MANGANESE TETRAPHENYLPORPHYRIN’

.. :PART II THE REDETERMINATION 0F ma

   
  

STRUCTURE OF PORPHINE ‘

TheSIs Iorthe Degree of Pb D
MICHIGAN STATE UNIVERSITY
BEITY MEI HORNE LEE CHEN

1970

 

III III III II IIIIIIIIIII L

3 1293 00694 7562

 

 

 

 

 

 

 

 

This is to certify that the

thesis entitled

Part I: The Structure Determination of Manganese
Tetraphenylporphyrin.
Part II: The Redetermination of the Structure
of Porphine.

presented by

Betty Mei-horng Lee Chen

has been accepted towards fulfillment
of the requirements for

PLJD degree in C(«cmtsgvj

 

 

(27:9qu

Major professor

Date Cflr;9‘ilLQ’H-

0-7639

 

 

JUI 9 ~ m

I]

 

 

 

ABSTRACT
PART I: THE STRUCTURE DETERMINATION OF MANGANESE
TETRAPHENYLPORPHYRIN
PART II: THE REDETERMINATION OF THE STRUCTURE OF PORPHINE
BY

Betty Mei—Horng Lee Chen

The structures of manganese tetraphenylporphyrin and
porphine were determined by means of three dimensional pray
crystallographic techniques. Both molecules crystallize in
the monoclinic space group P21/c with four molecules in
the unit cell. The unit cell dimensions for manganese
tetraphenylporphyrin are a = 14.56 R, b = 21.77 X, c =
17.02 X, and B = 135.60, those for porphine are a = 10.27 R,
b = 12.09 R, c = 12.36 R, and p = 102.20.

Manganese tetraphenylporphyrin was shown to coordinate
with an axial chlorine ion. The locations of the manganese
and chlorine atoms were determined by the heavy atom method;
the remaining atoms, including all the hydrogens, were
located from difference syntheses. All atomic parameters
were refined by the least squares method. The porphyrin
molecules in the crystal were stacked approximately perpen-
dicular to the 5* direction, with an acetone molecule from

crystallization trapped between adjacent porphyrin molecules.

Betty Mei-Horng Lee Chen

The Mn(III) ion in an approximately square-pyramidal
geometry is displaced 0.27 X from the mean plane of the
four basal nitrogen atoms toward the axial chlorine ligand.
The chlorine atom is slightly tilted («50) from the apical
position to keep a reasonable contact distance (3.45 R) to
a carbon atom belonging to the phenyl group of an adjacent
porphyrin molecule. The bond distances of ancl (2.36 R)
and Mn-N (2.01 X) , which are slightly shorter than ex-
pected, may be responsible for the high stability of this
porphyrin. The porphyrin skeleton is ruffled since one
pair of diagonal pyrrole groups is displaced below the NLS
plane while the other pair is above it with apparent devia-
tions of 0.3 — 0.5 R for the peripheral carbon atoms. The
porphyrin nucleus and phenyl groups were shown to be aromatic;
the former was electronically separated from the latter by
single bonds which join the phenyl rings to the porphyrin
nucleus. The dihedral angles between individual phenyl
groups and the NLS plane are 54.20, 123.50, 49.70 and 77.40
respectively.

The structure of porphine was determined previously
by Webb and Fleischer, with an alleged copper impurity and
a postulated "four half—hydrogen" structure for the central
hydrogen atoms. Since the peak heights of the half-hydro-
gens were only slightly greater than background, and since
the exact nature of these half—hydrogens with respect to

van der‘Waals contacts was not reported, a redetermination

Betty Mei-Horng Lee Chen
of the porphine structure was undertaken. In addition to
collecting a complete set of all independent reflections,
additional and more elaborate counting techniques were ap-
plied to those reflections which might contain a significant
contribution to the hydrogen atom structure. The results
indicated only two central hydrogen atoms bonded to one
pair of diagonal nitrogen atoms. The central hydrogen atoms
are coplanar to the porphine nucleus with N-H distances of
0.89 X and 0.92 8, respectively. The locations of H22 and
H24 are inclined toward N21 and N23 at angles of 5.80 and
4.50 relative to the line joining the two opposite nitrogen

atoms (N22—N24), respectively.

PART I: THE STRUCTURE DETERMINATION OF MANGANESE

TETRAPHENYLPORPHYRIN

PART II: THE REDETERMINATION OF THE STRUCTURE OF PORPHINE

BY

Betty Mei—Horng Lee Chen

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Chemistry

1970

3

\Q

070;?

ACKNOWLEDGMENT

The author wishes to express her appreciation to
Professor Alexander Tulinsky for his guidance throughout
the course of this study.

Appreciation is extended to Mr. Richard Vandlen and
to Dr. N. V. Mani for their assistance.

Appreciation is also extended to Dr. Alan Adler for
furnishing the samples of porphine and manganese tetra—
phenylporphyrin.

Appreciation is also extended to the Molecular Biology
Section of the National Science Foundation for providing
financial support.

Thanks are particularly due to her husband, Jing—

shyong, for his constant encouragement and assistance.

ii

 

 

TABLE OF CONTENTS
Page
DEFINITIONS OF SYMBOLS USED . . . . . . . . . . . . . ix
GENERAL INTRODUCTION . . . . . . . . . . . . . . . . . 1

PART I: THE STRUCTURE DETERMINATION OF MANGANESE

 

TETRAPHENYLPORPHYRIN . . . . . . . . . . . 5

I. INTRODUCTION . . . . . . . . . . . . . . . . . 6
1. Metalloporphyrins . . . . . . . . . . . . . 6

2. Review of Porphyrins and Metalloporphyrins. 7

3. Manganese Porphyrins . . . . . . . . . . . 12

II. EXPERIMENTAL . . . . . . . . . . . . . . . . . 15
1. Photographic Studies . . . . . . . . . . . 15
2. Diffractometer Intensity Data Collection . 18

III. STRUCTURE DETERMINATION . . . . . . . . . . . . 24
1. Introduction . . . . . . . . . . . . . . . 24

2. Location of the Manganese Atom . . . . . . 25

3. Electron Density . . . . . . . . . . . . . 31

4. Difference Density . . . . . . . . . . . . 33

5. Refinement . . . . . . . . . . . . . . . . 37

1) Weighting Scheme . . . . . . . . . . . 38

The Method of Least Squares . . . . . 39

(
(2)
(3) Phillips' Absorption Correction . . . 40
(4) Finding the Acetone Molecule . . . . . 46
(5)

Finding the Hydrogen Atoms . . . . . . 46
IV. STRUCTURAL RESULTS . . . . . . . . . . . . . . 49

V. DISCUSSION . . . . . . . . . . . . . . . . . . 69

 

 

TABLE OF CONTENTS (Continued)

PART II:

VI.

VII.

VIII.

IX.
x.

THE REDETERMINATION OF THE STRUCTURE OF
PORPHINE O 0 O O O O O O O O O O O O 0

INTRODUCTION . . . . . . . . . . . . . .

1.

UIIBCON

General . . . . . . . . . . . . . . .
Visible Spectroscopy . . . . . . . .
Infrared Studies . . . . . . . . . .
Nuclear Magnetic Resonance . . . . .

X-Ray Studies . . . . . . . . . . . .

EXPERIMENTAL . . . . . . . . . . . . . .

1.
2.
3.

4.
5.

The Problem of the Hydrogen Atoms . .
Preliminary X—ray Examination . . . .

Techniques for Measuring Intensities

(1) Stationary Crystal—Stationary Counter

Technique . . . . . . . . . . .

(2) Moving Crystal-Stationary Counter
Technique . . . . . . . . . . .

a. The X-ray Detector . . . . .

b. Constant-time Step Scan Technique.

c. Constant-count Step Scan Technique

(3) Moving Crystal-Moving Counter Technique

Data Collection . . . . . . . . . . .

Calibration Between Measuring Techniques

STRUCTURE DETERMINATION . . . . . . . . .

1.
2.
3.
4.

Isotropic Refinement . . . . . . . .
Anisotropic Refinement . . . . . . .
Extinction Correction . . . . . . . .

Weighting Scheme . . . . . . . . . .

RESULTS . . . . . . . . . . . . . . . . .
DISCUSSION . . . . . . . . . . . . . . .
REFERENCES . . . . . . . . . . . . . . .
APPENDICES

1.

2.

General Review of X-ray Diffraction

Observed and Calculated Structure Ampli-

tudes of CanTPP and Porphine . . . .

iv

Page

83

84
84
86
88
91
92

95
95
101
105

106

107
110
110
113
116
116
118

119
119
121
121
125
132
144
157

161

172

LIST OF TABLES

TABLE Page
1. Crystallographic Data for MnTPP . . . . . . . . . 19
2. Boundary Planes and Their Distances from the Center

of the Crystal . . . . . . . . . . . . . . . . . 44
3. Maximum Observed and Calculated Absorption Factors 45
4. Scale Constants for Each Reciprocal Level . . . . 45
5. Final Atomic Coordinates, Thermal Parameters and

Peak Heights for CanTPP . . . . . . . . . . . . 50
6. Coordinates, Isotropic Temperature Factors and

Peak Heights of Hydrogen Atoms . . . . . . . . . 54
7. Atomic Parameters of the Acetone Molecule . . . . 55
8. Parameters for the Equation, mlx + mzy + maz = d,

Selected to Fit Planes . . . . . . . . . . . . . 56
9. Dihedral Angles between NLS Plane and the Individual

Phenyl Plane and Angle between NLS Plane and

Mn—Cl Line . . . . . . . . . . . . . . 56
10. Atomic Deviations from Least—Squares Planes of

Individual Pyrrole and Phenyl Rings . . . . . . . 58
11. Atomic Deviation from the Least-Squares Plane of

Four Nitrogen Atoms . . . . . . . . . . . . . . . 59
12. Average Stereochemical Parameters of Porphine

Skeleton in Some Five Coordination Metallotetra—

phenylporphyrins . . . . . . . . . . . . . . . . 81
13. Intensities of (241) Reflection Measured by CTST

and SX Techniques . . . . . . . . . . . . . . . . 112
14. Step Scan Measurement . . . . . . . . . . . . . 114
15. Intensities of Reflection (412) Measured by CCST

and SX Techniques . . . . . . . . . . . . . . . . 115

 

 

 

LIST
TABLE

16.

17.
18.

19.

20.

21.

22.

23.

24.

OF TABLES (Continued)

Atomic Coordinates and Isotropic Temperature
Factors for Porphine (from Webb & Fleischer). . .

The Reflections Corrected for Extinction . . . .
Error for Intensity Less than 400 . . . . . . . .

Final Atomic Parameters and Peak Heights of Carbon
and Nitrogen Atoms of Porphine . . . . . . . . .

Final Coordinates, Isotropic Temperature Factors,
and Peak Heights of Hydrogen Atoms of Porphine .

Atomic Deviations from the Least-Squares Planes
of Individual Pyrrole, Inner Eight Atoms and
Four Nitrogen Atoms . . . . . . . . . . . . . . .

Average Pyrrole Bond Lengths in Some Free Base
Porphyrins and Porphine . . . . . . . . . . . . .

Average Pyrrole Bond Angles in tri—TPP and the
Porphine of This Work . . . . . . . . . . . . .

Fractional Coordinates and Peak Heights of Central

Hydrogen Atoms from Two Porphine Structure
Analysis . . . . . . . . . . . . . . . . . . . .

vi

Page

120
124

130

135

136

149

150

155

 

LIST OF FIGURES

FIGURE Page
1. (a) Manganese tetraphenylporphyrin, (b) Porphine 2
2. Geometry of metals in metalloporphyrins . . . . . 9
3. Flow chart for data collection procedure . . . . 22
4. Harker section of CanTPP . . . . . . . . . . . . 29
5. Harker Line of CanTPP . . . . . . . . . . . . . 30
6. Approximate crystal geometry for computing

absorption factors . . . . . . . . . . . . . . . 43
7. Porphine skeleton nomenclature . . . . . . . . . 47
8. Atomic deviatflxm (A) from NLS plane . . . . . . . 60
9. Atomic deviatkms from least—squares plane based
on inner sixteen atoms of CanTPP . . . . . . . . 61
10. (a) Bond distances (in A) . . . . . . . . . . . 62
(b) Intramolecular distances and dihedral angles 63
(c) Bond angles for CanTPP . . . . . . . . . . 64
11. A diagram in perspective of MnTPP molecule (ORTEP). 66
12. Crystal structure_9£ CanTPP viewed in the
projection along a . . . . . . . . . . . . . . 68
13. Intermolecular distances from Chlorine atom . . . 7O
14. Bond distances and bond angles of acetone molecule
of crystallization . . . . . . . . . . . . . . . 72
15. The geometry and the dimensions of square pyramidal
coordination in CanTPP molecule . . . . . . . . 78
16. Possible central hydrogen models . . . . . . . . 85
vii

LIST OF FIGURES (Continued)

FIGURE

17.

18.
19.

20.

21.
22.

23.

24.
25.

26.

27.

28.

29.
30.

31.

32.

33.

Mason's intramolecular hydrogen—bonded models for
porphine . . . . . . . . . . . . . . . . . . . .

Coproporphyrin . . . . . . . . . . . . . . . . .
Porphine numbering scheme . . . . . . . . . . .

Number of reflections (IFCI 3.1.0) XE scattering

angle (29) . . . . . . . . . . . . . . . . . . .
Dimensions of porphine crystals . . . . . . . . .
Errors (%) XE- intensity . . . . . . . . . . . .

Atomic deviations (A) from nuclear least squares
plane . . . . . . . . . . . . . . . . . . . . . .

Porphine bond distances (A) . . . . . . . . . . .
Porphine bond angles (degrees) . . . . . . . . .

Composite electron density of the hydrogen atoms
perpendicular to the ac plane . . . . . . . . .

The difference electron density in the vicinity
of the four nitrogen atoms . . . . . . . . . . .

The interatomic distances and angles of the
nitrogen and hydrogen atoms . . . . . . . . . . .

Deviations of porphyrin skeleton from planarity .
Porphine resonance forms . . . . . . . . . . . .

Polar coordinates of a reciprocal lattice point
(hkfi) for orthorhombic crystal system . . . . .

Maximum absorption factor X3 29 . . . . . . . .

Schematic representation of a four—circle
diffraction O O 0 O O O O O O O O O O O O O O O 0

viii

Page

90
90

97

100
102

128

137
138

139

141

142

143
146

152

163

166

170

—>

'—.K- -—->«
a ,b ,C

F(hk£)

mm)

or

DEFINITIONS OF SYMBOLS USED

Primitive translations or unit cell axes of
the crystal lattice, and their magnitudes.

Angle between C> and E”.

Primitive translations of the reciprocal
lattice.

Set of three integers with ranges from -oo
to 00.

Negative of the above set

Parallel lattice planes which intersect 35,
H> , and c at intervals of a/h, b/k, and
c/fi respectively.

Atom j's scattering factor or ability rela—
tive to a classical electron to scatter X—rays.
: exp — Bj(sin 6/A)2 isotropic temperature

factor of atom j

= exp ‘ (511h2 + 322k2 + 53332 + 2P12hk +
2813h£ + 2Bz3kfi) anisotropic temperature

factor of atom j.
Number of electrons belonging to atom i.

= xjg>+ yj5>+ sz: Position vector for atom j.
N I
= 2 f. (hkfi) exp 2wi(hx. + ky. + fiz.) struc-
j=1 3 3 J J

ture factor for the reflection from (h,k,£)
planes. N atoms per unit cell.

Intensity of the reflection from the (h,k,z)
planes.

Observed structure amplitude, whose square is
proportional to I(hk£).

Scattering angle.
Angular settings for the diffractometer.
Wavelength of X—ray radiation.

Absorption correction for the reflection
from the (h,k,£) planes.

Linear absorption coefficient.

Electron density calculated with structure
factors whose phases, S , are those of it
set of F (hkz) and whoge amplitudes are

IFo(hk£N. C

Difference\synthesis calculated with coef—

ficients lIFol — chl) and phases, SC.

= 2IIFoI - IFCII
2E0]

Residual index.

 

GENERAL INTRODUCTION

Porphyrins (Fig. 1a) are derivatives of porphine (Fig.
1b), a system in which four pyrrole rings are linked by
four methine carbon atoms to give a sixteen—membered macro—
cyclic ring. The porphyrins are found to be essential for
certain biological functions such as: (i) oxygen storage
and transport, as in myoglobin and hemoglobin; (ii) cellu—
lar respiration involving electron transport, as in the
cytochromes; and (iii) photosynthesis, as in the chloro—
phyll—containing chloroplasts. All these biologically ac-
tive substances consist of three distinct parts: the

Sporphyrin, a central metal atom, and a complicated molecular
environment.

Recently, manganese porphyrins have been considered to
be important in chloroplasts, since manganese is essential
in the energy converting unit of the plant. There is evi—
dence that the plant can restore its ability to reduce car—
bon dioxide and evolve oxygen by adding manganese ions back
to the energy system. Although there is little evidence to
indicate the function and environment of manganese, it has
been suggested that manganese is complexed with ligands of
biological interest such as porphyrins. Thus, the structural
properties of manganese-containing porphyrins may be of im—

portance and biological interest.
1

_ .

 

(a) Manganese tetraphenylporphyrin, MnC44H28N4.

 

(b)
(b) Porphine, C20H14N4

Figure 1.

 

3

Manganese tetraphenylporphyrin (Fig. 1a, hereafter
referred to as MnTPP) is a synthetic porphyrin. Single
crystals of MnTPP form in the monoclinic crystal system and
contain four molecules in the unit cell. Since space group
requirements dictate that each asymmetric unit contains one
complete molecule, the molecular structure of MnTPP is not
affected in any obvious way by crystal symmetry. For this
reason and others already mentioned, an X—ray crystallo—
graphic study of the structure of MnTPP was undertaken in
anticipation of perhaps providing information of biological
interest and utility, as well as adding to the general
understanding of metalloporphyrins.

In the other portion of this work, a redetermination
of the structure of porphine was carried out. As the parent
compound of the porphyrin series, the structure of porphine
is particularly important because any understanding of the
porphyrins must rest intimately upon the understanding of
porphine.

The central hydrogen atoms of the free base of porphine
and of porphyrins are known to influence the detailed struc—
ture of the porphyrin skeleton. Various techniques have
been used to probe properties of these central hydrogen
atoms. Low temperature visible Spectroscopy suggested the
existence of gi§_and trans isomers, inEII hydrogen atoms on
adjacent and on opposite pyrrole nitrogen atoms, respec~
tively. Attempts to detect hydrogen bonding between hydro—

gens and neighboring nitrogen atoms by infrared spectroscopy

4
were inconclusive. Nuclear magnetic resonance spectroS—
copy suggested the rapid exchange of the inner hydrogen
atoms. On the other hand, the X~ray diffraction analysis
of the triclinic form of tetraphenylporphyrin (tri-TPP)
showed that the two inner hydrogen atoms were localized
and located on opposite nitrogen atoms, whereas the results
of a similar study of the tetragonal form of TPP indicated
a disordered structure for the molecule (two equally prob—
able positions in the plane of the molecule 900 apart).
From the X—ray diffraction work of Webb and Fleischer, the
porphine molecule was reported to be essentially planar
with an average symmetry close to D4h(4/mmm) and to contain
four inner half—hydrogen atoms. The latter were suggested
to be due to a rapid interconversion of N—H tautomers.
However, since the crystals were also reported to contain
a 5-10% impurity of copper porphine and since the electron
densities of the half—hydrogen atoms were only slightly
above background, the situation of the central hydrogen
atoms remained unceratin. For these reasons and others to
be elaborated upon later, an X—ray crystallographic re—exam-

ination of the structure of porphine was undertaken.

 

PART I

THE STRUCTURE OF MANGANESE TETRAPHENYLPORPHYRIN

 

I . INTRODUCTION

1. Metalloporphyrins

The porphine skeleton with four pyrrole rings and four
methine carbon atom bridges is shown in Figure 1b. There
are fourteen replaceable hydrogen atoms, eight pyrrole
hydrogens, four methine hydrogens, and two central hydrogen
atoms bonded to nitrogen atoms. Derivatives which are pro—
duced by the replacement of inner hydrogen atoms by metals
aretie metalloporphines, while those whose outer hydrogens
are replaced by other groups are called porphyrins. The
four methine carbon atoms can also be replaced by aza—
nitrogen atoms forming azaporphines which, in turn, are
related to the phthalocyanines by fusion of a benzene ring
to each pyrrole. The two inner hydrogens of phthalocyanine
are also replaceable by a wide variety of metals.

Porphine is a planar molecule, made up of eleven con—
jugate double bonds, with considerable flexibility to fold
as demanded by environmental stresses and strains. Some
forces which can affect the conformation of the porphyrin
moiety are: (1) a central metal atom, (2) side-Chain sub-
stitutions on the porphyrin ring, and (3) intermolecular
forces from the environment of the molecule. Of greatest

6

 

7
concern in this work is the coordination of the central

metal atom and its effect on the porphyrin system.
2. Review of Porphyrins and Metalloporphyrins

Extensive reviews of structural studies of porphyrins
and metalloporphyrins have been written by Hoard1 and
Fleischer.2 The following on the geometry of metals in
metalloporphyrins is intended as a brief summary of these
reviews (see Fig. 2).

Since porphyrins consist of large conjugated systems
which can serve as tetradentate ligands, metallic cations
are able to be accommodated at the center of the system
with the four nitrogen atoms serving as ligands. The metals
of metalloporphyrins have been found in a variety of co—
ordinations. Four coordinate compounds formed by central
metal atoms bonded with the four pyrrole nitrogen atoms
havezgproximate square planar geometry. Although the por—
phine skeleton of these porphyrins is a conjugated system
and is usually assumed to be planar, some of the metallo—
porphyrins, such as CuTPP3 and nickel etio—I porphyrin4
have been found to possess nonplanar porphyrin rings.
Furthermore, there are small variations of metal—nitrogen
(M—N) distances from one porphyrin to another. The reasons
for the nonplanarity and the variation in M—N bond distances
are as yet not well understood.

Five coordinate metalloporphyrins are found to have

Square pyramidal geometry. In general, the metal is

Figure 2. Geometry of metals in metallOporphyrins.
(1) four—coordinate with a square planar geometry.

(2) tetragonal pyramid coordination of five—co-
ordinate metalloporphyrins.

3) six—coordinate metalloporphyrins.
(4) possible seven—coordinate metalloporphyrins.

(5) square antiprism of the eight-coordinate tin
phthalocyanine complex.

(6) manganese(III) phthalocyanine dimer.

(7) u—oxo—bis(porphyriniron(III) dimer.

 

,N
N
(II
o
I \
\ f/N',
n— III—II
’N\ CI
(3)
N<I [N
\‘ lN/l/
256‘
N ’ N
// ‘.\
N

 

10
displaced from the mean plane of the pyrrole nitrogen atoms
toward the apical ligand. For example, iron in high spin
ClFeTPP5 shows an out—of—plane displacement of about 0.4 R,
and vanadium in vanadyl—substituted etioporphyrin6 is 0.48 8
out of the plane. In some of these porphyrins, there is a
significant shortening of the axial bond between the
apical ligand and the metal. For example, the axial length
of Fe-Cl in ClFeTPP is 2.19 A, while the corresponding value

listed in International Tables for X—Ray Crystallography is

 

2.38 A. Similar shortening effects are also observed in
the o-Mg (2.07 A) bond of (H20)MgTPP7.

Six coordinate compounds display distorted octahedral
geometry; eight coordination is found as a square—antiprism
sandwich in the tin phthalocyanine complex,8 and higher co—
ordinate metallOporphyrins do not seem to form. On the
other hand, dimeric metalloporphyrins such as u-oxo—bis(por—
phyriniron(III))9 are known. Here, the iron atom has five
coordination and is about 0.5 8 out of the nitrogen plane
in the direction toward the oxygen bridge, with the Fe—O—Fe
angle being about 170°.

In general, the bond distances of the porphine core as
determined from X-ray studies do not correspond to an aver—
age of single and double bond distances nor a single—bond-
double—bond array of a conjugated double bond system.

The average carbon—nitrogen distance10 of most metallo—
porphyrins is about 1.37 A, which is shorter than the 1.42

A distance expected for a trigonally hybridized C—N o-bond,

 

 

 

11
but longer than the 1.27 A distance observed for the c=N
double bond. In the pyrrole ring, the average Ca~cb bond
length (where Ca is the carbon atom adjacent to the pyrrole
nitrogen while Cb is the carbon adjacent to Ca) is about
1.45 A, a definitely shorter value than the bond length of
1.49 A expected between trigonally hybridized carbon atoms,

while the average C bond length of 1.35 A indicates a

b'Cb
lengthening of the double bond value of 1.33 A.

The center-nitrogen distance (Ct—N), which indicates
the radius of the central hole of the porphyrin core, has
been observed in most cases to be smaller in metalloporphy—
rins than that of the corresponding free base porphyrins.
The bond distances of the metal-nitrogen (M—N) of metallo—
porphyrins have been observed to vary from 2.05 A in ferric
porphyrin to 1.95 A in nickel etio—I porphyrin. There seems
to be no direct relationship between the M—N bond length
and the size of metal atom. Furthermore, the metal atom
can be in or out of the mean plane of the four nitrogen
atoms. This effect has been carefully examined in iron
porphyrins by Hoard,10 who predicted that a low—spin iron
porphyrin would have iron in the nitrogen plane while the
metal in high—spin iron porphyrin would be 0.5 A out of the
mean plane. Indeed, this prediction has been verified by
the structure analysis of bisimidazoleiron(III) tetra~

phenylporphyrin.11

 

 

12

3. Manganese Porphyrins

Porphyrin complexes of Mg, Co, and Fe are known to
occupy central roles in chlorophyll, vitamin B12, and heme—
proteins. Recently, manganese porphyrins have received a
great deal of attention because of their possible link to
chloroplasts. Two reasons for this interest are: (1) the
relationship of manganese porphyrins in photosynthesis, and
(2) the coordination chemistry of this transition metal in
a porphyrin environment.

The chloroplast, which is the most essential component
in photosynthesis, contains protein, lipid, Chlorophyll,
inorganic ions and carotenoids. Among these components,
Chlorophylls and inorganic ions, such as manganese ions,
have been considered to be most important in the energy
transfer process.12:13 chloroplasts can be broken down into
subunits, with the smallest subunit, a quantasome, being
about 200 A in diameter. For each quantasome, there are
precisely two manganese atoms per 300 chlorophyll molecules.
In addition, there is evidence that manganese is an essen—
tial element for the oxygen evolving step of photosynthesis.
When manganese ions are re-added to the plant's environment,
its ability to evolve oxygen is restored, and the plant
can perform its normal function of reducing C02 and evolving
oxygen. All the evidence indicates that the presence of
manganese is a functional requirement of the chloroplasts.
However, the manganese is difficult to remove from chloro—
plasts, and its physical properties as such are not easily

observed.

 

13

Calvin14 has suggested that the manganese atoms in the
chloroplast are bound to porphyrin type ligands. He has
demonstrated that manganese porphyrin can undergo revers—
ible oxidation—reduction changes between Mn(II)-Mn(III) and
Mn(III)-Mn(IV), with the Mn(III) species being unusually
stable. This initial work supported the relevance of man—
ganese porphyrin as a possible photosynthetic model com—
pound.

The physical and chemical properties of manganese
porphyrins have been studied by Boucher.15116 Magnetic
susceptibility measurements in the solid and in solution,
at a number of different temperatures, yield an effective
magnetic moment in the range of 4.5 to 5.0 B.M. The ex—
pected value for a spin—free d4 manganese(III) complex is
4.9 B.M. These measurements suggest that there is no spin
pairing. The far infrared spectra show metal—anion
stretching absorptions in the region of 160 to 500 cm—1,
consistent with the strong binding of an additional ligand
in the axial coordinate position of the metal. In solution,
electronic spectra showed that six—coordinated manganese
porphyrins were present with various ligands. From these
Spectra it was concluded that manganese porphyrins have
significant metal—porphyrin N-bonding; however, the porphy—
rin—metal d—orbital w interaction is difficult to describe
quantitatively. Two possible geometries of the molecule
have been predicted. One possibility is that of tetragonal

geometry with the metal ion in the plane of four pyrrole

 

14
nitrogen atoms, with an axial anion and a solvent molecule
at somewhat larger distances from the metal. The other
possibility is that the metal atom is out of the plane of
the porphyrin (about 0.5 A), coming closer to the axial
aniono The latter geometry can be rationalized by saying
that because of the large size of the metal ion, it Cannot
fit into the nitrogen cavity. In any case, the exact
molecular structure of manganese porphyrins was still in
question. For such reasons, it seemed particularly ap—
propriate to carry out a detailed structural determination

of a manganese porphyrin.

II. EXPERIMENTAL

1. Photographic Studies

Photographic methods provide a quick and easy way to
obtain a general View of the geometry of a diffraction pat—
tern, the symmetry of the reciprocal lattice, and the
relative intensity distribution of a large number of re»
flections. Methods available to obtain such information
are oscillation and moving film photography (Weissenberg
and precession methods).

In the oscillation method, the crystal is mounted in
a manner such that some principle axis coincides with the
oscillation axis and the crystal is oscillated through a
small angle, i;§,, 5-100, around this axis by means of some
threaded gear or other mechanism. The photographic film
is placed in a cylindrical camera around the oscillation
axis. A small number of planes will come into a reflecting
position with this oscillating motion and will produce
spots on a film in the form of a series of separated layer
lines. The diffraction pattern recorded in this way can
provide useful information regarding the symmetry of the
crystal lattice and the Spacing of the lattice along the

oscillation axis.

15

16

Single crystals of MnTPP were grown by slow evapora~
tion of an acetone solution. The dark purple crystals ex—
hibited polyhedral morphology with many well—defined faces.
A crystal of suitable size (approximately 0.4 x 0.2 x 0.3
mm) and with good morphological quality was chosen for
photographic examination. A 100 oscillation photograph of
a crystal mounted with its largest dimension perpendicular
to the spindle oscillation axis showed that the intensity

distribution of the upper and lower halves of the photo—
graph were symmetrical with respect to the zero layer line.
This distribution indicated the presence of a mirror plane
of symmetry in the direct lattice perpendicular to the
oscillation axis and either a monoclinic lattice or one

with higher crystal symmetry (i.e., orthorhombic or higher).

 

In the Weissenberg film method, a single layer line nor—
mal to the oscillation axis is selected for observation by
means of a slotted screen which allows only the reflections
in that layer to be recorded on the photographic film. As
the crystal rotates, the film moves past the screen slot in
a synchronous way and reflections which occur at different
times are recorded at different translational positions
on the film. The moving film photograph displays the recip—
rocal lattice plane which is perpendicular to the oscillation
axis and can be used to determine the symmetry of these
planes and to index reflections. Photographs of several
successive layers of the MnTPP crystal were taken. The
lack of any further symmetry elements showed that MnTPP crys-

tallized in a monoclinic lattice. The unique b axis of the

 

17
monoclinic crystal system coincided with the oscillation
axis and the a* and c* reciprocal axes were selected so
that the zero layer photograph showed the reflections (h0£)
absent when the 3 index was odd. This Characteristic
extinction is due to a c-axis glide plane, and corresponds
to a reflection across a plane accompanied by a transla-
tion of c/2 parallel to the plane along the C axis.

In the precession method, the crystal oscillates about
an axis with the latter also undergoing an oscillation.

The net motion closely resembles a precession motion. Dur—
ing these motions, the film always remains parallel to the
reciprocal lattice plane which is perpendicular to the X—
ray beam in the absence of a precession angle, and thus
records the true, undistorted, geometry of the reciprocal
lattice plane. Precession photographs of MnTPP taken of
the reciprocal planes parallel to the b~axis (hkO and 0kg)
showed that OkO reflections were absent whenever k was
odd° This absence indicates the presence of a 2—fold screw
axis along the b axis of the crystal (i423, 2—fold rota"
tion plus b/2 translation along the rotational axis).

Thus, the preliminary studies of the crystal MnTPP
showed that the crystal belongs to a monoclinic system with
a space group possessing the following conditions for
systematically absent reflections:

OkO reflections, k = (2n + 1) = odd

h0£ reflections, z = (2n + 1) 2 odd.

From these conditions, the space group was uniquely

 

 

18
determined as le/c, space group No. 14, subgroup number 2,

as tabulated by the International Tables for X—ray Crystal-

 

lography.

2. Diffractometer Intensity Data Collection

A second crystal, which was slightly smaller than the
one used for photographic studies, with dimensions of about
0.25 x 0.15 x 0.15 mm (see Fig. 6) was used for intensity
measurements. The crystal was mounted on a goniometer head
whose axis was coincident with the T circle of a quarter
circle crystal orienter (see Figo 31 given in Appendix 1).
The orientation of the crystal with respect to the diffrac—
tometer axis was such that the unique b axis of the
crystal was also coincident to the m axis of the diffrac»
tometer. The a* c* plane was thus located in the equatorial
plane (X = 6). The unit cell dimensions of the crystal
were determined by measuring the angular orientation which
centered the intensity of 12 moderately intense reflections
well—distributed in reciprocal space and with large 26
angles. The angular coordinates were used with the method
of least squares to obtain the best unit cell parameters
and least squares orientation of the crystal. The results
are listed in Table 1.

The density of a single crystal of MnTPP was measured
by flotation in an aqueous silver nitrate solution and

indicated that there were four molecules in the unit cell.

 

19

The observed density of the crystal was 1.30 g/cm3; however,
the calculated density based on four MnTPP molecules in the
unit cell was only 1.17 g/cm3. The high observed molecular
weight (738 instead of 667) suggested the presence of ad—
ditional material in the unit cell. This material could
have been introduced at the time of preparation(ions) or
crystallization(solvent). The discrepancy was resolved

later during the structure determination.

Table 1. Crystallographic Data for MnTPP

Space . . * :
Group Monoclinlc P21/c Z 4
a 14.588 r 0.005 8 Empirical formula MnC44H28N4
b 21.765 r 0.006 M.W. = 667
c 17.023 r 0.006 D = 1.30 r 0.01 g cm‘3
obs
B 135.62 r 0.04 degree Dcal = 1.17 g cm"3

Volume 3773.8 r 3.4 is

it
Number of molecules in the unit cell.

The quality of the crystal chosen and the best quad-
rant for data collection can be ascertained by measurement
of the mosaic spreads of the crystal, essentially a measure—
ment of the degree of misalignment of the mosaic blocks
(minute perfect crystal blocks) which make up the real
crystal. For MnTPP, the reflections (080), (300), (300),
(006) and (006) were Chosen to measure the mosaic spreads.

The mosaic spreads of (300), (300), (006), and (006)

 

‘IIIIIIZZZL_______________________________________________________________

 

20
reflections (at X = 0°) were measured by: (1) presetting 29
at the center of the reflection as determined by use of a
left/right device which allows either the left half or the
right half of the diffracted beam to be selectively examined,
(2) off—setting the T angular setting to the background
level of the peak, and recording the intensity, I, of the
diffracted beam as a function of the angle T in increments
of 0.050 from background to background. The mosaic Spreads
of the (080) reflection (at X = 90°) were measured by: (1)
presetting 29max, (2) presetting T at the value of the
a*, C*, -a*, and —c* axes, (3) offsetting the w angle to
the background level and recording the intensity, I, as a
function of the w angle in increments of 0.050 from back—
ground to background. The mosaic spread of (006) was
found to have the maximum basal peak width which was 0.450.
All the remaining mosaic spreads were about 0.30 in width
and symmetrical in shape. The data collection was thus re—
stricted to the quadrant defined by the —a* axis (T =
298.50), and a* axis (T = 118.50) and including the c*
axis at T = 38.90.

A set of intensity data was collected with a Picker
4-Circle Automatic Diffractometer using the moving crystal—
moving counter technique (29 scan). In this technique,
the reflection was scanned and counted with the radiation
filtered through a nickel filter (9 filter) in order to
remove Cu Kfi radiation. A second scan was then made with

a balanced cobalt filter (a filter), i.e., one whose

 

21

absorption edge is at a wavelength just longer than the Ka
radiation being used. A flow chart of the data collection
procedure is shown in Figure 3. Within a 29 limit of
100°, the total number of reflections measured was 3978.
In order to ascertain which reflections should be considered
as unobserved, the lower limit of intensity corresponding
to the average background intensity fluctuation was deter-
mined as follows. Any measured intensity of reflections
which are systematically absent, 143., (hog) and (OkO) re—
flections k or B odd, should be mainly due to the
effects of background radiation. Using this assumption,
an average intensity of 7 counts/10 sec was obtained by
measuring 93 systematically absent reflections. Thus the
minimum observable intensity for reflection was set to be
slightly larger than this average background value.
Eliminating the unobserved reflections, systematically
absent reflections, and all redundant reflection (i hk0
reflections), a total of 2977 unique and observable reflec—
tions remained for the structure determination of MnTPP. I

If during the course of data collection procedure the
intensity of any of the monitor reflections (004), (700)
and (080) was outside the expected counting statistic
error, approximately the square—root of the original
intensity (JI ), the crystal was realigned and data col-
lection was resumed. Throughout the data collection the
intensity of the monitors did not fluctuate by more than

10% of their original value. Since there was no systematic

 

22

 

I Input variables j

 

 

 

[—~—1 Generate position of reflection
“I"llii__h-~
I

—_.___1_———-

Make
measurement

      
   
  
 

 

{F Check monitors/100 reflections l

 

Finished

 

Realign crystal, continue
) data collection

 

Figure 3. Flow chart for data collection procedure.

 

23
intensity decrease a decay correction was not considered
necessary.

The absorption of X-rays by the crystal (see Appendix 1)
showed a functional dependence on both 29 and T . Al—
though initially only an approximate absorption correction
was applied to the data in terms of both these angles, a
more accurate correction was applied later.

The intensities of all the independent reflections
were subsequently corrected for Lorentz and polarization
effects, and converted to a set of relative structure ampli—

tudes (|F|).

 

III. STRUCTURE DETERMINATION

1. Introduction

It is well known that an X—ray wave scattered by the
atoms of a crystal can be characterized by a quantity
F(hk£) called the structure factor. This quantity is a
complex number whose magnitude is the amplitude of the
scattered wave and whose orientation in the complex plane
is determined by the phase of the scattered wave. The
structure factors depend on the arrangement of atoms in
the crystal. If the magnitudes and phases of the structure
factors are known, the electron density distribution in the
unit cell can be calculated; conversely if the electron
density is known, structure factors can be obtained. The
fundamental difficulty encountered in crystallography is
that the magnitudes of the structure factors are obtainable
from measured intensities, but the phases cannot be
measured directly. Determination of the phases of the
structure factors is known as the phase problem.

There is no general solution for the phase problem.
However, it has been found that structures in which one or
a few atoms are markedly heavier than the remainder are
usually more easily solved than those in which all the atoms

24

25
are alike. The reasons for this are:(1) it is possible to
locate the heavy atoms in the crystal by methods which do
not require knowledge of the phases, and (2) once the heavy
atoms have been found they can serve as a trial phase model

from which the remaining atoms can be found.
2. Location of the Manganese Atom

The Patterson function is a Fourier series whose coef—
ficients are the squares of the structure amplitudes,
|F(hk£)|2. The structure amplitudes are directly derivable
from X—ray intensities. The Patterson function is related
to the electron density function, both of which can be
expressed mathematically as the following Fourier series

electron density:
p(xyz) = % ZZZ F(hkfi) exp ~2Fi<hX + ky + £2) (1)
hkfl
Patterson function:
P(uvw) = 12 222 |F(hk£)|2 cos 2N(hu + kv + fiw) (2)
V hkla

Then, (1) has a peak at each atom location, while (2) has

peaks corresponding to the end of the vectors between atom
th

locations. The coordinates of the r peak in (2) are
related to those of ith and jth peaks in (1) by
ur = xj — Xi, vr = yj — yi, and wr = zj — zi.

Thus for every pair of peaks in (1), there is a Specific

peak in (2).

 

26
Harker (1936)17 pointed out that in some cases much
useful information is concentrated in certain planes of the
three—dimensional Patterson function. For space group
P21/C, there are four equivalent positions:

(a) x. , y. , z.

(c) x. , 1/2 + yi , 1/2 — zi
(d) x. , 1/2 - yi , 1/2 + zi .

For atoms which are related by equivalent positions (a) and
(c), there is a corresponding peak in the section v = 1/2,
(u = 221' w = 1/2 — 221). This section (v = 1/2) is called
a Harker section. The same reasoning applies to atoms
related by (b) and (c), with the correSponding vector oc-
curing on the Harker line with coordinates, (u = 0 , v =
1/2 + 2y , w = 1/2).

If the crystal contains only a few heavy atoms in the
unit cell, the locations of these atoms can be solved by
the use of the Patterson function. The Patterson peaks are
approximately proportional to the product of atomic number

of the atoms giving rise to them (ZiZj); thus the peaks

 

due to the heavy atoms stand out against the background of
other smaller peaks. The overlapping of peaks which is
caused by finite widths can be reduced by a process known

as sharpening. Thus, the Patterson coefficients can be
modified to make the heavy-atom vectors appear approximately

as vectors between point atoms. Normally the scattering

27
power of an atom decreases as a function of (sin 9/I), but
sharpening can remove this fall—off characteristic by mak—
ing the scattering power equal to atomic number Z for

all (Sin 9/A). A common expression used for sharpening18

is
. = I" ‘=s- "2
)FpOInt) IFo/f , where f .2 (fm)i/.: (Zm)i
1—1 l~1
Zm is the number of electrons in an atom of m typeo
fm is atomic scattering factor of atom m.
Once the IF . I, s are obtained from the observable
pOlnt
IFOIS , they can be squared and used as the coefficients

for a sharpened Patterson function. The effect of sharpen-
ing enhances the heavy—atom vectors and makes peaks more
resolved.

MnTPP contains four Mn atoms in the unit cell and
their positions were found by the use of Patterson function.
The Patterson coefficients were sharpened with the Mn

atomic scattering factor

)Fpoint) : (ZMn/an) [FOI'
where ZMn is the number of electrons of the Mn atom (25),
and the denominator is the atomic scattering factor of Mn
atom, as obtained from the f—curve tabulated in International

Tables for X—ray Crystallography?4 The vector peak due to

 

Mn—Mn interactions showed clearly in the Harker section of
the Patterson map (shown in Fig. 4). The coordinates of Mn

atoms from the Harker section and Harker line (Fig. 5) are

 

 

Figure 4.

28

Harker section of CanTPP. Peak 1 is Mn-Mn
vector, peak 2 is Cl~Cl vector.

29

 

 

 

 

Figure 4.

30

 

.mmeczao mo TCAH HTMHmm .m Tasman

Q. . S1.)

v r/ C

\ .oon

-ooop

loom—

 

.ooou
A3>=vm

31
(in fractions of a unit cell):
x = —0.4766
y = 0.1142
2 = 0.0875.
The remaining atoms in the unit Cell were found by using

electron density methods.

3. Electron Density

The structure factor with one heavy atom in the unit
cell can be written as

F(hk£) = fH exp 2r1(th + kyH + 22H) +

(3)

g fn exp 2In(hxn + kyn + fizn)

where fH is the scattering factor of the heavy atom,

whose positional parameters are XH' yH, zH. If fH is
much greater than fn' then the first term will tend to
dominate the scattering factor expression. To a first ap-
proximation, the structure factor can then be represented
as

FC s’fH exp 277i(hxH + kyH + ng)

or in centrosymmetrical case

PC "=’ [F(hkg)

 

- Sc(hk,z) (3a)

where SC is the Sign of the calculated structure factor,
Fc’ and (P(hkfl)‘ is the observed structure amplitude. By
use of equation (3a), an electron density can be computed

from the calculated heavy atom phases and the magnitudes

 

32
of the (Fols'
p<xyz) IF0(hk£)) SC(hk£) cos 2r (hx + ky + Iz) (4)
where [F0[ is observed structure amplitude. Light atoms
found in this approximate electron density can then be
used to generate a new set of better phases. By continuing
this "bootstrapping" procedure, all atoms except the very
light ones can usually be found.

In the present work, an electron density was calculated
on the basis of the manganese atomic position derived from
the Patterson function. In this calculation some small and
phase undetermined reflections (|F0] < 10) were excluded.
Many peaks which were ascribed as light atoms appeared in
an approximate plane in the unit cell. However, at this
stage it was impossible to discern the expected molecular
geometry, probably because the phases based on just the Mn
atom contained considerable errors and introduced many
spurious peaks in the density along with the correct ones.
However, one strong peak was found approximately 2.5 A
away from the manganese atom and approximately perpendicular
to mean plane of peaks. The Harker section was re—examined,
and indeed, there was a vector due to an atom with approxi—
mately fourteen electrons. Anions that could possibly be
coordinated with manganese, introduced either during prepare
ation or crystallization, were considered.

Manganese porphyrin can be synthesized15 from a mixture

of divalent manganese acetate and free base porphyrin in a

 

33
reaction medium such as glacial acetic acid or N,N‘—di-
methylformamide.19 Dilute sodium halide solution is used
to extract and to purify the product. In the presence of
air, Mn(II) porphyrin is rapidly oxidized to the very
stable Mn(III) porphyrin, for which a halide complex has
been reported under these prepartory conditions.

Among possible anions, it was decided from the above
that chloride was the most likely anion bound to the
manganese atom; moreover, it also corresponded to about
the correct number of electrons. Thus, the peak from Harker

section and Harker line with coordinates,

x = 0.6350
y = 0.1667
2 = 0.2467

was assigned as Chlorine. This increased the expected
molecular weight to 702 a.m.u. and the calculated crystal
density based on four CanTPP molecules was 1.23 g/cm3
(Dobs = 1.30 g/cm3).
Another electron density phased with the Mn and Cl
contributions was calculated. This new map showed little

improvement of the light atom structure over the original

one except for the appearance of the chlorine atom.
4. Difference Synthesis

The difference synthesis is a Fourier series whose

coefficients are the quantities F0 — FC , AF,

 

34

Ap = 1-222 (lFol - IF I)“ 8 cos 2v(hx + ky + £2) (5)
V hkz C .

C

where SC is the Sign of the calculated structure ampli-

tudes |FC

 

. In the early stages of a structure determina-
tion, when the exact phases of [PC] are not known well, a
trial structure can sometimes be arrived at by calculating

a difference synthesis where dominating heavy atom contri-
butions are removed. Three criteria should be considered

in selecting the coefficients. In the first case, when

)Fol is approximately equal to (FC)(|F0| QZIFCI), the calcu—

lated phase is probably Close to the true phase. The

 

second case is then [Fol is much larger than )FC)()F0 AleC|).
Here, because FC is small, the calculated phase is fairly
uncertain due to the fact that small changes could cause
fairly large changes in FC. Thus, use of the calculated
phase for |FO| becomes very unreliable and can introduce

large errors. In the third case, where (EC) is much

larger than (F0|(|FCI>>|F0|), even though the discrepancy

is large the Sign of the difference is correct. Therefore,
the reflections used in a difference synthesis should be
mostly those satisfying the first and third cases.

Because an unambiguous location of the light atoms
could not be obtained from the |F0| synthesis due to the
many spurious peaks, a difference synthesis was computed.
Since the difference synthesis is very sensitive to the

scale constant between |F0| and (FCI, an accurate scale

constant must be applied to either the FC or IF0|(if|Fo|

35
is not on the absolute scale). The scale constant k can
be obtained from a WilSon plot of the data. A Wilson plot

is based on the equationzorz1

N
1n(<IFoI2>/ 2 £31) = ln k — 2B(Sin 6/1)2 (6)
i=1
where <[F0|2> is related to the average intensity, fOi is
the scattering factor of 1th atom, N is the total number

of atoms in the unit cell and B is an average thermal
parameter. By plotting the quantity ln(<[F0]2>/ g fgi)y§
(sin 9/A)2, a straight line can be obtained fromlwhich the
intercept is ln k and the Slope is 2B. In applying the
Wilson plot to the intensity data of MnTPP, the reflections
were separated into 12 ranges of 29, where each range con—
tained about the same number of reflections (approximately
250). Values for < ]F0|2> and (sin 9/A) were calculated
for each range. The quantity fOi was taken from f—curves
at the average (Sin O/A) for each range. The result of
this plot gave for B the value of approximately 4.0 32.
The value of the isotropic thermal parameter obtained was
about that expected for organic compounds (between 3 to
5 32)?2 The summation of observed and calculated structure
factors suggested for the scale constant a value of approxi—
mately 0.82. Since the value of k obtained from the
Wilson plot seemed unreasonable this latter value was used
in the structure factor calculations.

Initially, isotropic temperature factors of 3.5 82 and

4.5 A2 were assigned to Mn and Cl atoms, respectively. The

 

36
R—factor of the calculation, where R is defined as
Z )IF0) - {Fell/Z |F0|, based on the Mn atom alone was 0.69,
while the R-factor including both Mn and Cl atoms was 0.52.
The observed and difference syntheses calculated were based
on the latter structure.

The structure determination can be divided into three
stages. In the first stage, a difference, Apl, and observed
electron density, p01, were computed using 1266 reflections
whose calculated structure factors were greater than 14
electrons (on an absolute scale). By considering only
those peaks which occurred in both densities as possible
atoms, four nitrogen atoms and thirteen carbon atoms were
located with reasonable bond distances in the approximately
expected geometry. The structure factor calculation with
these seventeen atoms had an R—factor of 0.458. The same
structure factor calculation excluding the chlorine atom
from the calculation increased the R-factor to 0.507. Thus,
at this stage, it was decided that Cl atom was truly in
the crystal.

In the second stage, new observed and difference syn—
theses, P02: and A92 were calculated with 2037 terms whose
magnitudes were greater than 8 electrons (based on the struc—
ture factor calculation with R = 0.458). Twelve additional
carbon atoms were located. The observed electron and dif..
ference densities were plotted in the vicinity of each atom
to obtain better coordinates and to approximate individual

temperature factors. The heights of two peaks from p01

37
decreased in p02, with two new peaks forming near the
original peaks. Furthermore, the distances between the new
peaks and their adjacent peaks were closer to acceptable
bond lengths. Thus, the coordinates assigned to the old
peaks were replaced by those of the two new peaks for the
next calculation. A structure factor calculation using a
new scale constant of 0.75, including the Mn atom, the Cl
atom, flmr nitrogen atoms, and 23 carbon atoms had an R—
factor of 0.385.

In the third stage of the structure determination, new
difference and observed electron density maps, Apa and
p03, including 2725 terms, were calculated from which the
remaining 21 carbon atoms were found. Individual isotropic
temperature factors were then assigned to each atom by com—
paring the peak heights and shapes in the observed and
calculated density maps. A structure factor calculation
including the complete molecule, except hydrogen atoms, had

an R—factor of 0.235.

5. Refinement by the Method of Least Squares

Once a model of a trial structure has been prOposed, it
is usual to improve the preliminary coordinates of the atoms.
This process is known as refinement. Of the several methods
of refinement which can be used in crystal structure analy—

sis, that of least squares was used for CanTPP.

38
The principle of least squares, applied to a structure
refinement, is that the best values for a set of parameters
are those which minimize the sum of the squares of the
properly weighted differences between the observed and
calculated structure amplitudes for all independent reflec-

tions. The quantity to be minimized can be written

W
II
II. M 2

1 wi (IFO) _ )FC))2 I

i
where N is the total number of the independent reflections,
and wi is the individual weight of the observed structure
factor. The weight of the reflection is defined to be the

inverse of the square of the standard deviation of the cor—

responding observation

 

Usually, only relative weights can be estimated easily.

(1) Weighting Scheme

In order for the method of least squares to work best,
it is necessary to have a reasonable weighting scheme ap-
plied to the observed structure factors. The weighting
scheme, similar to that described by Hughes,47 which was
chosen for the refinement of CanTPP structure was

2.0

when |F0[.: 15.0 , o

I

0.1 X (F0

 

and when )Fo) > 15.0 , 0

Thus, when |F0| was greater than 15.0, the standard deviation

39
of the reflection was assumed to be directly related to
the magnitude of the observed structure amplitude; when

less than 15.0, the error was assumed constant.
(2) The Method of Least Squares

In the least squares refinement, the parameters which
are varied are the three coordinates of each atom, the
overall scale constant, and the individual temperature
factors. For the latter, each atom can be assumed to have
an isotropic temperature correction of the form of
exp(-B sin2 9/A2), or an anisotropic temperature correction
in terms of six parameters which describe a thermal ellipsoid
as:

T(hkfl) : exp ‘ (Diihz + Bzzkz + (3332 + Zfiizhk +

Zfilahg + 2823kfi) .

Individual isotropic temperature factors can be converted

to the anisotropic form by the relationships

.3 .3
511 = Ba*2/4 7 512 = Ba* - b*/4 , etc

where a* , b* , etc are reciprocal Cell constants.

The isotropic thermal parameters of the last structure
factor calculation, which had an R-factor of 0.235, were
converted into anisotropic parameters, and the weighting
scheme described above was applied before a least squares
calculation was performed using the program ORFLS.23 After

completion of one Complete cycle of refinement in which

40
atomic coordinates and anisotropic temperature factors
were varied, (atomic parameters of the 24 inner atoms were
allowed to vary first followed by the atomic parameters of
the outer atoms) the residual index, R, decreased to 0.173.
By readjusting the scale constant from 0.75 to 0.72, the
R—factor decreased further to 0.157. After another cycle
of refinement in which the anisotropic temperature factors
of only the Mn and Cl atoms were varied, the R—factor was
0.149. One further cycle of refinement on all parameters
brought the R—factor to 0.125. At this time the bond dis—
tances and angles of the model were calculated, and were
found to deviate in a significant way from those expected
on the basis of other porphyrin structures.

Because of the manner in which the crystal was mounted
(long direction perpendicular to the T—axis) the data were
affected by serious absorption problem. Since this effect
was only corrected in an approximate way, it was decided
to apply a more nearly accurate absorption correction at

this time based on a method proposed by Phillips.24
(3) Phillips‘ Absorption Correction

Generally, as a crystal rotates about the goniometer
axis at the angular setting X = 90° , the intensities of
an axial reflection vary as a function of the azimuthal
angular setting, T, for the corresponding reciprocal lat—

tice level. By measuring the intensities of an axial re—

flection as a function of T, a relative transmission T

41
(or absorption, A) curve can be obtained. The transmission
and absorption coefficients of the axial reflections have

the relationship:
A = 1/T = ImaX(T0)/I(T)

where To is the particular angular setting which gives
the maximum intensity.

In the Phillips“ absorption correction, the trans~
mission coefficients for any general reflection (hkfi) are

given approximately by the expression

TIth) = [T(Tinc) + T(Tref)]/2
where T. and T are the azimuthal angles of the
inc ref
incident and reflected beams. Both T. and T can
inc ref

be expressed in terms of T the crystal setting at which

hkfi’
the reflection plane (hkfi) is parallel to the incident X“

ray beam, more explicitly

¢inc ' (mhkfi " Ehkg) ' and ®ref ‘ (¢hk£ + éhkfi)
where th2 and éhkfi are the angular differences between
¢hk£ and the angles of the incident and diffracted beams

projected on the equatorial plane. For a four-Circle dif—

fractometer, ehkfi and éhkfi are given as

C - T = sin_1 (sin 9 cos X)
It should be pointed out that this semi—empirical method

can give only the relative values for each absorption cor—

rection; the additional scale constants corresponding to

42
the reciprocal lattice levels must be obtained from other
sources.
The absorption factor A can be obtained either by
experimental observation or by calculation by evaluating

the integral
A =f ~1- exp [-ILW + 3’ )1 dV
V V d B

where V is the volume of the crystal, u is its linear ab—
sorption coefficient, ya the path length along the primary
beam direction, and VB that along the diffracted beam
direction. This integral can be solved by numerical
methods (computer program, ORABS)25. Input to ORABS con-
sists of the unit cell dimensions, the linear absorption
coefficient, and the distances from the surface boundary
planes to an internal reference point. The absorption
curve can then be computed as a function of azimuthal angles
T and reciprocal lattice levels. The relative scale con—
stants between the corresponding reciprocal lattice levels
can be evaluated by considering the direction of least
absorption from each absorption curve.

The dimensions of an idealized CanTPP crystal and
the orientation of the three axes of the unit cell within
the crystal are shown in Figure 6. The linear absorption
coefficient of CanTPP is 41.0 cm_1, and the six boundary
planes and their distances from the center of the crystal
are listed in Table 2. The Calculated absorption curves

were in good agreement with the observed ones in both shape

43

.muouomw aoflumuomflm

m wupmeomm Hmummuo Tumaflxoummm .m Tusmflm

meansmaoo no

TIEEn—d l1.

 

 

 

ES mud ES mac

 

 

 

44
and magnitude, in Table 3 are listed the maximum absorp—
tion factors obtained from these observed and calculated
absorption curves. The scale constants obtained on the
basis of the least absorption in each absorption curve are

also presented in Table 4.

Table 2. Boundary Planes and Their Distances
from the Center of the Crystal.

 

Planes Distances (Cm)
100 0.0100
I00 0.0100
Iii 0.0075
T11 0.0078
1I1 0.0076
iiI 0.0075

A new data reduction was computed using this new ab—
sorption correction, but no significant improvement re-
sulted in the R-factor of the last cycle of refinement.

At this stage it became increasingly more evident that the
discrepancy between the observed and calculated crystal
densities was probably an important factor affecting the
residual index. After substracting the contribution to
the crystal density due to CanTPP, there still remained

approximately 40 a.m.u. of additional mass.

45

 

Reciprocal Levels

 

020
040
O60
O80
0,10,0
0,12,0
0,14,0
0,16,0
0,18,0
0,20,0

 

Table 3. Maximum Calculated and Observed Absorption Factors.
Absorption Curves in the (A ) (A )
Reciprocal Leyve‘lflo fy max Ob max Acal
020 1.70 1.70
040 1.73 1.69
060 1.68 1.65
080 1.60 1.57
0,10,0 1.54 1.55
0,12,0 1.47 1.52
0,14,0 1.43 1.43
0,16,0 1.33 1.36
0,18,0 1.26 1.29
0,20,0 1.17 1.22
Table 4. Scale Constants for each Reciprocal Level

Scale Constant

 

1.00
1.00
1.01
1.01
1.02
1.03
1.04
1.06
1.08
1.11

46

(4) Finding the Acetone Molecule

A difference electron density (at R = 0.125) was com-
puted and four relatively large peaks (~23 electron/A3)
were found in the vicinity of the Cl atom and the porphyrin
molecule. From an examination of the distances between
peaks, the corresponding angles, and the peak electron
densities, they were found to display the geometry expected
of an acetone molecule. By including Mn, Cl, the TPP mole-
cule, and an acetone molecule into the next structure
factor calculation, the R-factor was 0.129. After one
cycle of refinement on coordinates and anisotrOpiC tempera-
ture factors of all the atoms, the R—factor decreased to
0.085. After one more cycle on the coordinates and the
anisotropic temperature factors of Mn, Cl, and the acetone
molecule, the R-factor decreased to 0.078. Since the R—
factor had improved significantly, the Convergence of the
least squares calculation was assumed. An attempt was now

made to locate the hydrogen atoms.
(5) Finding the Hydrogen Atoms

The nomenclature of the atoms in the porphyrin mole—
cule is shown in Figure 7. Hydrogen atoms are named cor—
responding to the carbon atoms to which they are bonded. A
difference electron density based on the structure at an
R—factor of 0.078 was calculated to see if hydrogen atoms

would be observable. All hydrogen atoms were found at

47

PH44

PH45 PHlb PH”
"“3
4 PHI7
Pm C43
C42 PHI4
PI“? sz
P1147 \ 4 PHIS
C44 C41 /
PHAI/ \ \PHII
N4 \
34 cu
C33 \ / €12
3 N3 NI 1
C32 / \ cm
31 cu
\ /N2 /
”31.—"C24 \2‘ /PH21
/ 2 \ m.
"”37 PH32 P 22
C23
36 C22 2 PH24
P
H 3 PH33 PH27
PH25
PH35 ma. "'2"
Figure 7. Porphyrin skeleton nomenclature. Numbering of

phenyl and pyrrole groups is also indicated.

48

approximately the correct locations, but only 13 hydrogen
atoms which had the better peak heights and shapes were
selected to be included in the next structure factor calcu-
lation. The isotropic temperature factors of the hydrogen
atoms were assumed to be approximately 20% greater than
those of their adjacent carbon atoms before the former had
been converted to anisotropic values. One cycle of least
squares refinement in which the coordinates of all the
atoms (including H) and the anisotropic temperature factors
of all the atoms except the 13 hydrogen atoms were varied,
decreased the R—factor to 0.0720 Another difference map
was calculated and it showed the remaining hydrogens much
improved in peak heights and positions. These were included
in calculations and the R——factor became 0.067 after one
more cycle of refinement on all the coordinates and aniso-
tropic temperature factors. Since the acetone molecule
seemed to occupy the Crystal lattice incompletely, a
weight of 75% was applied to all of its atoms. The final
structure factor calculation gave R = 0.069 and the least
squares refinement was terminated at this point.

The calculated crystal density based on CanTPP and
including a 0.75 occupancy of acetone is 1.31 g/cm3, while

the observed density is 1.30 g/cm3.

IV . STRUCTURAL RESULTS

The final coordinates, anisotropic temperature factors,
the mean square atomic displacement (Hz) in the direction
of each principal axis, and peak heights of all the atoms
in CanTPP are listed in Table 5. The labeling of the
atoms has already been shown in Figure 7. The coordinates,
the peak heights, and the isotropic temperature factors of
the hydrogen atoms are shown in Table 6. The atomic param—
eters of the acetone molecule are listed in Table 7.

The procedure for fitting a set of points to a plane
or a line by a least squares method was described by
Schomaker5.1 The equation of a plane can be denoted as
mlx + mzy + m3z = d, where d is the distance from an
origin to the fitting plane. The parameters m1, m2, m3,
and d for the equations which best describe the individual
pyrrole rings, the phenyl groups, the four inner nitrogen
atoms, the sixteen-inner atoms of the porphyrin and the
nuclear least squares plane (NLS) which encompasses the
four pyrrole rings and four bridge carbon atoms are listed
in Table 8. The dihedral angles (in degrees) between the
NLS plane and those of each individual phenyl ring and the
angle between the NLS plane and the line between the Mn and
Cl atom are given in Table 9.

49

50

 

 

 

Table 5. The Final Atomic Coordinates, Thermal Parameters,
cooggigigiisln Anisotropic Temperature

Atom x y Z 311 922 933
Mn —0.4773 0.1150 0.0900 0.0067 0.0011 0.0056
Cl 0.6276 0.1673 0.2585 0.0010 0.0019 0.0061
N1 0.4000 0.0619 0.0756 0.0052 0.0013 0.0054
C11 0.2801 0.0789 0.0336 0.0093 0.0015 0.0074
C12 0.2413 0.0356 0.0695 0.0103 0.0016 0.0077
C13 0.6626 0.4926 0.3672 0.0078 0.0016 0.0081
C14 0.4342 0.0077 0.1351 0.0068 0.0015 0.0054
N2 0.6437 0.0427 0.1493 0.0067 0.0011 0.0064
C21 0.3663 0.4865 0.3183 0.0074 0.0013 0.0056
C22 0.2666 0.4461 0.2867 0.0079 0.0014 0.0065
C23 0.1951 0.4777 0.2963 0.0095 0.0013 0.0066
C24 0.7512 0.0381 0.1666 0.0063 0.0012 0.0058
N3 0.6266 0.1595 0.0721 0.0067 0.0012 0.0053
C31 0.7493 0.1448 0.1195 0.0063 0.0016 0.0057
C32 0.7238 0.2445 0.0747 0.0089 0.0021 0.0092
C33 0.8108 0.1974 0.1222 0.0111 0.0014 0.0092
C34 0.6085 0.2211 0.0415 0.0092 0.0016 0.0066
N4 0.3738 0.3243 0.4839 0.0063 0.0013 0.0063
C41 0.2497 0.3269 0.4387 0.0069 0.0013 0.0063
C42 0.1744 0.2749 0.3665 0.0073 0.0019 0.0072
C43 0.2549 0.2397 0.3722 0.0088 0.0018 0.0060
C44 0.3810 0.2695 0.4464 0.0081 0.0014 0.0065
PH11 0.2046 0.3704 0.4644 0.0078 0.0014 0.0065
PH12 0.0727 0.3606 0.4201 0.0057 0.0017 0.0074
PH13 0.9734 0.4045 0.3491 0.0087 0.0034 0.0105
PH14 0.8479 0.3964 0.3065 0.0090 0.0052 0.0127
PH15 0.8246 0.3440 0.3352 0.0117 0.0040 0.0160
PH16 0.9247 0.3004 0.4079 0.0157 0.0037 0.0190
PH17 0.0475 0.3099 0.4512 0.0123 0.0023 0.0125
PH21 0.4586 0.4712 0.3179 0.0083 0.0009 0.0057
PH22 0.4388 0.4128 0.2605 0.0073 0.0015 0.0047
PH23 0.5304 0.3659 0.3225 0.0117 0.0012 0.0085
PH24 0.5125 0.3112 0.2694 0.0131 0.0016 0.0111
PH25 0.4037 0.3038 0.1563 0.0127 0.0019 0.0091
PH26 0.3123 0.3498 0.0952 0.0126 0.0023 0.0095
PH27 0.3307 0.4052 0.1470 0.0119 0.0022 0.0065
PH31 0.8071 0.0864 0.1575 0.0061 0.0015 0.0053
PH32 0.9326 0.0772 0.1929 0.0074 0.0013 0.0072
PH33 0.0460 0.0598 0.3016 0.0064 0.0023 0.0076
PH34 0.1642 0.0541 0.3320 0.0070 0.0028 0.0122
PH35 0.1730 0.0664 0.2579 0.0114 0.0024 0.0140
PH36 0.0611 0.0846 0.1509 0.0117 0.0021 0.0145
PH37 0.9406 0.0895 0.1173 0.0114 0.0021 0.0093

51

and Peak Heights of MnClTPP.

 

 

 

Peak

Mean Square Atomic Hei ht

_Earameters Displacements* (X?) ge/ 3)
0.0002 0.0047 0.0002 2.01 2.36 3.22 34.9
0.0003 0.0057 —0.0004 2.59 3.89 4.59 19.9
0.0006 0.0039 0.0003 1.57 2.82 3.25 7.1
0.0000 0.0070 0.0001 2.25 2.85 4.36 6.1
0.0002 0.0071 0.0002 2.91 3.03 4.54 5.5
-0.0000 0.0062 -0.0000 2.53 3.13 4.54 5.3
-0.0003 0.0049 —0.0001 1.97 2.73 3.22 5.5
—0.0000 0.0051 —0.0001 1.85 2.12 3.68 7.0
—0.0004 0.0051 ~0.0007 1.87 2.56 3.62 5.9
-0.0007 0.0059 -0.0002 1.72 3.03 3.89 5.4
—0.0004 0.0061 —0.0003 2.39 3.09 4.07 5.3
0.0002 0.0044 -0.0002 2.05 2.67 3.45 6.2
0.0003 0.0046 0.0004 1.97 2.26 3.25 7.6
0.0000 0.0048 -0.0000 1.92 2.94 3.25 6.0
0.0004 0.0071 0.0008 2.70 3.65 5.76 5.3
-0.0003 0.0081 0.0004 2.10 3.82 5.30 5.5
0.0005 0.0062 0.0005 2.59 2.85 4.18 5.8
—0.0004 0.0049 -0.0002 1.87 2.70 3.68 6.6
—0.0004 0.0050 0.0001 1.78 3.10 3.65 5.7
-0.0009 0.0049 -0.0009 2.39 3.75 5.01 5.2
~0.0007 0.0055 —0.0006 2.82 3.00 4.18 5.5
-0.0009 0.0059 —0.0006 1.94 2.56 4.10 5.8
0.0001 0.0055 0.0003 2.31 2.97 4.25 6.6
-0.0008 0.0046 -0.0011 1.92 2.79 5.34 5.7
0.0002 0.0072 0.0000 3.00 6.37 6.59 4.7
—0.0003 0.0077 —0.0001 3.16 8.19 9.78 4.1
-0.0022 0.0111 —0.0005 2.33 8.55 9.73 4.1
-0.0017 0.0154 —0.0006 2.23 7.44 10.87 4.1
-0.0007 0.0100 —0.0000 2.97 5.01 7.11 4.8
-0.0002 0.0054 —0.0001 1.75 2.53 3.51 6.3
-0.0004 0.0045 —0.0002 2.23 2.61 3.35 6.3
-0.0002 0.0082 —0.0003 2.20 3.00 5.17 6.5
-0.0000 0.0100 —0.0002 2.94 3.42 6.41 5.3
—0.0005 0.0082 —0.0008 3.13 4.55 5.63 5.2
—0.0006 0.0075 -0.0013 3.45 5.38 6.64 4.7
—0.0003 0.0070 -0.0006 2.53 4.44 5.01 5.2
0.0002 0.0044 0.0002 2.10 2.76 3.19 6.2
0.0001 0.0059 —0.0000 2.10 2.56 5.18 5.8
0.0007 0.0042 0.0004 2.42 4.55 5.76 5.1
0.0007 0.0058 0.0001 2.56 5.34 9.13 4.7
-0.0000 0.0101 -0.0001 3.38 4.55 8.24 4.7
~0.0001 0.0110 —0.0004 2.76 4.03 8.39 4.9
—0.0003 0.0084 —0.0006 2.88 3.96 5.59 4.7

52

 

 

 

Table 5. Continued.

Coordinates in Anisotropic Temperature

Fractions 4 _
Atom X Y Z 511 322 533
PH41 0.4927 0.2457 0.4808 0.0095 0.0015 0.0080
PH42 0.4930 0.1810 0.4509 0.0091 0.0017 0.0090
PH43 0.4717 0.1680 0.3612 0.0250 0.0021 0.0158
PH44 0.4901 0.1085 0.3432 0.0232 0.0034 0.0161
PH45 0.5244 0.0636 0.4146 0.0089 0.0046 0.0152
PH46 0.5412 0.4254 0.0041 0.0198 0.0025 0.0128
PH47 0.5238 0.3650 0.0233 0.0184 0.0011 0.0089
ox104 0.9-10 0.3—5 0.8-9 0.3—64 1 - 9 1 - 45
*In the direction of each principal axis.

 

53

 

 

Peak

Mean Square Atomic Hei ht

pgfarameters Displacements* (32) 194 3}
512 513 523 SWZfii SWZGZ 8w2fi§ Po
~0.0007 0.0075 -0.0006 2.02 2.70 4.90 5.9
-0.0015 0.0073 —0.0019 1.92 2.67 6.37 5.5
—0.0036 0.0175 —0.0040 1.38 4.97 12.50 4.6
-0.0044 0.0168 —0.0032 3.72 4.62 12.70 4.4
—0.0002 0.0083 -0.0037 2.45 4.86 14.80 4.5
~0.0013 0.0068 0.0003 4.36 6.41 15.99 3.7
w0.0013 0.0070 -0.0002 1.82 5.05 11.28 4.9

1 — 11 1 — 45 1 - 19

54

 

Table 6. Coordinates, Isotropic Temperature Factors, and
Peak Heights of the Hydrogen Atoms.
Peak
Hei hts

Atom X y z B e/§3
HC12 0.1460 0.0419 0.0461 5.0 0.4
HC13 0.6644 0.4472 0.3372 4.6 0.4
HC22 0.2521 0.4055 0.2724 4.1 0.5
HC23 0.1339 0.4528 0.2940 4.3 0.4
HC32 0.8952 0.1971 0.1435 5.4 0.5
HC33 0.7306 0.2926 0.0662 5.4 0.4
HC42 0.0663 0.2663 0.3201 4.2 0.5
HC43 0.2319 0.1957 0.3274 4.3 0.5
HPH13 0.9900 0.4520 0.3388 6.3 0.4
HPH14 0.7801 0.4309 0.2810 7.7 0.3
HPH15 0.7495 0.3310 0.3030 7.3 0.3
HPH16 0.9145 0.2574 0.4471 10.4 0.5
HPH17 0.1045 0.2772 0.4941 6.8 0.5
HPH23 0.6089 0.3745 0.3935 5.2 0.4
HPH24 0.5867 0.2796 0.3119 6.4 0.4
HPH25 0.4036 0.2602 0.1263 8.3 0.5
HPH26 0.2275 0.3440 0.0002 6.0 0.4
HPH27 0.2656 0.4466 0.0937 5.3 0.5
HPH33 0.0347 0.0476 0.3632 4.2 0.6
HPH34 0.2588 0.0500 0.4203 5.7 0.5
HPH35 0.2658 0.0548 0.2839 7.2 0.3
HPH36 0.0577 0.1032 0.0888 7.4 0.5
HPH37 0.8660 0.0994 0.0365 5.9 0.5
HPH43 0.4000 0.2000 0.2830 10.6 0.3
HPH44 0.4332 0.1167 0.2667 10.9 0.3
HPH45 0.5373 0.0242 0.3870 8.0 0.3
HPH46 0.5297 0.3564 0.0944 8.4 0.4
HPH47 0.5827 0.4534 0.0673 5.8 0.3

55

 

 

Table 7. Atomic Parameters of the Acetone Molecule.

Atom X Y Z 511 322 P33 @12
01 0.8601 0.0380 0.5021 0.0285 0.0050 0.0212 0.0015
C2 0.9001 0.0860 0.5075 0.0152 0.0020 0.0105 0.0025
C3 0.9576 0.1030 0.4626 0.0192 0.0092 0.0113 0.0054
C4 0.9120 0.3621 0.0686 0.0320 0.0067 0.0110 ~0.0096

0x104 18-54 8 — 30 3 - 30 8 — 14 1 _ 27 11—16 1 - 16

Peak

Hei ht

Atom 613 623 8v2ޤ 8w2ޤ 8wzޤ e/ 3
01 0.0139 0.0016 8.44 11.95 18.27 3.0
C2 —0.0013 0.0027 0.81 6.28 23.89 3.3
C3 0.0133 0.0028 2.02 6.41 19.43 2.8
C4 0.0121 —0.0013 3.65 5.97 25.83 2.6

0x104 3 - 40 4 — 16

 

56

 

Table 8. Parameters for the Equation, mlx + mzy + m3z = d
Selected to Fit Planes.
Planes m1 m2 m3 d
lst Pyrrole 2.321 11.87 11.76 0.682
2nd Pyrrole -1.338 6.826 12.39 1.298
3rd Pyrrole —5.342 5.542 15.14 —1.385
4th Pyrrole —5.590 10.781 13.97 -0.404
lst Phenyl -5.536 -10.58 14.01 —2.980
2nd Phenyl 1.319 - 8.341 -13.22 4.960
3rd Phenyl —0.008 20.86 3.433 2.280
4th Phenyl 11.60 — 4.116 ~ 2.852 4.521
NLS —3.757 8.992 1.356 0.021
Inner 16 Atoms —3.727 9.049 13.53 0.047
Inner 4 Nitrogen ~3.753 9.190 13.50 0.041

 

Table 9. Dihedral Angles between the NLS Plane and the
Individual Phenyl Planes and the Angle between
NLS Plane and Mn—Cl Line.
Plane Dihedral Angle

(degrees)
lst Phenyl 54.2
2nd Phenyl 123.5
3rd Phenyl 49.7
4th Phenyl 77.4
Angle between NLS plane and Mn—Cl line* —— 85.3O

*
The equations for the line between Mn and Cl atoms are:

x = 0.575 + 0.004 t, y = 0.141 + 0.022 t, and
z = 0.174 + 0.071 t, where t is a parameter with real
values.

57

The atomic deviations from the calculated least squares
planes on the basis of different groups of atoms are listed
in Tables 10 and 11. The atomic deviation for each atom
in the porphyrin skeleton from the NLS plane is shown in
Figure 8, and the atomic deviation for each atom from the
least squares plane of the inner sixteen atoms is shown in
Figure 9. The various bond distances of the porhyrin
skeleton are presented in Figure 10a, and Figure 10b, with
the corresponding bond angles in Figure 10c. The MnTPP
molecule drawn in perspective in terms of its vibration
ellipsoids is shown in Figure 11 (ORTEP).26

The structure of CanTPP crystal viewed on the bc
plane is shown in Figure 12. There are four molecules
packed in each unit cell, with the molecules stacking nearly
perpendicular to the 3* direction. The molecules in the
unit cell are related by the following symmetry operations:
molecule II can be generated by rotating molecule I about
a 2-fold axis at z = 1/4 and x = 1/2, followed by a
translation of 1/2 along the b axis; the same rotation
and translation generate molecule IV from molecule III; the
pair of molecules I and IV and the pair II and III are re~

lated by a center of symmetry.

 

 

58

Talole 10. The Atomic Deviations from the Least—Squares
Planes of the Individual Pyrrole and Phenyl Rings.

 

 

 

 

 

 

 

 

Atom d,§g) Atom d,§R}
First Pyrrole Second Pyrrole
N—1 0.011 N-2 —0.018
C~11 —0.005 C~21 0.012
C-12 —0.003 C-22 ~0.002
C—13 0.010 C—23 ~0.009
C—14 ~0.013 C-24 0.016
s.d* 0.011 s.d 0.014
Third Pyrrole Fourth Pyrrole
N-3 0.012 N-4 -0.017
C—31 -0.008 c—41 0.017
C-32 0.006 C—42 -0.010
C—33 0.001 C—43 0.000
C—34 —0.011 C—44 0.010
s.d 0.010 s.d 0.014
First Phenyl Second Phenyl
PH12 —0.017 PH22 0.002
PH13 0.001 PH23 0.005
PH14 0.013 PH24 «0.005
PH15 —0.011 PH25 —0.004
PH16 —0.006 PH26 0.011
PH17 0.020 PH27 —0.010
s.d 0.014 s.d 0.008
Third Phenyl Fourth Phenyl
PH32 ~0.002 PH42 0.026
PH33 0.008 PH43 —0.019
.PH34 —0.005 PH44 0.001
LPH35 ~0.003 PH45 0.011
LPH36 0.009 PH46 ~0.013
PH37 -—0 .006 PH47 ~0 . 005
€3.d 0.007 s.d 0.016

9(-

Standard deviation.

59

Tailole 11. Atomic Deviations from the Least Squares Plane
of Four Nitrogen Atoms.

5.29515. ”€1.13. .2.
N1 0.047
N2 ~0.047
N3 0.047
N4 ~0.047

s.d 0.054

 

60

 

Figure 8. Atomic deviations in (R) from the nuclear
least squares plane (NLS).

 

 

61

 

Figure 9. Atomic deviations in (A) from the
least squares plane based on the inner
sixteen atoms of CanTPP.

62

‘ 1-06 ’
‘\ {0.9“ ‘ 0'83 .

. L348 ' ~ 1373 ,’

1.383

 

Figure 10a. Bond distances (in 8), Broken lines
indicate C-H bond distances.

 

 

 

63

 

 

 

Rama r 2 0h]
\ I
f \ I It“
,' \ , ..
I \ ’
‘ 3646 Li ’1’, 3.148
3.571
“I
I
I
I
, 3.355 \
\
f .
3-57 3.536 \
Z 3. I75 T
\ 2A9
\\ 1
\ 2.834 2.806 , ’
2.022 Cl ’2
| 1
——Mn—— 1.999/
/ 2.793 2.021 2.825 .
’ \
T ’ \
2... 7
3 133
L 3.057 - 2 28
I
\\ ’
‘ I

\
3"52 I, {\\\\‘\\‘3 243
< ’ \ - a .
Q ‘ ‘ "
v23) [\33! 4

Figure 10b. Intramolecular distances. The numbering of-
the phenyl groups is indicated in the figure.
The dihedral angles from phenyl groups 1,2,3,
and 4 to the NLS plane are 54.20, 123.50,

49.70, and 77.40 respectively.

I

64

Figure 10c. CanTPP bond angles (degrees). Angle between
line Mn—Cl and NLS plane is 85.50.

L N1,Mn,N3 = 166.90
4 N2,Mn,N4 = 161 .70
2 N1,Mn,cl = 100.00
4N2,Mn,Cl = 101.00
zN3,Mn,Cl = 93.10
2 N4,Mn,Cl = 97.20

the standard deviation of the angles of the
carbon—carbon and carbon—nitrogen bonds is
approximately 0.6 N 1.0 degree.

 

65

 

Figure 10c.

66

 

Figure 11. A diagram in perspective of the MnTPP molecule
(ORTEP).

 

67

Figure 12. Crystal structure of CanTPP as viewed in the
. . A .
progection along a . The solid bar represents
the approximate least squares plane of the
porphine core.

 

 

 

 

 

 

 

 

 

V. DISCUSSION

The data presented in Table 5 indicate that the aniso—
tropic temperature factors of the carbon atoms generally in—
crease as the distance of the atoms increases from the center
of the molecule. Hence the peripheral carbon atoms have
decreased peak heights and increased standard deviations in
atomic coordinates. Such characteristics have also been ob—
served in the Mg(H20)TPP and free base tri-TPP structures.
These observations are assumed to be due to the contribution
of quasi—rigid body angular oscillations.

An acetone molecule of crystallization was found between
adjacent CanTPP molecules. The closest approach of the mole—
cule to the porphyrin is through the central carbon atom of
the acetone to the chlorine atom of CanTPP; the interatomic
distance of 3.58% does not indicate that any particularly
significant interaction is occurring (see Fig. 13). As is

typical of solvent molecules trapped in a crystal lattice,

 

the large temperature factors of the acetone molecule indi—
cate that it is either disordered with respect to the acetone
molecules in neighboring unit cells or that the acetone lat~
tice site is only partially occupied. A somewhat related
case in which a solvent molecule of pyridine was included in
the phthalocyanine complex of manganese(III)27 was observed.
Two planar and parallel manganese phthalocyanine—ring systems
which are joined by an oxygen atom midway between the two

69

 

70

Mn(3)

1§BPH2H41

(:u31

PH4H3)

 

N
PH43
Cl(2)

\3 73

3.58

Mn(2)

acetone

hAn(U

5..

Figure 13. Intermolecular distances from the chlorine atom.

_+

 

 

71
manganese atoms have two pyridine molecules coordinated to the
manganese atoms on either side of Mn—O—Mn bridge (see Fig. 2).

The bond distances and bond angles of the acetone of
crystallization are shown in Figure 14. The numbers in paren—
theses are those reported for an acetone molecule in the gas
phase.28 Although large discrepancies exist between the two,
there is sufficient correlation between the bond lengths,
angles and planarity of the molecule to state confidently
that it is an acetone molecule of crystallization.

The residual densities in the final difference electron
density map were in the range of 0.11 to 0.18 e/g3 in the re—
gion of the CanTpp molecule. Due to the large thermal motion
of the atoms in the acetone molecule, the peak heights of
its carbon atoms were much lower than those in the CanTPP
molecule. Either thermal motion or disorder prevented loca—
tion of the hydrogen atoms in the acetone molecule. The ran—
dom residual electron density in the vicinity of the acetone
molecule was of the order of 0.65 e/Ra, somewhat greater
than the average peak height for the hydrogen atoms of the
CanTPP molecule.

The bond distances of the porphyrin skeleton as
listed in Figure 10a have an average C—N bond distance of
1.384 f 0.009 A, an average Ca—Cm bond distance of 1.394 1
0.009 X (where Ca is the carbon atom adjacent to the
pyrrole nitrogen, and Cm is the methine carbon atom),
and an average C—H bond distance of 1.07 i 0.09 X, The
reported values of bond distances in an aromatic system
(such as benzene) listed in Volume III of the International

Tables for X—ray Crystallography are C-C bond of

 

72

O
1

1.16 A
(1,215)

126.8°C 1223.1o )
1.5) 2 121.5
(‘2 1o99°

(116.1) 1.46 A

1.53 A (1.515)
15
(1.5C ) c4
3
ACETONE
Figure 14. Bond distances and bond angles of the

acetone molecule of crystallization.

 

73

1.395 i 0.003 X, and C—H bond of 1.084 1 0.006 X. The
comparison of the bond distances reported in literature
with those determined in this structure analysis shows that
the average Ca-Cm and C—H is close to the expected value.

From Figure 10a, the average bond distance on the
basis of different groups of atoms in CanTPP has a some—
what different meaning. The average Ca—C bond distance

b

is 1.433 i 0.007 R and the average c is 1.356 1

b—Cb“
0.008 A (where Cb is the carbon atom adjacent to Ca).
The former bond length is shorter than the 0 bond length

of 1.49 8 between Sp2 hybridized carbon atoms, while the
latter is longer than the expected double bond value of
1.33 8, This behavior is commonly observed in most of the
porphyrins. The other C—C bond distance joining the bridge
carbon atom and the terminal carbon atom of the phenyl
group has an average value of 1.493 A, typical of a 0

bond in trigonally hybridized carbon atoms. Because of
possible steric interference between phenyl hydrogen atoms
and pyrrole hydrogen atoms if the phenyl groups were co—
planar to the porphyrin core, the phenyl groups are rotated
out of the NLS plane. Thus, the w electron systems of
the phenyl rings are isolated from the corresponding sys—
tem in the porphyrin core by pseudo—single bonds. As is
indicated in Table 10, the phenyl and pyrrole rings are
essentially planar as individual entities. The dihedral

angles between the individual rotated phenyl groups and the

 

74
NLS plane are 54.20, 123.50, 49.70, and 77.40. The large
variation in the angles shows indirectly the crystal pack—
ing forces.

The standard deviations of the molecular parameters
are in the range between 0.007 and 0.009 R for Ca—Cb,
Cb—Cb , Ca-Cm and C—N bonds. The standard deviations of
the crystallographic structure parameters from the last
cycle of the least squares structure factor calculation
based on the errors of carbon and nitrogen coordinates are
in the range between 0.006 and 0.013 A for C—C and C-N
bonds. According to Cruickshank's statistical significance
tests52:53 comparing the errors of the molecular parameters
to those of the crystallographic structure parameters, the
errors in the molecular parameters are insignificant, since
they fall within the value of three standard deviations of
the crystallographic structure parameters.

The atomic deviations from the least squares plane
based on the inner sixteen atoms of the porphine core are
given in Figure 9. Although the atomic deviations of the
nitrogen atoms, which range from 0.04 to 0.07 X, are prob—

ably not significant, every other pyrrole atom (149;,

 

C14, C24, C34, and C41) shows an appreciable atomic devia—
tion of approximately 0.25 A, alternating above and below
the least squares plane. The bridge carbon atoms, PH11,

PH21, PH31, and PH41, deviate approximately 0.1 X from the

mean plane. One can conclude from these atomic deviations

 

75
tzlaat the inner sixteen-membered ring is decidedly nonplanar,
jLI) contrast to the sixteen—membered ring found in tri—TPP
‘wJIuose carbon atoms are approximately within the plane.

From the many porphyrins whose structures have been
Cflxetermined, it is obvious that deviations from the planarity
c>:f the NLS plane vary uniquely from one porphyrin to
Einother, depending on the particular molecular structure

Eind various crystallographic packing forces. In the pre—

ssent case of CanTPP, the atomic deviations from the indi-

\7idual planes of each pyrrole and phenyl group are within

t:he error of the determination (see Table 10). However,

(:onsidering the whole porphyrin skeleton, one pair of

(diagonally opposite nitrogen atoms, N1 and N3, is dis-
]placed about 0.05 A slightly above the mean plane of the

nitrogen quartet, while the other pair is diSplaced about

the same distance below the plane (see Table 11). The

peripheral carbons of the pyrroles have an apparent (0.3—
0.5 g) deviation from the NLS plane in the same direction

as their corresponding nitrogen atoms (see Fig. 8). Be—

cause of this alternating arrangement, the porphine core

of CanTPP is ruffled in a puckered way. Furthermore, the

atomic deviations show approximate 4 symmetry.

In the structure of free base tri—TPP, each individual

pyrrole was found to be planar, but the departure from the
planarity of the porphine core differs in a significant way

from CanTPP. In tri-TPP, one pair of pyrroles carrying

 

76
1:11e central hydrogen atoms is inclined away from NLS plane,
Vvidile the other pair is approximately in the plane. In
Eiddition, the atomic deviations from the NLS plane of
<2 thTPP are substantially more pronounced than those ob~
55erved in tri—TPP.

Figure 15 shows the details of the central part of
tzhe CanTPP molecule. It can be seen that the four nitro-
ggen—nitrogen distances are similar, and the nitrogen-
czhlorine distances are not equivalent. The difference of
(3.22 R between N2—Cl and N3-Cl corresponds to a difference
caf 7.90 between the angles 1N2, Mn, Cl and 1N3, Mn, Cl.
In other words, the apical chlorine atom is slightly in—
clined toward the N3 atom. Calculations show that the
chlorine atom is inclined about 4.70 from the normal of the
plane of basal nitrogen atoms. Thus, the square pyramid
coordination of the manganese by the four nitrogens and one
chlorine is somewhat distorted. Examination of the geom—
etry around the chlorine atom shows an acetone molecule and
two phenyl groups belonging to two different adjacent
molecules to be the close neighbors (see Fig. 13). If the
chlorine atom were at the apical position of the square
pyramid, the contact between Cl atom and PH44 atom of the
other CanTPP molecule would be much shorter than 3.45 2,
about the minimum van der Waals contact distance. There«

fore, the chlorine atom, by tipping itself away fromihe

apical of the square pyramid, is able to keep a reasonable

 

 

77

Figure 15. The geometry and the dimensions of square
pyramidal coordination in CanTPP molecule.

Nl—Cl 3.346 R Mn—Nl 1.999 R LNl,Mn,Cl = 99.980

N2—Cl 3.392 Mn—N2 2.021 A N2,Mn,Cl = 101.04

N3-Cl 3.171 Mn—N3 1.992 A N3,Mn,Cl = 93.12

N4—Cl 3.297 Mn-N4 2.022 /_ N4,Mn,Cl = 97.21
Average Mn—N distance 2.008 8

Average center—nitrogen, Ct—N, 1.989

Out—of—plane displacement, Mn—Ct,0.273

78

CI

3.346

 

 

Figure 15.

79
contact distance to the surrounding atoms. In a similar
manner, the phenyl group with the PH44 atom has also ad~
justed its angular rotation so as to avoid other close
constraints and contacts with adjacent molecules due to
the crystal packing arrangement.

Of other interest is the fact that the Mn atom is
displaced 0.27 A from the mean nitrogen plane, and the
bond length of Mn-Cl of 2.363 A is somewhat shorter than
expected. Although there are no other convincing axial
bond length data available for five coordinate compounds,
general references tth—Cl bond distances in a variety of
compounds can be found for comparison. The Mn-Cl bond
distance in manganous chloride dihydrate29 (MnCl2-2H20)
is 2.57 8, while Mn-Cl distance in the complex of hexa~
methylenetetramine with manganous chloride3O (abbreviated
HMT, MnC12'2(CH2)6N4'2H20) is approximately 2.47 X. It
can be said that the longer bond distance in MnC12‘2H20 is
expected due to the ionic character, while the shorter
length in HMT corresponds to some covalent bond character.
Consequently, the Mn-Cl distance of 2.363 A in CanTPP
suggests that there is significant covalent bond character.
In addition, the average Mn—N distance of 2.008 A is also
somewhat shorter than that expected by covalent radii
estimates (2.04 X)_ The shortening of both the Mn—Cl and
Mn-N distances might be responsible for the relative high

stability of this unique porphyrin.

 

80

The shortening of axial ligand distance of square
pyramid geometry is also found in ClFeTPP. A qualitative
consideration by molecular orbital studies suggested10
that the 3 dz2 orbital of the metal combined with an
appropriate o—type orbital of axial ligand to give a
strong bonding and a weakly antibonding orbital. Also,
the 4s and 4 pZ orbitals of the metal can further con—
tribute to the bonding.

The structural parameters of some five—coordinate
metallotetraphenylporphyrins are listed in Table 12. Be—
cause Mg(H20)TPP, ClFeTPP, and (H20)ZnTPP31 crystallize in
the same disordered structure type, the precision of param—
eter determination is not so good as desired. However, it
can be seen that the radius of the central hole of the
porphine core Ct-N of CanTPP is the shortest of all these
tetraphenylporphyrins. There appears to be a contraction
of about 0.05 R in going from the Ct-N value of 2.043 A
of porphine to that of 1.989 A of CanTPP. This contraction
might be the cause of the ruffling of the porphyrin core
upon metal and side—chain substitutions. In addition to
the shortening of Ct—N distance, the Mn—N bond distance of
2.008 X is somewhat shorter than that of 2.04 X estimated
from covalent radii. The other bond length Ca~N, Ca-C

b

and C are approximately the same as those of other

b'cbn
tetraphenylporphyrins. A comparison of the bond lengths
of CanTPP and porphine indicates a slight expansion of

the Ca—N bond, and a slight contraction of the Ca—Cb

 

Table 12.

81

Average Stereochemical Parameters of the Porphine
Skeleton in Some Five Coordination Metallotetra-
phenylporphyrins (two free base molecules are

given for comparison).

CanTPP M9(H20)TPP ClFeTPP (H.0j2nTPP tri-TPP Porphine*

M-N 2.008 2.072 2.049 2.05 —— ——
th—N 1.989 2.054 2.012 2.04 2.065 2.043
a-N 1.384 1.376 1.384 1.38 1.369 1.379
a—Cb 1.433 1.431 1.446 1.430 1.442 1.442
b—cb. 1.356 1.360 1.380 1.37 1.351 1.355
a—cme 1.394 1.415 1.395 1.42 1.398 1.382

A 0.273 0.27 0.383 0.20 —— ——

aMetal—nitrogen distance.

bCenter-nitrogen distance.

Cca is the carbon atom adjacent to pyrrole nitrogen.

d

C is the carbon atom adjacent to Ca'

b

eCm is the methine carbon atom.

f A is the out-of—plane displacement of the central

metal atom.

.X.
From the structure determination in Part II.

82

bond, but the C bond, as in general, is relatively

b—Cb‘

insensitive to metal substitution.

PART II

THE REDETERMINATION OF THE STRUCTURE OF PORPHINE

83

VI. INTRODUCTION

1. General

Porphine (Fig. 1b) is the parent compound of all the
porphyrins. The bond distances, the bond angles and the
planarity of this molecule form the basis of all comparisons
among the porphyrins. Porphine crystallizes with a mono—
clinic space group in which each asymmetric unit contains
one complete molecule. With such an arrangement, the
structure of porphine can be expected to be relatively
free from any crystalline imposed symmetry or distortion
and to approximate the molecule in its free state. There—
fore, accurate structural parameters, which are important
for the discussion of the general characteristics of
porphyrins, are particularly important for this molecule.

Since porphine is a conjugated system, its carbon~
nitrogen skeleton can be represented in terms of several
resonance forms. The usual structural assignments to the
free base of porphine lead to several possible configura-
tions for the center imino hydrogen atoms:32 1) hydrogen
atoms on opposite nitrogen atoms (Fig. 16, I), 2) hydro—
gen atoms on adjacent nitrogen atoms, (II), 3) hydrogens
in an ionic form, (III), and 4) hydrogen atoms occupying

84

85

 

 

 

IV ( Reson once structures)

Figure 16. Possible central hydrogen models
(from Dorough & Shen (1950))32

86
equivalent bridging positions between two nitrogen atoms,
(IV). In early studies, neither isomer I nor isomer II
could be conclusively isolated, even though a great number
of free base porphyrin compounds had been investigated.
It was thus concluded that the Structure of porphine was
that of either an inseparable equilibrium mixture of
isomers I and II or some other species (III or IV), in
which the hydrogen atoms were bonded in an entirely dif-
ferent manner. The inner—hydrogen structure of the free
base porphine and other porphyrins has been studied by
infrared and visible Spectroscopy, nuclear magnetic resonance,
and X-ray diffraction. These studies will be discussed

briefly.
2. Visible Spectroscopy

Studies of the visible absorption spectra of porphine
and some derivatives of it were carried out by Erdman and

Corwin.33 They observed that the absorption Spectrum of a

porphine in which one of the two inner hydrogens had been
replaced by a methyl group was identical with the absorption
spectrum of the corresponding unmethylated free base. These
results were interpreted to mean that the replaced hydrogen
was bonded covalently since the methyl group was certainly
bonded covalently, and the ionic and the resonance hydrogen
bridge structures (see Fig. 16, III and IV) were precluded.
However, the covalent character of inner hydrogens implied

that porphine could exist as structural isomers.

 

87

Subsequently, the visible spectrum of the free base
of a tetraphenyl porphyrin (TPP) was studied by Dorough
et al.32 The free base dissolved in E.P.A. (which is a
mixture of ether, isopentane and alcohol) forms a clear
glass without crystallizing at low temperature. The ab-
sorption spectrum of the solution was observed at room
temperature andthe<flass at liquid—air temperature. The
low temperature spectrum exhibited a blue shift for the
long wavelength absorption band, and a red shift for the
short wavelength band, the relative heights of these bands
were interchanged, and at the low temperature the fine
structure of some small bands was resolved. However, the
spectra of the metalloporphyrins of Sn(II) and Ag(II)
showed no shifting of bands at the two different tempera—
tures. Since divalent metals are presumably bonded equi—
valently to all nitrogens, the metallo—spectra led to the
interpretation that isomeric metallo—structures were impos-
sible. Hence, the behavior of the free base suggested
that more than one species was present.

Emission Spectra provide an experimental method for
obtaining information concerning whether or not a given set
of absorption bands is due to one or more absorbing species.
A fluorescence spectrum is physically and absolutely char—
acteristic of a given substance and results from an elec—
tronic transition from the lowest vibrational level of the
first excited state to the ground state. If a sample con—

tains two different species it will exhibit two absorption

 

88
bands which can be excited by a particular wavelength of
light and thus two different fluorescence spectra will be
obtained. Fluorescence spectra which could corroborate
the conclusions drawn from visible absorption spectra have
been carried out32, but they contained so many overlapping
bands they could not be interpreted easily. However, they
appeared to support the proposition that the free base
existed as an equilibrium mixture which resulted from the
tautomerism of the imino hydrogen atoms.

Theories have been developed which attempt to predict
the structural properties of some free base porphyrins and
metalloporphyrins. Molecular orbital calculations of por-
phine by Gouterman34 predicted that the spectrum of the
structure with the two central hydrogens on adjacent nitro—
gens would resemble closely that of the "opposite" tautomer,
since the energy of each of four B and Q bands was predi—

1 of its counterpart. Thus the

cated to fall within 500 cm—
calculation suggested that any ”adjacent" tautomer present
in solution would be very difficult to detect spectro—

scopically.
3. Infrared Studies

In the first systematic study of the infrared spectra
of porphyrins (in Nujol), Falk and Willis35 found that the
N—H stretching vibration appeared as a weak band at 3280-
3300 cm_1. In dilute carbon tetrachloride solution,

porphyrins gave N-H stretching bands around 3320 cm_1.

 

89
A comparison of the N-H stretching bands of pyrrole and
indole in dilute solution led to the conclusion that inter-
molecular hydrogen bonding had to be present, but, the ex—
act nature of this bonding was not suggested.

Subsequently, from solid state infrared spectroscopic
studies of porphine and many of its derivatives, Mason36
concluded that the nitrogen atoms of the porphine nucleus
were extensively hydrogen bonded. To account for the
observations he proposed three possible intramolecular
hydrogen—bonding schemes for the free base porphyrin (see
Fig. 17). In the first model, the hydrogen atoms were
attached to adjacent nitrogen atoms and hydrogen bonded to
the remaining nitrogen atoms (Fig. 17a). In the second,
the hydrogen atoms were bonded to opposite nitrogen atoms
and were hydrogen bonded to the adjacent nitrogen atoms
(Fig. 17b). In the third, the hydrogen atoms were sym—
metrically located between each pair of nitrogen atoms
(Fig. 17c). At the time the dimensions of the porphine
nucleus were not known, so these models were examined on
the assumption that the dimensions of the porphine core
were very close to those of phthalocyanine37 (an azapor—
phine), whose approximate structural parameters were avail—
able. From the latter, Mason concluded that the first
model would be less stable than the others due to the pene—
tration of each hydrogen atom into the van der Waals sphere
of the other. Using similar assumptions and scale models

of the porphine core, Badger, et al.,38 excluded the third

 

90

 

(a)

Figure 17. Mason‘s intramolecular hydrogen—bonded
models for porphine.

 

M
M =CH3

P = c H2C 112cooc143

Figure 18. Coproporphyrin.

 

91
model, which had symmetrical hydrogen bonds, because the
N...N distances of 2.65 and 2.76 2 found for phthalocyanine
would clearly cause the N...H bonds to be unsymmetrical.
Thus through the process of elimination, the second model

was considered the most reasonable.
4. Nuclear Magnetic Resonance

High resolution proton nuclear magnetic resonance
spectra of free base porphyrins have been reported by
Becker, Bradley, and Watson.39 The spectra were inter—
preted in terms of a "ring current" in the v conjugated
system as indicated by the heavy line in the porphine skele—
ton of coproporphyrin I (as shown in Fig. 18). In copropor-
phyrin I, the methyl groups attached to the two types of
pyrrole rings are at different distances from the W electron
distribution and should thus experience a different local
electrical field. However, the single sharp CH3 line ob—
served in the nmr spectrum indicated the methyl groups were
magnetically equivalent. Furthermore, at the freezing
temperature of solvent, CDCl3 (—63°C), no broadening of the
CH3 line was observed. Thus rapid tautomerism, which would
average the properties of the pyrrole rings, was suggested
as the only possible interpretation of the CH3 magnetic

equivalence. Calculations showed that the rate of the

tautomerism of NH proton should be much greater than 200 sec-

1

 

92

5. X—ray Studies

Several conflicting models of the inner hydrogen atom
structure of porphine emerged from the visible, infrared
and nuclear magnetic resonance spectroscopic studies. How—
ever, the X—ray diffraction crystal structure studies of
tri—TPP40, tetragonal TPP41 and porphine42 suggest that the
central hydrogen atoms are bonded to diagonal nitrogen atoms.

The structure determination of tri-TPP shows two inde—
pendent pyrroles and phenyl groups. Although the individual
pyrrole and phenyl groups are planar, the porphyrin core is
nonplanar, as indicated by the fact that one pair of the
centrosymmetrical pyrroles is essentially coplanar to the
nuclear least squares plane (NLS) of the porphyrin ring,
while the other pair, carrying the central hydrogen atoms,
is inclined approximately 16.60 to this plane. The slight
deviation of the two central hydrogen atoms from the NLS
plane gives H—H contact greater than the in-plane distance.
The four bonds which connect the methine carbon atoms to
the terminal carbon atoms of the phenyl groups are abnormally
long (1.5 X), and separate the phenyl rings electronically
from the porphyrin ring .

The crystal and molecular structure of tetragonal TPP
were determined by Hoard,et a}. They found that in each
molecule the central hydrogen atoms are bonded to opposite
nitrogens. The crystal structure achieves the space group
symmetry requirement (84—4) statistically by using a stereo-

chemical species in which hydrogen atoms are attached to a

 

 

93

diagonal pair of nitrogen atoms which in turn are in orienta~
tions differing by a 900 rotation. The.H—H separation is
about 2.1 X,

The bond parameters of the pyrrole of tetragonal TPP
are almost identical to the average of the two pairs of
crystallographically independent pyrroles of tri-TPP. Since
tetragonal TPP has the molecular symmetry of a fourfold in—
version axis, the four pyrroles are crystallographically
equivalent. For this reason, the pyrrole with a central
hydrogen is indistinguishable from that without a hydrogen
atom. Therefore, a precise determination of the inner
hydrogen atom structure in tetragonal TPP is limited.

The structure of porphine was originally determined
by Webb and Fleischer.42 They reported the porphine mole—
cule to be planar, with approximate D4h(4/mmm) symmetry,
with four half-hydrogens bonded to the nitrogen atoms. The
latter was explained as due to the interconversion of N-H
tautomers first suggested by Becker on the basis of nuclear
magnetic resonance work.39 During the structure refinement
of the porphine, a peak corresponding to 2-3 electrons was
observed at the center of the ring, and it was assumed to
be due to a 5-10% impurity of copper porphine. When this
electron density at the center of the molecule was removed
with a calculated contribution, the four peaks which appeared
in the vicinity of the nitrogen atomswere assumed to be half-
hydrogen atoms. Since peak heights of the half—hydrogen

atoms, 0.31, 0.42, 0.29 and 0.44 e 2-3, were only slightly

94
greater than the background of 10.2 e 8-3. Their structure
determination of the central hydrogens of porphine was at
best unreliable. Furthermore, even though the N—H bond
distances were reported, the exact nature of the half—hydro—
gen atoms in relationship to van der Waal"s hydrogen con—

tacts was not considered.

VII. EXPERIMENTAL

1. The Problem of the Hydrogen Atoms

The atomic resolution usually obtainable with CuKa
radiation, approximately 0.8 A, is sufficient to resolve
hydrogen atoms bonded to carbon or nitrogen atoms. Since
hydrogen atoms appear only as weak features on the observed
electron density of heavier atoms, they are commonly found
from a difference synthesis which provides a means for find—
ing hydrogen atoms by subtracting from the observed elec-
tron density the density due to the heavier atoms. Since
a difference synthesis is used, the observed structure ampli—
tudes ((Fol), the calculated structure amplitudes ()FC|),
the phases, and the scale constant between (Fol and ‘Fci
are important factors in determining the hydrogen locations.
To locate hydrogen atoms with certainty, accurate struc-
tural parameters of the nonhydrogen atoms, which relate to
the |Fcls , and accurate intensity data, which relate to
lFols, are required.

Since the hydrogen atom structure of the porphine
molecule, particularly the central hydrogens, was the
principal interest inxedetermining the structure, it was
desirable to know which reflections had a substantial
hydrogen atom contribution before intensity data collection

95

96

was undertaken. In addition to collecting a complete set
of intensities for all independent reflections, additional
and more elaborate counting techniques could be applied to
those reflections with an expected significantly measurable
hydrogen atom contribution, thus minimizing counting errors,
and adding7more significance to the hydrogen atom locations
as revealed in a difference synthesis. The reflections
which were to be examined in greater detail were ascertained
yia a structure factor calculation in which were required
the approximate atomic parameters of the hydrogen atoms and
the cell parameters of porphine. The necessary structural
parameters were obtained from the structure determination
of porphine by Webb and Fleischer.42

The numbering scheme for the carbon and nitrogen atoms
in porphine is given in Figure 19. The hydrogen atoms are
numbered corresponding to the atoms to which they are bonded.
The hydrogen atom structure factor calculations included
the methine and central hydrogen atoms, the latter in three
different combinations. These combinations arise from the
fact that the central hydrogen atoms might be associated
with different sets of pyrrole nitrogen atoms. The four
structure factor calculations which were computed were
based on the following structures:

1 H22, H24 structure

[\3

H21, H23 structure

(.0

( )
( )
( ) Four one-half hydrogen structure
(4) Four methine hydrogen structure (H5,H10,H15, and H20).

97

 

98
In (1), a structure factor calculation was based on a set
of two opposite inner central hydrogen atoms bonded to two
pyrrole nitrogen atoms. The second calculation (2) was
computed using the other set of two opposite central hydro—
gen atoms. In (3), half weights were applied to each of
four central hydrogen atoms, H21, H22, H23, and H24. This
central hydrogen atom structure was the one reported by
Webb and Fleischer, which is said to be due to rapid ex—
change between N-H tautomers. Structure calculation (4)
included those hydrogen atoms which are bonded to the bridge
carbon atoms of porphine, since these hydrogens were consid—
ered important for certain crystal packing properties which
might be associated with tri—TPP. All structure factor
calculations were confined to the scattering angle of 29
less than or equal to 50°, since the mean scattering factor
for a hydrogen atom is less than 0.2 electron beyond this
region.

The magnitudes of the four sets of structure factors
based on the different models of hydrogen locations were
compared. Reflections which might contain significant
hydrogen atom contributions were then grouped according to
the following scheme: (1)|FC|> 2.0 in any of the structure
factor calculations, and (2) 1.0 <|FCL5 2.0 in all the dif—

ferent calculations QF = 8.0 for central and 16.0 for

ckmax)

methine hydrogen atom calculations). The former included

about 10% of all the reflections considered and the latter

 

99
about 20%. The calculated PC for two reflections (523)
and (500) are given as examples.

Reflections Four 1/2H H21, H23 H22, H24 .Four Methine H
Structure Structure Structure Structure

 

(523) < 1.0 1.0 e 1.0 2.3

(500) 1.2 1.1 1.3 1.6

After such a process of elimination, eighty reflections
considered to be most sensitive to the atomic parameters

of the hydrogen atoms were chosen for measurement with more
elaborate counting techniques to minimize counting errors.
The details of these techniques will be discussed in a
later section.

The distribution of structure factors of the central
and methine hydrogen atoms of porphine in relationship to
the scattering angle (29) was also investigated using the
four sets of structure factor calculations. A graph of the
number of reflections whose calculated structure amplitudes
had a value [FC] : 1.0 is shown as a function of the scat—
tering angle in Figure 20. Hence, the reflections which
occur at medium scattering angles (300 to 45° of 20) may
contain significant hydrogen atom contributions and are
important for an accurate determination of the hydrogen

atom structure.

 

100

 

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o

 

ow o... ow
395%va 2|

8 91
o

\

mIIIIIIllllllllIn1lllIIIIIIIIIMN|\|\\\\\\\\\AU

quuoznum smooucmc wamnlmso HDom .m
wusuosnum ammonpws-wsflsuoe usom .N

mquposnum mmm .Hmm cam www.mmm .H
m>nso

accrue—woe *0 .02

.00

 

101

2. Preliminary X-ray Examination

Single crystals of porphine in the form of dark-red
square platelets were grown by slow evaporation from a
benzene solution. The space group was known to be P21/c
with the unique b axis located along one of the diagonals
of the plate. If the b axis is mounted precisely along
the spindle axis of the Weissenberg camera, mirror sym—
metry perpendicular to the spindle will be seen in an
oscillation photograph. Therefore, oscillation photo—
graphs were used to find the b axis of the crystal and
for preliminary alignment of the crystal.

A crystal with the approximate dimensions of 0.2 x
0.275 x 0.05 mm (shown in Fig. 21) was used for the X—ray
(CuKa) data collection which was carried out on a General
Electric XRD—5 Diffractometer equipped with a quarter circle
single crystal orienter. The porphine crystal was mounted
with the unique b axis along the 0 axis with the a*c*
plane in the equatorial plane of the diffractometer when
the angular X setting of the diffractometer is at zero
degrees. The angular settings of twelve reflections, which
were well-distributed in reciprocal space were carefully
measured and subjected to a least squares analysis from

which the best orientation and the unit cell dimensions

 

were obtained. The unit cell dimensions and their estimated

standard deviations are:

102

ES no.0

 

 

.mampmhso wcanmnom mo maoamJQEaD .HN mudmflm

EE nkmd Illllllli

 

\_

 

EEoNo

 

 

 

EEnNo.o\Tll EE mN—d 1
w

 

 

SEW—.0

 

 

 

 

 

103
a 10.271 1 0.003 R
b 12.089 1 0.003
c 12.362 1 0.004
B 102.17 1 0.020 .

Mosaic spreads, which among other things are used for
determining the quality of a crystal, were measured on cer-
tain reflections by offsetting the azimuthal angle of the
reflection to background level and then recording the inten—
sity in 0.050 steps across the peak until the background was
encountered again. Since the peak shapes of these mosaic
spreads were symmetrical with a maximum peak width of about
0.30 close to the base of the peak, the crystal was judged to
be of sufficient quality to allow intensity data to be col—
lected in any quadrant. For convenience, data were collected
in the quadrant which was bounded by ia* through +c*.

The reflections (040) and (0,12,0) were the only observ-
able reflections along the b* axis. However, (0,12,0) was
weak and not suitable for accurate measurements. Therefore,
an absorption correction was based on the (040) reflection
and was measured before and after data collection with the
average of the two measurements serving as the correction.

The maximum absorption occurred at the 0 values corresponding

to the —a* axis with a value of 1.07 (AmaX(—a*)), and the a*
axis (Amax(a*)) with a value of 1.14. The ratio Amax(a*)/
A aX(—a*) = 1.06 indicates the discrepancy in the intensity
m

measurements along the a* and ~a* directions. Anomalous ab-
sorption effects by a crystal can cause such disagreement be-

tween the intensities of equivalent reflections along the a*

104
direction, namely I(hk0), and those along —a* direction,
I(hkO). The average ratio obtained between the reflections
of these two zones (hkO, hkO) was 1.03, obtained from the
expression
< I hko > = 1.03 i 0.02
I hkO _
n—53

n is number of unique reflections.

The average ratio of 1.03 based on 53 measurements was con—
sidered more reliable than the ratio of 1.06 obtained from
the absorption curve. Therefore, the absorption curve was
adjusted slightly in the regions of the -a* and a* di—
rections to have the ratio of 1.03 instead of 1.06. This
adjustment gave the maximum absorption correction of 1.09
at the —a* and 1.12 at the a* direction.

The empirical absorption curve was used with Phillips“
method (see Part I) to correct for the absorption of X—rays
by the crystal. Basically, the procedure for evaluating
the absorption factor as given by Phillips is: (1) cal—

culate the azimuthal angles of incident and diffracted

beams,
¢inc = (¢hkg ' Chm) 7 ¢ref = (¢hk£ + 6hkz)
where
(th = 6hk£ = sin—1(sin 6 cos x),
¢hk£ is the 0 value of the reflection,

and (2) obtain the absorption factors A(¢inc) and AMref

)

105
from the absorption curve. Then, the absorption factor is

given by

A1hk2) = 1/T(hk2)

 

1
(T(¢inc) + T((DrefH/g

 

2
- 1/A(<1>inc) + 1/A(<I>ref)

3. Techniques for Measuring Intensities

In a crystal structure determination, the intensities
of all the reflections obtained from intensity—data measure—
ments form a set of relative integrated intensities; from
these intensities a set of structure amplitudes can be
derived by applying various geometrical and other correction
factors. The integrated intensity, I, can be expressed as

(see Appendix 1)

 

where I0 is the uniform intensity of the incident beam,

wv is the angular velocity of the crystal, and E is the
total energy of the diffracted beam. The equation indicates
that the integrated intensity of a reflection is prOpor—
tional to the total energy reflected by the crystal at a
reflecting position. The measurement of the integrated
intensity of a reflection is made by recording the number

of quanta entering the detector as the crystal rotates a

small angular range about the Bragg position. During this

 

106
measuring process, the detector (or a counter) can be
either kept stationary or given a small movement relative
to that of the crystal. Accordingly, some of the various
techniques used for measuring intensities are: (1) sta-
tionary crystal - stationary counter, (2) moving crystal -

stationary counter, and (3) moving crystal - moving counter.

(1) Stationary Crystal—Stationary Counter Technique*

This technique, as its name implies, involves no
mechanical motions whatsoever during the measurement of the
intensity. It depends on the apparatus and optics of the
experimental arrangement. The conditions required in order
to achieve a valid integrated intensity measurement43 are:

1) The intensity distribution across the width of
the X—ray source must be uniform.

2) The apparent width of the source must exceed; a)
the width of the reflection taken at the base of
the mosaic spread curve, b) the dispersion of the
spectra range to be measured, and c) the size of
the crystal as it must be completely bathed in the
X—ray beam.

3) The width of the aperture at the counter must be
greater than the apparent width of the source.

4) The response of the counter must be uniform across
the entire aperture used, and

5) If the source intensity varies with time, monitor
reflections measured at definite intervals must be
used to record the fluctuation of X—ray intensity.

9(—
Hereafter, referred to as SX.

 

107

The SX technique offers speed and simplicity in data col-
lection, but cannot be used to measure high—order reflec—
tions whose spectral components, Kai and Kaz, have angular
separations greater than the width of the counter.

In this work, the SX technique was used to measure
the intensities of all reflections within a limiting sphere
defined by 29 : 100°. A crystal of appropriate size was
chosen so that it was totally immersed in the X—ray beam.
Before the intensity of each reflection was measured, the
angular settings of the reflection were adjusted so that
the diffracted intensity was maximized. The intensity was
measured at the adjusted angular settings for a ten second
period with a nickel filter and then with a cobalt filter
(see balanced filter discussion in Appendix 1). The inte—
grated intensity of a reflection was taken to be the dif—
ference between the intensity recorded with the nickel

filter and that recorded with the cobalt filter.
(2) Moving Crystal - Stationary Counter Technique*

In this measuring technique, the detector is fixed at
the Bragg angle, 26, of the reflection and the crystal is
rotated with respect to the omega, w, angle (see Appendix 1).
The conditions for a valid integrated—intensity measurement
are:

1) The crystal must be rotated through an angle large

enough to cause every volume element to diffract

96
Hereafter referred to as MX.

 

108
from the full width of the source.

2) The counter aperture must be large enough to ac-
cept all the radiation of the desired spectral
range which is diffracted during the rotation of
the crystal.

3) The response of the counter must be uniform across
the full aperture.

4) Each and every increment of the angular position
of the crystal rotation carries the same weight
in the summation of the diffracted intensity.

The MX technique can be executed either by a continuous
scanning motion in angular rotation or by a step—by—step
motion. In the present work, a manual step-scan method
was used in the intensity collection of the eighty reflec—
tions which had been considered to have an important contri—
bution to the structure of the inner and methine hydrogen
atoms of the porphine molecule.

The step scan of the MX technique consisted basically
of using a count—six—drop—two omega (w) scan procedure
(Wyckoff, 1967).44 The intensity is measured at each of
six steps of the most sensitive angular position (w) and
the four largest measurements are used to compute the in—
tensity of the reflection. The reasons for applying this
procedure to this work are: (1) to increase the tolerance
of the most sensitive angular setting (w), and (2) to have
the best efficiency of total counting time.

Two methods, constant—count timing and constant—time

 

109
counting can be used to record the intensity at each step in
the w scan procedure. The counting rate in the constant~
time—counting procedure consists of accumulating counts dur-
ing a predetermined time T, and dividing the count accumula—
tion, Nj' by T. The other method, constant-count, is to
measure the time tj required to accumulate the predetermined

number of counts, c. The expressions for the counting rate,

Ij' in each method are:
Ij = Nj/T for constant—time counting
and Ij = c/tj for constant—count timing.

The corresponding estimated variances of these methods as

derived by A. J. C. Wilson45 are:

2 :
act(1j) Ij/T
2 N 2
6CC(Ij) Ij/c

where the subscripts ct and cc denote constant—time and con-
stant—count, reSpectively. The variance of the intensity for
a reflection can be minimized by proper adjustment of the
time of measurement for the constant-time method, or by a
careful choice of the predetermined count for the constant-
count method. The variance of intensities in the constant—
time count is directly proportional to the intensity, Ij’
while that in constant—count method is proportional to the
square of the intensity. Therefore, the magnitude of the
intensity of the reflection should also be taken into the
consideration to choose which of the measuring techniques
should be used for that reflection. In this work, the con-
stant—time step scan technique was used for the intensity
measurement of low intensity reflections, 142;, integrated

intensity of a reflection less than 200 counts/10 seconds

 

110
as determined from SX measurements, and the constant—count
step Scan technique was used for medium and high intensity
reflections. Details of the application of these measuring

techniques will be discussed later.

a. The X-ray Detector.

The electronic circuitry in the detection and counting
unit of G.E. XRD—5 Diffractometer consists of two main
parts, the Electronic Time Register and the Scaler. The
Electronic Time Register consists of six glow transfer
counter tubes from which time information can be obtained
by observing the relative position of the small glow dis—
charge in each of six glow tubes.

The scaler circuits standardize and accumulate the
pulses received from the Xeray detector. In addition,
various control circuits are available to provide for man~
ual, preset counts and preset time counting. The pulses
accumulated by the scaler in one counting cycle, defined as
the time necessary to accumulate a specified number of pulses
or a specified time interval, are displayed by eight Decimal

Counting Units.
b. Constant—time Step Scan Technique*

This method requires the number count, Nj’ for each step
to be accumulated for a predetermined time interval, 1. The
predetermined time, T, is selected by a switch on the XRD—5

scaler units, and Nj is indicated by visual read~out scalers.

The counting rate, Nj/T, is recorded and calculated.

9%
Hereafter referred to as CTST.

 

 

 

111

The step—scan was performed with respect to the most
sensitive angular position (w). The scan extended approxi-
mately 10.10 from the calculated position and the step scan
was carried out in 0.040 increments. The intensity was
measured for a preset time of 100 seconds at each of the
steps and the four largest measurements were totalled to
give the intensity of the reflection (count—six-drop—two,
Wyckoff, 1967).44 The crystal was then moved to the @—
position displaying the highest intensity and the back—
ground was recorded at this position for 100 seconds with
a balanced cobalt filter. Intensities measured for the
(241) reflection are given as an example of this measuring
technique, along with the corresponding SX values (see
Table 13). The intensities of the (241) reflection ob—
tained from the two measurement techniques, can be compared
on the basis of relative error, C, (Parish, 1965)46 to see
which measurement has the least error. The relative error
in the constant—time measurement is inversely proportional
to the square root of the total number of counts accumulated
at the Bragg position, 1:3,, 1 0 lflfN. The number of
counts accumulated by the SX technique is 97, and that
by the CTST technique is 3774. Thus the ratio between the

two relative errors can be written as,

€CTST : ./97 N 1
esx N/3774 6

112

Table 13. Intensities of (241) Reflection Measured by CTST
and SX Techniques.

 

 

Intensity CTST SX
¢ Accumu—
Settings Time lating
(degree) (sec) counts
278.30 100 917
278.34 100 939
278.38 100 948
278.42 100 960
278.46 100 927
278.50 100 894
background
at
278.42 100 139
INi 94 c/10 sec* 97 c/10 sec
ICO 14 13
Inet 80 84
*
2 = = 1
(iNi)CTST (939 + 948 + 960 + 927)/400 3774/400 94 c/ 0 s

(ICO)CTST = 139/100 =

14 c/10 s.

113
This calculation indicates that the relative error of (241)
reflection obtained from CTST technique is much smaller than
that from the SX technique. In addition, the step scan
technique across the peak position eliminates slight varia—
tions in peak shapes resulting in a better integrated in—
tensity. Therefore, intensities derived by the SX technique
were removed by the CTST procedure before conversion to

the corresponding structure factors.
c. Constant—Count Step Scan Technique*

This measuring technique is essentially the same as
that of CTST technique except that the time, tj’ to accumum
late a constant number of counts, c, is recorded. The
number of counts to be used at each step was determined
according to the intensity scheme listed in Table 14. The
reflection (412) is used to compare this measuring technique
to the SX technique (see Table 15). Based on Wilson"s

estimated variance, the SX method gives

2 : : = 2
osx Ij/T (237 c/lOs)/10s 2.4 c/s

and CCST has a variance of

2
= Ig/C : 24 X 24 C s) : 0.2 c/52

02
CCST 4000

This estimated variance indicates that the intensity of this

reflection as determined by the CCST technique is about an

.x.
Abbreviated as CCST.

 

Table 14.

Intensity Range
(c/lOs) of SX

I < 200

200 i I < 2000

2000 ; 1 < 10,000

I 1 10,000

114

Step Scan Measurement.

Counting Count at
Technique Each Step
const. -—
time
const. 1000
count
const. 10,000
count
const. 100,000

count

Time at
Each Step
(seconds)

100

Back—
ground
at Peak

100 s.

100 c.

1000 C.

10,000 c.

 

115

Table 15. Intensities of Reflection (412) Measured by SX
and CCST Techniques

 

Intensity CCST SX
T NO.
Settings Count for Time
(degree) Each Step (sec)
278.24 1000 40.62
278.28 1000 38.31
278.32 1000 35.97
278.36 1000 34.71
278.40 1000 35.55
278.44 1000 39.22
background
at
278.36 100 25.92
INi 277 counts/10 sec* counts/10 sec
ICO 39 37
Inet 238 237
*(INi)CCST = 4000/(38.31 + 35.97 + 34.71 + 35.55) = 277 c/lOs
(1C0)CCST = 100/25.92 = 39 c/lOs

 

 

116
order of magnitude better than that measured by the sx tech-
nique. Therefore, the latter procedure was replaced by the

former for the hydrogen structure determination of porphine.

(3) Moving Crystal—Moving Counter Technique (20-5can)*

In the MX—MC intensity measurement technique, the
counter moves at twice the angular displacement of the crys—
tal. The conditions necessary to obtain a valid integrated

intensity are very similar to those for the MX measurement.

4. Data Collection

With the scattering angle limit of 1000 a total of
1725 reflection intensities were measured using the SX
technique. In order to estimate the intensity limit for
unobserved reflections, the systematically absent reflec—
tions of the (hog) zone and the (OkO) reflections were
measured. For these 88 reflections, the average intensity
was 5 counts/10 seconds. Therefore, reflections with in~
tensities greater than 5 counts/10 seconds were taken to
be observed reflections. After rejecting the unobserved
and redundant reflections (ihkO), 1206 independent reflec~
tions remained to compute structure amplitudes.

During the course of the intensity data collection,
the reflections (500), (040) at a 0 value of c*—axis
and (040) at a T value of a*-axis were used to monitor

any intensity fluctuation of the X—ray source and/or the

96
Abreviated as MX—MC.

 

117

alignment of the crystal during each interval of measure-
ment. A total of 32 monitor measurements were taken through—
out the data collection. The standard deviations of the
intensities of these monitor reflections were 1.2% for the
(500), 1.8% for the (040) reflection along the c*—axis, and
1.1% for the (040) along 5* direction. These deviations
indicate that the intensity fluctuation of X—ray source was
insignificant and the crystal remained well—aligned through—
out the data collection.

In space group P21/c the intensities of the (hkO)
and (hkO) reflections are equivalent. A comparison of these
equivalent reflections was made in terms of a residual
index Re expressed as

R : 6%[I(Ek0) — kI(hkO)

)
e 6§(I(hk0) + kI(hk0))/2

 

where k is the scale constant of 1.03 obtained from the
average ratio of the intensity of (hkO) to that of (hk0).
Theoretically, the intensity of an (hkO) reflection should
be equal to that of an (hkO), but discrepancies which are
due to absorption and other such experimental causes are
found in practice. The R—value obtained with 67 equivalent
reflections was 3.8%. The residual index is an indication
of the reliability of the data and is certainly acceptable,

especially when considered in terms of the lFl's.

 

118

5. Calibration Between Measuring Techniques

Since various intensity measuring techniques were used,
systematic errors could arise between different sets of
data due to possible scaling errors. Calibration constants
between the sets were evaluated by comparing the average
ratio of the intensity measured by the SX technique to
that measured by the CTST technique, and by comparing the
average ratio of intensity measured by the SX method to
that determined by the CCST method. They are

ISX >

ICTST n=24

I
< f_§§_ > = 1.00 i 0.04
CCST n=54

where n is the number of the reflections used in the

averaging. Since these average ratios were very close to
unity, it was not necessary to correct the intensities of
the same reflection measured by different techniques, and
the intensity measured by the SX technique was directly
replaced by that measured by the step—scan method for use

in the structure amplitude calculations.

 

VIII 0 STRUCTURE DETERMINATION

1. Isotropic Refinement

A trial structure based on the coordinates reported by
Webb and Fleischer (abbreviated W&:F)42 and isotropic tempera—
ture factors for the four nitrogen and twenty carbon atoms
(see Table 16) were used to compute a set of initial struc—
ture factors. The R-factor for this calculation was 0.142,
and decreased to 0.139 after one cycle of least squares re-
finement of all the parameters (with unit weight). After
some small calculated structure factors were eliminated,
1177 (out of 1206) reflections were used to compute the
first observed electron density, p01 , and the first dif—
ference electron density, Apl . All the hydrogen atoms
were located from Apl at approximately the expected posi-
tions in the difference density map. The most striking dif—
ference from the W&F structure was the presence of only two
central hydrogen atoms which were attached to two opposite
nitrogen atoms. The peak heights of the two central hydro—
gen atoms were approximately O.3 e/g3 for H22, and 0.4
e/R3 for H24; these peak heights were somewhat lower than
the average peak height (0.5 e/g3) of the remaining hydro-
gen atoms. In addition to these features, residual electron

119

 

 

 

120

 

Table 16. Atomic Coordinates and Isotropic Temperature
Factors for Porphine (from Webb & Fleischer) .
(Coordinate i std. dev.)a x 104
Atom x 1 OX y i 0y z i oz B(22)
Cla 1978 i 2 4489 i 2 3114 i 2 .2
CZB 2661 i 2 5349 i 2 3825 i 3 .1
C33 2884 i 2 6059 i 2 2912 i 3 .
C4a 2351 i 2 5645 i 2 1614 i 2 4.
C5m 2396 i 2 6123 i 3 405 i 3 4.
C6a 1903 i 2 5735 i 2 —848 i 2 4.3
C7B 1966 i 2 6234 i 2 —2098 i 3 3
C8B 1393 i 2 5596 i 2 —3069 i 3 .
ng 949 i 2 4684 i 2 -2449 i 2 .
C10m 292 i 2 3836 i 2 —3099 i 2 .
Clla —154 i 2 2962 i 2 -2520 i 2 .
C12B -850 i 2 2097 i 2 —3221 i 3 .
C138 —1105 i 2 1407 i 2 —2309 i 3 .
C140 —566 i 2 1829 i 2 —1016 i 2 .
C15m —621 i 2 1362 i 2 199 i 3 .
C16a —126 i 2 1756 i 2 1444 i 3 .4
C17B —182 i 2 1253 i 2 2697 i 3 .3
C18B 418 i 2 1870 i 2 3669 i 3 .
C19a 862 i 2 2780 i 2 3046 i 2 .0
C20m 1549 i 2 3604 i 2 3702 i 2 .4
N21 1811 i 2 4682 i 2 1782 i 2 .
N22 1283 i 1 4794 i 2 —1108 i 2 .
N23 7 i 1 2770 i 2 —1188 i 2
N24 517 i 1 2686 i 2 1698 i 2 .

aStandard deviations estimated by least squares analysis.

b

work.

The coordinates x,

z are equivalent to z, x of the present
This Table was taken from L. B. Webb, Ph.D. Thesis,

Department of Chemistry, University of Chicago, Chicago,

Illinois,

1965.

121
densities found in the vicinity of the outer pyrrdle car-
bon atoms in Apl suggested anisotropic thermal motion for
the outer carbon atoms of the porphine molecule. Thus,
the individual isotropic temperature factors were converted
into the corresponding anisotropic temperature factor form
for carbon and nitrogen atoms and the least squares refine-

ment was continued.
2. Anisotropic Refinement

One cycle of least squares refinement in which the co-
ordinates and anisotropic temperature factors of the inner
12 atoms were allowed to vary, followed with another cycle
in which the atomic parameters of the outer 12 carbon atoms
were allowed to vary, decreased the R-factor about 1% for
the first cycle and another 2% in the second cycle to 0.109.
Examination of the observed and calculated structure fac—
tors indicated the largest discrepancies to be concentrated
in some large, low—order reflections, such as (022),

]F0( = 137.5 and tii = 161.4. This observation is charac—
teristic of secondary extinction, and an attempt to correct
for extinction was made before proceeding with further re—

finement.
3. Extinction Correction

Secondary extinction is related to the amount of mosaic
character of crystals. When the X—ray beam must penetrate

deeply into the mosaic crystal before it reaches mosaic

 

122
blocks which have parallel reflecting planes as those blocks
near the surface, there is an attenuation of the beam reach—
ing the deeper mosaic blocks. This effect is known as
secondary extinction and is most pronounced for reflections
at low (sin 9/%) where the intensities are generally large.
As a result, the observed values for intense reflections
are systematically less than their calculated values. There
are several methods by which secondary extinction can be
detected and corrected. The extinction correction for the
intensity data of porphine was made by remeasuring the low
order reflections with a small crystal. The small crystal
has fewer planes in the reflecting position at the given
time, and thus the attenuation of X-ray beam is less than
that for a large crystal.

A small crystal with the dimensions of 0.15 x 0.125 x
0.025 mm (see Fig. 21) was used for intensity measurements
of reflections which might be affected by secondary extinc—
tion. The volume ratio between the large crystal and the
small crystal is 5.88. All reflections distributed in the
hemisphere with i h : 4, k L 4 and g i.4 were measured by
the use of a Picker 4—Circle Automatic Diffractometer.
Proper scaling between different instruments as well as
crystals was made by using reflections not affected by ex~
tinction. The average ratio obtained between structure

amplitudes of the small crystal, [F and the structure

smalli’

l
, was

amplitudes of large CrYStal' iFlargel

 

123

IF 1
<—-F—li£9-‘i-> =1.61:0.06
' small‘ n=30

where n is the number of reflections.

 

The residual index in terms of [F | and [F |, over
small large
extinction—unaffected reflections, was assessed by
2||Flargei _ 1'6lFsmallH
RE : V, :- 3.3%
Ai<|Flargel + 1'lesmallI)/21

This number indicated that the two sets of structure ampli—
tudes, based on two different sized crystals, measured by
different diffractometers and methods were in good agreement.
It is of note that the thirty reflections which were used

to determine the average ratio of the structure amplitudes
had amplitudes (IFOI) ranging from 3 to 74 (absolute scale).
The average intensity ratio can be written as the square of
average ratio of structure amplitude. The average ratio of
intensities had a value of 2.6 which does not correspond to
the volume ratio of 5.88. This is probably due to the fact
that the automatic diffractometer is more sensitive for
X—ray detection.

The structure factor calculation (excluding hydrogen
atoms) computed after six strong low—order reflections from
the large crystal which showed pronounced secondary extinc—
tion were replaced by the new structure amplitudes (see
Table 17) and an R-factor of 0.10. A difference electon
density was then calculated and examined, from which all

the hydrogen coordinates were obtained. Individual

124

Table 17. The Reflections Corrected for Extinction.

Reflection |FC( (F0 large [F0 small
( 022) 161.4 137.5 160.6
( 122) 108.8 95.5 111.1
( 013) 100.1 89.7 99.8
( 023) 122.7 116.3 129.7
( 113) 121.4 107.0 122.3
( 123) 166.3 155.2 172.8

 

125
isotropic temperature factor‘ for each hydrogen atom was
approximated to be 20% greater than that of its adjacent
carbon and nitrogen atom in the porphine molecule. These
isotropic values were then converted to anisotropic tem—
perature factor form. The structure factor calculation
(hydrogens included) of the porphine molecule had an R—
factor of 0.086, and after one cycle of least squares re—
finement of all coordinates of carbon and nitrogen atoms,
the R-factor decreased to 0.078. With one cycle of least
squares refinement of anisotropic temperature factors of
the 12 outer atoms followed by another cycle of refining
the 12 inner atoms, the R-value went to 0.072 for the former
and to 0.068 for the latter. Performing one cycle of least
squares on all the hydrogen coordinates, the R—factor im—
proved to 0.067. At this point the refinement by least
squares was altered by basing it on a different weighting

scheme.
4. Weighting Scheme

As it has been mentioned in Part I, the method of least
squares applied to the structure refinement consists in sys—
tematically varying the atomic parameters so as to minimize
the quantity

wi(|F0| _ ‘FC‘)2
1

W
H
n' M :5

l
where the sum is taken over all independent structure ampli—

tudes and wi is the weight of an observation. Each

126
weight wi is to be taken as the inverse of the square of
the standard deviation of the corresponding observation,
and may be estimated from the agreement of independent
measurements or from considerations of the way the measure—
ment was made. Factors which were taken into consideration
for the weighting scheme for the porphine intensity data
were counting statistics, the instrumental instability, and
the reliability of the measurement. Three different weight—
ing functions were used according to the intensity of the

reflection. They were as follows

a) 12,000 > I > 400 (Intensity, I, is counts per 10 sec)

0 = 0.04 X lFol where o = I/Jw
_ 1/ 2 _ 1 —2
or W - O - W2 ‘FO‘
Since the weight is inversely proportional to {F0|2, this

weighting scheme is similar to that of Hughes .47 The
constant of 0.04 (4%) is the error estimated for unit
weight observations. Generally, data in this intensity
range were very reliable, as evidenced by the small fluctu—
ation observed for the monitors (~2%) throughout the data
collection. In addition, the counting statistics,~fI, can
be expressed in terms of the percentage counting error,
Jl/I, which is small in this intensity range. The two
extreme conditions can be illustrated. For an intensity,
I, equal to 12000 counts/10 sec, the counting error is
less than 1%; for I equal to 400 counts/10 sec, the

counting error is 5%. The latter value correSponds to

127
approximately 3% error on structure amplitude, since the

standard deviation of [Fl, 0 is approximately one—half

Fl
the standard deviation of intensity, OI. Thus the average
error for an observation in this intensity range was assumed

to be slightly greater than 3%, or 4%.

b) 1 > 12,000

0 = 0.04 x 1/12000 x )FOJ .

In this intensity range, the error of the observation is
assumed to be linearly dependent on the magnitude of the
intensity. Because extinction and crystal mis-setting
problems are more pronounced for very intense reflections,

the errors increase to account for these effects.
c) 400 i 1 > 5

The error for an observation in this range was obtained
from a curve derived from plotting the error (%) as a func-
tion of the intensities (shown in Fig. 22). The boundary
conditions, I = 5 and I = 400, were selected so that the
relative error was 100% for the fermer and 4% for the lat—
ter. This curve was then constructed by fitting three
selected points, determined as follows:

(1) when I = 68, the error is 15%. This error was
the maximum counting error for the (306) reflection which
was one of the seven reflections selected in the intensity
range between 5 and 200 count/10 sec and was measured re—

peatedly.

 

128

100 _ error

80

60

40-

2O

 

 

 

250 ' 400 600
—-—> Intensify(counfs/IOsec)
Figure 22. Error (%) y_s_ intensity (I).

 

129

(2) The second point is that when I = 234, the error
is 8%. This point was determined from the reflection (110)
whose counting error of 8% was the largest among five I
selected reflections in the intensity range from 200 to 300
counts/10 sec.

(3) The third point is that when I = 300, the error
is 5%. This point was obtained from the (425) reflection,
as one of the five reflections whose intensities were in
the range of 300 to 400 counts/10 sec.

In order to make the calculation of weight easier in
this region, the curve was divided into 10 regions and the
errors for estimating the standard deviation of a reflection
are shown in Table 18.

The weighting scheme was applied to all the reflections
except the (100) and (200) reflections. These reflections
were not improved by the extinction correction, since the
size of the second crystal used was not small enough to
correct completely their secondary extinction effects.

Zero weight (w = 0) was then applied to these two reflec-
tions to exclude them from the refinement.

When the new weights were applied and two cycles of
least squares refinement of coordinates and anisotropic
temperature factors of all the carbon and nitrogen atoms
were performed, the R—factor lowered to 0.059 and the
weighted R—factor to 0.041. The difference between the R—

factor and the weighted R—factor is

 

130

Table 18. Error for Intensity Less than 400.

Intensity Range Error
300 Z I x 400 0.05
250.: I a 300 0.06
200 L; I -, 250 0.07
150 ;.I < 200 0.08
125 ;.I < 150 0.09
100 :.I < 125 0.11

75.: I x 100 0.14
50.; I x 75 0.23
25 :_I 1 50 0.53

5 :.I x 25 1.00

131

2 F0 — k FC
2 lFo‘
211/2

weighted R = [ZW(IF0| _ lec1)

 

[21w |F0|3]1/2
where k is the scale constant between (F0| and ch”
Since one additional cycle of least squares on all the
hydrogen coordinates had no apparent effect, the refinement
of the porphine structure by least squares was terminated
with a final R—factor of 0.059 and weighted R-factor of

O .041 .

 

 

IX . RESULTS

The final coordinates, anisotropic temperature factors,
the mean square atomic displacement (62) in the direction
of each principal axis, and peak heights of all the carbon
and nitrogen atoms are listed in Table 19. The final co—
ordinates, isotropic temperature factors and the peak
heights of the hydrogen atoms are shown in Table 20. The
isotropic temperature factors of the peripheral pyrrole
hydrogens were approximated to be 20% greater than the
average isotropic temperature factors of their adjacent
pyrrole carbons (B = 5.6 X); the isotropic temperature fac-
tors of the remaining hydrogen atoms were estimated to be
20% greater than the average isotropic temperature factors
of their adjacent atoms (B = 4.6 R).

The atomic deviations from different least squares
planes based on the individual pyrrole rings, the plane de—
fined by the four nitrogen atoms, and the plane based on the
eight inner pyrrole carbon and nitrogen atoms are given in
Table 21. The atomic deviations from the nuclear least
squares plane (NLS) of the porphine molecule are shown in
Figure 23; the standard deviation (excluding hydrogens) is
0.02 X, The porphine bond distances and angles are shown

in Figure 24 and Figure 25, respectively. The standard

132

 

 

 

133

Table 19. Final Atomic Parameters and Peak Heights of

Coordinates in

 

 

 

Fractions Anisotropic Temperature

Atom x y Z 511 322 533

N21 0.1757 0.4670 0.1809 0.0121 0.0066 0.0063
ClA 0.3113 0.4476 0.1978 0.0112 0.0086 0.0071
C2B 0.3825 0.5359 0.2657 0.0148 0.0102 0.0072
C3B 0.2904 0.6068 0.2877 0.0177 0.0092 0.0071
C4A 0.1613 0.5628 0.2353 0.0142 0.0076 0.0061
C5M 0.0418 0.6121 0.2388 0.0160 0.0067 0.0058
N22 —0.1116 0.4801 0.1282 0.0113 0.0077 0.0065
C6A —0.0846 0.5743 0.1918 0.0151 0.0075 0.0057
C7B —0.2088 0.6244 0.1970 0.0186 0.0090 0.0077
C8B —0.3077 0.5598 0.1391 0.0135 0.0109 0.0076
C9A —0.2475 0.4672 0.0955 0.0091 0.0105 0.0066
C10M —0.3120 0.3826 0.0292 0.0102 0.0114 0.0070
N23 —0.1183 0.2775 0.0014 0.0102 0.0075 0.0069

C11A —0.2527 0.2953 —0.0146 0.0133 0.0084 0.0064
C12B —0.3260 0.2092 -0.0855 0.0151 0.0097 0.0079
C13B —0.2330 0.1407 —O.1097 0.0169 0.0092 0.0082
C14A —0.1038 0.1823 —0.0579 0.0151 0.0069 0.0067
C15M 0.0171 0.1358 —0.0623 0.0154 0.0075 0.0073
N24 0.1682 0.2671 0.0520 0.0103 0.0065 0.0071
C16A 0.1425 0.1741 —0.0141 0.0150 0.0149 0.0056
C17B 0.2661 0.1232 —0.0198 0.0185 0.0083 0.0087
C18B 0.3661 0.1863 0.0412 0.0157 0.0079 0.0085
C19A 0.3046 0.2768 0.0861 0.0112 0.0074 0.0068
C20M 0.3699 0.3598 0.1559 0.0099 0.0092 0.0073

0X104 0.1— 4 0.1- 4 0.1- 3 0.1—-4 0.1— 2 0.03-2

*
In the direction of each principal axis.

 

134

Carbon and Nitrogen Atoms of Porphine.

 

 

Peak
, Mean Square Atomic Hei ht
Parameters Displacements* (82)_‘ le/a3)

612 813 623 8w2ui 85253 8wzޤ p0

0.0008 0.0023 -0.0001 3.48 3.82 4.92 7.6
—0.0006 0.0026 0.0014 3.31 4.66 5.54 6.2
—0.0044 0.0015 —0.0002 3.75 4.28 8.23 5.9
-0.0041 0.0019 —0.0014 3.48 4.81 8.43 5.5
—0.0009 0.0017 0.0003 3.48 4.36 5.92 6.0
0.0007 0.0020 0.0006 3.22 4.03 6.54 6.0
0.0026 0.0025 0.0005 3.22 3.65 5.75 7.2
0.0030 0.0029 0.0003 3.06 3.61 6.91 5.9
0.0053 0.0038 0.0012 3.58 4.21 9.17 5.3
0.0047 0.0041 0.0021 3.45 3.89 8.49 5.4
0.0029 0.0021 0.0017 3.00 3.58 6.96 6.2
—0.0004 0.0011 0.0013 3.75 4.32 6.91 5.8
~-0.0001 0.0017 0.0013 3.41 4.14 5.09 7.4
—0.0008 0.0022 0.0013 3.25 5.09 5.50 5.9
~0.0037 0.0009 0.0004 4.06 4.54 8.08 5.5
—0.0052 —0.0001 ~0.0000 3.51 4.85 9.17 5.2
-0.0023 0.0015 0.0005 3.41 3.99 6.82 5.9
-0.0014 0.0022 —0.0009 3.82 4.70 6.27 5.9
0.0020 0.0025 0.0005 2.97 3.89 5.01 7.9
0.0069 0.0021 0.0034 2.79 3.78 6.45 6.0
0.0053 0.0040 0.0011 3.25 4.89 9.01 5.7
0.0050 0.0043 0.0020 2.91 4.32 8.28 5.6
0.0022 0.0029 0.0024 2.73 3.78 6.01 6.1
0.0001 0.0021 0.0016 3.68 4.03 5.84 5.9
0.1—3 OJn»5 0.1-2

135

Table 20. Final Coordinates, Isotropic Temperature Factors,
and Peak Heights of Hydrogen Atoms of Porphine.

 

 

 

 

Isotropic
Temperature Peak
Atom Coordinates Factors Heights
X* y z B(32) p(e R_3)
H22 —0.0458 0.4358 0.1183 5.5 0.5
H24 0.1042 0.3167 0.0633 5.5 0.5
H2B 0.5058 0.0367 0.2067 6.5 0.5
H3B 0.7033 0.1750 0.1650 6.5 0.5
H5M 0.9575 0.1842 0.2117 5.5 0.5
H7B 0.2242 031958 0.2700 6.5 0.5
H8B 0.4133 0.0533 0.3783 6.5 0.6
H10M 0.5850 0.3808 0.0192 5.5 0.5
H12B 0.5650 0.2825 0.3958 6.5 0.4
H13B 0.7433 0.4325 0.3400 6.5 0.5
H15M 0.0125 0.4300 0.3875 5.5 0.5
H17B 0.2750 0.4458 0.4342 6.5 0.5
H18B 0.4685 0.1742 0.0542 6.5 0.5
H20M 0.4758 0.3533 0.1708 5.5 0.6

*
Coordinates of hydrogen atoms were obtained from difference
density map.

 

136

Table 21. Atomic Deviations from the Least Squares Planes
of Individual Pyrrole, Inner Eight Atoms, and
Four Nitrogen Atoms.

 

Atom d(8) Atom d(R) Atom d(g)
Pyrrole N21 Pyrrole N22 Pyrrole N23
N21 —0.02 N22 ~0.01 N23 0.04
Cl —0.02 C6 0.01 C11 0.00
C2 ~0.00 C7 —0.03 C12 —0.01
C3 -0.01 C8 —0.00 C13 0.01
C4 0.00 C9 0.01 C14 —0.01
s.d.* 0.01 s.d. 0.02 s.d. 0.02

Pyrrole N14 Four Nitrogen Eight Inner Atoms
N24 0.01 N21 0.01 Cl 0.03
C16 —0.01 N22 —0.01 C4 -0.02
C17 0.00 N23 0.01 C6 w0.03
C18 —0.00 N24 —0.01 C9 0.02
C19 0.00 s.d. 0.01 C11 0.02

s.d. 0.01 C14 —0.01
C16 ~0.02
C19 0.01
s.d. 0.02

3(-
Standard deviation

137

 

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125.3
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11o.2. N23
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1094 124.]
108.4 1 26-4
Figure 25.

Porphine bond angles

139

127. 5 0
124.5 107'
107,1
106.3
N21
109.3
125.2
125.6
126.5
125.0 126.5
108.5
N 24
107.8
107.4
125.1 108.6
127 °-3
.7 '2 107,3

(degrees).

 

140
deviation of the lengths and angles of carbon—carbon and
carbon—nitrogen bonds are approximately 0.004—0.007 X and
0.3—0.50 respectively, based on the standard errors of co—
ordinates of carbon and nitrogen atoms in the last cycle
of least squares refinement.

The composite difference electron density (based on
the structure factor calculation excluding all hydrogen
atoms) projected onto the ac plane is shown in Figure 26.
The first contour is drawn at a level of 0.12 e 2—3 with
each additional contour occurring at 0.12 e R-a. In addi—
tion, the difference electron—density in the vicinity of
four nitrogen atoms is given in Figure 27; the electron
densities of hydrogen atoms as well as the residual densi-
ties (~ 0.1 e 8—3) due to background fluctuation in this
region are indicated. Figure 28 shows the interatomic
distances and angles of the two central hydrogen atoms with

respect to the four nitrogen atoms in porphine molecule.

141

 

Figure 26. Composite electron density of the hydrogen
atoms perpendicular to the ac plane.

Figure 27.

 

142

 

The difference electron density in the vicinity
of the four nitrogen atoms. The length of b
axis is divided into 60 sections, and the num—
bers in parenthesis are the section number cor—
responding to the y—coordinate of the ato s or
the residual density (greater than 0.1 e '3)
along the b axis.

143

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X. DISCUSSION

The deviations of the atoms from the least squares
plane of each pyrrole indicate that the individual pyrroles
(see Table 21) are essentially planar within the error of
the structure determination («’0.01-0.02 R), In addition,
from the small atomic deviations from the least squares
plane formed by the inner eight atoms, the plane of four
nitrogen atoms, and the NLS plane, one can conclude that
the porphine molecule is also essentially planar. In con—
trast to this planarity of the porphine molecule, the por—
phyrin skeletons of some free base porphyrins and some
metalloporphyrins are found to be very ruffled. Factors
which might influence the observed departure from planarity
could be either metal or side—chain substitution, and/or
forces arising from crystal packing. Examples of nonplanar
porphyrin skeletons are illustrated in Figure 29. The
NiEtio—I, CuTPP, and tetragonal TPP crystallize in tetragonal
forms and the independent structural parameters determined
are restricted to one quarter of the molecule due to the
space group symmetry relations. From Figure 29 it can be
seen that the nonplanarity of NiEtio—I manifests itself in
pronounced deviations of peripheral pyrrole carbon atoms

144

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147

(N 0.3 g) from the plane fitting the methine and pyrrole
atoms, while CuTPP is nonplanar in a different way: the
bridge carbon and some of the pyrrole carbon atoms (~ 0.2-
0.4 8) show the largest deviations. In the case of tri—TPP,
the maximum deviation is found to be the pyrrole nitrogen
atom which carries the central hydrogen atom (~ 0.2 R);
in addition, the pyrrole group is inclined with respect
to the NLS plane (i 6.60). The nonplanarity of CanTPP is
different from all the cases mentioned above. The atomic
deviations for CanTPP (see Fig. 8, Part I) are found to
fall into the following groups of decreasing atomic devia—
tions:

d(Cb) ; m

where C Cm’ and N denote the peripheral pyrrole car—

b'
bon, the methine carbon and the nitrogen atoms, respectively.
Furthermore, the atomic deviations have approximately 4
symmetry. All these different types of nonplanarity found
in porphyrin systems suggest that the porphyrin skeleton is
indeed very flexible.

The bond distances shown in Figure 24 have average bond
lengths of 1.379 1 0.008 X for C-N, 1.381 1 0.008 X for Ca‘
Cm, and 1.04 i 0.03 X for C—H. The corresponding bond

distances given in Volume III of International Tables for

X—ray Crystallography are, C—C of 1.395 i 0.003 g in

 

aromatic systems, and C—H of 1.084 i 0.006 R in benzene.

A comparison of the reported values with those of this

148
determination shows that the bond distances of C-C and C—H
are very close to the expected values.

Also of interest are the average distances within the
pyrrole ringso The average Ca-N, Ca—Cb and Cb-Cb, distances
of tri—TPP, tetragonal TPP, porphine from W&F, and from
this structure determination are listed in Table 22; the
average of these bond distances on the basis of pyrrole
with and without central hydrogen in tri—TPP and porphine
are also included. A comparison of the average bond dis—
tances of the pyrrole with the hydrogen atom to those of
the pyrrole without the hydrogen atom in porphine, indicates
the differences: +0.004 R for N-Ca, —0.021 X for Ca-Cb, and
+0.020 R for Cb-Cb,. The corresponding values found in
tri-TPP are +0.01 2 for N—Ca, —0.028 8 for Ca—Cb, and +0.008

R for C -C Even though the magnitudes of the bond-length

b b"

differences are different in the two cases, the pyrrole
with hydrogen attached seems to have larger N—Ca and Cb—Cbl

bond lengths, and a contracted Ca—C bond length. In

b
addition, comparison of the average pyrrole bond angles of
the pyrrole with a. hydrogen atom to the average pyrrole
bond angles of that without a hydrogen atom in the porphine
structure is +2.50 for A Ca'N'Ca’ —1.9° for A N,Ca,Cb, and
0.70 for A Ca’cb’cb (see Table 23). The corresponding
values found in tri—TPP are 3.00 for A Ca'N’Ca’ -3.00 for

A N'Cacb’ and 1.30 for A Ca,Cb,Cb. Such comparisons could

not be extended to the tetragonal TPP since its pyrrole rings

are similar.

 

149

 

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150

Table 23. Average Pyrrole Bond Angles in tri—TPP and the
Porphine of this Work.

Porphine
tri-TPP (present work)
Pyrrole Pyrrole Pyrrole Pyrrole
N-H N—H
A Ca,N,Ca 109.2 106.2 108.6 106.1
A N,Ca,Cb 107.3 110.3 107.9 109.8

A c ,c ,c 108.1 106.8 107.9 107.2
a b b

 

151

It is interesting to note that porphine and the por—
phyrin nucleus of tri—TPP can be described as correSponding
to a structure of hybrids of the two predominant classical
resonance forms of the porphine molecule. These two forms
are shown in Figure 30(a) and (b); Figure 30(c) is an at—
tempt to represent the expected nature of the hybrid. The
average pyrrole bond distances of porphine and tri-TPP are
shown; the bond distances of tri—TPP are indicated in par—

entheses. In the hybrid form, the distance in

Cb —Cb
pyrrole 1 should show increased double bond character (shorter
bond length) compared to the equivalent distance in pyrrole 2.
Likewise, the C~N distance in pyrrole 2 should show decreased
double bond character compared to that in pyrrole 1. Trends
towards these proposed results have been observed in the
porphine and tri-TPP structures.

The most striking difference between this structure
determination and that of W&F is the existence of two cen—
tral hydrogen atoms bonded to two opposite pyrrole nitrogen
atoms. These hydrogen atoms, H22 and H24, have peak heights
of about 0.5 e 8‘3 (background level N 0.1 e R_3) as indi—
cated in Figure 27. The N22—H22 and N24—H24 bond distances
are 0.89 g and 0.92 K, respectively. The locations of the
imino hydrogen atoms are slightly off the line joining
their opposite nitrogen atoms; a deviation of 5.80 toward
N21 is found for H22 and of 4.50 toward N23 with respect to
N22—N24 for H24. These departures make the central hydro—

gen van der Waals contact (2.31 X) slightly larger (0.01 X)

 

152

(0)

 

1.3450347)

 

Figure 30. Porphine resonance forms.

153
than the contact between two hydrogen atoms lying on the
line of N22-N24. It is noteworthy that the central hydro—
gen atoms are essentially coplanar to the porphine molecule,
as shown by their small atomic deviations from the NLS
plane (see Fig. 23, 0.05 R for H22 and —0.09 8 for H24).
The central hydrogen structure of the porphine is different
from that of tri—TPP. In tri—TPP case the central hydrogen
atoms are slightly inclined from the NLS plane, presumably
in order to keep a reasonable contact distance.

It is of additional interest that the distance between
the pair of pyrrole nitrogen atoms which carry the central
hydrogen atoms is 0.06 8 longer than the corresponding dis—
tance of the other pair of nitrogen atoms. A similar value
of 0.14 R is found in tri—TPP. This slight elongation of
the N—N distance tends to increase the distance between the
central hydrogens.

A comparison between the central region of the porphine
molecule as reported by W&F and this work was made. It can
be seen from the difference electron density in the vicinity
of the nitrogen atoms projected on the ac plane (see
Fig. 27) that only small residual electron densities other
than the hydrogen atoms (about 0.1 e X_3) can be found.

This observation suggests strongly that: (1) the sample of
porphine used for this work does not contain a metal impurity
at the center of the porphine molecule, and (2) only one

pair of diagonal central hydrogen atoms is bonded to diagonal

nitrogen atoms. The coordinates and peak heights of the

154

central hydrogen atoms of the two structures are listed in
Table 24. The pair of alleged "half-hydrogen atoms", H21
and H23 are of peak heights of about 0.3 e R_3; the corre—
sponding locations are found to lie in negative regions in
the present difference electron density. By comparing
these peak heights (0.3 e 273) with the background level
of 0.2 e 2'3 in the structure reported by W&F, one can see
that hydrogen atoms, H21 and H23 could be error fluctua-

tions of the background. a

Final Remarks

A comparison of the observed structure amplitues of
this work with those of W&F gave an Rd-factor, indicating
the discrepancy between the two sets of data, which was
0.13, where
n
X

Rd:

liFol ‘ lFo‘w&Fi/ g 1F01

and n is the total number of reflections of the present
structure determination (n = 1206). This Rd—value indicates
a substantial disagreement between the two sets of data.

Factors which may have contributed to this disagreement are

as follows.

1) Extinction Correction

A secondary extinction correction was made in this
work. The crystal used for the main intensity measurement

had a size of 0.20 x 0.275 x 0.05 mm, while the crystal

 

155

6 MHOB mflflu.

.xno3 mflnp mo x .N

EOHM pocflmuno mum mommfiucmumm 030 GA mnmflfis: one

Q

on ucmam>HSWm mum MMO3 m3; Eonm N .x mmumcflonooom

 

Am.ov v.6 Aon.oV moH.o Asfim.ov wom.o Ammo.ov 860.0 was
Am>flummmcv m.o wmo.ou Hmm.o mmo.o mam
Am.ov 4.0 beeo.osv wmo.o- Ammv.ov mme.o QAwHH.ov ooe.o mum
Aw>flnmmmcv m.o mmH.o mm6.o mee.o Ham
Muoz Amlm 0V N w x Eoufi
ucwmwum #3 flow m
3866

.mmmwamc4 enquSHum ooflsmnom 039

Eomm mEoum somonpxm Hmnuqmu mo musmflmm mem pom mopmoflonooo HMQOHpomum .vm mHQMB

156
used by W&F work was 0.36 X 0.36 x 0.20 mm (reported as 0.50
mm along the diagonal of one face). The latter is approxi—
mately eight times larger than the former. It is well known
that secondary extinction effects are much more pronounced
for larger crystals. Thus, strong low—order reflections can
contribute to the large discrepancy between two sets of

data due to extinction.
2) Counting Error

The counting error of 7% of intensity data (80 out
of 1206 reflections) from this work was minimized by using
w (omega) step—scan measuring techniques. Thus the set of
[Fo"s of the present data is probably affected by more
favorable counting statistics and this could contribute to

the discrepancies with W&F data.

REFERENCES

10.

11.

12.
13.
14.
15.

16.

REFERENCES

J. L. Hoard, J. Amer. Chem. Soc., 87, 2305 (1965).

 

E. B. Fleischer, Accounggof Chemical Research, 3,
105 (1970).

E. B. Fleischer, C. Miller, and L. E. Webb, J. Amer.
Chem. Soc., §§I 2342 (1964). ““““‘

E. B. Fleischer, J. Amer. Chem. Soc., 85, 146 (1963).

 

J. L. Hoard, G. H. Cohen, and M. D. Glick, J. Amer.
Chem. Soc., 89, 1992 (1967).

R. C. Petterson, Acta. Cryst., B25, 2527 (1969).

R. Timkovich, and A. Tulinsky, J. Amer. Chem. Soc.,
21, 4430 (1969)

 

W. E. Bennett, D. E. Broberg, and N. C. Baenziger,
Inorg. Chem., in press.

E. B. Fleischer, and T. S. Srivastava, J. Amer. Chem.
Soc., 91, 2403 (1969).

J. H. Hoard in "Structural Chemistry and Molecular

Biology," A. Rich, and N. Davidson Ed., W. H. Freeman
and Company, San Francisco, Calif., (1968), pp 573-594.

R. Countryman, D. M. Collins, and J. L. Hoard, J. Amer.
Chem. Soc., 91” 5166 (1969).

P. A. Loach, and M. Calvin, Biochemistry, 2, 361 (1963).
P. A. Loach, and M. Calvin, Nature, 202, 343 (1964)o

M. Calvin, Rev. Pure Appl. Chem., 15, 1 (1965).

L. J. Boucher, J. Amer. Chem. Soc., 22» 6640 (1968)

 

L. J. Boucher, and J. J. Katz, J. Amer. Chem. Soc;,
89” 134 (1967).

157

 

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

32.

158
D. Harker, J. Chem. Phys., 4, 381 (1936).

R. W. James, "The Optical Principles of the Diffraction
of X~rays," Cornell University Press, New York (1965)

A. D. Adler, J. Inorg. Nucl. Chem., 32} 2443 (1970).

H. Lipson and W. Cochran, "The Determination of Crys-
tal Structures," Cornell University Press, New York
(1966), pp 73-76.

J. S. Rollett, "Computing Methods in Crystallography,“
Pergamon Press, Long Island City, New York (1965),
pp 133-139.

G. H. Stout, and L. H. Jensen, "X—ray Structure Deter—
mination," The Macmillan Company, New York (1968),
pp 242.

W. R. Bushing, K. 0. Martin, and H. A. Levy, "A Fortran
Crystallographic Least—squares Program," Report
ORNL—TM—305, Oak Ridge, Tennessee (1962).

C. T. North, D. C. Phillips, and F. S. Mathews, Acta.
Cryst., A24, 351 (1968).

D. J. Wehe, and W. R. Bushing, "A Fortran Program for
Calculating Single Crystal Absorption Correction,"
Oak Ridge National Laboratory, Report ORNL—TM—229 (1962).

C. K. Johnson, "ORTEP, a Fortran Thermal—Ellipsoid
Plot Program for Crystal Structure Illustrations,"
ORNL—3794, Oak Ridge National Laboratory, Oak Ridge,
Tenn., 1965.

L. H. Vogt, A. Zalkin, and D. H. Templeton, Inorg. Chem.,
6, 1725 (1967).

L. E. Sulton, et al., "Tables of Interatomic Distances
and Configuration in Molecules and Ions," Burlington
House, London (1965), pp 99.

A. J. C. Wilson, Structure Report, 16, 184 (1952).

Y. C. Tang, and J. H. Sturdivant, Acta. Cryst., 5, 74
(1952).

M. D. Glick, G. H. Cohen, and J. H. Hoard, J. Amer.
Chem. Soc., 82, 1966 (1967).

G. D. Dorough, and K. T. Shen, J. Amer. Chem. Soc.,
12, 3939 (1950). '

33.

34.

35.

36.
37.

38.

39.

40.

41.

42.

43.

44.

45.

46.

47.

48.

49.

50.

51.

159

J. Erdman, and A. H. Corwin, J. Amer. Chem. Soc., 68,
1885 (1946) . “N

M. Gouterman, G. Wagniere, and L. C. Snyder, J. Mol.
Spectroscopy, 11, 108 (1963).

J. Falk, and E. Willis, Austral. J. Sci. Res., 4, 579
(1951).

S. F. Mason, J, Chem. Soc., 976 (1958).
J. M. Robertson, J. Chem. Soc., 1195 (1936).

G. M. Badger, R. T. Harris, R. A. Jones, and J. Sasses,
J. Chem. Soc., 4329 (1962).

E. D. Becker, R. B. Bradly, and C. J. Watson, J. Amer.
Chem. Soc., 83, 3743 (1961).

 

S. Silvers, and A. Tulinsky, J. Amer. Chem. Soc., 82”
3331 (1967).

M. J. Hamor, T A. Hamor, and J. L. Hoard, J. Amer.
Chem. Soc., 86, 1938 (1964).

L. Webb, and E. Fleischer, J. Chem. Phys., é§x 3100
(1965).

T. C. Furnas, ”Single Crystal Orienter Instruction
Manual," General Electric Company, Milwaukee (1957).

H. W. Wyckoff, M. Doscher, D. Tsernoglou, T. Inagami,

L. N. Johnson, K. D. Hardman, N. M. Allewell, D. M.
Kelly, and F. M. Richards, J. Mol. Biol., 21, 563 (1967)o
A. J. C. Wilson, Acta. Cryst., A23, 888 (1967).

W. Parrish, Phillips Technical Review, 11, 206 (1965).

 

E. W. Hughes, J. Amer. Chem. Soc., 63” 1737 (1941).
U. W. Arndt, and B. T. Willis, "Single Crystal Dif-
fractometry," University Press, Cambridge (1966),
pp 15—30, 234—236. .

M. J. Buerger, ”Crystal—Structure Analysis," John
Wiley & Sons, Inc., New York (1960 .

C. G. Darwin, Phil. Mag., 43” 800 (1922).

V. Schomaker, J. Waser, R. E. Marsh, and G. Bergman,

Acta. Cryst., 12” 600 (1959).

 

 

160
52. D. W. J. Cruickshank, Acta. Cryst., 2, 65 (1949).

53. D. W. J. Cruickshank, and A. Robertson, Acta. Cryst.,
6, 198 (1953).

54. International Tables for X—ray Crystallography (1962),
Vol. III, pp 202—207. Birmingham: Kynoch Press.

APPENDICES

APPENDIX 1

GENERAL REVIEW OF X--RAY DIFFRACTION48'49

1. Bragg's Law and its Application

Diffraction, considered as the reflection of X«rays
from planes (hkfi) of a crystal lattice, can be expressed
in a simple form

2 d(hk£) sin 9 = n1
where h, k, g, and n are integers, 0 is the angle at which
the incident and reflected beam intersect the planes (hkfi)
and d(hk£) is the spacing of lattice planes which are

parallel and intersect the unit cell edges 57, ES, E7,
at n(a/h), n(b/k), and n(c/fi). Mathematically, these con—

ditions can lead to equations with different forms. The

most common expression is in terms of the reciprocal lat—
tice with corresponding reciprocal cell parameters a*, b*,
and c*. The parameters, a*, b*, and c* can be considered

as vectors with the following properties

31? -E*‘=5"—5¢=E¥-E‘=1

and
312 .323 .Ezfiéi ~E>=S¥ .83-}? .5’:
34? ~E”_0

162
Consider, in the reciprocal lattice, a vector ?> =
55* + k5* + 23¢ constructed between the lattice point hkfi
and the origin, with a magnitude of 1/d(hk£), and perpen-
dicular to the lattice plane hkfl in direct space. The
reciprocal lattice vector E* can then be interpreted in
terms of certain angular settings by the use of polar co—
ordinates. An example based on the orthorhombic crystal

system is shown in Figure 31.
2. Mosaic Crystal

Most crystals possess irregulatities in their atomic
arrangement, in the form of dislocations, point defects,
and the like. These irregularities tend to destroy the
coherence between the components of the incident beam
scattered by different parts of the crystal. The crystal
can be divided, effectively, into small regions, about
10,000 2 across, which are sufficiently perfect to reflect
the X-ray beam coherently, but between which there is loss
of coherence. These perfect regions are known as ”mosaic
block". A crystal possessing mosaic blocks is known as a

mosaic crystal.
3. Integrated Intensity

When a crystal is rotated with uniform angular velo-
city, wv, through the hkfi plane in an incident X—ray beam
whose uniform intensity is I0, the integrated intensity, I,

of the diffracted beam, whose total energy is E0, can be

163

 

 

 

b
(th)
d‘ f
.. fkb‘
3 TT’ ' , 0
¢ , ,
,1’1’6
— - ”( hon

. u /
d =((h 012+(kb>+(lc"3‘)2
sin}(: k H/d’

29 = 2 sin“ < 1/23 1
t0n¢= |c*/h0'

0:1/0
b*=l/b
8 = 1 / C

Figure 31. Polar coordinates of a reciprocal lattice
point (hkfl) for orthorhombic crystal system.

 

164
expressed as
E0 (“V
I0

The integrated intensity should be corrected for effects
of systematic errors. These types of errors generally
arise from absorption and extinction effects and if they
are significant, affect the precision of the structure

determination.
4. Absorption

The absorption of the incident X-ray beam is dependent
on the length of the path of the X—ray beam through the
crystal. As a result, in a typical, nonspherical, crystal,
the amount of absorption is a function of the angular
orientation. The absorption correction procedure for a
single crystal may be simplified by grinding the crystal
into the shape of a sphere to make the X—ray path through
the crystal equal in all directions. However, this grinding
process is only applicable for those crystals, which neither
fragment nor cleave during shaping.

An absorption correction procedure has been suggested
by Furnas (1957)43 for the unshaped crystal. The method
makes use of the fact that the azimuthal angle, 0 , of
some reflection planes can be changed without destroying
the Bragg reflecting conditions. To apply this method to

the CanTPP crystal, whose unique b axis was at X = 90°,

 

165

the (OkO) reflections were chosen for the absorption meas~
urement because diffraction from these planes is independent
of the azimuthal setting. The variation of the intensity
of an axial reflection with reSpect to 0 at X = 900
will be an indication of the absorption of X~rays as a
function of crystal orientation.

The intensities of the (OkO) reflections of the CanTPP
crystal were measured in increments of 100 over the 1
range in which the X~ray intensity data were taken. The
absorption factor, by which each reflection, hkfi, was

multiplied depending upon its 9 value, was

 

Akm) = I (%)/1(1)

max

and can be obtained by plotting the quantities Ak(¢) as

a function of the 0 angle. For the CanTPP crystal the
maximum absorption factor from each absorption curve was
observed to be linearly dependent on the 20 angle

(Fig. 32). The absorption for each independent reflection
was then computed as a function of its 1 angle and its
scattering angle, 20.

Other ways to correct for absorption include the method
of Bushing and Wehe (1962)25 of absorption factor based on
the shape of the crystal and the semi—empirical method
developed by Phillips et al.,24 and have been discussed

in Part I.

 

166

@erl
00w

.mm ImM muouomm ooflumHOQO 8553me

08

.mm 665636

 

XOE

Q—

QN

 

5. Extinction

The effect of absorption is to attenuate the X-ray
beam as it passes through the crystal. An additional at«
tenuating effect is extinction which is known to be of two
different kinds, classified as primary and secondary ex—
tinction.

Primary extinction relates to an interference process
which reduces the intensity of a beam as it passes through
a crystal. Given a set of planes in the position to re—
flect the incident beam, the reflected beam can be at the
proper angle for further reflection by another set of planes
(second time or more). Thus, this interference effect will
cause part of reflected beam to be out of phase and de-
crease its intensity. The primary extinction effects are
more serious in perfect crystals than in mosaic crystals
In the latter case, the perfect planes cannot extend over
appreciable ranges for multiple reflections with the mosaic
blocks.

Secondary extinction is commonly encountered in single
crystal work and its effect can be very serious for struc—
ture refinement. For a given set of planes at the reflect-
ing position, the deeper planes will receive less incident
intensity and therefore reflect less power than the upper
planes. This interference effect is usually more pro~
nounced for reflections at low sin 0/% values and a cor-

rection can be made for it. Methods for correcting for

168
secondary extinction are: (1) an empirical method derived
by Darwin (1922),50 (2) the use of a small crystal to re—
measure those reflections which are most seriously affected
by extinction, and (3) quenching the crystal in liquid
nitrogen to break up the mosaic blocks into even smaller

blocks.
6. Conversion of Intensities to Structure Amplitudes

The structure amplitude of a reflection is related to

the intensity as

L = 1 sin 20,
]F(hk£)( = §l%%&&l , where /
P = (1 + cos2 26)/2,

and K is a constant which depends on the crystal size,
incident beam intensity and a number of other fundamental
constants. The polarization factor, P, arises because the
degree of polarization of the eray beam varies with the
reflection angle. The Lorentz factor, L, arises because
the time required for a reciprocal lattice point to pass
through the sphere of reflection varies both with its posi—
tion in reciprocal space and the direction in which it

approaches the reflecting Sphere.

7. Diffractometer

In a four—circle diffractometer the crystal has three
rotational degrees of freedom, a number sufficient to give

any vector, any arbitrary orientation in space referred to

169
axes in the crystal, The three circles (see Figure 33) are
the w—circle, the x-circle which is carried on the w—circle
and whose axis is normal to the w—axis, and the m—circle
which is mounted on the X—circle and carries the goniometer
head supporting the crystal.

The X-ray source is set in a fixed position with re—
spect to the crystal orienter and the detector is mounted
on the 29 circle. The angle between the detector and the
direct beam can be set to any desired value within the
range of the instrument.

In addition to the four-circle elements described, the
diffractometer includes a regulated power supply for the
X-ray tube, scalers for counting the pulses produced by
the detector, a rate meter for displaying on a chart re~
corder the rate at which pulses are being received, and a
pulse—height analyzer for discriminating against pulses
which are either much weaker or much stronger than those

expected for the characteristic energy being used.

8. Unwanted X-ray Radiation

The radiation emitted from an X—ray tube is not mono—
chromatic. The desired kq radiation is always accompanied
by a KB component of somewhat shorter wavelength and both
Ka and Kfl are superposed on the background. Unwanted
radiation can be removed by use of balanced filters which

are made with a pair of metallic foils, one foil of which

 

170

   

Single crystal

Incident beam

 

 

Figure 33. Schematic representation of a fourwcircle
diffractometer.

 

171

has an absorption edge just covering the Ko radiation
and the other an edge covering KB. The intensity of each
reflection is measured once with each filter, and the dif-
ference is taken to be the intensity.

 

APPENDIX 2

1. Observed and Calculated Structure Amplitudes of CanTPP.

2. Observed and Calculated Structure Amplitudes of Porphine.

Appendix 2

1. Observed and Calculated Structure Amplitudes of CanTPP

"‘ K L no») '(LAlL: H l L VIM-a) V‘LILC) n L V(UH>) VlLAL‘.) '03 K I~ 1(0-3) V(LILC)

»°—ar ,_ —

     

.61“ 2.1060 5-

 

172

173

VlC‘LC)

n— x—L—vruv:l_YrcALCY u x L VIU|~>I

mum N‘x L nun» uurc; n K 1. rim-,5)

 

 

a ,_°”1—' 0.1.Ir—IA/N7

 

JIIDJJ'I

 

_-/_:_4_ o.un_ 4.15.11...
7 6 '4 o,>ur >.wu

19]

 

u 4 L nun) HCALC) u 1k L Hon) nuLC) ~ 1 g run-:1 nu.“ n :1 1. Hons) HCALc)

    

 

 

.1 17.4.5101 45.547;

.0111 “.1194
.un_n.uvv
.00

 
   

s .17
_'_d_n_ : _‘N
-a 7 3 > 4.41“

 

u n L nun) NLALC‘I n l L "03)! VIIJALCI n 4 L Vlurb) HCALC) n x L "mun HLALLI

 

11.1"!) '(CALC,

VICALC) n K L va-M HEALTT u '14 L vu-n HLALL) - x ~

A ' x L nun)

 

o 2‘.

177

N x L HIM-Bl V(I.ALC) .- n u. Hal-M HLML) ~ 4 L up»)! Hun.) I K L Nuns) VlLALC)

~ I.JM|4

I

 

- Infillk,
b.06hll

 

n a L V(w-)| VH,ALL N K L Hut-3) HCALC) n 4 L nun-5) vuALc) n R L vu-n VILALCI

 

 

" I} 10 7.1‘1‘11 A.2Vl¢ 1]
._\_.L . -
" 15 IO J$.>7lf‘ 45.00.50
7-5 0__ID_>5 Vlil‘_ol;l295

‘U.VOJl| ll.01hJ

 

MWM‘LJHL
-u 12 12 29.301" 37.1671

 

 

 

 

 

.
o

v»
No

u

u . u u w o o ‘10 g u A)» o u o a V o u o 9 AIM a

v‘v Au.~

 

 

 

o D ‘00 u ;

 

10
10

 

 

 

0
0.2000
14.5000

6.2000
0.0000

Observed
1(085) V(CALC)
17.0000 19.5205
4.3000 ‘.1204
1 .0000 15.097
0 .2000 70.5570
.0000 6.A411
.0000 .3350
.3000 2.5000
.2000 7.5112
.2000 2.7711
3.1000 2.61l9

3.1239
5.9917

and Calculated Structure Amplitudes of

 

 

a 2 A ul—nan)» . w v

 

 

 

~10 o w1r .

 

» p v r

 

11005)
7.2000
3.3000
57.0000

M
o
a
a
o

»
A
o
a
a

 

3.2000
7.0000

V(CALC
H.06F0
4.6102
0? 172‘

 

    

1.9 I)
0000'!

179

 

» u unn

 

 

 

r

 

71005)
1.7000
3.4000
1.4000
6.4000
0.2000

10.0000
3.7000
0.1000

15.2000
9.1000
7.1000
5.2000

 

I» «59- A399 M a
q.
1
u
n

V(CALC)

u :3 0-9‘ n
u
b
c
a

N
N
N
a
c

 

1
‘.715I
4.0.91

< V ‘ V

 

x

F

u »
-Voauuabuunnvflooanuomubbuuurracoo.Vuoouobhhunurwoaroooo

 

y

oouuwoouuuu-uuunev

» u u u
9- ..., c

r

 

 

Porphlne
1.095) 7(CALC)
10.7000 19.5921
3.3000 1.67“
0.2000 3,090}
.2000 10.33“
10.2000 9.5507
1.0000 3.012
00.0000 02.7200
7.3909 1.0722
0.5000 7.00
12.0000 11.7900
10.9000 10.2150
19.5000 10.7030
.00 5.0050
0.9000 7.7090
3.2000 2.7090
17.0000 10.490.
3.700 3.0170
0.9000 4.0030
12.0000 12.2731
25.0000 20.9471
5.000 0.0909
5.5000 5.4700
4.5000 3.1031
10.1000 10.9002
5.000 0.0110
15.1000 15.0211
0.100 2.500
20.9000 19.030
20.0000 23.0967
1.700 .570
.5000 2.1771
.2000 0.0030
3.0000 2.2050
10.5000 10.0939
7.4000 0.0712
0.3000 0.23-2
0.9000 9.1101
9.0000 9.3900
0. 000 0.0197
0.0000 5.1394
35.000 32.0300
10.7000 13.0002
1 .7000 10.0500
.0000 1.0919
1 .4000 17.3072
1 .9000 13.051
1 .7000 12.2709
1 .0000 19.2713
2 .00 22.301
.3000 1.1715
.0000 0.0900
7000 3.1517
.3000 1.7094
.5000 9.2090
1.5000 0.0017
1 .3000 10.5003
1 .3000 12.7510
1 .5000 20.5971
11.7000 13.0002
4.9000 5.2001
.500" 6.3727
.2000 0.0115
1 .1000 12.5539
.900 9.0031
.2000 3.0725
1 .0000 10 0507
.000 .0520
.9000 10.7070
1 .1000 10.1170
.5000 .535
0.3000 3.1110
4,1000 3.0001
.100 10.0007
1 .0000 11.0333
.7000 9.5203
.7000 .1027
.‘000 10.1020
.5000 .7020
.10 0.9032
9 .0000 100.0007
12 .7000 133.5235
16.3000 10.400
0.0000 0.5950
.0000 .7909
10.0000 17.0101
‘.20 .0734
21.5000 2 7995
15.70 1 .5539
122.3000 12 .5201
03.90 0 .0000
172.0000 10 .7090
02.0000 0 .0000
.90 0 .9153
01.2000 0 .9739
0.0000 .3100
.1000 .2903
0.0000 .4155
3.1000 .9570
3.5000 0071
10.3000 .7011
0.5000 .0971
3.1000 .1427
10.0000 1 .5243
7.0000 .0301
3.5090 22
7.4000
.7000
0.0000

 

 

uuuuuuuuu r

anodONVOwAuBNVV

9-1-9-

51»..-
OovoflbwooumbbuunvPFOOOOODVVOOWUAuuNMN-vb-H

 

~9-

oooOVVamhbuuuw

.-

 

 

9.1.71.
“VOW“.buNHOVVouuAAuuMHouOoowv‘AuuNNI-l

180

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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