NOV 1 1 "3‘9?

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ABSTRACT
STUDY OF HINDERED INTERNAL ROTATION IN SOME

SUBSTITUTED AMIDES BY NUCLEAR MAGNETIC
RESONANCE SPECTROSCOPY

BY

William Chung-Tsing Tung

A Varian HA-lOO high-resolution nuclear magnetic
resonance (NMR) Spectrometer was used for measuring the
proton magnetic resonance Spectra of several symmetrically
and asymmetrically N,N—disubstituted amides over a wide
range of temperatures. Due to inconsistencies in the
Varian temperature charts, the ethylene glycol and methanol
chemical-Shift thermometers were carefully recalibrated.

A detailed description and discussion of the two cur—
rently most pOpular approximation methods used in the study
of the relationship between the rate of internal rotation
about the central C—N bond of symmetrically disubstituted
amides and the various observed line-Shape parameters, are
presented. The theoretical two—site exchange line—Shape
equation was programmed to fit the experimental Spectra
to a set of line—Shape parameters by a least—squares method.
The best setscflfparameters were extracted from the observed

line Shapes by this curve fitting procedure and the

William Chung-Tsing Tung

theoretical Spectra were plotted for visual comparison with
experimental Spectra. Both computer programs were written
for the CDC-3600 computer.

In the case of symmetrically disubstituted amides, all
three methods (intensity-ratio, peak-separation and total
line-shape) were used to study the rate of internal rotation
as a function of temperature. The results of these studies
are reported and discussed. Deuterated N,N—dimethylform—
amide (DMF) was used to eliminate the effect of Spin—Spin
interaction between the formal proton and the protons of
N—methyl groups and so obtain a more reliable rotational
energy barrier for DMF. A superposition technique was also
used to estimate the effect of Spin-Spin coupling on the
energy barrier of this amide using the digital computer.

A study of factors influencing the rotational energy
barrier obtained for N,N—dimethylcarbamoylchloride has been
made. It is shown that the methods of preparing and handling
the sample, as well as the method of referencing the NMR
signals,have an important effect on the values obtained for
the energy barrier.

The total line-Shape analysis method was also applied
to evaluate the energy barriers of N-methyl-N-ethylacetamide,
N-methyl—N—n-butylacetamide, N-methyl-N-iSOpr0pylacetamide,
N-methyl-N-cyclohexylactamide and N-methyl-N-benzylformamide.
The results qualitatively indicate that the order of the
values of the energy barriers of these asymmetrically di—

substituted amides is parallel to the order of polarity

William Chung-Tsing Tung

of the N-alkyl groups.

The observed Spectra of N-methyl-N—n-butyltrimethyl-
acetamide, N-methyl—N-o-naphthylacetamide and N—methyl-N-
phenylacetamide indicate that either the rates of internal
rotation about the central C-N bonds of these amides
were too fast,even at quite low temperature (-ZOOC),to be
detected or the bulky N-Substituted groups lead to a single
stable isomer in the accessible temperature range.

The frequency factors obtained in this laboratory are

12 1 ..
+ to 10 7 sec 1. These are somewhat

in the range of 10
higher than those reported earlier (5,4), but they are in
good agreement with the more recent values. The high values
are attributed to the increase of entropy in going from the
ground state of a disubstituted amide molecule to the transi-
tion state.

The rotational energy barriers in a number of N,N-
dimethylamides have been redetermined using the total line-
Shape analysis method. The new values are, in general, much
higher than those reported from intensity—ratio or peak-
separation studies. The effect of substituents on the
barriers has been discussed.

The effect of solvents on the rotational energy barrier
in DMF has been investigated. It is found that solvents of
lower dielectric constant than the amide itself lower the
barrier. These solvents appear to break up the dimers and
polymeric Species which are important in the pure amides

and which tend to raise the barriers to internal rotation.

STUDY OF HINDERED INTERNAL ROTATION IN SOME
SUBSTITUTED AMIDES BY NUCLEAR MAGNETIC

RESONANCE SPECTROSCOPY

BY

William Chung-Tsing Tung

A THESIS

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

DOCTOR OF PHILOSOPHY

Department of Chemistry

1968

ACKNOWLEDGMENTS

It is with sincere appreciation that I acknowledge
the encouragement and counsel of Professor M. T. Rogers
under whose direction this investigation was conducted.

I also wish to express my gratitude to the National
Institutes of Health, Division of General Medical Sciences
and the American Chemical Society, Petroleum Research
Fund,for SUpport of this work.

To Debbie, my wife, I want to offer my everlasting
appreciation for her constant encouragement and under-
standing during this phase of my education.

 

ii

TABLE OF CONTENTS

INTRODUCTION . . . . . . . . . . . . . . . . . .
HISTORICAL BACKGROUND. . . . . . . . . . . . . .
THEORETICAL BACKGROUND . . . . . . . . . . . . .

Introduction. . . . . . . . . . . . . . . .
Chemical Shifts . . . . . . . . . . . . . .
Solvent Effects on Chemical Shifts. . . . .
Spin-Spin Splitting . . . . . . . . . . . .
Double Irradiation. . . . . . . . . . . . .
Bloch Formulation of the Nuclear Induction

EXperiment . . . . . . . . . . . . . . .
The Line-Shape Equation with Exchange . . .
Computer Programs for Exchange Calculations
Chemical Shifts of the Methyl Proton Peaks.

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

Preparation of Amides . . . . . . . . . . .
Spectrometer. . . . . . . . . . . . . . . .
Temperature Calibration . . . . . . . . . .

RESULTS. . . . . . . . . . . . . . . . . . . . .

Computer Methods in NMR Studies of Rate
Processes. . . . . . . . . . . . . . . .
Methods for Evaluating Rotational Energy

Barriers in Amides. . . . . . . . . .
Method I--The Intensity-Ratio Method.
Method II--Peak-Separation Method . .
Method III--Total Line-Shape Analysis

Treatment of Data . . . . . . . . . . . . .

High-resolution Spectra . . . . . . . . . .
N, N-DimethylprOpionamide . . . . . . . .
N, N-Dimethylacrylamide . . . . . . .

Asymmetrical N, N-Disubstituted Amides . . .
N- Ethyl— N-methylacetamide. . . . . . . .

iii

Page

15

15
19
25
27
50

51
56
41
46

51

51
55
56

59

59

59
59
62
65
64
67
67
69
69
71

TABLE OF CONTENTS - Cont'd.

N—n-Butyl-N-methylacetamide. . . . . . .
N-Cyclohexyl—N-methylacetamide . . . . .
N-IsoprOpyl—N-methylacetamide. . . . . .
NsMethyl-N-benzylformamide . . . . . . .
N-n-Butyl-N-methyltrimethylacetamide . .
N-Methyl-N-d-naphthylacetamide . . . . .
N-Methyl-N-phenylacetamide . . . . . . .
Hindered Internal Rotation in Substituted
Amides . . . . . . . . . . . . . . . . .
N,N-Dimethylformamide. . . . . . . . . .
N,N-Dimethylacetamide. . . . . . . . . .
N,N-DimethylprOpionamide . . . . . . . .
N,N-Dimethylacrylamide . . . . . . . . .
N,N-Dimethyltrichloroacetamide . . . . .
N,N-Dimethylcarbamoylchloride. . .
N-Methyl-N-ethylacetamide. . . . . . . .
N-Methyl-N-n-butylacetamide. . . . . . .
N-Methyl—N-cyclohexylacetamide . . . . .
N-Methyl-N-iSOprOpylacetamide. .
N-Methyl-N-benzylformamide . . . . . . .

DISCUSSION . . . . . . . . . . . . .‘. . . . . .

Methods for Obtaining Rate Data from NMR
Spectra. . . . . . . . . . . . . . . . .
Method I--The Intensity-Ratio Method . .
Method II--The Peak-Separation Method. .
Method III--Total Line-Shape Analysis. .

Errors in the Measurement of Rotational
Barriers . . . . . . . . . . . . . . . .

Rotational Barriers in Symmetrically Substi
tuted Amides . . . . . . . . . . . . . .

Solvent Effects on Rotational Barriers in
Amides . . . . . . . . . . . . . . . . .

Rotational Barriers in Unsymmetrically N,N-
Disubstituted Amides . . . . . . . . . .

SUMMARY. . . . . . . . . . .

BIBLIOGRAPHY . . . . . . . .

APPENDICES . . . . . . . . .

Appendix I -- NMRFIT. .
Appendix II -— NMRPLOT.
Appendix III -- NMRTAU.

iv

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74
74
77
77
8O
8O

80
8O
85
85
85
85
84
141
141
141
141
141

160
160
160
162
165
165
171
177
179
185
187
195
195

200
207

LIST OF TABLES

TABLE Page

1. Energy barriers restricting rotation about the
central C-N bond of substituted amides. . . . . 11

2. Some rotational barriers for substituted
amides in solution. . . . . . . . . . . . . . . 15

5. Rotational barriers in unsymmetrically N,N-
disubstituted amides. . . . . . . . . . . . . . 14

4. Boiling points of substituted amides. . . . . . 52

5. Temperature dependence of the rate of internal
rotation about the central C-N bond of pure
DCON(CH3)2O o o o o o o o o o o o o o o o a o o 89

6. Thermodynamic and kinetic parameters for
internal rotation about the central C-N bond
of pure DCON(CH3)2 from different methods. . . 9O

7. Temperature dependence of the rate of internal
rotation about the central C-N bond of pure
HCON(CH3)2 with C6H5C(CH3)3 as internal refer—
ence. . . . . . . . . . . . . . . . . . . . . . 92

8. Thermodynamic and kinetic parameters for
internal rotation about the central C-N bond of
pure HCON(CH3)2 with C6H5C(CH3)3 as internal
reference . . . . . . . . . . . . . . . . . . . 95

9. Temperature dependence of the rate of internal
rotation about the central C-N bond of pure
DCON(CH3)2 in F3CCOOH solution. . . . . . . . . 95

10. Thermodynamic and kinetic parameters for in-
ternal rotation about the central C-N bond of
DCON(CH3)2 in F3CCOOH solution. . . . . . . . . 96

11. Temperature dependence of the rate of internal
rotation about the central C-N bond of
DCON(CH3)2 in €2H2c14 solution. . . . . . . . . 98

LIST OF TABLES - cont'd.

TABLE

12.

15.

14.

15.

16.

17.

18.

19.

20.

21.

22.

Thermodynamic and kinetic parameters for in-
ternal rotation about the central C-N bond
of DCON(CH3)2 in c2H2c14 solution. . . . . . .

Temperature dependence of the rate of internal
rotation about the central C-N bond of
DCON(CH3)2 in C6H5C(CH3)3. . . . . . . . . . .

Thermodynamics and kinetic parameters for in-
ternal rotation about the central C-N bond of
DCON(CH3)2 in C6H5C(CH3)3. . . . . . . . . . .

Temperature dependence of the rate of internal
rotation about the central C-N bond of
CH3CON(CH3)2 . . . . . . . . . . . . . . . . .

Thermodynamic and kinetic parameters for in-
ternal rotation about the central C—N bond of
CH3CON(CH3)2 . . . . . . . . . . . . . . . . .

Temperature dependence of the rate of internal
rotation about the central C-N bond of
CH3CON(CH3) 2 o o o o o o o o o o o o o o o o o

Thermodynamic and kinetic parameters for in-
ternal rotation about the central C-N bond of
CH3CON<CH3> 2 o o o o o o o o o o o o o o o o 0

Temperature dependence of the rate of internal
rotation about the central C-N bond of
CH3CON(CH3)2 in F3CCOOH. . . . . . . . . . . .

Thermodynamic and kinetic parameters for in-
ternal rotation about the central C-N bond of
CH3CON(CH3)2 in F3CCOOH. . . . . . . . . . . .

Temperature dependence of the rate of internal
rotation about the central C-N bond of
C2H5CON(CH3)2. . . . . . . . . . . . . . . . .

Thermodynamic and kinetic parameters for in-

ternal rotation about the central C-N bond of
C2H5CON(CH3)2. . . . . . . . . . . . . . . . .

vi

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99

101

102

106

107

109

110

112

115

115

116

LIST OF TABLES — cont'd.

TABLE

25.

24.

25.

26.

27.

28.

29.

50.

51.

52.

55.

Temperature dependence of the rate of internal
rotation about the central C-N bond of
CH2 =CHCON (CH3) 2 o o o o o o o o o o o o o o o o

Thermodynamic and kinetic parameters for in-
ternal rotation about the central C-N bond of
CH2=CHC0N(CH3)2. . . . . . . . . . . . . . . .

Temperature dependence of the rate of internal
rotation about the central C-N bond of
CC13CON(CH3)20 o o o o o o o o o o o o o o o o

Thermodynamic and kinetic parameters for in—
ternal rotation about the central C-N bond of
CC13C0N(CH3)2. . . . . . . . . . . . . . . . .

Temperature dependence of the rate of internal
rotation about the central C-N bond of
CC13CON(CH3)2. . . . . . . . . . . . . . . . .

Thermodynamic and kinetic parameters for in-
ternal rotation about the central C—N bond of
CC13CON(CH3)2. . . . . . . . . . . . . ... . .

Temperature dependence of the rate of internal
rotation about the central C-N bond of
C1CON<CH3)20 o o o o o o o o o o o o o o o o 0

Temperature dependence of the rate of internal
rotation about the central C-N bond of
C1CON(CH3)2O o o o o o o o o o o o o o o o o 0

Temperature dependence of the rate of internal
rotation about the central C-N bond of
ClCON(CH3)2. . . . . . . . . . . . . . . . . .

Temperature dependence of the rate of internal
rotation about the central C-N bond of
ClCON(CH3)2. . . . . . . . . . . . . . . . . .

Temperature dependence of the rate of internal

rotation about the central C-N bond of
ClCON(CH3)2. . . . . . . . . . . . . . . . . .

vii

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119

121

122

124

125

126

127

151

155

154

LIST OF TABLES - cont'd.

TABLE

54.

55.

56.

57.

58.

59.

40.

41.

42.

45.

44.

45.

Thermodynamic and kinetic parameters for in-
ternal rotation about the central C-N bond of
ClCON(CH3)20 o n o o o o o o o o o o o o o o 0

Temperature dependence of the rate of internal
rotation about the central C-N bond of
C1CON(CH3)2. . . . . . . . . . . . . . . . . .

Thermodynamic and kinetic parameters for in-
ternal rotation about the central C-N bond of
C1CON(CH3)2. . . . . . . . . . . . . . . . . .

Temperature dependence of the rate of internal
rotation about the central C-N bond of
CH3CON(CH3)C2H5. . . . . . . . . . . . . . . .

Temperature dependence of the rate of internal
rotation about the central C—N bond of
CH3CON(CH3)C4H9. . . . . . . . . . . . . . . .

Temperature dependence of the rate of internal
rotation about the central C—N bond of
CH3CON(CH3)C6H11 . . . . . . . . . . . . . . .

Temperature dependence of the rate of internal
rotation about the central C-N bond of
CH3CON(CH3)CH(CH3)2. . . . . . . . . . . . . .

Temperature dependence of the rate of internal
rotation about the central C-N bond of
HCON(CH3)CH2C6H5 . . . . . . . . . . . . . . .

Temperature dependence of the rate of internal
rotation about the central C-N bond of
HCON(CH3)CH2C5H5 . . . . . . . . . . . . . . .

Thermodynamic and kinetic parameters for in-
ternal rotation about the central C-N bond of
some N,N-dimethylamides. . . . . . . . . . . .

Effect of various factors on the rotational
energy barriers in N,N-dimethylcarbamoyl-
chloride (DMCC). . . . . . . . . . . . . . . .

Thermodynamic and kinetic parameters for in-
ternal rotation about the central C-N bond of
some unsymmetrically N,N-disubstituted amides.

viii

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158

159

142

144

148

154

156

158

168

169

170

LIST OF FIGURES

FIGURE

1.

2.

10.

11.

12.

Proton magnetic resonance Spectrum of
CH3CH2CON(CH3)2. Internal reference: HMDS. .

Proton magnetic resonance Spectrum of
CH2=CHCON(CH3)2. Internal reference: HMDS. .

Proton magnetic resonance Spectrum of
CH2CON(CH3)(CH2CH3). Internal reference: HMDS

Proton magnetic resonance Spectrum of

CH3CON(CH3)(CH2CH2CH2CH3). Internal reference:

HMDS . . . . . . . . . . . . . . . . . . . . .

Proton magnetic resonance Spectrum of
CH3CON(CH3)(C5H11). Internal reference: HMDS.

Proton magnetic resonance Spectrum of
CH3CON(CH3)CH(CH3)2. Internal reference: HMDS

Proton magnetic resonance Spectrum of
HCON(CH3)CH2C6H5. Internal reference:
t-butylbenzene . . . . . . . . . . . . . . . .

Proton magnetic resonance Spectrum of
(CH3)3CON(CH3)(CH2CH2CH2CH3). Internal refer-
ence: mDS . O O O O O O O O O O O O O O O O O

Proton magnetic resonance Spectrum of
CH3CON(CH3)(d-C10H7).Internal reference: HMDS

Proton magnetic resonance Spectrum of
CH3CON(CH3)(C5H5) in CC14 solution. Internal
reference: HMDS . . . . . . . . . . . . . . .

The observed and calculated proton magnetic
resonance Spectra of DCON(CH3)2. . . . . . . .

Temperature dependence of observed and calcu-
lated Spectra of DCON(CH3)2. . . . . . . . . .

ix

Page

68

70

72

75

75

76

78

79

81

82

85

87

LIST OF FIGURES - cont'd.

FIGURE

15.

14.

15.

16.

17.

18.

19.

20.

21.

22.

25.

24.

25.

26.

Plot of 10910 T against 103/TO K for pure
DCON(CH3)2. . . . . . . . . . . . . . . . .

Plot of 10910 T against 103/TOK for pure
HCON(CH3)2 with Spin—Spin coupling correction
included by superposition, with C6H5C(CH3)3
as internal reference . . . . . . . . . . . .

Plot of loglo T against 103/TOK for
DCON(CH3)2 in F3CCOOH solution. . . . . . . .

Plot of 10910 T against 103/TOK for” 0.67
mole fraction of DCON(CH3)2 in C2H2Cl4 solu-
tion. . . . . . . . . . . . . . . . . . . . .

Plot of log 10 T against 103/TOK for
DCON(CH3)2 in C6H5C(CH3)3 solution (410.7
mole fraction). . . . . . . . . . . . . . . .

Temperature dependence of observed and
calculated proton magnetic resonance Spectra
Of CH3CON (CH3) 2 o o o o o o o o o o o o o o 0

Plot of 10910 T against 103/TOK for pure
CH3CON(CH3)2, with TMS as internal reference.

Plot of loglo T against 103/TOK for pure
CH3CON(CH3)2, with HMDS as external reference

Plot of 10910 T against 103/TOK for
CH3CON(CH3)2 in F3CCOOH solution. . . . . . .

Plot of 10910 T against 103/TOK for pure
C2H5CON(CH3)2 . . . . . . . . . . . . . . . .

Plot of loglo T against 103/T0K for pure
CH2=CHCON(CH3)2 . . . . . . . . . . . . . . .

Plot of loglo T against 103/TOK for pure
CC13CON(CH3)2, with HMDS as external reference

. 0
Plot of 10910 T against 103/T K for pure
CC13C0N(CH3)2. with TMS as internal reference

Plot of 10910 T against 103/TOK for pure
C1C0N(CH3)2, with cyclohexane as external
reference . . . . . . . . . . . . . . . . . .

Page

91

94

97

100

105

104

108

111

114

117

120

125

126

128

LIST OF FIGURES - cont'd.

FIGURE

27.

28.

29.

50.

51.

52.

55.

54.

55.

56.

57.

58.

59.

40.

Plot of loglo T against 103/TOK for
ClCON(CH3)2 saturated with 02, TMS as intern-
al reference. . . . . . . . . . . . . . . . .

Plot of 10910 T against 103/TOK for unpuri-
fied ClCON(CH3)2, not degassed, with HMDS as
external reference. . . . . . . . . . . . . .

Plot of loglo T against 103/TOK for highly
purified ClCON(CH3)2, with HMDS as external
reference . . . . . . . . . . . . . . . . . .

Plot of 10910 T against 103/TOK for pure
ClCON(CH3)2, with TMS as internal reference .

Plot of 10910 T against 103/TOK for pure
ClCON(CH3)2. with HMDS as external reference.

Plot of 10910 T against 103/TOK for pure
CH3CON(CH3)C2H5 . . . . . . . . . . . . . . .

Plot of loglo T against 103/TOK for pure
CH3CON(CH3)C4H9 . . . . . . . . . . . . . . .

Temperature dependence of observed and calcu-
lated proton magnetic resonance Spectra of
CH3CON(CH3)(C6H11). . . . . . . . . . . . . .

Plot of 10910 T against 103/TOK for pure
CH3CON (CH3)C6H11 o o o o o o o o o o o o o o o

The observed and calculated Spectra of
CH3CON(CH3)CH(CH3)2 . . . . . . . . . . . . .

Temperature dependence of observed and calcu—
lated proton magnetic resonance Spectra of

CH3CON(CH3)CH(CH3)2 . . . . . . . . . . . . .'

Plot of loglo T against 103/TOK for pure
CH3CON(CH3)CH(CH3)2 . . . . . . . . . . . . .

Plot of loglo T against 103/TOK for pure
HCON(CH3)CH2C5H5 (from benzyl protons). . . .

Plot of loglo T against 103/TOK for pure
HCON(CH3)CH2C6H5 (from the formyl doublet). .

xi

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140

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152

155

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159

INTRODUCTION

Rotation about the central C-N bond of amides and
substituted amides is not free and the energy barrier
restricting rotation is believed to arise, in part at least,
from the partial double-bond character of this bond (1).
The only general method for measuring these rotational
energy barriers depends on detailed analysis of the nuclear
magnetic resonance line shapes at various temperatures.

Phillips (2) proved that the doublet observed for the
N-methyl protons of N,N-dimethylamides was the result of a
chemical Shift difference between the two methyl groups A

and B.

/ CH3 (A)

R \ CH3 (B)

He also noted that the components of the doublet gradually
coalesce on raising the temperature and that the resulting
Single line becomes narrower at high temperatures.

Gutowsky and Holm (5) develOped a theory relating the proton
line Shape to the rate of rotation about the C-N bond and
evaluated the rotational energy barriers in N,N-dimethyl-

formamide (DMF) and N,N-dimethylacetamide (DMA) from

measurements of the rates of rotation at different tempera-
tures. Application of the Arrhenius equation (rate =
Ae-Ea/RT) to this rate process permitted values of the
rotational energy barrier Ea and the frequency factor A to
be evaluated.

Because of the general interest in the origin of ro-
tational energy barriers, and also because the NMR method
provides the only precise method for studying a series of
substituted amides, many investigations have been made since
1956. Rogers and Woodbrey (4) Showed that the original peak-
separation method (5) was not capable of great precision and
deve10ped an intensity-ratio method which was used to study
substituent effects on the rotational energy barriers in
symmetrically N,N-disubstituted amides. They also studied
the effect of solvents on these barriers (5).

Allerhand and Gutowsky (6) develOped the Spin-echo
method for determining rates of internal rotation in amides
and applied it to determining the rotational energy barriers
in N,N-dimethylcarbamoyl chloride (DMCC) and in N,N-dimethyl-
trichloroacetamide (DMTCA). This method has the advantage
that it greatly extends the range of temperatures which can
be studied. Their values were consistently higher than those
of Rogers and Woodbrey and detailed investigation Showed
that the intensity-ratio method is subject to certain
systematic errors in unfavorable cases. It became clear

that only by detailed fitting of observed line Shapes to

those calculated with variable sets of parameters could
reliable rate constants be obtained.

The present research program consists of three parts:
(1) Re-examination of the high-resolution NMR method for
determining rotational energy barriers and develOpment of
computer techniques for total line-Shape analysis, (2) Ap-
plication of the methods so develOped for treating proton
exchange between two sites,without any approximations or
assumptions,to a re-examination of the symmetrically
N,N-disubstituted amides, and (5) Extension of the total
line-shape analysis techniques to the measurement of
rotational energy barriers in a series of unsymmetrically
N,N-disubstituted amides which had not been previously

studied.

HISTORICAL BACKGROUND

High-resolution nuclear magnetic resonance (NMR)
Spectrosc0py may be used to determine the rates of many
processes. In 1955 Gutowsky and McCall (7) Showed that
for protons exchanging between two Sites the rate of
exchange may be related quantitatively to the line shape
provided the rate falls within certain limits. Since then
the NMR method has been used to measure the rates of many
proton interchange processes.

In his book Pauling (1) postulated that rotation about
the central C-N bond of amides would be restricted since
the bond Should have considerable double—bond character and
this was confirmed by Phillips (2) from an NMR study of
N,N-dimethylamides. Phillips (8) also discussed several
types of molecules in which internal rotations could be
studied by the NMR method. Phillips (2) Showed that peaks
correSponding to the two methyl groups A and B in N,N-di-
methylformamide (I) were chemically Shifted in the NMR
Spectrum and that these peaks coalesced at higher tempera-
tures to a Single peak located at the average position.
From a theoretical study, Gutowsky and Holm (5) Showed that
the apparent peak separation 5v of the partially coalesced
doublet could be related to the lifetime 2T of a given set

4

of protons at one Site. They were able to evaluate the
rate of interchange of methyl protons in I between sites
A and B, and so the rate of interchange between isomers I
and II, for two amides. This may be considered a first

order rate process with rate constant k = 2T.

Q§C_N/£m(m o§h_N/rm(m
\
R”’ ‘\‘CH3 (B) R’/’ CH3 (A)
I II

Treating the interchange as a rate process governed by the

Arrhenius equation

k = Ae-Ea/RT

I

they obtained values for the energy barrier Ea hindering
rotation about the central C-N bonds in N,N-dimethylformamide
(DMF) (I, R=H) and in N,N-dimethylacetamide (DMA) (I, R= CH3)
of 7.: 5 and 12.1 2 kcal/mole, reSpectively. The large
probable errors reflect the fact that the linewidths are
comparable to the chemical shifts between the peaks at the
low Spectrometer frequency (v0: 17.755 Mhz) which they used.
Loewenstein and Meiboom (9) Showed that the mean life-
time T of exchangeable nuclei at a chemical site could be
related to r, the ratio of maximum to central minimum v-mode
intensities. Rogers and Woodbrey (4) deveIOped the intensity—
ratio method and applied it to the evaluation of internal

rotation energy barriers in an extensive variety of

substituted amides. In addition they treated the process

as governed by the absolute reaction rate theory equation

AFt

kT 7fi

i and AS* of

and obtained values of the parameters AF#, AH
that theory assuming the transmission coefficient K to be
unity. They also studied the effect of solvent on the

energy barriers (5).

Fraenkel and Franconi (10) compared actual with calcu-
lated line shapes through two parameters, the intensity
ratio r and the width of the collapsed doublet S. By this
method they evaluated the barrier to internal rotation in
DMF and in the protonated Species DMF-H+ and Showed that
the latter was larger by 5.1 kcal/mole. Their work indi-
cated that protonation occurs on oxygen rather than nitrogen
and this was later proved conclusively by GilleSpie (11)
from NMR studies of solutions of DMF and DMA in fluoro-
sulfuric acid. Neuman (12) programmed the general line-shape
equations of Rogers and Woodbrey (4) to obtain energy
barriers from the intensity-ratio method for DMF, DMA and
dimethylthioacetamide (DMTA) in formamide solution.

Allerhand and Gutowsky (6) applied the Spin-echo tech-
nique to determine exchange rates in the N,N-dimethyltri-
chloroacetamide (DMTCA) and N,N-dimethylcarbamoyl chloride
(DMCC). They Showed that accurate values of the exchange

rates for the protons could be obtained by determining the

decay amplitude of successive echoes in a Carr-Purcell

train and the method has the advantage that it can be used
to measure much more rapid exchange rates than can the high-
resolution methods. It has the disadvantage that no other
protons but the two exchanging sets can be present Since

the resolution is low. Reeves (15) extended this method

to N,N-dimethyltrifluoroacetamide (DMTFA) and to N,N-di-
methylformamide-d1 to obtain new values for the energy
barriers in these amides.

Fryer, Conti and Franconi (14) reviewed all work up to
1965 on energy barriers hindering internal rotation in
amides. They Showed that values obtained in various labora-
tories disagreed beyond the stated limits of error and they
attempted to locate systematic sources of error and to
develOp other line-Shape parameters. They were able to Show
that both the peak-separation method and the intensity-ratio
method were subject to systematic errors particularly as a
result of the inhomogeneous broadening of the lines in mag—
netic fields at present attainable.

It became clear about this time that the best way to
obtain reliable values of exchange rates and of energy
barriers from high-resolution NMR data would be to compare
the complete eXperimental Spectrum with Spectra calculated
using various parameters and select the parameters to give
best agreement between theory and eXperiment. Allerhand
et a1. (15), showed that good agreement between high-

resolution and Spin-echo methods could be obtained for

energy barriers if adequate computer methods were used to
treat the data in each case. It has become necessary to
reinvestigate all the values of energy barriers obtained
using the older methods since systematic errors led to
values which were, in general, too low.

Neuman (16) used total line-shape analysis to rein-
vestigate the rotational barriers in DMCC and obtained a
value,Ea = 16.9.i 0.5 kcal/mole,somewhat higher than that
reported by the Spin-echo method (16) (Ba = 14.0.1 0.9
kcal/mole). The same method was used (17) to obtain a new
value for the rotational barrier in DMA-d3, Ea = 19.6.i 0.5
kcal/mole; the deuteration of the acetyl methyl protons
eliminates the Spin coupling across the C-N bond and improves
the accuracy of the results. They used the line—shape
equations of Gutowsky and Holm to generate values of signal
intensity versus frequency for exchange between equally
pOpulated sites for various values of the exchange rate 2T.
The results were plotted and compared visually with eXperi-
mental Spectra; a computer program develOped by Roberts and
Gerig was used in their work. Conti and von Philipsborn
(18) have also reinvestigated several amides using every
precaution to eliminate systematic errors and report values
of DMF, DMF-dl, DMF-H+ and DMF-dl-H+ which should be quite
reliable. Unfortunately these new and carefully-obtained
results from the high-resolution method still differ in

several cases from those obtained by the best Spin-echo

techniques and the source of these discrepancies is not
known.

Although most of the research so far has concentrated
on symmetrically disubstituted amides, the NMR method may
also be used to obtain rotational barriers in unsymmetrically
substituted materials. The earliest report of barriers in
such compounds was that by Franconi (19) who reported Ea =
11, 12, and 11 kcal/mole for CeHSCHCHsNCH3CHO, C3H5CH2NCH3CHO
(MBF) and (C6H5)2CHNCH3CHO, reSpectively. Mannschreck (20)
obtained the relative amounts of isomers I and II by the NMR
method in a series of compounds R3CONR1R2 where R3 = 2,4,6-
trimethylphenyl and R1, R2 are various alkyl groups. He eval-
uated (21) the rotational barriers for the particular compound
with R1 = CH3, R2 = benzyl, and R3 = 2,4,6~trimethylphenyl
in quinoline solution and reports AF¢ = 25.1 kcal/mole.
If R3 = 2,4,6-tribrom0phenyl, AF: = 25.5 kcal/mole. Gehring
§£_§;, (22), determined the barriers in several N-alkyl—
N-vinyl-amides by the peak—separation method. Gutowsky,
Jonas and Siddall (25) have made the only reliable study of
any unsymmetrically substituted amide for MBF where Ea =
22.7 kcal/mole or 25 kcal/mole,depending on whether the
formyl or benzyl doublets are analyzed. A direct measure-
ment from the eXperimentally determined equilibrium constant
gave the value 20.0 kcal/mole. An intensive study of con-
formational isomerism in the much more complex N-acetyl—N-

methyl-2,4,6—trinitroaniline (24) has also been made.

10

The values which have been reported for energy barriers
hindering internal rotation in pure substituted amides are
listed in Table 1 while Table 2 lists values obtained in
solution. Table 5 summarizes the data for the unsymmetrical-
ly substituted amides. In only a few cases have the values
been determined by fitting the complete observed line Shape
to the theoretical expression. All values determined by
other methods must be considered as only estimates subject

to very large probable errors.

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.m UHQMB

THEORETICAL BACKGROUND

Introduction

Many atomic nuclei behave as though they are Spinning
charged bodies and the circulation of the charge produces a
magnetic moment along the axis of rotation. Nuclei such
as 1H, 13C, 15N and 19F are Spherical, have no quadrupole
moment and their Spin quantum number I = 1/2. ‘When these
nuclei are placed in a magnetic field H, taken as the Z
direction, they will line up with the field (I2 = +1/2) or
against the field (I2 = -1/2). The energy difference between
these two levels, AB, is prOportional to the magnetic field
strength H at the nucleus and is equal to th/ZW, where 7
is the gyromagnetic ratio of the nucleus. AS for other
type of Spectrosc0py, NMR involves absorption of electro-
magnetic radiation whose energy AE is related to the fre-
quency v of the rf oscillator by the equation AB = hv.

To observe nuclear magnetic resonance absorption a fixed
frequency can be applied and the field varied until the
equation v = yH/Zw is satisfied; energy is then absorbed by
the nuclei. In a typical eXperiment this flow of energy
induces a current in the receiver circuit which is detected

and recorded.

15

16

In a uniform static field Ho the energies of the
two Spin states are separated by an energy ZuHo, where u
is the maximum component of the nuclear magnetic moment.
For an assembly of nuclei (I = 1/2) at a certain thermal
equilibrium temperature T the ratio of the pOpulations of

the two states is

$2.: ZQEEQ. ,, _ SEES
N1 exp ( kT ) __1 kT .

The probabilities of a given nucleus being in either the
upper or lower state are Quip—‘12:?) and §(‘1+Hy%%) , reSpectively.
The mean nuclear magnetic moment in the direction of the
main field is

_ 2
u=u [§(1+%) -‘2-(1-E’]-:—T9)]= 9%

and, in a unit volume containing N nuclei, the correSponding

paramagnetic volume susceptibility is

XO=EB=§BE
H0 kT

Let n_ and n+ be the number of nuclei in the upper and lower

states, reSpectively; the difference n = n+ - n_ (excess

number of nuclei per time) is a function of time. If ne is
denoted as this difference after equilibrium is reached

the rate of change of pOpulationS can be eXpressed as

dn/dt = - (n — ne)/T1 ,

17

where T1, the Spin-lattice relaxation time, is a measure of
the rate at which the Spin system comes into thermal
equilibrium with the other degrees of freedom. The Spin—
lattice relaxation time is related to W, the mean of the
two probabilities for the Spin-state transitions upward

W_ —>W+ and downward W+ ->W_ by the eXpression

T =: —1— = - 1
1 2w (w_—-> w+)+(w+—> w_) '

The experimentally observed line is always broader
(covers a range of several frequencies) than the sharp
signal at one frequency predicted by the quantum mechanical
calculation. There are several causes for the broadening.
First, it is due to Spontaneous emission Since the lower
limit of any Spectrosc0pic line width is determined by the
finite lifetime of the upper state. The broadening caused
by this is negligibly small (25). Second, the Spin-lattice
relaxation can cause line broadening. The finite lifetime
of the two states is important because of the possibility
of transitions between them being induced by the other
molecular degrees of freedom. The line broadening can be
estimated from the uncertainty principle AEAugfi, and this
implies that the uncertainty in the frequency of the absorp—
tion is 1/2wAt.

In the case of solids or highly viscous liquids the
direct interaction of the magnetic dipoles causes greater

broadening than that from the Spin-lattice relaxation process.

18

Here the nuclei stay in the same relative positions for a
long time but the nuclei are in a variety of fields because
of the changing local magnetic field from the neighboring
dipoles. This relaxation process is characterized by the
Spin-Spin relaxation time T2. In a fluid of low viscosity,
molecules undergo random motion (Brownian movement) and it
can be Shown (26) that, providing this motion is very fast,
the local dipolar fields average out to a very small value.

A third cause of line broadening is the interaction of
the given nuclear moments with neighboring nuclei having an
electric quadrupole moment (I > 1/2). Quadrupolar broaden-
ing is important for protons attached to nuclei such as
nitrogen (I = 1 for 14N) and often makes the absorption
peaks for such protons difficult to detect.

A final cause of line broadening is the inhomogeneity
always present in the static magnetic field Ho over the
volume of the sample. The observed Spectrum at a fixed
frequency can be considered as a superposition of the
Spectra from molecules at all different parts of the sample
each in a slightly different static field. Line widths in
high resolution NMR are ordinarily limited by the inhomo-

geneous broadening.

Chemical Shifts

 

The magnetic field strength at a particular nucleus
is usually less than the strength of the applied field Ho,
because the motions of the electrons result in a diamagnetic
shielding effect. The local field experienced by the
nucleus is H = Ho(1 - 6), where 6 is the screening constant
and depends only on the position of the particular nucleus
in the molecule. Consequently, the resonance signal pro-
duced by each kind of hydrogen will come at a different
field strength. The difference in field strengths at which
the signals are obtained for nuclei of the same kind, but
located in different magnetic environments, is called the
chemical Shift. It is dependent on the field strength.

It has been Shown (27) that the screening constant for

the nucleus of atom A may be written as

6A=6AA+oAA+zoAB+oA (a)

d B$A ring

where odAA is the diamagnetic Langevin—type circulation of
electrons on atom A. The contribution of the local dia-
magnetic currents on the hydrogen nucleus itself can be

estimated from the Lamb formula

AA e2 E
6d 'gaaz'f 7 dT .

 

to
- V‘
to .

:v;b
‘5.

n)
(n

‘.

5o

(3

f)

(I)

n)

20

Here p is the electron density of the electrons associated
with the hydrogen atom and may be represented by “(15'
where A measures the effective number of electrons in the

_g.

hydrogen ls atomic orbital wls(=w e-r in atomic units).
The eXpreSSion for 6d may then be integrated and eXpressed

as

A e2
smchAo .

The second term of Equation a results from the mixing of
ground and excited electronic states by the magnetic field
which produces a paramagnetic current on this atom. POple
(28) has shown that an excited state contributes to the
local paramagnetic current on an atom if it correSpondS to
the transfer of an electron between p-orbitals or d-orbitals.
It vanishes for electrons in a S-orbital Since these have
zero angular momentum. Fluorine chemical shifts are largely
dominated by the paramagnetic term, but for hydrogen this
term is generally small. The term ZGAB is the Shielding
contributed by the electrons of allB:fie other atoms in the
molecule while oiing is the contribution from a ring current
which cannot be localized on individual atoms. The combined
effects of the diamagnetic and paramagnetic currents on
other atoms is largest if the electrons on a near-neighbor
atom have a large and anisotrOpic magnetic susceptibility.
Consider a nucleus of Spin I at a distance R from an

axially symmetric anisotropic molecular grouping whose mag-

netic susceptibility is X". along the z axis and XI along

21

the x and y axes. If the line from the nucleus to the group
makes an angle 9 with the z axis and the field H is along

the z axis (as indicated in the diagram), then it may be

 

Shown that (5) z
fozz = le (1-5cosae)/'R3
6yy = Xl/R3
oxx = XI (1-5Sin28)/'R3

 

x
and the average correction to the Screening for a molecule

in solution becomes
A6 = (XH - X1)(1-5cosge)/5R2 .

The ring current contribution has been evaluated (28)
for aromatic ring systems. When the magnetic field is applied
perpendicular to the plane of the ring a circulation of the F
electrons is induced which is equivalent to a current. The
ring acquires an induced magnetic moment in a direction
Opposite to the applied field. If the applied field is in
any other direction the induced moment will be different

and 6r is quite anisotrOpic. POple has Shown that A6 =

ing
6" - 61 may be written

2 2
_ e R
A6 _ 2mc2 (R+d)3 ’

where R iS the ring radius, and d is C—H bond length for the

particular case of aromatic hydrocarbons.

22

Complete calculation of the chemical shielding for a
molecule is rarely possible since the required wave functions
are not usually known. Only for protons in very Simple
molecules have accurate quantum mechanical calculations been
possible. However, various empirical schemes have been
proposed to correlate chemical shifts.

Primas, Arndt and Ernst (29) postulate that the chemical
shift of a particular nucleus can be considered as the sum
of several characteristic contributions from the various

groups; the chemical Shift can be estimated empirically from

T=TQ+ZC.T.
J 3

Where T is the T value of a hydrogen nucleus, To = 9,067,
Tj is the contribution from a group and Cj is the number of
times such a group occurs in the molecule. In their paper,
detailed information concerning the choice of parameters To
and Tj is given.

Maslov (50) devised a semiempirical method for calcu-
lation of chemical shifts and magnetic Shielding constants.

He used an "equation of weighted averages":

where S = Zéj is the valency of the coordinating group,
common for all representatives of the chosen family of mole-
cules which are related in structure. Bi and Bj are the

value of a particular prOperty, such as chemical shift and

a:

¢u

nu

Aa\-

25

magnetic shielding constant, for molecules j which are given
in the paper, and for molecule i which is unknown. This
method has advantages over Simple additivity relationships.
He gives extensive tables of Bj values for various families
of organic molecules.

Many other workers have tried to correlate qualitatively
chemical Shifts and molecular prOperties. Packer (51) has
found that the 31F chemical Shifts in (CF3)2PX compounds
depend linearly on the electronegativity of the X group, and
that deviations from this relationship are probably due to

the magnetic anisotrOpy of the P-X bond.

Solvent Effects on Chemical Shifts

 

When molecules are dissolved in a solvent there are
additional contributions to the chemical Shifts of solute
nuclei from the solvent molecules. The commonly used eXpres-
sion for the chemical Shift 5 observed for a particular

Species in solution is (52,55):

where the contributions to 5 are: 6B from the bulk magnetic

susceptibility of the solution; 5A from the anisotrOpic

diamagnetic susceptibility of the solvent molecules; 5W

from van der Waals interactions with the neighboring mole-

cules; 5E from the polar effect caused by the charge dis-

tribution in the neighboring molecules which leads to an

n v.
N hi
I

:~r:
'5‘ \

...,
3t -.

AI.

V a

,. .
on.
1%.;

N‘tu
‘4
4 V

AC

VA

5'.
V..

24

electric field acting on the solute molecule thereby
perturbating its electron structure and hence magnetic
Screening constant, and be from the formation of solute-
solvent complexes.

In the presence of the external magnetic field the
solvent molecules will be diamagnetically polarized and
this polarization may produce a magnetic field at the nucleus
and consequently contribute to the screening constant of the
given nucleus. This secondary field depends upon the shape
of the sample. It is zero for a Spherical sample and is
2wxv/5 for a cylindrical sample.

The anisotroPic term 6A, depends on the shape of the
solvent molecules, their magnetic anisotrOpy and their
orientation with reSpect to the solute molecule and the mag-
netic field. Solvent molecules such as benzene, which have
disc-like Shapes, will have large induced moments when the
ring is at right angles to the field, and Since their shape
enables them to lie closer to the solute molecule when they

are in the configuration a; than in the configuration a2

C> . 1. a

1L
\
H

I
a1 a2 a3 a4

 

 

 

 

25

the contribution of a; may be expected to dominate. This
would lead to a mean diminution of the external field at the
solute protons and, consequently, a resulting shift to high
field because the secondary magnetic field due to the in-
duced magnetic moment is prOportional to the inverse third
power of the separation.

Using the same argument, rod-like solvent molecules
such as carbon disulfide and acetylene, whose largest magnetic
susceptibility is along the axis of the rod, would lead to a
low-field Shift. The arrangement a4 becomes the most Sig—
nificant one and leads to an enchancement of the applied field.

For a disc-like solvent molecule close to-a solute mole-
cule the screening constant is 6A = -2n(x,l - xl)/5R3, where
X” and X1 are the magnetic susceptibilities parallel and
perpendicular to the symmetry axis, R (whose magnitude R must
be large in comparison to the molecular dimension) is the
vector from the origin of the solvent molecule to the center
of the solute molecule, and n is the number of solvent mole—
cules which are considered close enough to contribute to 6A.
The magnitude of R, is PDT/cos e, where 1) is the unit vector
along the molecular Symmetry axis of the solvent molecule and

e is the angle between R and I: leerse the screening con-

stant for the case of rod-like solvent molecule is exPressed
as 6A = +n(X“ - Xl)/5R3.
Schug (55) assumed that liquid solutions are completely

random in nature and that the anisotrOpic shift is therefore

26

directly prOportional to the volume fraction of the aniso-
tropic Species; he then tried to calculate the anisotrOpic
shift 6A produced by cylindrically symmetrical solvent
molecules. He found that including all the anisotrOpic
molecules in the solution, rather than nearest neighbors
only, provided theoretical anisotrOpic Shifts comparable to
those observed.

In case of polar solutes the interactions between the
solvent and solute molecules perturb their electronic
structures and the resulting distortion leads to a solvent
dependent nuclear screening constant term, the van der Waals
term. This arises because the electronic environment of the
nucleus is distorted by the interaction between the solute
and solvent molecules causing the solute electrons to be
attracted by the neighboring molecules. The diamagnetic
screening is therefore reduced and nuclear resonance occurs
at lower field strength. This contribution can be expressed

as (54.55):

= 5_ 2n2 -2 viva
4¢h(2n+1))a ‘15-)(vi+v2)

I

6W

where n is the refractive index of the solvent, a is the
solvent molecular radius, h is Planck's constant, v1 and v2
are the mean absorption frequencies of the solvent and solute,
and O correSponds to a bonded hydrogen atom.

For polar solutes the observed large solvent chemical

shifts are due to the effect of the reaction field. This is

35(

an:

I
It”.

i..-

FA
“.4...

(I)
:‘1‘

“f

27

a secondary electric field arising in the polar or polariz—
able solvents under the influence of solute molecules

which carry a permanent dipole moment. The model used by
Onsager (56) and Buckingham (57) assumes that the entire
molecule is reduced to a point dipole in the center of a
cavity surrounded by an isotrOpic, homogeneous, polarizable
continuous medium of fixed dielectric constant. They (57)
showed that the electric field at a particular nucleus
arising from a polar group in the remainder of the molecule
can lead to ' chemical Shifts prOportional to the first
power of the field strength. The change in the proton
screening constant of a proton of an X-H bond when it is

subject to an electric field E is equal to
A6 = -2 x Io‘leEz - 10’18E2 ,

IMhere E2 is the component of E (e.s.u.) in the bond direc-
tlion. An electric field in the X-H direction would be
‘SJQpected to draw the electronic charge between the nuclei
tO‘ward the X atom, thereby causing its resonance to occur at
:LCJme magnetic field strength, while a field in the H—X

<51irection leads to resonance at higher fields.
g§pin-Spin Splittipg‘

A systematic study of multiplet Splitting by Gutowsky
Eirld.McCall (58) showed that fine structure may arise in

Eil‘lymolecule containing two or more nuclei which resonate at

28

different field strengths; that is, if the nuclei are either
of different isotOpic Species or are chemically shifted.

The multiplet fine structure is caused by mutual magnetic
interactions between the nuclear Spins giving rise to a set
of values of the total magnetic field at a given nucleus.
The interactions are transmitted by the bonding electrons
(59) and the magnitude of the interaction is the Spin-Spin
couPling constant J.

The interaction can be divided theoretically into three
parts (40,41). In the first of these one nuclear magnetic
moment induces orbital electronic currents which consequently
induces magnetic fields at the site of the second nucleus.

In the second, the electron Spins interact with the magnetic
.moment of one nucleus producing an electron Spin polarization
‘which is then transferred to the adjoining nuclei. However
'the two parts just mentioned are very small in comparison
VWith the third part which is the Fermi contact interaction
(arnd is the most significant contribution to the overall Spin-
Spin coupling. In this the interaction between nuclear
moments and the Spins of electrons in s-orbitals produces an
electron Spin polarization prOportional to the density of the
S electron at the nucleus. In molecular orbital theory the
SD in coupling constant, JAB’ may be written in terms of the wave
functions of the ground and excited states wi’ (03.. Summing
c3‘7eer'OCCUpied and unoccupied levels for i and j, reSpectively,
occ unocc.

J o - 2 2 (wiwj)A (wiwj)B
AB . .
1 J (ej - 6i)

 

1‘

CN

29

where (ej-ei) is the energy difference between the ground

state Si and the unoccupied excited state Ej and is always

positive. From the above eXpression the Sign of the coupling

constant depends on whether the molecular orbital is sym-

metric of asymmetric. The symmetric molecular orbitals

have the same Sign at atom A and atom B, and the asymmetric

molecular orbitals have different signs. For transitions

from symmetric to symmetric or from asymmetric to

asymmetric molecular orbitals, the contribution to J, the

Spin-Spin coupling constant, is negative. ‘Transitions

from symmetric to asymmetric molecular orbitals, or vice

versa, gives a positive contribution to the coupling constant.

Pople (41) used this molecular orbital theory in the

study of Spin—Spin COUpling between directly bonded

atoms where the contact term is usually dominant. His calcu—

lations indicate that the coupling constant is negative when
<Dne of the atoms is fluorine. For long-range Spin-Spin
idateractions over four or five chemical bonds. the theoretical
Study becomes much more difficult. It can be treated as a
"Iparticle in a box" problem. The linear paths are more
earnergetically favorable than those with high curvature in
tilde long-range delocalization of electrons (42). Hence long-
ITEange COUplingS are largest when a linear path can be drawn
13<etween the coupled nuclei to include the intervening bonds

Ipiarticularly when these latter form a conjugated system.

50

Double Irradiation

When two non-equivalent magnetic nuclei A and X are
coupled together by indirect Spin-Spin interaction, the
absorption peak for each nucleus is Split into a multiplet.
If one of these nuclei (X, say) can be made to transfer
rapidly between its various Spin states then the multiplet
for the other nucleus (A) will average out to a Single
peak located at the center of the original multiplet.

This process occurs naturally if one of the nuclei possesses
an electric quadrupole moment since the fluctuating electric
field gradients arising from molecular motions will induce
transitions between the Spin states of the nucleus with

the quadrupole moment. The decoupling can also be induced
artificially (45—45) by application of a second rf field at
the resonance frequency of the X nucleus while observing the
A nuclei at their resonance frequency. Sufficient rf power
at the X resonance frequency will then induce transitions
among the Spin states of the X nuclei and the A resonance
peaks will not Show multiplet structure from coupling with
X nuclei.

Bloom and Shoolery (46) have made a quantum mechanical
analysis of the effects of radiofrequency fields on nuclear
Spin coupling. They were able to predict the nature of
intermediate Spectra between the unperturbed multiplets
and the totally collapsed multiplets when the second radio-

frequency was changed. The double resonance method has

51

been applied to the measurement of chemical shifts (44)
and to the determination of the relative signs of coupling
constants (48).

Bloch Formulation of the Nuclear
Induction Experiment

 

To describe the time dependent variation of the com-
ponents of the total nuclear magnetic moment per unit volume,
Bloch used a set of phenomenological equations (26). First,
a set of coordinates Should be defined. Let Z be the di-
rection of the magnetic field, with field strength Ho, and
X be the direction of the rf field with angular frequency w
and amplitude 2H1. The three components of the total field

vector H; are:

Hx = 2H1 coswt ; Hy = O ; Hz = Ho (1)

If the vector M=(MX,My,Mz) is the resultant nuclear moment
per unit volume, the primary purpose of the theory is to
formulate the variation of this vector with the time.

Let the resultant angular momentum vector of all the
nuclei in a unit volume be A; Then, from the classical
mechanical definition of torque, the torque acting on the

nuclei is

= T (2)

fi‘lg I

and T'is also equal to (M'x H). The magnetic moment M'is

equal to the product of the angular momentum and the

52
gyromagnetic ratio,
M'= 7A . (5)

Combining equations 1, 2, and 5, the time variation
of the total magnetic moment vector M (or macrosc0pic

moment), can be written

filé”.

=7[l‘-’1XH]- (4)

For a set of nuclei with Spin 1/2 in a steady magnetic field
H0 along the Z direction the Z component of (M X'H) vanishes,

and the X and Y components are

g%%-= woMy (5)
EME¥ = '(DOMX (6)
dM _

.5? _ o (7)

where we = 7H0 is the angular frequency of the Larmor
precession.

By introducing apprOpriate damping terms, the relaxation
effects can be added to above equations. Mz will vary and
approach an equilibrium value of Mo. For N nuclei of Spin

1/2 in a unit volume, Mo may be written

2
Mo = filial-I'D— = XQHQ . (8)

The rate of approach to equilibrium is dependent on the Spin-

lattice relaxation time T1:

sz = _ M2 - Mg (9)
dt T1 .

For the same reason the X and Y components must also be modi—
fied. According to the solutions of Equations 5 and 6, the
component perpendicular to Ho rotates with the Larmor fre-
quency about the Z axis. Individual nuclei will get out of
phase due to relaxation effects and MX and My will decay to
zero. By analogy with the argument for the longitudinal
component, the change of MX and My will also have an exponen-

tial character governed by the equations,

0 — 1

MX - - (—T2)MX (10)
. — - 1—

My — (T2)My (11)

where the time constant T2 is called the transverse relaxa-
tion time.

Up to this point, the discussion is only concerned with
the nuclei in a fixed field HO along the Z direction. In
the NMR experiment an additional field H1, perpendicular to
Ho and rotating with angular frequency w, must also be con-
sidered. The vector H in Equation 4 then will have additional
components Hx = H; coswt, Hy = — H1 sinwt and H2 = H0. The
complete Bloch equations can be obtained by combining the

contributions from Equations 9, 10, 11, and 4:

= ' _ y—X
MX 7 (MyHo + MzHlsinwt) T2 (12)
n = 7 (M choswt - M Ho) - ES. (15)
y 2 X T2

54

M

z = 'H-Mlesinwt - Mychoswt) - 5111—4-51 (14)

T1

Equations 12, 15, and 14 are derived with reSpect to a set

of fixed axes; they can be transformed to a set of axes
rotating with frequency w about the Z axis. The new compon-
ents of Mare M2, L1, and v, where u and v are the in-phase and
out-phase components of M Since they are parallel and perpen-
dicular to the direction of H1, reSpectively. The relation-

ships between components are

MX = ucoswt - vsinwt (15)
My = usinwt - vcoswt (16)
and
u = choswt - Mysinwt (15-a)
v = -M Sinwt - M coswt . (16-a)
x Y

The Bloch equations in the rotating coordinate system
can be obtained by substituting Equations 15 and 16 into the

Bloch equations for the fixed coordinate system and are:

§§+%g+<oo—o)v=o <17)
dt T2 0 1 z

sz M _

Ef—t + z_____Q.T1M _ “y HIV :7. O (19)

where wo — w = 7H0 - w and w; = 7H1,

55

In most NMR eXperiments the steady state solutions of
the above set of equations are of interest. They can be
solved by requiring the time derivatives to be zero and M2
to be constant. The values of M2, u, v then become:

u = M0 YHngéwo " (1)) (20)
1 + T:(wo — w)2 + y 2H1T1T2

 

 

_ YHlT
V “M0 1 + T§(wo -- (3)5 + yZHETng (21)
= 1 - T§(wo - w)2
M2 M0 1 + T§(wo - w)‘ + VEHETITg (22)

The rate of absorption of energy per volume is -MXde/dt
and Mx can be obtained by reconverting the above components

to the fixed laboratory axes. Then,

 

= ;_ 22(wQ-w)2H1coswt + 2Hl§inwt
Mx 2 MOVTZ 1 + T§(wo-w)2 + 72H§T1T2 (25)

InSpecting -deHx/dt, it is seen that there is a term prOpor-
tional to coswtsinwt which averages to zero and a term pro-
portional to sinzwt that averages to 1/2. The average rate

of absorption of energy per unit value is then

 

ngfmng 2 . (24)

:L + Tau». - or? + THiTiTa

This expression has a maximum value when w is in the vicinity
of the Larmor frequency. With a small oscillating magnetic

field, H1 << i/VJTng , Equation 24 becomes

_ waETM
9(V) - 1 + T§(CDQ-(D)2 (25)

 

56

which has a peak value of 2T2. In Equation 25, g(v) is
called the line-Shape function which in practice, however,

cannot always be approximated by a Lorentz—type curve.
The Line-Shape Equation with Exchange

The Bloch equations can be directly generalized to in-
clude the effect of exchanging nuclei (49). Let nuclei X
transfer back and forth between two different molecular
environments A and B, where A and B are sites with different
local fields giving two absorption peaks Shifted by +6w/2
and -6w/2 from their average angular frequency 6w. Time
Spent in the transition state can be assumed to be Short and
can be disregarded. The lifetimes of X at Site A and Site B
are denoted by TA and TB, reSpectively. In other words, the
probability of X at site A moving to site B is 1/TA, and
for the reverse process in 1/TB. The rate of exchange of

(protons between the two Sites can be expressed by the follow~

ing equations (12):

 

dNA = - 4.
a? T NA (26)

A

(inB = - 4...
Ht— TB NB (27)
24 = EB (28)

TA TB
T = TATE (29)

T “I" T

57

where NA and NB are the number of labeled X nuclei at Site A

and site B, t is the time, and pA and pB are the fractions

of X nuclei at Site A and Site B at time t, reSpectively.
Having the above consideration in mind, the magnetiza-

tions can be written as the sum of the contributions of A

and B systems:

u = uA + uB (50)

v = vA + vB (51)
= A B

M2 M2 +Mz , (52)

where v, u and M2 denote the components of X nuclear mag-
netization. which are in-phase and out—of—phase with the effective
rotating components of RF field, and in the direction of the
large stationary field, reSpectively.

.The Bloch Equations 17, 18 and 19 can be modified to

accommodate the kinetic effects and take the forms (46)

uA + AQAVA = —uA/T2A + uB/TB (55)
uB + AvaB = -uB/TgB + uA/TA (54)
v - Aw u = -v /T + v /T - wIMA (55)
A A A A 2A B B 2

' __ _ B

vA AwBuB — vB/TgB + vA/TA wle (56)
'A A A B

-w = T _ T

Mz 1vA Mo/ 1A Mz/TIA +.Mz/ B (37)

B B B B
4b = T — T
Mz 1V Mo/ 1B Mz/TlB + Mz/ A (58)

58

In the preceding equations Mg and Mg are the equilibrium
Z magnetizatiomsof X nuclei at site A and site B; AmA and

Aw? are the differences between QA’ mg and w,the angular

frequency of the RF field, reSpectively. T1 and TgA can

A

be defined as:

1 1

 

 

 

1
= -——— +-—— 59
TlA TlA TA ( )
T1 = T1 +i— (40)
2A 2A TA

and Similar definitions hold for T18 and T23; TlA and TgA
are the longitudinal and transverse relaxation times of

nuclei X at Site A, and TlB and TgB of nuclei X at Site B.

By comparing Equations 55-40 with the original Bloch
equations the reason for the modification made becomes evi-
dent. Equation 55 has two additional terms on the right

hand side, -uA/T and uB/TB. The first term measures the

A

rate at which uA decreases due to the chemical exchange of

u magnetization out of A Site; and the second term measures

the rate at which uA increases because of the chemical ex-

change of u magnetization from Site B to Site A. The same
argument is also applicable to Equations 54 to 58.

In order to apply Equations 55 to 58 to reaction rate
determinations, the assumption that the relaxation times

T1 T2 T1 and T2B are independent of T and T must be

A' B A B

made. This assumption is most readily realized when the X

A!

nuclear relaxation is due to time—dependent perturbations

59

-I _I
A and TB .

The modified Bloch equations also imply the requirement that

which are of high frequency relative to T

the X nuclear magnetizations<mfthe A and B systems are inde-
pendent of one another (except for the chemical kinetic
exchange effect).

For Slow passage in an NMR eXperiment

uA = uB = VA = VB = M2 = M2 = 0 (41)

which transforms the set of coupled differential Equations
55-58 to,a complete set of ordinary simultaneous linear
equations in Six unknowns which can be solved numerically.
Equations 55 to 59 can be applied to the case of hindered

internal rotation in disubstituted amides which is a typical
two-site' exchange problem. If the RF saturation iS neglig-
ible, the total Z magnetization Mz becomes unaffected by the
kinetic process (50):

M =MA+MB=M =MA+MB=E£=££ (42)

z z z; o o o pA pB -

By summing over all X nuclei, the RF magnetization can be

written as

—= ' = = +' '
M u + 1v MA + MB uA lvA + uB + lVB (45)

Substituting Equations 28, 59, 40, 42 and 50-55 into the

above expression the resulting equation is

M ___ "inMO (TA + T3 +(TATB+pApB) ) (44)
(1 + TABA) (1 + TBBB)-1

 

40

1. _1_.,
-1AwB and BB — lAbA . (45)

where 8 =
A TgA TgB

The real part of Equation 44 gives the diSperSion u-mode
line-shape equation and the imaginary part gives the absorp-
tion v-mode line-Shape function in terms of the rate

constant:

 

 

u = -w1Mo[QP-{1-T(pB/T2A + pA/TaB))R] (45)
v = "wlMo[P(1 + T‘PB/?2A + PA/TaB)) + QR] (47)
P2 + R‘
where
p=T[E—-1—;—-Aw2+(-§%>21+EB +8.9. =s-mw2
2A 2B ~ T2B TZA

Q = T[Aw - ggqu - pB)]

1 Ow 1 1
—.—._ + __—
T23)] T2 (T23 T2A

and R Aw[1 + 1(—-1——+
T2A

£52 (

2 pA ' pB) °

When a set of line-Shape parameters is known, the intensities
at the correSponding values of m can be calculated from
Equation 47. Upon differentiating this equation with reSpect

to Am, the resulting equation has the following form:

2T2AAw5 + 5T288w4 + 412cAm3 + (BD-AE)Aw2

+ 2(CD-AF)A<B + (CE-BF) = o (48)

where

“p1
V1.

VOL;

41

 

p p
_ 2 . = 2 __B. .. _A.
A — T (TA/TZA + pB/TgB), B T éw(T2 T2)
B A
_. £422 _ 2 §_ T 2 2 +
c - T(2 ) [1-(pA pB) + T] T2AT2B [1 + pA + pB
pB PA 1 1 A
T(———-+-———) + T ( + ) +
TgA TgB ] pApB TEA TEE I?
D = [1 + T(—i—'+ —;—)]2 - 2TS
T2A T2B
E = éw(D + 21S) [ - + T( 1 - —;—)]
PA pB T2 T2
B B
E2 -1
and F = S2 +-—— (D - 218) .

4

When Equation 48 is solved, one of two cases can occur.
With a large value of T (slow exchange) three of the five
solutions of the fifth~order equation are real and correSpond
to the two maxima and the central minimum of the uncoaleSced
doublet. In case of small T, in other words fast exchange.
only one solution is real, the central maximum for the

coalesced doublet.
Computer Programs for Exchange Calculations

In the last few years the application of electronic
computers to the exchange problem has been reported (51,12,
52). T. Nakagawa (55) reported a computer program based on
Equation 47 which gives intensities correSponding to a set
Of line—Shape parameters. The program is very Simple; it is
essentially a couple of do-lOOps with no adjustments included.

TWo programs written by Gutowsky's group (55) and one by

42

Saunders (55) have been used on several NMR problems. Line
shapes of fluorine magnetic resonance Spectra and the con-
formational isomerization of 1,1-difluorocyclohexane have
been studied with the first program (53). In this program
the rate constant is the only variable parameter, and often
the single-parameter curve fitting does not yield very
satisfactory results because Equation 47, on which the program
is based,makes the assumption that the values of the line
widths and the peak separations in the absence of exchange
hold for the entire temperature range. In this laboratory,
as well as in several others (54,15,25), this assumption is
found not to be valid. This point will be discussed quanti-
tatively in the Discussion section of this report.

Saunders (55) program has been used to study exchange
among many sites. A correction to the line-shape function
for field inhomogeneity can be built into the computer pro—
gram by use of the convolution integral; this permits the
introduction of any desired line shape. .Let the intensity
function without correction be Y'(w) and the desired function
be S (w), the corrected intensity function is then expressed
as

Y'(w) = fOOS(w-w')I'(w')dw . <49)
"CXD

Anet (56) used the approach mentioned above in the study of
ring inversion in cyclohexane-dii; he reported that the
results from the programs with and without the convolution

integral were almost identical.

43

All three principal methods (42,51) will be subject
to a significant systematic error if each of the doublet
peaks is itself a Spin-Spin multiplet from coupling with
other protons; for instance, in N,N-dimethylformamide the
two N-methyl peaks are each Split into a doublet by Spin
coupling between the formyl proton and the methyl groups.
With this complication the procedure for evaluation of the
exchange rate constant must be modified. Four approaches
can be used.

(1) IsotOpic substitution: When the formyl proton in

DMF is substituted by deuterium the coupling constant
becomes negligibly small, because the ratio of the coupling
constant of the two isot0pes with the third nucleus is pro-
protional to the ratio of their gyromagnetic ratios which is
0.1555 for deuterium and hydrogen.

(2) Double irradiation: In the case of DMF the secondary
doublet can be eliminated by irradiation at the frequency of
the formyl proton using an external oscillator or noise
generator. This method permits decoupling the protons when
enough rf power can be introduced.

(3) Quantum mechanical approach: When two nonequivalent
protons exchange between the two sites and couple with each
other to form an AB Spin system, the coupling complication
can be resolved theoretically by using the density matrix
method. The basic formulation is worked out by Kaplan (57)

and Alexander (58,59). The theoretical line-Shape equation

44

describing the two exchanging protons can be calculated

by deriving the Boltzmann equation for the average density
matrix, and the exchange process is described by exchanging
the indices of the Spin coordinates in the Spin wave func-
tion. The equations derived with this approach have been
used in several exchange problems (60,61,62). A very eXplicit
application is the study of conformation and internal rota-
tion in a nitroaromatic amine by Heidberg §£_3l, (65). The

equation used is:

= -y.,.b+ - Sa+ “y b - Sa_
v C( 2 + 2; 2 ) (50>
a+ + b+2 a_2 + b_

 

 

where

[(wo-w) i;§J]2 - (1-1+ T2-1)2 - 62 - fiJZ + T-2

W.
H
l

l

b _+_ = 2[(wo-w) _téJ] (1‘ + Tg‘l) :J/y

'Y i = (mo-(1)) i J

U)
ll

Z/T + 1/T2 .

It describes the line shape for a system of two exchanging
protons which couple with each other. If the coupling constant
J in the equation is equal to zero Equation 50 will be re-
duced to a Simpler form, identical to the classically derived
Equation 47. This approach could be used for the disubsti—
tuted amides, but the quantum mechanical derivation becomes
extremely complex because of the large number of Spins in

this problem and has never been reported.

45

(4) SUperposition: The doublets at each N-methyl peak
can be considered as the superposition of two sets of
identical methyl doublets with centers separated by (J; +
J2)/2, where J; and J2 are the COUpling constants between
the two methyl groups and the formyl proton. Method III can
be modified to accommodate this improvement.

In order to evaluate the activation energy for the ex—
change process in N,N-disubstituted amides the classical

Arrhenius rate equation (64,65) can be written as

log T = log £—- + Ea (51)
2A 2.505 RT

 

Where T is the inverse of twice . the rate constant of the
exchange process, R is the molar gas constant, A is the fre-
quency factor and Ea is the activation energy, or the energy
barrier of the system. «The quantities A and Ea can be
evaluated from the lepe and the intercept of the best
straight line when log t is plotted gs. 103/T0K.

Assuming that this exchange process obeys the absolute
rate equation (66), the free energy of activation AF¢ for

the internal rotation problem can be written as

t _ i

- RT ln(rate constant-h)/(KkT)

2.505RT log ZTKkT/h

2.505 RT(10.519 + log T + log 2T)

(52)

46

where h is Planck's constant, k is the Boltzmann constant
and K is the transmission coefficient, which is equal to

unity when every activated complex breaks up to give products.

Chemical Shifts of the Methyl Proton Peaks

 

Much research has been done on the assignment of the
peaks of the doublet to the reSpective methyl groups in N,N-
dimethyl amides. The resonances correSponding to the two
N-methyl groups of N,N-dimethylformamide can be distinguished
because each is Split into a closely-Spaced doublet by Spinu
Spin coupling with the formyl proton (67) and the coupling
constants differ. The high~field signal in pure DMF is
most strongly coupled to the formyl proton and so is Egagg
to the formyl proton. In N,N-dimethylacetamide the two
N-methyl resonance peaks may also be distinguished because the
high-field signal is broader. -Each component of the doublet
is presumably an unresolved quartet with the coupling con-
stants to the acetyl methyl proton different. (The N-methyl
resonance which Shows the greater broadening must be Egang
to the acetyl methyl group.

A second method for assigning the N-methyl resonances
is based on the fact that addition of an aromatic solvent
produces large changes in the relative chemical Shifts of the
two N-methyl groups (67). AS the concentration of the N,N-
dimethylamides decreases, both N-methyl resonance signals

are shifted to higher fields but the original lower-field

47

signal Shifts by a much larger amount. At a certain concen-
tration the doublet coalesces* and further addition of sol-
vent causes the original low-field Signal to cross over the
original high-field peak, with consequent change in the Sign
of the chemical shift between them.

This phenomenon can be explained by the fact that the
amide molecules associate with the aromatic solvents in such
a way that the nitrogen atom with its fractional positive
charge is Situated close to the region of high H electron
density of the aromatic ring and with the negatively-charged
carbonyl oxygen atom as far from the center of the ring as
possible. The amide molecule retains its planar configura—
tion so the solute and solvent molecules become parallel and

c0p1anar as shown below:

In this arrangement the N-methyl group Egagg to the
carbonyl oxygen atom will be near the center of the ring
and, consequently, the diamagnetic anisotr0py of the benzene
ring will affect this N-methyl group more than the other,
tending to shift it to higher magnetic field. Hatton (67,68)
measured the chemical shifts of N-methyl groups of DMF in
both aromatic and non-aromatic solvents. In non-aromatic
Solvents the mean chemical shifts of the two peaks due to

the N-methyl group do not change with reSpect to the internal

48

reference. However, the peak separation between them de—
creases as the mole fraction of the amide is reduced. This
is probably due to the mutual interaction of the amide mole—
cules by dipolar association.

Of considerable importance in the present studies of
rates of internal rotation in the N,N—disubstituted amides is
the question of whether or not the peak separation changes
with temperature. It can only be precisely measured at
temperatures low enough that exchange broadening is small.
It has then been usual to use this value at all higher tempera-
tures in the calculation of rate constants. However, Whittaker
and Siegel (69) made measurements on the temperature dependence
of this separation, over the accessible range, using solutions
of amides in acetone-d6, hexamethyldisiloxane and CFC13 as
well as the pure amides. They noticed that the maximum value
of chemical shift at low temperature is strongly dependent on
the nature of the solvent. The peak separation decreases
rapidly as concentration decreases, but different limiting
values are reached at infinite dilution in different solvents.
This behavior indicates the possibility of dimerization or
hydrogen bond formation. They also found that the peak
separation increases as the temperature decreases from the
coalecence point but tends to level off at some intermediate
temperature. (When the temperature is reduced even further,
the rate of increase of the peak separation may change

indicating that effects other than internal rotation must

49

enter. They suggest that the correct peak separation éwo
in the absence of exchange can be obtained by plotting the
observed peak separation 6w vs. temperature. This will yield

a plot of the following type:

6w

(5&0

 

 

 

and the correct value of 6mg is obtained by a 'reasonable'
extrapolation (perhaps to the freezing point) of the linear
portion "a" of the curve.

The unusual behavior of the 6w gs TO curves may be
explained qualitatively. The planar amide molecules tend
to associate (68), and this association may change the
magnetic anisotroPy of the carbonyl bond since it has been
shown (70) to be quite sensitive to the charge distribution
in the bond.

The average half-life of a given dipolar interaction
increases with decrease in thermal motion and increase
viscosity. Consequently, the average magnetic anisotroPy of a
carbonyl bond increases with decrease in temperature and
the chemical Shift of the methyl groups should increase as
temperature decreases. «This exPlainS the sudden change in

sloPe at temperatures lower than "a". At high temperatures

50

the fast rotation about the C-N bond probably prohibits
significant dipolar association because of the steric
effects. Based on this mechanism, the Ea obtained from the

high temperature data Should be more reliable.

n§ is

EXPERIMENTAL
Preparation of Amides

The compounds used in this investigation are listed in
Table 4:, along with their boiling points and appr0priate
literature references. N-methyl-EI-butylacetamide and
N-methyl-N-cyclohexylacetamide are prepared (67) by the ad-
dition of one mole of acetyl chloride in ether (or benzene)
Slowly with stirring into an ether (or benzene) solution of
two moles of the reSpective amine. Sub-zero temperatures
should be maintained at all times, but freezing should be
avoided. The mixture is then allowed to warm up to room
temperature with stirring. After several hours, the amine
chloride is dissolved in a minimum amount of water. The
aqueous layer is then extracted three times by ether (or
benzene) and the organic extract is combined with the original
organic portion which contains the desired amide. The com-
bined organic solution is then washed with minimum amount
of 20% potassium carbonate solution, in small portions, until
neutral. The organic layer is dried over anhydrous
potassium carbonate overnight, and the amide collected by

vacuum fractional distillation.

51

52

.N .Z

.MUHmEmo ..UCH

.qu & paw M Eoum Ummmnousm
.>uoumuoflma mflnu CH vmummmumu

U

.N .z .Hmummnuom ..ume.mHmoHEm£o UHcmmHo cmaummm Eoum Ummmzousm

Q

.b .2 .c3mq Hflmm .mcmmfioo oamaucmflum umnmflm Eonm Ummmnuusmm

 

 

 

 

o.mm m o.mm m o.mm Amm¢oucvxmmovzoommo
o.mm ma chumm ea m.om «Ammovmoxmmovzoommo
o.sm ows msm ma omanmms Adamoouooxmmoozoommu
0.0m om» oma mm o.m« Ammmovxmmovzoommo
o.mm mos m.msa oa m.mm mxmmovzoommmo
p.4m mm soaumm m o.m¢ mxomovzoomoummo
p.mm «we o.sma om o.mm «Ammovzooao
o m N.mm mxmmovzoomaoo
n.mm cos a.mma m 0.44 mxmmovzoonmo
m.am owe o.mmd owe m.ama mammovzoom
mocmummmm .mm EB .03.m.m .mm 55 .0D.m.m ocsomEou .ll
mnmumumqu Uw>nmmnO<

 

 

.mmUHEM Umusuflumnsm mo mucflom mCHHHom .w. mHQMB

an

an“.

“’5‘

A

I
.a

to

7m!

of

55

N-methyl-N-ethylacetamide is prepared by addition of
an aqueous solution of two moles of NaOH slowly into an
aqueous solution of one mole of N—methyl-N-ethylamine hydro-
chloride. One mole of acetyl chloride is then added gradual-
ly to the above mixture. ,The temperature should be kept
between 0 and 100C throughout the eXperiment. The aqueous
layer is separated and then extracted several times by either
ether or benzene. The organic extract is combined with the
original amide layer and dried over anhydrous potassium car-
bonate. The solvent is evaporated and the amide is collected
by vacuum fractional distillation.

N-methyl-N-iSOpr0pylacetamide is prepared by addition
of one mole of acetyl chloride slowly with stirring to an
aqueous mixture of one mole of N-methyl-N-iSOprOPylamide and
one mole of sodium hydroxide. The temperature should not ex-
ceed 100C. The remaining procedures are the same as for the
preparation of N-methyl-N-ethylacetamide.

The purity of t—butylbenzene, trifluoroacetic acid” 9-
tetrachloroethane and hexamethyldisiloxane was checked by NMR
Spectra after vacuum fractional distillation. All the sample
tubes are sealed at a pressure of 10" mm of Hg and a small
amount of HMDS is added to the sample as an internal reference.
HMDS is a good internal reference for this study because it
has a higher boiling point (about 1009C) than the con-
ventional reference, tetramethylsilane, TMS (b.p. 27°C).

At room temperature the chemical shift of HMDS is 0.05.:

54

0.005 ppm from TMS. After the sample tube is sealed, it

is tested by heating in an oil bath to a temperature twenty
degrees above the highest desired probe temperature. In
general practice chemical Shifts are measured against a
reference compound and the most common reference compounds
for protons are water, benzene, TMS and HMDS. The chemical

Shifts are given here as the dimentionless numbers
= _. -1 6
5 (HC Hr)Ho x 10 ppm

where HC is the resonance field for the nucleus in the
particular molecular environment and Hr is the resonance
field for the reference compound. Ocasionally an external
reference was used to eliminate the solvent effect. This iS
done by sealing the reference compound in a capillary tube
which in turn is supported in the center of the sample tube
by Teflon plugs. The results using the external reference
technique are not entirely satisfactory for two reasons.
First, at high temperatures the vapor pressure of the sample
tends to push the Teflon plugs upward out of the sample
region. ,Second, the capillary tube can cause very high Spin-
ning noise, due to the high sensitivity of the 100MHz instru—
ment. Also, the relative chemical Shifts measured by the
external reference technique must be corrected for the dif~
ference in the bulk diamagnetic susceptibility x between

the compound and the reference material. The correction

factor for a cylindrical sample is

R

S

r
s

e

N
9'

3913f

F, U
AN» 4

Z aU 1r PuJ
.13 v s a «Q
“In n0. u h N...

55

_ .21
6 + 5 (X

corr obs X)'

ref-

In some cases the correction factor is found empirically to

be 20-50% greater than the theoretical Value 2vAX/5 (71,72).
A6 can be measured by the method (75) suggested by Frei and
Berstein.~ They used two small reference containers, one
Spherical and one cylindrical in the regular 5mm sample tube.
The difference between the two sharp signals from the two
reference cells, is linearly dependent upon the volume sus-
ceptibility of the sample contained in the sample tube accord-

ing to the eXpreSSion

5Cy1(R) - ésph(R) = [gCy1- gsph][Xv(R) - Xv(s)] ,

where the chemical shifts are in ppm and g is a geometrical
constant which depends only on the Shape of the interface

between the reference and sample. (9 -gs h) can be deter—

cyl p

mined by calibration with liquids of known volume suscepti-

bility. In the ideal case it is equal to %£ .

§pectrometer

 

A Varian HA-100 high-resolution proton-stabilized NMR
Spectrometer was used in this investigation. A V-4511(100
MHz) fixed frequency rf unit and a V-4555 variable temperature
probe were used to obtain the proton magnetic resonance sig-
nals. A V-5506 flux stabilizer is used to stabilize the Ho

magnetic field to about one part in 108. The V-4554A

r‘f

L4)

13

("f

a

56

internal-reference proton stabilization unit provides NMR
stabilization by locking the magnetic field to a reference
proton signal of the sample. Frequencies were counted with

a Hewlett-Packard 5245L frequency counter.

Temperature Calibration

 

The temperature of the sample is controlled by a V-4541
variable temperature system which has a temperature range of
-60-2000C. At ambient temperatures and above the nitrogen
gas is heated inside the probe to the desired temperature
and allowed to flow around the sample tube. For low tempera—
ture studies liquid nitrogen is used to cool the nitrogen
gas. The temperature controller circuits limit the maximum
temperature variation at the heat sensor to.i 1°C.

.Since the temperature dial on the V-4541 has a calibra-
tion accuracy of only.i 5 degrees, ethylene glycol and
methanol chemical-shift thermometers are used for more accur—
ate work in the high-temperature range (GO—160°C) and the
lowetemperature range (-400 to 40°C), reSpectively.

These two chemical—Shift thermometers have been care-
fully calibrated in this laboratory using a copper-constan-
tan thermocouple which was inserted in the Spinning sample
tube and the voltage output recorded on a Sargent recorder.

A least-squares analysis of each set of data provided the
necessary temperature-chemical shift correlation eXpressionS.

These correlations were used in all the following experiments

57

to provide precise values of the sample temperatures.
For the high-temperature range the resulting expres-

sion is
TOK = -(6)1.017 + 464.9 (A)

where 6 is the difference between the two chemical Shifts
in ethylene glycol. For the low-temperature range the

calibration equation is
TOK = -(6)1.076 + 464.7 (B)

where 6 is the difference between the two chemical shifts
in the methanol Spectrum.

A cross check has been made between the above ca1i~
brated temperatures and the temperatures from the calibra-

tion charts provided by Varian, and the results are listed

 

 

below:

Ethylene Methanol

glycol A6 Varian (Eq. A A6 Varian Eq. B
155 Cps 52°C 54.30c 146 cps 57.5°c 34.5°c
159 28 50.2 150.5 52 29.8
165 24 26.1 154.5 27 25.5
167 20 22.06 158 25 21.7

 

All the results in a given row are from the same temperature
setting on the V—4541 unit. .Columns 2 and 5 are obtained
from the charts provided by Varian.Associates and it is

evident that these two columns are not consistent in the

58

region where they overlap (20 to 400C). The values in
columns 5 and 6 are obtained from Equations A and B,
reSpectively, and are quite consistent,so these two equations
can be used with confidence.

In addition to using the differences of the chemical Shifts
of ethylene glycol and methanol, Glew (74) used a mixture of
5 mole percent tetramethylsilane, 61 mole percent m—chloro-
phenol and 56 mole percent trifluoroacetic acid as an NMR
thermometer. This mixture is useful in the temperature
range -10 to +5OOC. The analytical expression for this

thermometer is

o = _ _
T C 87.961 1.0756(6OH 5ArH)

where 60 and éArH are the phenolic and the aromatic ring

H
proton chemical shifts in cps, reSpectively. The sensitivity
of this thermometer is claimed to be 1.8 times greater than
that of methanol but it was not used in this work. Duerst
(75) has a similar thermometer which employs a mixture of

51.8% water, 48.1% methanol and 0.1% HCl, by weight. The

temperature and chemical shift relationship is

TOC = 160.0 - 90.5 (s)

where S is the peak separation in ppm between the two Sharp

signals.

“KP:

1‘ ‘(It‘

RESULTS

Computer Methods in NMR Studies
of Rate Processes

 

Methods for Evaluating Rotational Energy
Barriers in Amides

Several methods have been used in the last ten or
eleven years to determine the energy barriers for internal
rotation in molecules from NMR data. Three of them will
be discussed here.

Method I--The Intensity-ratio Method

Woodbrey and Rogers (4,50) imposed the requirements
EEK-(<6w>> Egg" pA = p3, and TA = TB = ET on Equations 47
and 48 to obtain an eXpression for rate constant 1/2T in
terms of the ratio r of the maxima to central minimum
of the doublet:

i“?
1 = fléflz[r'+-(r2 - r) ] . (55)

24 J?
The method then consists of measurement of the intensities
of the maxima and of the minimum of the doublet correSpond-
ing to the two different magnetic environments for the
N-methyl groups in the N,N-disubstituted amides. The in-

tensity ratio is obtained at each temperature and, combining

59

ra‘.

CT‘

60

it with the peak separation in the absence of exchange, the
-rate constant 1/21’ can be evaluated from Equation 55.

This method is, in general, used for exchanges with
intermediate rates and the applicable temperature range is
usually only about 25 degrees. For obvious reasons, the
upper temperature limit is the coalescence temperature.

The intensity ratio can be measured quite accurately in the
moderatelycfast exchange region but the errors are the
largest in the Slow—exchange region where small fluctuations
in the base line and the central minimum will cause a large
error in the value of the intensity ratio. Inhomogeneous
broadening also tends to cause systematic errors.

A mathematical evaluation of this method was made by
Allerhand and Gutowsky (15) who Showed that, for a given
6wT20 product, the percent error in calculating the rate con-
stant increases with decreasing exchange rate and decreases
with an increasing value of the 6wT20 product.

In the case where the natural line widths 1/T2A and
1/T2B are comparable in magnitude to the peak separation in
the absence of exchange,the overlap effect should be con-
sidered. Woodbrey and Rogers (50) substituted 26w = 5wobs
and T —)-oo into Equation 48 to solve for a corrected 6w.

A slight improvement may be made on the value of the energy
barrier when the value of 6m corrected for overlap is used.

The improved intensity-ratio method can be programmed

for the digital computer and the computation procedures are

61

summarized as follows:
1. Substitute T -+'aa, pA, TgA, T23 and 6abo into
Equation 48 to calculate the corrected peak separa~

tion in the absence of exchange.

2. Use the corrected peak separation 6w. the line
shape parameters mentioned above and Equation 48 to
solve for the precise positions of the maxima and

the minimum, varying T each time by a small increment.

5. For each set of frequencies found in step 2 above,
the correSponding relative intensities of the maxima
and minimum can be obtained from Equation 47 so the

ratios of the maxima and the minimum are obtained.

4. Compare all the calculated intensity ratios from
step 5 with the eXperimental intensity ratios and
choose the one closest to the eXperimental value .
The correSponding T is the best value for that

particular experimental Spectrum.

It is obvious that this computation is very time con-
suming because it requires the computer to solve a large
number of fifth-order equations. A computer program,
BARRIER, has been written for this calculation. For a
typical experimental Spectrum, 250 T values ranging from

10“

to :105 are used,requiring 20 minutes time on the
Control Data 5600 computer. This procedure is seen to be

rather impractical, particularly in view of the systematic

we
eel
en

. 0.
M6.

62

errors inherent in the intensity-ratio method.
This program is not included as an Appendix since it
was not extensively used in this research; however, the

program is available.

Method II--Peak-Separation Method
The peak-separation method was develoPed by Gutowsky

and Holm (5). When the line widths JL-are small compared

T2
to the peak separations 600 in the absence of exchange the
ét'terms can be neglected in Equation 48. Neglecting over—

lap, the experimentally observed peak separation 6we can

be expressed as

 

(—)=_/1-7r?§'52 . (54‘)

When Equation 50 is written in terms of cycles/sec. the

equation has the following form

 

= L'J6v2 - avg . (55)
e

fa—

In this method the frequency separation in the proton mag-
netic resonance Spectrum of the N-methyl doublet at differ-
ent temperatures is measured. From Equation 55 the corres-
ponding rate of internal rotation 1/2T’ can be calculated
for each temperature. Fitting the data to an Arrhenius-type

-Ea/RT

rate equation, 1/ZT = Ae , the energy barrier Ea and

the frequency factor A can then be obtained from the lepe

65

and the intercept of the straight line plot of log 1/2T
yg. 1/TOK. The least-squares method may be used to obtain
the best values of Ea and A.

The program NMRTAU was written for the CDC-5600 com-
puter to carry out the above Operations. It prints out T
values at each temperature,and the values of Ea and log A
evaluated by the peak separation method,using a least—squares
fit of the data (Appendix III).

6mg becomes decreasingly sensitive to rate of exchange
as the exchange becomes slower. At very low temperatures,
where the exchange is quite slow, the error in determining
6we becomes large. The other shortcoming is that the major
change in the peak separation with exchange rate takes place
over a very narrow temperature range, 0.45 3T6w g 2. For
fast exchange, the rate constant obtained from Equation 55
is always inaccurate (48). The peak separation method is,
therefore, not a reliable technique for obtaining precise

kinetic data.

Method III--Total Line-Shape Analysis

From Table 1 values of the internal rotation energy
barrier for a given amide are seen to vary widely, depending
on which particular approximation method (intensity-ratio
method or peak-separation method) was used. Both are subject
to large systematic errors and disadvantages. The most
logical and desirable method is to determine the exchange

rate from the high resolution NMR Spectra by using Equation 47

64

directly, without further assumptions or approximations.
-When a set of adjustable line-Shape parameters T, pA,
6w, 1/T2A, 1/TZB, and Aw are substituted into Equation 47,
the complete Spectrum can be calculated. The computer
program NMRFIT (Appendix I) will compute the Spectrum based
on any given set of the above parameters. The calculated
Spectrum is then compared with the experimental Spectrum
and the computer will continue to search for the best combi—
nation of the parameters until the value of 2 (calculated

1

.)2 is not improved by further

intensityj - observed intensity 1
changes. The program NMRFIT is thus able to extract the best
combination of the above parameters to fit a given eXperi-
mental Spectrum. It must be kept in mind that NMRFIT is
only a numerical Operation and it is possible that the iter-
ation procedure may StOp before reaching the best fit. This
is possible if it is trapped in a local minimum. To avoid
such a situation the input parameters should be as close to
the true values as possible.

The best parameters selected by NMRFIT are then used as
input in the program NMRPLOT (Appendix II) which will plot

out the entire calculated Spectrum so it can be checked

visually against the eXperimentally determined Spectrum.
Treatment of Data

The line-shape Equation (47) was derived from the modi-
fied Bloch equations and kinetic considerations. The ideal

approach for extracting line-Shape parameters from the

65

experimental Spectrum is to substitute a number of sets of
parameters into the theoretical equation,calculating a
theoretical Spectrum in each case, comparing these with the
observed Spectrum and identifying the set of parameters
which will provide the best fit. The comparison can be
done either visually or mathematically. The most common
mathematical criterion used is the least—squares curve fit-
ting procedure (76,77,78).

The ordinary least-squares Operation involves three

steps (79). First, suppose the line-Shape equation is

Yi = Axi + BUi + czi + Dwi (56)

where Yi is the intensity at a particular frequency, and

A, B, C, D are the line-Shape parameters such as peak
separation, half-width at half-height and exchange rate
constant. The other variables Xi, Ui, Zi and Wi are simple
functions of the frequency. Second, the sum of the Squares

of the absolute deviations of the calculated values of Y

from those observed should be minimized:

 

Yi - (Axi + BUi + czi + DWi) = Dev (57)
_ 2 = 2
ZlYi (Axi + BUi + czi + DWi)] (Dev) (58)
82(Dev)2 _ _ =
6A - Z(-2)[Yi (Axi + BUi + CZi + DWi)]Xi O (59)

Differentiation of 2(Dev)2 reSpect with B, C, and D yields

= 2

66

ZU.Y. = AZX.U. + BZU.2 + 022.0. + D2W.U. (61)
J. l 1 1 l l .‘L l l

221. = Azxz. + BZU.Z. + 022? + Dzw.z. (62)
J. J. l J. l J. l .‘L .‘L

2w.Y. = Azx.w. + BZU.W. + czz.w. + DZW.2 (65)
1 l l l l J. l J. 1

Third, Equations 60, 61, 62 and 65 can be solved Simultan-
eously for the values of line-Shape parameters, A, B, C and
D, which will give the best fit.

The ordinary least-squares treatment of data occasion-
ally gives experimentally impossible results and, in other
cases, reasonable values for the parameters can only be ob-
tained by treating part of the data rather than the entire
set of values.

Instead of solving the above set of equations directly,
an alternate procedure can be used. The estimated para-
meters are substituted into the line-Shape equation in such
an order that the least certain parameter will be adjusted
first. An arbitrary adjustment increment or variation func—
tion is assigned to each parameter. The sum of the squares
of the differences between the calculated and observed in-
tensities is compared with that obtained in the previous
trial (80). If this sum is smaller than the previous sum,
it indicates that the correction adjustment is in the
right direction, otherwise the Sign and magnitude of the
previous adjustment increment are changed. This procedure
was programmed and the description of the program and the

flow chart are given in Appendix I.

67
High-resolution Spectra

The proton magnetic resonance Spectra reported on the
following pages are obtained from the HA-100 MHz high-resolu—
tion Spectrometer at room temperature. The chemical Shifts
were measured in ppm from the internal reference HMDS,
chosen as zero. Indication will be given when other reference
compounds are used.

The Spectra of N,N-dimethylformamide, N,N-dimethyl-
acetamide, N,N-dimethylcarbamyl chloride and N,N-dimethyltri-
chloroacetamide can be found in Woodbrey's thesis (50). In
the Spectra of these compounds the two N-CHa groups give
rise to a doublet. The signal at the higher field is due to
the methyl group which is in a position Egagg to the carbonyl
oxygen atom, while the one at the lower field is due to the
gg§_methyl group. In the case of N,N-dimethylformamide, the
two peaks of the original doublet are further Split into
(inflfletsrw the formyl proton. The coupling constants are
0.7 and 0.9 cps for the low and high field peaks,
reSpectively. This additional Splitting is not observed for

the other amides mentioned above.

N,N:Qimethylp£9pionamide

The proton magnetic resonance spectrum of N,N-dimethyl-
prOpionamide is given in Figure 1. One N-methyl group has
a resonance signal at 2.91 ppm and that of other N-methyl is

located at 2.77 ppm. The quartet between 2.555 ppm and 210.7

68

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2mm em.o mfi.m
smm.o mdo.a so.m mm.m mm.m. es.m am.N
. _ _ _ _ _ _ a _
.mozmumocmummmu HmeumucH .mxomovzoommoamu
. mo asuuommm mocchmmu oaumcmme cououm .a mnsmwm

 

 

69

ppm is due to the methylene protons, whereas the triplet
between 1.015 ppm and 0.867 ppm arises from the methyl
protons of the ethyl group. These multiplets result from
the Spin-Spin coupling between the methyl protons and the

methylene protons of the ethyl group.

fl,N:Qimethylacrylamide

The proton magnetic resonance Spectrum of pure N,N-
dimethylacrylamide is shown in Figure 2. The doublet at
2.98 ppm and 2.857 ppm arises from the two N-methyl groups.
The peak at 2.857 ppm arises from the N-methyl group which
is gig to the carbonyl oxygen atom. The line widths of the
two peaks are about the same, because of the negligible
Spin—Spin coupling with the proton of the vinyl group.

The remaining Signals are from the protons of the vinyl
group. Such a complicated Spectrum arises when the chemical
Shifts and the Spin-Spin coupling constanfisare comparable

and it can be analyzed by standard methods as an ABC Spectrum.
Asymmetrical N,N-Disubstituted Amides

In this type of compound, the intensities of the two
components of the N-methyl doublet are different, because the
equilibrium prOportions of the two isomers differ. The rela—
tive pOpulations of the two rotational isomers are prOpor-
tional to the relative intensities of the two N-methyl

peaks.

 

.emm.m omm.m

 

_ E

 

Cs

 

70

am¢.m wwm.m dwfi.m . nwm.w

 

.Nm¢.m mmm.m Nmm.m dOO.® fihfi.© www.m fid>.m Wfim.©
a. — — . _. ~ _ _ q _ _

L «1)..

 

 

 

 

 

.mazmumocwnmmmn HmcumucH .NAomUVZOUmU u mmo
mo Esuuowmm mucmcommn oaumamme cououm .N musmflm

 

 

 

71

N-Ethyl-N-methylacetamide

The proton magnetic resonance Spectrum of N-ethyl-N-
methylacetamide is Shown in Figure 5. The resonance peaks
at 1.92 ppm and 1.895 ppm arise from the CHa-CO groups of
the two rotational isomers. The quartet at 5.27 ppm is
from the N-methylene protons and the 'doublet' Splitting
of this quartet is from the two rotational isomers. The
methyl signal at 2.901 ppm and the N-C-CH3 triplet at 1.040
ppm are assigned to the reSpective N-alkyl groups which are
in a position Eggpg to the carbonyl oxygen atom, while
N-methyl peak at 2.741 ppm and the N-C-CH3 triplet at 0.955
ppm are associated with groups located gig to the carbonyl
Oxygen. ,The different line widths of the two methyl peaks
are probably a result Of weak Spin-Spin coupling with the
O=C-CH3 protons. The difference in Spin-Spin coupling con-
stants is averaged out at elevated temperature, and conse-

quently the line widths become equal.

N-n-Butyer-methylacetamide

The proton magnetic resonance Spectrum of pure N-n-
butyl-N-methylacetamide is shown in Figure 4. The triplet
at 5.225 ppm is from the N-CHz protons and the rather large
line width of this triplet is probably caused by the super-
position of two triplets from the two rotational isomers.
The doublet at 1.94 ppm and 1.885 ppm is from the acetyl
protons of the two rotational isomers. The N—methyl peak

at 2.74 has been assigned to the group which is in a position

72

 

mmm.o moo.d

 

 

 

 

 

 

 

 

map;
266 mpm.o mem.o 660.2 Hma.a mm.e
it. A q) — — fix). \ ‘ —
aim smzm

 

 

 

 

Hom.m
_

 

 

)} q

 

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HmcumucH .AmmommovhmmoVZOOmmo mo
Esuuowmm monocommu Uflumcmma cououm .m wusmflm

 

 

 

see mmmé ‘ mm:

 

75

 

Hem?“ 60min H¢>.N mmm.m mmm.m emmé...
_ _ _ .

 

 

 

 

 

 

.mozmumocmumwmu
HmcnmucH .AmmommommommovAmmovzoommo
. mo Eduuowmm mocmcommu Oauwcmme cououm .d wusmwm

 

 

74

cis to the carbonyl oxygen atom and the trans N-methyl peak
is located at 2.895 ppm. The unresolved signal at 1.541

ppm is from the N-C-CHg-CHg protons.

.N-Cyclohexyl-N-methylacetamide

The proton magnetic resonance Spectrum of N-cyclohexyl-
N-methylacetamide is shown in Figure 5. The peaks of the
acetyl protons of the two rotational isomers are located at
1.942 ppm and 1.89 ppm. The N-methyl peak at 2.644 ppm is
assigned to the group which is gig to the carbonyl oxygen
atom, while the peak at 2.752 is assigned to the N-methyl
group Egggg to the carbonyl oxygen atom. The two broad and
weak peaks at 4.245 ppm and 5.508 ppm are from the protons
at the 1-position of the cyclohexyl rings of the two rota-

tional isomers.

N-ISOprOpyl-N-methylacetamide

The proton magnetic resonance Spectrum of the N-iso-
propyl-N-methylacetamide is Shown in Figure 6. The acetyl
proton peaks are at 1.928 ppm and 1.876 ppm. The N-C-(CH3)2
resonance peaks appears as two doublets at 1.112, 0.99 ppm
and 1.047, 0.916 ppm. The N-methyl peak at 2.609 ppm and
the methine septet at 4.726 ppm are assigned to the isomer
in which these groups are located gig to the carbonyl oxygen
atom, while the N-methyl peak 2.726 ppm and the methine
septet at 4.016 ppm are assigned to the isomer in which the

reSpective groups are trans to the oxygen atom. The relative

 

 

 

 

 

 

 

 

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76

 

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98.05601“ mhmJu

 

mm.o mafia - mmm.H
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In

H):

(I?

ir

77

pOpulation is about 60% for the isomer with the N-methyl

group trans to the carbonyl oxygen atom.

NeMethyl-N-benzylformamide

The proton magnetic resonance Spectrum of N-methyl-N-
benzylformamide is shown in Figure 7. The peaks from the
N-methyl protons and benzyl protons gig to the carbonyl
oxygen atom are located at 1.521 ppm and 5.168 ppm,
reSpectively, while those from the N-methyl protons and
benzyl protons giggg_to the carbonyl oxygen atom are at 1.548
and 5.168 ppm, reSpectively. The low field doublet is from
the formyl_protons in the two rotational isomers. The unre—

solved signal at 5.956 ppm is from the ring protons.

N-n—Butyl-N-methyltrimethylacetamide

The proton magnetic resonance Spectrum of N-n-butyl-N-
Inethyltrimethylacetamide is shown in Figure 8. In this
Espectrum only one set of N-alkyl resonances is found. The
‘Nemethyl resonance is located at 2.957 ppm and the N-CHa
triplet is at 5.272 ppm. The high-field strong Single peak
is from the t-butyl protons. The unresolved high field
Signals are assigned to the protons of the N-C-CHg-CHg-CHa
group. No doublet appears for the N-methyl group when the
sample temperature is increased from -200C to 800C indicat-

ing that there is only one isomer in this temperature range.

78

 

5mm

 

 

 

 

 

 

HNM.H mem.d dmm.m mwa.m mmm.m mm.m mmo.s
_ _ _ _ _ _ _
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.mmoummuammovzoom mo Esuuommm OOSMSOme Uflumcmmfi couonm .w musmwm

 

 

 

79

 

5mm

mwm.o

mmd.d

5mm.N th.m

 

 

 

 

 

 

 

 

.mazm "wocmumwwu
HmcumucH .AmmommONmommovAmmovzoovmxnmov
mo Esuuommm DUSMOOmOH oaumcmmfi cououm

 

.m musmflm

 

 

1%

Ta

80

N-MethyigN—a-naphthylacetamide

The proton magnetic resonance Spectrum of the solution
of N—methyl-N-a-naphthylacetamide in CHC13 is shown in
Figure 9. Only one peak is found for the N-methyl protons
at 5.46 ppm and the proton signal from the acetyl methyl
group is located at 1.865 ppm. The solvent peak is at
7.648 ppm. When the sample temperature is varied from —200C
to 65°C, no evidence for the existence of a second rota—

tional isomer was obtained.

N-Methyl-N:phenylacetamide

 

The proton magnetic resonance Spectrum of N-methyl-N-
phenylacetamide in CCl4 solution is Shown in Figure 10.
Again only one isomer is found in the temperature range
-200C to 600C. The resonance peaks at 5.126 ppm and 1.706
are assigned to N-methyl protons and acetyl methyl protons,
reSpectively. The unresolved ring Signal is located between

7.241 ppm and 7.174 ppm.
Hindered Internal Rotation of Substituted Amides

The hindered internalrotationslabout the central C-N
'bond of some N,N-disubstituted amides were studied, and the

results are reported as follows:

N,N-Dimethylformamide_

__v—i

The experimental and calculated data are tabulated in

Table '7 and Figure 14. The internal rotation of pure

81'

 

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m¢m.w

 

 

 

 

 

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82

 

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85

DMF-d1 and its solutionsin.F3CCOOH,S—C2H2Cl4and $~C(CH3)3
were also studied and the. results are tabulated in
Tables 5, 9, 11, and 15, reSpectively. These data are
plotted as 10910 T against 103/TOK in Figures 15, 15,

16, and 17.

N,N—Dimethylacetamide

This compound has been studied in both the pure form
and in solution in F3CCOOH. The calculated and experimental
data are tabulated in Tables 15, 17, and 19, respectively.
The data obtained by total lineQShape analysis (T.L.S.) are

plotted as loglo T against 103/TOK in Figures 19 through 21.

N,N-Dimethylpropionamide
The results for DMP were evaluated by all three methods
and tabulated in Table 21 and the results from T.L.S. are

plotted as loglo T against 103/TOK in Figure 22.

N,N—Dimethylacrylamide
The data are tabulated in Table 25, and the results
from T.L.S. are plotted as loglo T against 103/TOK in

Figure 25.

N,N-Dimethyltrichloroacetamide
The results for DMTCA are tabulated in Tables 25 and 27
and the T.L.S. outputs are plotted as loglo T against

103/TOK in Figures 24 and 25.

 

1:2.

84

Egg-Dimethylcarbamoylchloride
The results for different samples of DMCC are tabulated
in Tables 29 through 56, and the T.L.S. outputs are plotted

as loglo T against 103/TOK in Figures 26 through 51.

85

 

 

mom.emm

.mxmmovzooo
mo mnuuwmm OUGOCOmmH oaumamms Sououm Amcfla

Owuuovv Omumaaoamo can AOSHH Owaomv Om>ummno one

 

.HH musmflm \

 

 

86

 

 

semen

.O.ucoo dd musmflm

 

 

 

 

Figure 12. Temperature dependence of observed and
calculated Spectra of DCON(CH3)2.

Observed Calculated

 

422-20K

412.50K

405.9OK

 

 

-88

 

 

 

Figure 12 cont'd.

60K

 

0°K

579.

570.

 

50K

 

 

 

89

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90

 

 

 

 

Table 6. Thermodynamic and kinetic parameters for
internal rotation about the central C-N bond
of pure DCON(CH3)2, from different methods.

Method E Log 2A AF$ O

kgal/mole 575.8 K
kcal/mole
*

I.R. 16.22 10.56 20.688

p.s.* 6.441 5.212 20.08

T.L.A. 27.19 16.67 21.156

-)(-

= 16.2 Hz.

FR = 603g)

s.~

 

91

 

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**

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*

 

 

 

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Ta

95

Table 8. Thermodynamic and kinetic parameters for in-
ternal rotation about the central C-N bond of pure
HCON(CH3)2 with C5H5C(CH3)3 as internal reference.

 

 

 

Method Ea Log 2A AF;75 9
kcal/mole kcal/mole
+
I.R. 14.67 9.606 20.56
p.s.+ 5.006 _5.599 19.66
T.L.A.* 25.52 14.7 20.99
**
T.L.A. 24.15 15.06 20.99

 

+FR = 15.8 Hz.
*
With no Spin—Spin coupling correction.

am-
With Spin~Spin coupling correction by superposition.

94

 

0.0-

 

 

 

 

.P
m
0
g
-2.0
o
L 1 1
2 46 2.5 2.6 2.7
1 Os/TOK
Figure 14. Plot of 10910 7 against 103/TOK for pure HCON(CH3)2

with Spin-Spin coupling correction included by
superposition, with C6H5C(CH3)3 as internal
reference.

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*
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95

 

 

 

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96

Table 10. Thermodynamic and kinetic parameters for internal
rotation about the central C-N bond of DCON(CH3)2
in F3CCOOH solution.

2W
#

 

Method Ea Log 2A AF557 9
kcal/mole kcal/mole

I.R.* 14.0 10.55 16.55

p.s.* 6.154 6.711 16.17

T.L.S. 16.76 12.09 16.46

 

*-
FR = 15.0 Hz.

97

 

 

 

 

 

Figure 15. Plot of logic T against 103/TOK for DCON(CH3)2
in F3CCOOH solution.

98

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99

Table 12. Thermodynamic and kinetic parameters for internal
rotation about the central C—N bond of DCON(CH3)2 in
Se-C2H2C14 solution.

 

 

4

 

Method Ea Log 2A AF 0
kcal/mole 579'9 K
kcal/mole
I.R.* 15.45 10.15 20.9
p.s.* 6.499 5.22 20.47
T.L.S. 16.96 12.14 21.01

 

*FR = 15.9 Hz.

0.0

Loglo T

-2.0

100

 

 

 

 

 

2.42

Figure 16.

2.5 2.6 2.7
1 O3 /T°K

Plot of loglo T against 103/TOK forr%*0.67 mole
fraction of DCON(CH3)2 in C2H2Cl4 solution.

101

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102

Table 14. Thermodynamic and kinetic parameters for internal
rotation about the central C-N bond of DCON(CH3)2
in C5H5C(CH3)3.

 

m

 

Method Ea Log 2A AFgaooK

. kcal/mole kcal/mole
I.R.* 14.56 9.657 20.76
p.s.* 14.76 9.719 20.65
T.L.A. 21.65 15.61 20.92

 

*-
FR = 9.7 Hz.

105

 

Loglo T

 

 

 

l l l

2.46 ' 2.5 2.6 2.7
103/TOK

 

Figure 17. Plot of loglO T against 103/TOK for DCON(CH3)2
in C5H5C(Cf13)3 solution (~'0.7 mole fraction).

104

 

Observed Calculated

 

 
 

557.7°K

/\S:>OK/\
/\/\:528 50K/\/\

Figure 18. Temperature dependence of observed and calcu-
lated proton magnetic resonance Spectra of
CH3CON(CH3)2.

 

 

 

105

 

 

Figure 18 cont'd.

‘ Observed Calculated

 

.5220K

m

 

 

 

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107

Table 16. Thermodynamic and kinetic parameters for internal
rotation about the central C-N bond of
CH3CON(CH3)2.**

 

 

 

t
Method Ea Log 2A AF5500K
kcal/mole kcal/mole
I.R.* 12.71 9.746 17.925
p.s.* 15.17 11.59 17.674
T.L.A. 22.56 16.06 16.199

 

*
TMS as internal reference.
66*

FR = 17.2 Hz.

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m.m
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108

 

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109

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110

Table 18. Thermodynamic and kinetic parameters for internal
rotation about the central C-N bond of
CH3CON(CH3)2.**

t

 

Method Ea Log 2A AF529 6
kcal/mole kcal/mole
I.R.* 17.29 12.69 18.0
P.S.* 10.55 8.567 17.75
T.L.A. 27.16 19.0 18.56

 

* FR = 17.2 Hz.
**
HMDS as external reference.

 

 

111

 

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115

Table 20. Thermodynamic and kinetic parameters for internal
rotation about the central C-N bond of CH3CON(CH3)2

 

 

 

Method Ea Log 2A AF2950K
kcal/mole kcal/mole
I.R.* 18.24 14.91 16.055
P.S.* 24.25 19.55 16.144
T.L.A. 24.54 19.57 ' 15.72

 

* ..
FR = 6.9 Hz,

Loglo T

114

 

0.0—

 

 

 

 

Figure 21. Plot of loglo T against 103/TOK for CH3CON(CH3)2
in F3CCOOH solution.

115

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116

Table 22. Thermodynamic and kinetic parameters for internal
2 rotatiOn about the central C—N bond of
C2H5CON(CH3)2.

 

 

 

t
Method Ea Loglo 2A AF524.50K
kcal/mole kcal/mole
I.R.* 15.65 10.65 17.17
p.s.* 17.65 15.61 17.12
T.L.A. 21.44 15.92 17.2

 

*FR = 15.9 Hz.

117

 

0.0-

 

 

 

I AJ I
2.96 5.0 5.1 5.2

103/TOK

 

Figure 22. Plot Of loglo T against 103/TOK for pure
C2H5CON(CH3)2.

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119

Table 24. Thermodynamic and kinetic parameters for internal
rotation about the central C-N bond of
CHgéCHCON(CH3)2.

 

 

 

Method Ea Loglo 2A AF518.8
kcal/mole kcal/mole

I.R.* 9.645 6.45 16.65

p.s.* 9.092 7.901 16.66

T.L.S. 17.82 15.95 16.66

 

*
FR = 15 Hz.

VHO.H.\ OOH
H.m

 

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Table 26. Thermodynamic and kinetic parameters for internal
rotation about the central C-N bond of
CC13C0N(CH3)2. **

Method Ea Loglo 2A AFEQ5 6oK

kcal/mole '
kcal/mole

I.R.* 14.21 12.49 15.02

p.s.* 15.71 12.15 15.02

T.L.A. 22.11 18.47 15.013

= 28.6 Hz.

**

HMDS as external reference.

125

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125

Table 28. Thermodynamic and kinetic parameters for internal
rotatiOn about the central C-N bond of
CC13CON(CH3)2.**

 

 

1

 

Method Ea L091 0 2A AF 0
kcal/mole 293.6 K
kcal/mole
I.R.* 16.71 14.42 14.96
p.s.* 14.66 15.05 14.97
T.L.A. 21.07 17.66 14.96

 

*
FR = 28.6 Hz.

**
TMS as internal reference.

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127

Table 29. Temperature dependence of the rate of internal
rotation about the central C-N bond of
C1CON(CH3)2.**

a
—“=====_——_———

 

103/TOK pA* Loglo 1*
5.456 0.55 0.10924
5.05 0.5018 0.580
5.181 0.424 -1.0044
5.155 0.5046 -1.250
5.110 0.5055 -1.525
5.070 0.502 -1.495
5.029 0.4829 -1.758
2.974 0.4925 -1.958

 

,AEa = 21.91 kcal/mole

Loglo 2A = 16.21

AF521.5°K

*Results from T.L.S.

**Not degassed,

= 17.56 kcal/mole

cyclohexane as external reference.

Loglo T

0.0

128

 

 

 

 

 

[ l 1
3.0 3.1 3.2
lea/TOK
Figure 26. Plot of logic T against 103/TOK for pure

ClCON(CH3)2, with cyclohexane as external
reference.

129

Table 30. Temperature dependence of the rate of internal
rotation about the central C-N bond of

C1C0N(CH3)2.**

 

 

 

103/TOK pA* Loglo 0*
5.618 0.515 0.5
5.482 0.4829 0.172
5.515 0.4959 -0.616
5.274 0.509 -1.162
5.184 0.505 -1.168
5.125 0.509 -1.5401
5.096 0.495 -1.444
5.072 0.505 —1.555
5.015 0.508 -1.755

 

AEa = 17.7 kcal/mole

Loglo 2A = 13.45

1

AF517.5°K

= 18 .17 kcal/mole

*-
Results from.T.L.S.
*

*
Saturated with 02 and TMS as internal reference.

130

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151

Table 31. Temperature dependence of the rate of internal

rotation about the central C-N bond of

ClCON(CH3)2.**

 

 

 

 

103/TOK pA* Loglo 1*
3.618 0.4650 0.4623
3.422 0.4989 -0.1910
3.315 0.5006 -0.875
3.262 0.5095 -1.2479
3.184 0.5141 -1.277
3.125 0.5033 -1.438
3.096 0.4815 -1.541
3.072 0.5074 -1.64
3.02 0.5088 -1.751

Ea = 13.79 kcal/mole

Log 2A = 10.88

AF517.50K = 17.79 kcal/mole
*Results from T.L.S.

**From K and K, not purified, not degassed, cyclohexane

as internal reference.

152

 

0.0-

 

1 1 4

5.1 A 5.2 5.5

 

 

 

103/TOK

Figure 28. Plot of loglo T against 103/T0K for not purified
C1CON(CH3)2, not degassed, with HMDS as external
reference.

155

Table 32. Temperature dependence of the rate of internal
rotation about the central C-N bond of
ClC0N(CH3)2.**

 

 

 

103/TOK PA* Loglo T*
5.511 0.4950 -0.412
5.181 0.5054 -1.025
5.168 0.4952 -1.047
5.155 0.4947 —1.217
5.086 0.5180 -1.584

 

Ea = 20.02 kcal/mole

Log 2A = 14.93

1

AF514.5oK = 17.4 kcal/mole

*
Results from T.L.S.

**
Highly purified (V.P.C.), degassed, HMDS as external

reference.

Loglo T

154

 

0.0—

 

 

] 1 l

 

Figure 29.

5.1 5.2 5.5
103/TOK

Plot of loglo T against 103/TOK for highly
purified C1C0N(CH3)2, with HMDS as external
reference.

 

155

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136

Table 54. Thermodynamic and kinetic parameters for internal
rotation about the central C-N bond of
ClCON(CH3)2.**

 

 

 

¢
Method Ea Loglo 2A AF514.50K
kcal/mole kcal/mole
I.R.* 11.8 9.609 16.89
P.S.* 12.5 10.08 16.84
T.L.S. 21.56 16.06 17.14

 

*-
FR = 11 Hz.

**
Highly purified, degassed, TMS internal reference.

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159

Table 56. Thermodynamic and kinetic parameters for internal
' rotation about the central C-N bond of
C1C0N(CH3)2.**

 

 

 

Method Ea Loglo 2A AF§14 5oK
kcal/mole kca1/0ole
I.R.* 12.9 10.57 16.9
P.S.* 11.24 9.19 16.95
T.L.S. 25.16 17.52 17.1

 

*FR = 11 Hz.

**HMDS as external reference.

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141

NFMethyl—N—ethylacetamide
This compound was studied by T.L.S. and the calculated
results are tabulated in Table 57 and plotted as 10910 T

against 103/TOK in Figure 52.

N-Methyl-N-n-butylacetamide
The internal rotation of this compound was studied by
T.L.S. and the results are tabulated in Table 58 and plotted

as 10910 T against 103/TOK in Figure 55.

NfiMethyer-cyclohegylacetamide
The results from T.L.S. of this compound are tabulated
in Table 59 and plotted as 10910 T against 103/TOK in

Figure 55.

NeMethyer-isoprOpylacetamide
The results from T.L.S. of this compound are tabulated
in Table 40 and plotted as loglo T against 103/TOK in

Figure 58.

N-Methyl-N-benzylformamide
The results from T.L.S. of this compound are tabulated
in Tables 41 and 42, and plotted as loglo T against 103/TOK

in Figures 59 and 40.

142

Table 57. Temperature dependence of the rate of internal
rotation about the central C-N bond of
CH3CON(CH3)C2H5.

 

 

 

*
103/TOK pA* K=EA Log 1 o 1* FR*
3 rad/sec
5.070 0.49957 0.998 -1.192 100.48
5.042 0.50694 1.028 -1.505 100.56
5.014 0.50514 1.021 -1.447 100.55
5.002 0.52475 1.104 —1.552 100.28
2.987 0.50171 1.007 —1.602 101.89
2.960 0.51488 1.061 —1.716 100.05
2.957 0.50476 1.019 -1.710 98.477
2.940 0.51552 1.056 -1.818 105.59
2.954 0.50882 1.056 -1.855 106.52
2.905 0.49797 0.9919 -2.055 116.97
2.900 0.50667 1.005 —2.055 112.51
2.880 0.49255 0.971 -2.465 117.19
2.865 0.49292 0.972 -2.168 105.29

 

Coalescence point = 103/TZK 3 2.9.
*Results from T.L.S.

Ea = 22.85 kcal/mole

Log 2A = 16.55

AF558.20K - 17.7 kcal/mole

145

 

 

 

 

L l l

 

2.9 5.0 5.1
- 103/T°K

Figure 52. Plot of logic T against 103/TOK for pure
CH3C0N(CH3)02H5.

144

Table 58. Temperature dependence of the rate of internal
rotation about the central C-N bond of
CH3€0N(CH3)C4H9.

 

 

 

103/TOK pA* K = 35- Log T* FR*

pB rad/sec
2.996 0.55854 1.17 -1.557 95.695
2.994 0.55501 1.15 -1.528 92.0
2.960 0.55757 1.16 -1.725 99.04
2.957 0.52949 1.125 -1.699 95.59
2.951 0.55245 1.159 -1.857 98.677
2.919 0.55555 1.15 -1.905 98.867
2.988 0.55682 1.159 -2.057 105.54
2.880 0.55545 1.145 -2.158 105.28
2.870 0.55551 1.14 -2.158 102.11

 

Ea = 24.2 kcal/mole
Log 2A = 17.59

AF* 0

542.6 K = 17.64 kcal/mole
Coalescence point = 103/T2K a 2.95.
*Results obtained from T.L.S.

145

 

 

 

 

 

2.9 3.0
103/T0K

Figure 55. Plot of loglo T against 103/T0K for pure
CH3CON(CH3)C4H9.

146

 

 

Observed . Calculated

 

 

550.20K

  

524.70k

Figure 54. Temperature dependence of observed and
calculated proton magnetic resonance Spectra
of CH3C0N(CH3)(C6H11).

 

 

147

 

 

Figure 54 cont'd.

 
 

32.219430.

514.10K

505.1OK

 

 

 

148

Table 59. Temperature dependence of the rate of internal
rotation about the central C-N bond of

CH3CON(CH3)C-C5H11.

 

 

 

103/TOK pA* K = 5— Log T* FR*

B rad/sec
3.277 0.54209 1.184 -0.519 70.506
5.184 0.55304 1.237 -1.208 70.081
3.14 ' 0.53812 1.165 -1.401 69.62
3.118 0.53740 1.182 -1.525 72.112
3.107 0.53542 1.15 -1.544 70.261
3.102 0.5059 1.023 —1.678 80.555
3.08 ’ 0.52832 1.12 -1.696 73.38
3.08 0.50537 1.02 -1.85 78.833
3.029 0.49833 0.993 -1.952 72.543

 

Ea = 26.2 kcal/mole
Log 2A = 19.58 .
¢ _
AF521.9°K - 17.06 kcal/moée ”
Coalescence point = 103/TCK = 5.07.

*Results from T.L.S.

149

 

Loglo T

 

 

 

 

5.0
103/TOK

Figure 55. Plot of loglo T against 103/TOK for pure
CH3C0N(CH3)C5H11.

150

 

 

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152

 

Observed Ca1culated_

 

 

330.8°K

 

322.3°K

Figure 57. Temperature dependence of observed and calcu-
' lated proton magnetic resonance Spectra of
CH3CON(CH3)CH(CH3)2.

 

 

 

155

 

Figure 57 cont'd.

  

318.9°K

 

 

 

 

154

Table 40. Temperature dependence of the rate of internal

rotation about the central C—N bond of

CH3C0N(CH3)CH(CH3)2.

 

 

 

103/T0K pA* K = 25- Log 1* FR*

pB rad/sec
5.27 0.52148 1.089 -0.608 72.864
5.17 0.5554 1.259 -1.269 70.445
5.15 0.56507 1.289 -1.594 72.140
5.15 0.56552 1.29 -1.495 72.595
5.11 0.56459 1.296 -1.572 72.868
5.10 0.546 1.205 -1.68 76.465
5.07 0.5284 1.12 -1.819 78.295
5.06 0.526 1.11 —1.908 78.150
5.02 0.55 1.15 -2.062 72.507

 

Ea = 26.77 kcal/mole
Loglo 2A = 19.81

* _
AF521.50K — 17 kcal/mole o I”
Coalescence point = 103/TCK = 5.1.
*Results from T.L.S.

155

 

0.0 -

L091o T

r
5.2

 

 

 

 

5:1
103/T°K

Figure 58. Plot of loglo T against 103/TOK for pure
CH3C0N(CH3)CH(CH3)2.

156

 

 

 

Table 41. Temperature dependence of the rate of internal
rotation about the central C-N bond of
HCON(CH3)CH2C5H5.***

103/TOK PA* K = 25- Log T** Log T* FR*

pB rad/sec
2.660 0.45464 0.8556 -1.127 -1.126 125.68
2.651 0.46424 0.8665 -1.185 -1.185 127.28
2.617 0.46065 0.854 -1.518 —1.518 124.45
2.595 0.45165 0.845 -1.524 -1.524 125.56
2.565 0.46894 0.885 -1.546 -1.546 125.88
2.537 0.44872 0.814 -1.64 -1.840 123.39‘
2.511 0.45956 0.85 -1.825 -1.825 150.46
2.481 0.46796 0.88 -1.912 -1.912 125.51
2.446 0.49468 0.9789 -2.165 -2.164 155.22

 

Ea = 25.24 kcal/mole

Log 2A = 14.57

A *

F394.5°K

= 20.88 kcal/mole

Coalescence point = 103/TZK g

*-
Results from T.L.S.

**

Superposition technique is used and J1 and J2 are assumed

to be 0.4 CpS and 0.6 ops.

**

*
T.L.S. on the benzyl f

2.48.

doublet.

157

 

 

 

 

l I
2.5 2.6

103/TOK

 

Figure 59. Plot of loglo T against 103/TOK for pure
HC0N(CH3)CH2C5H5 (from benzyl protons).

158

Table 42. Temperature dependence of the rate of internal
rotation about the central C—N bond of

 

 

 

HC0N(CH3)CH2C5H5.***
103/TOK PA* = 25- Loglo T* FR *
pB rad/sec
2.660 0.54595 1.2024 -1.005 110.69
2.651 0.52486 1.1046 -1.262 111.47
2.617 0.57959 1.5468 -1.501 115.41
2.595 0.52920 1.124 -1.581 110.4
2.565 0.58659 1.418 -1.596 115.1
2.557 0.55102 1.227 -1.755 117.55
2.511 0.20404 0.25 -1.766 165.57
2.481 0.51246 1.0511 -2.025 124.89
2.446 0.49656 0.9865 —2.162 125.05

 

Ea = 22.87 kcal/mole
LOglo 2A = 14.41

AF394.20K = 20.68 kcal/mole

a/

Coalescence point = 103/T2K = 2.48.

*Results from T.L.S.
*-
T.L.S. on the formyl doublet.

**

159

 

 

 

 

 

103/T°K

Figure 40. Plot of logic T against 103/TOK for pure
HCON(CH3)CH2C6H5 (from the formyl doublet).

DISCUSS ION
Methods for Obtaining Rate Data from NMR Spectra

The values reported in this thesis for the energy
barriers hindering internal rotation in substituted amides
have been obtained using three different methods for ana-
lyzing the NMR data. These are the peak—separation method,
the intensity-ratio method and the method of total line-
shape analysis. These methods will now be discussed from
the viewpoint of selecting the 00st practical procedure for

applications to chemical problems.

-Method I--The Intensity-Ratio Method

This method is based on the measurement of the ratio
of maximum to central minimum intensities in a partially
coalesced doublet. Any factors which produce errors in
this ratio will reduce the accuracy of the results. These
factors include Spin-coupling in the case where it is small
enough to broaden the lines but not sufficiently large to
give higher multiplets. In molecules such as DMF this
introduces an important error and must be taken into account

in the calculations or eliminated. A second error may arise

160

161

from overlap of the components of the doublet if the chemi-
cal shift between them is not large compared to the line
width. This can be corrected for in the calculations (4).
but makes it difficult to measure energy barriers when the
chemical shift is less than about 5 Hz. The most important
error in this method arises from the inhomogeneous broaden-
ing of the lines when the static magnetic field varies over
the sample volume and, particularly, when the field inhomo-
geneities change during a given series of measurements.
Even though care is taken to tune the Spectrometer for maxi—
mum field homogeneity at each temperature the line widths
in the absence of exchange are limited by this factor and
it varies from one measurement to another. Line broadening
from this source decreases the maxima and builds up the
minima giving intensity ratios which are too small. A sys—
tematic error is thereby introduced into the rate constants
and the energy barriers. It is this factor which is
primarily reSponsible for the energy barriers being too low
when determined by the IR method. A final difficulty is
that the intensity ratio can only be determined with pre—
cision from the temperature where exchange broadening first
causes the doublet components to overlap,up to the coales-
cence temperature. This range is scarcely large enough for

the accurate determination of energy barriers.

162

Method Il--ThePeak-Separation Method

This method requires the precise measurement of the
apparent chemical shift between doublet components at
various temperatures. It is more difficult to make this
measurement precisely than it is to measure the intensity
ratio, particularly near the coalescence point where the
peaks are broad and flat, and it is subject to the same
disadvantages as the former method. When the chemical shift
in the absence of exchange is small,overlap must be con-
sidered. Gutowsky and Holm (5), who originally applied
this method to the study of energy barriers in DMF and DMA,
at a Spectrometer frequency of 17.755 Mhz, suggested that
going to higher Spectrometer frequencies would reduce the
overlap error. The temperature range accessible by this
method is unusually small because in the region of Slow
exchange the peak separation changes only very slowly as
the rate of rotation changes while in the region near the
coalescence point the errors in the measurement are large.
Woodbrey (50) has discussed the dependence of the peak separa-
tion on rate of exchange. The peak-separation method is the
easiest but the least effective one to use in practice.

The disadvantages of these first two methods and their
range of effectiveness have been discussed by Fryer gt_:__a_]_..
(14). They develOped a system for combining several tech—
niques, using data points obtained by each only in the

temperature range where that method gives best results'..

165

In this way they obtained plots of rate constant Xi
temperature covering a wide range of temperature with

reasonable precision.

Method III--Total Line—Shape Analysis

The only generally satisfactory method for extracting
kinetic results from NMR data is to compare the actual
line shape observed with Spectra calculated using various
combinations of the NMR parameters. To obtain the best
values of these parameters some curve fitting procedure is
required and the digital computer is the only rapid way to
achieve this. It has been shown in this work that, for
exchange between two sites, the parameters required are:
(1) the chemical shift FR in the absence of exchange, which
may itself depend on temperature; (2) the relative pOpula-
tions of protons at sites A and B, pA and p3; (5) the in-
dividual line widths in the absence of exchange 1/T2A and
1/T2B; and (4) the rate constant for the exchange process
1/21.

The chemical Shift in the absence of exchange FR has
been assumed constant over the entire temperature range
employed in most previous studies. However, it has been
recently shown (25) that it often does change with tempera-
ture. It should, therefore, be introduced into the line—
Shape analysis as an adjustable parameter to be determined
at each temperature. The curve fitting procedure used in

this work has provided the values of FR shown in the final

164

column of each of the above tables. It is seen that they
tend to decrease with increasing temperature until about
the coalescence temperature when this trend seems to stOp
and even reverSe. At low temperatures the amides are highly
associated (69) and these changes in FR must result partly
from the changes in degree of association with temperature.
The pOpulation factors PA’ pB should be exactly 0.5
for symmetrically substituted amides but the computer may
select a slightly different value Since the eXperimental lines
are not always completely symmetrical. For the unsymmetrical
amides pA may take values other than 0.5, but should approach
0.5 with increase in temperature. In practice this factor
changes only slightly with temperature and Gutowsky was able
to use the constant value of pA = 0.54 over the entire
temperature range covered in his investigation of N-methyl-N-
benzylformamide (25) without introducing appreciable error
into the rate constants. In this work the program NMRFIT
provides values of pA} pB at each temperature.
The line widths 1/‘1‘2A and 1/‘I‘2B should be equal for
the symmetrically substituted amides and at low temperatures
should be about equal to the line width for the reference.
AS the temperature increases and exchange broadening becomes
important the "natural" line widths become relatively unim-
portant and the computer tends to select very small values
for these parameters. These values have no particular sig-

nificance and the rate constants are not appreciably altered

165

if these values are fixed throughout at the values they
have in the absence of exchange.
Errors in the Measurement of
Rotational Barriers

Values reported for the rotational barriers in a given
amide have varied widely. Thus for N,N—dimethylformamide
values from 7 to 28.2 kcal/mole have been reported (Table 1),
with frequency factors ranging from 103 to 1017. Wbodbrey
investigated in detail the random errors in these parameters
as determined by NMR and showed that the 90% confidence
limits for values of Ba were usually within.i 1 kcal/mole
of the reported values. The large deviations from one
laboratory to another, and even within the same laboratory
when measurements are made under different conditions (Table
2), must come from important systematic errors.

Fryer, Conti and Franconi (14) attempted to determine
the reasons for great Variations observed. They considered
particularly the effects of field inhomogeneities and
gradients (which lead to non-Lorentzian line Shapes) and
the systematic errors associated with the methods for
analyzing NMR data. In this work we have considered the
possible effects of impurities, of dissolved oxygen, of the
standard used (external or internal) and of the number of
data points taken and the temperature range covered. The
results for a study of N,N-dimethylcarbamolychloride are

Shown in Table 44. In each case the field has been Optimized

166

at each temperature, using the 100 MHz instrument, and the
total line-shape method for analyzing the data has been used.

It is seen at once that impurities lower the rotational
barrier markedly. Even with purified samples the line
broadening from dissolved (paramagnetic) air may be signifi-
cant as Shown by the fact that a sample saturated with oxygen
gas gave a much lower barrier (17.7 kcal/mole) than that
obtained under Optimum conditions (21.4 kcal/mole).

The use of an external reference appears to lead to
systematic errors which produce values of the rotational
barrier which are too high. Since Spinning sidebands become
more significant with the arrangement used for external
referencing the intensity distribution is altered and this
result is not unreasonable. The most reliable values for
DMCC appear to be Ea = 21.4 kcal/mole and log A = 16.1 ob-
tained with internal TMS reference. It may similarly be
noted that the use of external HMDS reference for DMA gave
a value of Ea larger by 4.5 kcal/mole than that obtained
with internal TMS. The lower value is preferred in each
case since the best values reported from other laboratories
for DMCC and DMA are 16.9 and 20.6, reSpectively (Table 1).

Although the values reported here for the rotational
barriers in the N,N-dimethylamides agree fairly well with
the most recent numbers from the literature and differences
are still well beyond the rather small statistical errors

(about 0.0.5 kcal/mole) computed by probability theory in

167

the usual manner. The conclusion must be that all the im-
portant factors determining these values have not been
isolated and fully taken into account yet. The present
values (Tables 45, 44, and 45) represent the results of
reducing all the known systematic errors to a minimum.

One possible source of the differences between the
present results and those reported in the literature is the un-
known effect of the internal reference material which must
be used in our work to provide a stable lock Signal.

A rather large amount of reference (0.2-0.5 mole fraction)
must be used and a solvent effect on the barrier is quite
possible. Use of an external reference gives less reliable
results because of Spinning problems. Use of an external
lock requires (in our laboratory) going to a Spectrometer
frequency of 60 MHz where the chemical Shift is smaller
and the errors correSpondingly larger. For this reason we
have no completely reliable data on the amides with which
to compare our internally referenced samples. Most other
authors have used internal TMS in unsPecified amount so
similar observations hold. The Spin-echo measurements are,
however, made with pure materials as are all our externally
referenced measurements.

It has frequently been noted by investigators in this

¢ . o 0
obtained in various labora-

field (16) that values of AF
tories tend to agree quite well; the disagreement is in the

values of Ba and log A. For this reason we should

168

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171

particularly stress the interpretation of the AFi values
when discussing substituent effects. Our values of AF:
almost always agree.i 0.2 kcal/mole with the best litera-
ture values.

The values of Ea obtained by the computerized versions
of the peak-separation method and the intensity-ratio
method are included in the tables of data for the various
‘compounds. These values are consistently lower than those
obtained by total line-shape analysis. Since they are less
reliable than the latter they will not be used in the dis-
cussion.

Rotational Barriers in Symmetrically
Substituted Amides

The energy barriers for internal rotation about the C-N
bond in the disubstituted amides are much higher than those
for internal rotations in ethane, amines, alcohols and
ketones, all of which have values about 5 kcal/mole (57).
The extra height of the barrier for internal rotation about
the C-N bond in amides is believed to result from large
partial double bond character in the C-N bond. There is a

variety of evidence that

I .
§ /R .p‘\ N+/ R.
/

/ ..
R \ R.. R \ R

II III

172

structures 1' and II' contribute about equally to the
resonance hybrid (97,99). However, there has not been
enough data of sufficient reliability to evaluate the effect
of substituents R, R', R" on the rotational barrier deSpite
the many articles which have appeared on the subject (see
HISTORICAL BACKGROUND). -Since the substituent effects
should lead to a better understanding of the origin of the
barrier an attempt has been made to obtain more precise
values for a series of N,N-dimethylamides. The results
are summarized in Table 1.

The value obtained here for the rotational barrier in
DMF (24.2 kcal/mole) is close to the mean of the best two
values available in the literature and there now appears to
be reasonable agreement that this value is in the range
24.: 2 kcal/mole. The higher value (27.4 kcal/mole) ob-
tained with DMF-d1 and internal TMS may reflect the diffi-
culty of using this standard for the measurements at higher
temperature since it is volatile and boils out of the solu-
tion causing the internal-lock signal to be erratic; the
higher value is, therefore, considered less reliable. Any
isotOpe effect should be small and less than the uncertain—
ties in our values for the barriers. The value for DMF-d1
will be free of any error from overlap effects but the DMF
result has been corrected for overlap so any residual error
from this source should be small. A careful Spin-echo

study of DMF-d1 has yielded a value Ea = 22 kcal/mole (95)

173

and the less reliable study of Franconi §£_§l, (14), made
by a combination of approximate methods, a value Ea = 27.4
kcal/mole.

The value of 22.6 kcal/mole found here for the rota-
tional barrier in N,N-dimethylacetamide is close to the
best value in the literature, 25.0 kcal/mole. Neuman and
Jonas (17) have reported 19.6 kcal/mole for DMA-d3 but this
difference may represent a true isotOpe effect, at least in
part. They suggest that the decreased electronegativity
and hyperconjugation plus the smaller effective size of CD3
relative to CH3 could lead to a decrease in AFt in the
deuterated compound. However, our best value for AF* (18.2)
in DMA is identical with theirstthMA-ds so no isotOpe effect
on AFt has been established.

Three factors may be of particular importance in deter—
mining the size of the rotational barriers. (1) Increasing
steric size of the substituent group might be eXpected to
lower the barrier as a result of relief of steric strain in
proceeding from the planar ground state to the rotational
transition state in symmetrically substituted amides.

(2) Increasing resonance donation of charge (by hyperconju-
gation in this case) should also lower the barrier since
cross—conjugation would tend to compete with the principal
resonance which provides the large partial double-bond

character. Thus, contributions of structures such as III

would reduce the partial double—bond character of the

174

central C-N bond and so the barrier. (3) Increasing in-

ductive donation of charge from the group X will tend to

favor form II and reduce the barrier. Neuman and Jonas (17)
have shown that these ideas are in semi-quantitative agree-
ment with experiment by correlating AFtwith the substituent
constants 6* and ES which measure polar effect and combined

steric size and resonance effect, reSpectively.

* in different

Finally, in comparing values of Ea or AF
compounds possible solvent effects must be borne in mind.
Even in going from one pure amide to another differences in
size and shape of the molecules, and in dielectric constants
of the liquids, may alter rotational energy barriers.
Further effects from internal reference materials used in
the NMR studies are probable.

A significant decrease is observed in both AF¢ and Ea

* = 21.0, Ea = 24.2) to DMA (AF: =

on going from DMF (AF
18.2, Ea = 22.6). Substitution of hydrogen by methyl will
both increase the size of the grOUp and its ability to
donate electrons inductively and both these factors should
lower the rotational barrier. Hyperconjugation may also

be significant through the contribution of additional

structures of type IIILwhich also would reduce the barrier.

175

/ c —— N\
HE/C H+ CH3
III'

A further decrease in Ea and AF: is observed in going
from DMA to N,N-dimethylprOpionamide and can be attributed
to both the increase in steric size of the group and in the
inductive donation of charge when the methyl group is re-
placed by ethyl group.

It was suggested by Rogers and Woodbrey (4) that sub-
stituents in which cross conjugation with carbonyl oxygen
would be important should lead to decreased double-bond
character in the central C—N bond and lower barriers. The re-
sults for N,N-dimethylacrylamide (Ea = 17.8, AF: ='16.7) and

* = 17.1) bear

N,N-dimethylcarbamoylchloride (Ea = 21.4, AF

out this hypothesis,although the effects are not large.
In the case of N,N-dimethyltrichloroacetamide the

rotational barrier (Ea = 22.1 kcal/mole) is very close to

* is 5.2 kcal/mole lower. The trichloromethyl

DMA but AF
group is much more polar than methyl which would tend to
increase the barrier but the larger size should Oppose this
and evidently is the more important factor since a net de-
crease is Observed.

The limited data available on substituent effects in
N,N-dimethylamides indicates that the polar effect of the

group is Of relatively small importance since even the most

polar groups (CF3, CC13) lead to rotational barriers not

176

greatly different from DMA. Steric effects appear to be
more important since all the compounds studied have lower
rotational barriers than DMF. Resonance effects are per-
haps most important since a substantial dr0p in the
barrier occurs when groups capable of conjugating with
the carbonyl group are introduced (¢, CH2=CH-, Cl). Much
more research will be required to evaluate the influence
of each of these factors.

The rotational energy barriers for DMF and DMA in
trifluoroacetic acid solution, where the principal Species
are eXpected to be DMF-H+ and DMA-H+, have been measured.
The values for DMF-H+ (AF* = 18.5, Ea = 16.8) are surpris-
ingly low since previous investigators have reported much
higher values for DMF-H+. One might expect a higher barrier

than in DMF itself since protonation on the oxygen atom

\ — +/CH3 O\ _ +/CH3
/c — N /c — N\
\CH3 R CH3

IV . I

occurs and the contribution of resonance structure IV should
be more important for the cation, where there is no separa-.
tion of charge, than the correSponding structure (I) would
be for DMF where there is a large separation of charge. It

may be noted that although their absolute values are higher

than ours,Conti and von Philipsborn (18) did observe a

decrease of 5.4 kcal/mole in Ea and Of 2 kcal/mole in AF*

177

on going from DMF-d to DMF-d-H+. It may be that steric
strain is greater in the protonated Species thus destabi—
lizing the ground state and lowering the rotational
barrier. The eXpected increase in barrier on protonation
does occur with DMA, however. Here Ea(24.5 kcal/mole) has
increased 1.9 kcal/mole going from DMA to DMA-H+ although
AP* has decreased by 2.5 kcal/mole. It was not possible
to make precise measurements of the cations in 100% sul-
furic acid because of the high viscosity; Franconi and
Fraenkel (10) reported such measurements for DMF-H+ but
found that exchange protolysis was the dominant process
with DMA.
Solvent Effects on Rotational Barriers
in Amides

The effect of added solvent on the rotational barrier
in DMF has been investigated by studying solutions of DMF-d1
in S-tetrachloroethane andiJIt—butylbenzene. Choosing
Ea = 24.2 as the best value for the barrier in DME,and
neglecting any deuterium isotOpe,effect,the rotational
barrier is lowered by 2.6 kcal/mole in going from the pure
material (containing, however, t—butylbenzene as an internal
reference) to a solution with about 0.4 mole fraction S-
C2H2Cl4. Since the dielectric constant of S-tetrachloro-
ethane ( 8.2) is considerably lower than that of pure DMF
(57.8 at 25°C) the polar ground state of the amide molecule

should be destabilized relative to the less polar transition

178

state and the barrier lowered as is observed. Similarly,
going from DMF containing only enough t-butylbenzene to
maintain a lock signal to DMF containing about 40 mole
percent solvent has lowered the barrier from 24.2 to 21.6
kcal/mole. Neuman g£_§;, (16), however, found a slight
increase for the rotational barrier for DMCC on dilution in
carbon tetrachloride (but a decrease in AF: of 0.5 kcal/
mole). Our results indicate that both Ea and AF: are lowered
on dilution in a solvent of dielectric constant lower than
that of the pure amide.

It should be noted that any solvent (other than an
amide solvent) will tend to break up the structure believed
to be present in these liquids. The structure arises from
two factors--hydrogen bonding between two or more COplanar
amide molecules and van der Waals forces between the planar
molecules which tend to stack with their planes parallel.
Both these factors will tend to increase the energy necessary
for rotation of the -N(CH3)2 group. There will be a tendency
then for solvent molecules of other types to lower the
rotational barriers by breaking up this structure.

If the hypothesis is correct that solvents of higher
dielectric constant stabilize the ground state more than
the excited state, then solvents Of dielectric constant
higher than the pure amides should increase the barrier.
This appears to be true since Neuman and Young (12) report

a value of Ea = 26.5 kcal/mole for a 10 mole percent solution

179

Of DMF in formamide and a value of Ea = 24.7 for a 10 mole
percent solution of DMA in formamide and the dielectric
constant Of formamide (e = 109.5 at 25°C) is higher than
that of DMF (8 = 57.8) or DMA (8 = 57.9). Neuman and
Jonas (17) also find that the value Of Ea for DMA is
1 kcal/mole higher in 9.5 mole percent dimethylsulfoxide
(e = 48.9) than for the pure liquid. Unfortunately, no
other data for solvent effects on rotational barriers have!
been reported using total line—shape analysis and the
precision of the Older work is in doubt.
Rotational Barriers in Unsymmetrically
N,N-Disubstituted‘Amides

A number of older measurements made by the peak separa-
tion method (Table 5) have been reported for unsymmetrically
N,N-disubstituted amides. However, these are subject to
considerable uncertainty and the only reliable values,
derived from total line-shape analyses, are those for the
barriers in N-methyl-N-benzylformamide (25) and N-acetyl-N-
methyl-2,4,6—trinitroaniline (24). In this investigation
N-methyl—N-benzylformamide was studied to permit comparison
with the work of GutowskyIand rotational barriers for four
N-methyl-N-alkylamides not previously studied have been
Obtained by the total line~shape analysis method.

In the case of N-methyl-N—benzylformamide the formyl
proton is a doublet which coalesces at higher temperatures

and the methylene protons of the benzyl group are a chemically

180

shifted doublet which also coalesces on heating so both
can be used to evaluate rotational energy barriers. The
values so derived, Ea = 25.2 kcal/mole from benzyl protons
and Ea = 22.9 kcal/mole from formyl protons, may be com-
pared with the values Ea = 25.0 kcal/mole (benzyl) and

Ea = 22.7 kcal/mole (formyl) obtained by Gutowsky §t_§l,
(25). The agreement is good and, in the case of the AF:
values, is excellent. They also determined Ea by a direct
equilibration method and obtained a value of 20.1 5 kcal/
mole. Our values agree better with each other than do
those Of Gutowsky perhaps because we corrected for Spin
coupling between the formyl and benzyl protons. This was
done by estimating the gig and trans couplings and super-
posing two doublets separated by (J; + J2)/2. Although
the fine structure is not resolved the line broadening from
the Spin-coupling will introduce errors into the rate con-
stants unless corrected for. The corrections are small
(see Table 41).

In the series of substituted acetamides studied here

(VSVIII) the rotational energy barriers are, reSpectively,

CH3 \\CH2CH3 CH3 CH2CH2CH2CH3 CH3 CH 2\CH2
CH
v VI VII {CH2— \CH2

0% ”H3

— N
CH; \CH’CH3

H3
VIII

181

22.9 kcal/mole, 24.2 kcal/mole, 26.2 kcal/mole and 26.8
kcal/mole. This order roughly follows the order of in-
creasing Size of the groups. The steric substituent con-

stants E (98) for CgHs, 27C4H9, QfCBHll and ifC3H7 are,

S
reSpectively, -0.07, -0.59, -0.79 and -0.47, with cyclohexyl
out of line. However, if the values of AF¢ are compared
then the order is exactly that that of the ES constants
(AF: = 17.7, 17.6, 17.1 and 17.0 for V-VIII, reSpectively).
However, the barriers would not be expected to increase with
increasing size of substituent, but rather to decrease
because the steric strain would be relieved in the rotational
transition state. It therefore appears that the increasing
electron donating powers of the groups must be the dominant
effect. The 6* constants for C2H5, n-C4H9, ngBHll and
i-C3H7 are -0.100, -0.150, -0.150 and -0.190, reSpectively.
Electron donating substituents on nitrogen could increase
the rotational barrier by stabilizing the polar structures
Of type II which are reSponSible for the partial double-bond
character of the central C-N bond. A more electronegative
substituent such as 2,4,6-trinitrophenyl Should then lower
the value of Ea and Weil g£_gl. (24) report Ea = 19.7 kcal/
mole for N-methyl-N-acetyl-2,4,6-trinitroaniline.

The Spectra of N-methyl-N-n-butyltrimethylacetamide,
N-methy1-N-d-naphthylacetamide, and N-methyl-N-phenylacetamide

were also studied, but only one N-methyl resonance peak

182

was observed for each amide. It could be that: (1) the
rate Of rotation about the central C-N bond is very fast
(1/Tc:2W(VA - VB)) and only an average of the two N-methyl
resonance peaks is observed, (2) the two N-methyl resonance
peaks have the same chemical shift, or (5) only one isomer
is present. The first possibility is not likely, because
all three amides have been studied in the temperature.range
of -200C to 650C, and there is no evidence for two rota-
tional isomers, The second possibility is also improbable,
because all the other disubstituted amides did give two
distinctive N-methyl resonance peaks, SO the chance for
these three amides to all accidentally have equal chemical
shifts for gig and trans methyl groups is very small. The
explanation for the observed single N-methyl resonance peak
then must be that there is one dominant isomer, and the
steric effects of the bulky substituent group slow. the
internal rotation about the central C-N bond in these amides.
These amides may not be planar in the ground state as a
result Of steric interactions.

An inSpection Of the tables containing the activation
parameters obtained from different methods indicates that
the values of energy barriers and of log A have tended to
increase when increasing care has been taken in conducting
the experiments and in analyzing the eXperimental Spectra.
In several cases, the frequency factors are larger than the

usually accepted value for unimolecular reactions,

185

6 x 31.0123ec‘1 at 5000K. However, this is not unexpected.
From transition state theory the discrepancy reflects an
entrOpy increase in going from the normal amide to the

I observed may

transition state. The large values of AS
be rationalized in the following way. »Amide molecules

are known to be approximately planar, hence in the ground
state the resonance structure II is favored. The transi—
tion state for the internal rotation process is non-planar,
and its electronic structure will be better represented

by structure I. In the ground state an amide molecule

tends to dimerize with another amide molecule to form a

rigid configuration such as X.

R R
\--.. /

Néfl

/// \\

R \ 5-
\6- 0

Comparing the configuration of the more polar ground state
with the less polar activated state it can be seen that in
the activated state the amide molecule has less constraint,
or more degrees of freedom than in ground state, conse-
quently a positive activation entrOpy is expected in going
from ground state to the activated state. There may even

. . . . . . t
be an additional pOSitive contribution to AS because of

184

desolvation, since it Should be more difficult to solvate
the non-planar transition state. The high values Of the
frequency factorsfor internal rotation about the central

C-N bond in amide molecules are thus reasonable.

SUMMARY

(1) Two approximate methods, the intensity-ratio and
peak-separation methods for determining rate constants
from NMR data,have been evaluated and shown to lead to
systematically low values for rotational energy barriers in
amides.

(2) A total line-shape analysis method has been develOped
for obtaining rate constants from NMR data over a wide
temperature range. It fits the exPerimental curve to a
"best" set of NMR parameters by a least-squares method and
performs all computations and curve plotting using the CDC-
5600 computer.

(5) A study has been made of the effects of such
factors as sample purity, dissolved oxygen and method of NMR
referencing on the rotational barrier of N,N-dimethyl-
carbamoylchloride.

(4) The barriers hindering internal rotation in a series
of substituted N,N-dimethylamides have been obtained by the
total line-Shape analysis method and compared with previous
values. (Substituent effects have been discussed.

(5) The effect of solvents on the rotational barrier in

N-N-dimethylformamide has been studied.

185

186

(6) The barriers hindering rotation in a series of
unsymmetrically N,N-disubstituted amides have been
determined by the NMR method and the factors affecting the

rotational barriers discussed.

B IBLIOGRAPHY

10.

11.

12.

15.

14.

15.

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192
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31, 585 (1957).

 

APPENDICES

 

APPENDIX I
NMRF IT

Description of variables:

P(1) is the T value or the inverse of twice the rate constant.

P(2) is the pOpulation fraction of the lower field component
of the doublet.

P(5) is the position Of the center Of the doublet.

P(4) is the peak separation Of the doublet in the absence
of exchange.

P(5) is the half width at half height of the lower field
component in the absence of exchange.

P(6) is the half width at half height of the higher field
component in the absence of exchange.

. N is the number of experimental points.

COMPOUND identifies the Spectrum.

X(I) is the experimental frequency reading.

Y(4,I) is the eXperimental intensity at X(I).

Y(5,I) is the calculated intensity at X(I).

Y(6,I) is Y(4,I)-Y(5,I), at X(I).

Y(5,I) is the calculated intensity of the first doublet.

Y(2,I) is the calculated intensity of the second doublet,

which is to be superimposed onto the first doublet.

B is the intensity adjustment constant.

C(I), I=1 to 6, are the initial adjustment increments.

TR is the number of times the program passed through a
given point in SIZE.

TRY is the desired number of trials.

195

194

Flow Chart for
NMRFIT

 

 

[Read N,00NPOUND P(5)

 

 

Read estimated
P(I)$I=l929495,69
I

 

 

 

[Print N,CONPOUND ‘)

I

Print P(I)'s

'END 'yes ‘{fllE’E»

I 0
Read X(I), I

 

 

 

 

 

 

 

 

[
71(461)

 

 

 

Define starting 8
adjustment increments

 

 

 

 

 

[Cali ADJ‘ I

 

 

 

 

 

Print Y(4,I),X(I),
1(8,I);I=l,...N

 

1
[Print P(1) I

END

195

Flow Chart of ADJ’

TRIAL=0.0 _
T=large number ’
_V=1 + C(K) -

 

 

E
[Call SIZEI

 

T0=Old sum Of Sq.
T=sum Of Sq. from SIZE
TRIAL=TRIALS + l

  

 

 

[P(K)=P(K)+v

 

 

 

 

IEhange Sign and»
ladjust C(K)
I

 

 

 

 

 

lReadjust C(K) i

Print SO,TR.TRIALS
J,K,P(K).C(K),B

. I 5
he turn I

 

 

 

 

 

 

* Ref.80

196

 

 

I Define V I
_ J :'

 

 

 

to calculate

1
Use lineshape eq.
Y(5,I)'s

 

I
Displace P(5) 1
Iby (J1+J2)/2I
I

 

[Use lineshape eq.
tO calculate Y(2,I)‘s

Y(3.I)=B~x (Y(5,I)+Y(2,I))’-

 

2:;(Y(4.I)*Y(3,I))2=so‘

 

 

- Define TR 7
and functions 0
governing A,B

 

 

 

—h

[Adjust Y(5,I) by-
A factor

 

 

 

I 2:£(Y(4,I)-Y(5,I))2=SQ I

 

   
     

 

Change Sign
and reduce V

 

 

 

 

Return tO ADJ

 

 

 

 

 

 

(W (3 l3 (3 (3 (3

m

22

q
C.

11

15

197

DQOGQAV NwR FIT

COMMON X. Y9 P. Co 90 C09 TQYqo_N9 K0 Jo L9 TD. R09 TA. TR
DINFNGION X(ZOO).Y(6.1PO)~R(6).¢(6).R(1).OO(6)

THIS RROCRAM IS TO FIT Tr? FXDFCIVHNTAL OOU=LVT OF DTSURRTITUTFO
AMIDE OR ANY Two SITF EXCHANGE RROOLAm

x IS THE FREOOEHCY IN CYCLES AND Y Is IN RELATIVE INTRNSITY
P(1) IS THE TAO 0(2) 19 THE RFLATIVS PODULATICN DF'THE Two SITES
9(3) IS THE CENTER OF TH? Two RsAKs R(4) P(5) R(6) ARR THE

PEAK SER .HALF CD THE LIMOwIOTHER AT THE ABSENCF OF EXCHANGF
FORMAT (I30A891E1000)

READ 1.N.CCMPOOMO.R(3)

FOQMAT (5E10.0)

READ 3. R(1).D(2).R(a).R(6).R(6)

R(a)=R(4)*6.2R32*1.025

FOQMAT (*IQATA CF CRSCTRUN *nn)

RRINT 4.COTDOUMO

FORMAT (6F)O.3)

PDIJT 5.9(1).D(2).R(3).R(a).R(s).R(é)

FCQNAT(/* PK N0 CCN‘T “3 CON§T “DJ INT
50 TR TRIALS*/)
RRINT 22

IF (NoLEoO) 63 T0 15

DO 110 (zloNofi

FCQMAT (8F1003)

READ 29X(I)vY(491)9X(I+1)0Y(401+1)0X(I+2)oV(4oI+2)oX(I+3)oY(aq1+3)
CONTlqu

$0 = 1.0

TQY9 = 25.0

on.“
90:0.4
C(1)=0o2 $ C(Z)=\.OO: 5 C(3)=c,og
C(4)33002 $ C(G):O.CE $ C(6):0.0?

DO 14 NB=1013

DO 14 K=196

CALL ADJ
CONTINUE

FOQMAT (* X C!
DRINT 7c

FOQMAT (IFIOCIOQFIdOC)

03 339 I=1.”

DQINT 80 X(I)'V(79!)0Y(4~I)9V(691)
CONTINUF

FOQW0T(///*LUGTAU=*9 Flno3)

A=ALCG C(D(1))

PQINT 690

GO TO 10

C CWT 151;):

E‘JD

(“J

S Y CAL Y OQS Y DIP: *)

198

SUPQOUTINE ADJ

COMMON X0 Y9 F3, Co no COO TQYQQ N0 (<0 J! Lo TR. "109 TAO TR
DIP/)ENSION X(203)0Y(69103)9?(F))o“(€))9F‘(1)QRC(6)
TOTALQ = 000

T = QUQQQO.Q

V=l.O+C(‘<)

DO 8 N1 = 102

CONTINUE

CALL SIZE

T0 = T

T = SO

TRIALS = TQIALS + 100

IF (TRIALS - TRYS) 5.0.0

CONTINUE

IF (T - TC)6o-'o7

CONTINUE

D(K)=:’(K)*V

GO TO 3

CONTINUE

C(K) =-C(K)

V=l.O + C(K)

p(K)=D(K)*V

CONTINUE

CONTINU‘:

C(K)=C(K)*TDI:‘~LS/IC.C

FOQVAT (I69I1004X04F120402F600)

pQINT loJo".0p(<)9C(K)090900TQ0TQIAL§

RETURN

END

SUBQOUTINE SIZE

COM‘-ION X9 Y9 P, C. 89 SO. TPYSQ Na K. J. Lo TR. .,Co TAO TF3
DI‘JENSION X(ZOQ)9Y(60100,op(6)oC(6)CDXI)075C193)

5:000

V=OoO.25*(L5-BO /f~BS-F(T?-PC)
80:8

CONTINuE

DO 11 I = loN

D=X( I )-D(3)

Q=Q*60?9?2*10O2m

TP=10/(D(6)*éo2’7")?*1oh2:)

TA=lc/(p(5)*(5025332*10n?:)
PP:P(1)*(1./(T/\-x-T;-‘2)—.'?%f3+(£3(q)/:?.)¥D(4)/2.)+(1.—D(2))/Trx+p(p)/TA
C:P(1)*(fQ-p(4)-}(L‘(2)%2.-1.)/?_,)
RQ:Q%(I.+P(I)‘((1./T.1+1./T7.’))+p(1)if-D(4)¥r(I./T7-‘s-—1./TA)/2.+
1p(4)*(p(2)*20*10)/?o

Y(5OI ):(ppfi-(1.+D(1)-X-D(?)/Tr~3+-f3(1)-K'(1.—p(2))/T;’.\)+
lC-X-QR)/(PI-“T~";3F3+ixé-f-X'l‘rQ)

J1=~’)o7 $J2:Q.’3

199

DS=X(I)‘(D(3)+(JI+J?)/29)
QS=Q§*602832*19095
PT=D(I)*(Io/(TA*TR)-Qg*pc+((p(4j‘JI+J2)/?o)*((p(4)'JI+J2)/?9))+
1(Io-p(?))/TQ+D(2)/TA
0029(1)*(QS-(p(4)-JI+J?)¥(p(2)¥?o-I9)/29)
QT:QS*(1.+D(I)*(1./TA+Io/TC))+D(I)*(D(4)’JI+J2)*(Io/TQ-I./TA)/
129+(p(4)’JI+J2)*(D(?)*29-I9)/?o
Y(29I)=(pT*(Io+p(I)*p(2)/Tfi+p(I)*(Io*p(2))/TA)+
IOO*RT)/(pT*pT+QT*QT)
Y(39I)=B*(Y(59I)+Y(29I))
Y(69I)=Y(49I)‘Y(39I)
SO=Y(69I)*Y(69I)
§=S+SQ
J=2
11 CONTINUE
GO TO 4
4 CONTINUE
TQ=093
DO 8 N2 = I94
A = 190 + V
5 CONTINUE
839*A
SD = S
S = 090
TQ=TQFIOO
DO 6 I = I9N
Y(39I)=Y(39I)*A
Y(69I)=Y(49I)-Y(79I)
§O=Y(69I)**?
S = S + $0
6 CONTINUE
IF (5 - SO) 59797
7 CONTINUE
=-V*0025
8 CONTINUE;~
pETURN
END
'QUN9IC9IOCCC9I

APPENDIX II

NMRPLOT

The purpose of this program is to calculate and plot
out the Spectrum from a given set of line—shape parameters
correSponding to those from the program NMRFIT which best
fit the experimental Spectrum. The program can plot out
Spectra on the same scale as those obtained eXperimentally,
so the calculated and observed Spectra can be compared by

superimposing one on the other.

Description of symbols:

KAPPA identifies the Spectrum.

KSCALE is the scale factor. If it is 1, the plot has a
50 cycle/sec sweep width, and if it is 2 a 100 cycle/
sec sweep width.

YY is the highest intensity, in centimeters, of the experi-
mental Spectrum. This will set the upper limit of the
calculated Spectrum.

RECORD is the compound name.

TAU is the inverse of twice of the rate constant.

PA is the fractional pOpulation for the low field peak.

R and S are the half width at half half height of the two
doublet peaks in the absence of exchange.

FR is the peak separation of the doublet in the absence of
exchange.

CEN is the Center position of the doublet.

TOTAL is the calculated intensity.

Notes:

1) In order to produce the Spectrum which best fits the experi-
mental one the line shape parameters Should be taken from
the output of NMRFIT.

2) Before the plotter starts, the pen is at the right hand
side of the paper.

200

5)

4)

5)

201

The statement CALL PLOT (200,x,5) requests the total
number of inches desired for all the Spectra to be
plotted. In this case, the request is 200 inches.

If more than one Spectrum is desired, the data cards for
the additional Spectra should be provided in the same
order as given in the comment statements at the beginning
of the program.

The program will correct the frequency readings by a
calibration factor, such as 1.025 in the statements 555
and 5. This quantity means that 1 cycle/sec. is equal
to 1.025 cm. This factor is dependent on the instrument.

202

Flow Chart for NVRPLOT

IIIRead J,KAAPA I” '
_ I 1 f

I Request total NO.I
Of inchs Of plot 1

I

I Read PA R,S,FR,TAU I

 

 

 

--—_.

YY,N,RECORD,CEN

 

 

 

Print out input CI ”1'

Read and )
_ convert X(I B
yes to rad./sec.

 

 

 

n0

 

Convert input tO
rad./sec.

 

 

 

 

[______I Call INTEN ,]

 

 

 

Calculate
intensity at
corresponiing
frequency

 

 

 

 

 

I BIC=IOIAL(1)

 

 

 

 

 

- !
I BIG-TOTAH I) I— < o—fI BIG=TOTAL(I) I
_ , I w ,

30

-——-no—————-I I=KRANGE

 

 

 

 

yes

 

.. _ A __--..»...._

205

 

  

 

 

SX=1./(O.254x0.6285)~ . sx=1./(O.508xo.6285) -

 

 

 

 

 

 

Plot X,Y A
scale
Plot calculated
spectrum

, )I ’77 I
IPlot $EI3, I B

 

 

 

 

 

 

 

L——-no

.A <$—————-no

 

yes

 

END

(300000

0000000

('7

()

204

DDCGDIV NHQDLOT
DlerSICN TOTAL(RCOC)9KADDA(10)9XC(1Cn,,VIInn).Y(Inn).PrN(I)
.CMVCN TOTAL .
IF J IS III EXPT DTS WILL BE INCLUDFO
IF J IS 7CRO .I:T DATA CAQO us mLAN<.FXRT RTS NCT READ IN
ST CARD IS J »
2ND CARD ‘5 IJENT‘FICATICN C? SDECTRLV
3R3 1 FOR so CYCLE stFRT RIDTR.2 FOR 100 CYCLF S.w.
«Th CARD TAU AND YY WHICH IS THE HIGHFST FXRT. DOINT IN CM
R'S'FQ' AS DR’INT/UT FQOM NVPFIT
5TH pA9R939FR WHICH ADE DODULATICN.LIMF WIDTHQ AND pEAK SFD.
AT THE AUSFNCE OF ROTATInN
6TH NUMUFD CF SPECTDAgQECCTDzCPWDD NA”F9DQCITIQN OF CENIEP CF [WHO
PEAKS
7TH X9Y9S ARE THE QFLATIVF FQCQUFNCY AND INTFNsITY I: CFNTVETFD
FOR MORE THAN ONF SRFCTRA. R1REAT THE Aaovs CROPS .

2 FORMAT (4510.0)
4 FORMAT (2510.0)
6 FORMAT (Ions)
8 FOQWAT (II)
32 FORMAT (8310.?)
334 FOQMAT (13)
7:0 FORMAT (/94H PA=EII.5.HX.AH PS=FII.5.=X.
13H R:€12.6.2X.3H F=EIZ.6.2X.1CH RFAK RFR=GII.€)
751 FORMAT (/o‘H TAU=812.6)
READ 334.J
Q QEAC 5. (ADDA

pEAD 89 KSCAL:

pQIVT 69 KAPOA

CALL DLOT (4OO9X93)

CALL pLOT (OOO9OOO9C9IDC.91CQ.)

CALL PLOT (0.00‘2O9929I09991C39)
3 DEAD 49TAU9YY

IF (TAU) 88.9.1
I 9500 29p39FR9Q9S

DQINT 7509 SAoDVBQZPoSoF-‘r‘

IF (JoLE-C) GO TO 333
101 FCQIV'TAT (13.0.8.1?! ..fi)
100 DEAD 1019N9EECCR3oCEN

DO 3I9I=I9N94
PEA? 329X(I)9V(I)9X(I+I)oY(Y+1)o¥(I+2)~Y(I+?).X(I+?).Y(1+3)
xc IS x COORO CflLCUD FUO” RFAOIN x
31 CONTINUE

DO 333. I=1oN
XC(I)=(FR/I.Ogs—(CFN/I.CPS—X(I)))%6.2932

333 CONTINUE
CUR/EQT CYCLES/RFC. TC RADIAws/cgg,

(‘3

21

11

205

:Q:FQ/1002R
Q=Q*602832/10n2m
D=R*5.2932/1.02§
DI’QI‘JT 7510 TAU
pB:].—DA

szA-DB
w=DA*R+PU*S
O:1.+TAU*(D+3)
VW:-FQ

YM=20 *FQ

KQANGE=Yv/O.125

DO 10 I=10KDAWGF

CALL INTFVCTAUOQQSQFQQWQDOCQTCTAL(I)OVVOPAQDW)
VM=VV+00125

PIG=TOTAL(1)

DO 20 1:2 QKQANGF
tF(QIS-TOTAL(I)) 25020920
BIG=TOTAL(!)

CONTINUE

YY=YY*IOOo/205¢

SY=YY/SIC

GO TO (2109?). KQCALF
SX=lo/(OoL;4*0062537)

THIS IS SCALEU TO 1 CYCLF/CM.
GO TO 30

SX=I./(O.?OR*O.GPQ7P)

THXS lg SCALE“ TO 2 CYCL:Q/Cvo
CALL pLCT (0.3,0.fi,0,1§n..1np.)
X=C

DO 11 1:109

X3X+EoO/2054

CALL pLCT (OofloXeloIOO..1“O.)
CALL DLOT (ColoXololcogolCCo)
CALL PLOT (OoOoX~I~100.0100.)
CALL pLOT (00090.5910]CO.0100.)
Y=C

DO 222 121017

Y=Y+1o

CALL pLOT (Y.O..1.10“..1F7.)
CALL pLOT (Y.7010101q00.1000)
CWLL.DLCT (YO000019100091000)
CALL D CT (000.300.101FO.QIOA.)
Vlt'fitco 12?.)

DO 76 IzloKpAHGF

CALL pLOT (TQTAL(I)0VIV0103Y1?X)
VIF“‘=VI"‘+OO 12E.)

CC‘VT I .JUE

CALL pLCT (0.990.0920CV9Q7)

'RUNcIoEQoZIOUoI

l

88
89

CALL
IF

CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL
CALL

pLOT

(JoLE-O)
DO 77

206

(OO‘WOOQ’WQCQIOI’T..CX)
CO TO 333

I=10N
Y(I)=Y(I)/2.SQ

PLOT
PLOT
PLOT
PLOT
PLOT
pLOT
DLOT
PLOT
PLOT
PLOT

CONTINUE

CALL
CALL
CALL

PLOT
pLOT
PLOT

GO TO 3

CALL
END

S'JBQOUT I NE

PLOT

X3FQ/20
PIK:TAM*(Q*S—C*F+X¥x)+w

QIN=TAV*(F-P*X)

QIN==*O+TA”*X*(Q-Q)+D*x

DIQ:DIN¥-DII\3+L{ IN¥TIM
TOTAL=(pIN*(Io+TAV*(PN*P+PA*$))+QIV*QIfl)/D[D

END

(Y(I)QXC(X)OEOIOanqy)
(OOOQOOOOCQIOOQQIOCQ)
(OOOSQOQOQEQIOOOQIPOQ)
(0005900C591)
(-CoOEoOoO5QI)
(-C.050-0005913
(00050-000501)
(00050000.!)
(000000992)
(Y(I)OXC(I)QOQICO.99Y)

(0009000029100.9QX)
(ODO‘CQOOQQIOOQQIOOQ)
(11.500009201000‘1000)
(OOCQOOO"195YQSX,

INTF':N(TAVQQQQOFF-29717990OQTCTALqF'QDAat”?)

TEST DATA FOR AN CNSYAWETQICAL DCUHLCTI

APPENDIX III
NMRTAU

In this program the rate constants for exchange between
the two sites are calculated. The program consists of two
parts. The first part of the calculatiOn is based on-Woodbrey's
intensity-ratio method and the second part of the calculation
is based on Gutowsky's peak-separation method (15). ,No cor-
rection for overlap of the doublet components is included
in this program because the observed line widths are small
in comparison to the peak separation of the doublet. The in-
puts are the observed lineshape parameters, intensities at
two maxima and central minimum, peak separations at each
temperature and in absence of exchange, and the temperatures
at which Spectra were taken. The output is a list of temper-
atures and the correSponding 1/(2 rate constant) or l/T
values and the energy barrier and the frequency factor

obtained by each method.

Description of symbols:

TEM is the experimental temperature in OC.

BIG is the relative intensity of the first maximum.
SMA is the relative intensity of the central minimum.
BIGG is the relative intensity of the second maximum.
SPE is the peak separation at TEM.

FR is the peak separation in the absence of exchange.

207

TAM

TAU

FRE

208

is the inverse of twice of the rate constant from the
peak-separation method.

is the inverse of twice of the rate constant from the
intensity—ratio method.

and EN are the energy barriers in kcal/mole from the
intensity-ratio and peak-separation methods.
reSpectively.

and FE are the logarithms of the frequency factors from
the intensity-ratio and peak-separation methods,
reSpectively.

209
Flow Chart for NMRTAU

 

 

[ Read in N

I

[Read TEMJBIG,

 

 

SMA,BIGG,SPE,
FR

T'—

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

    

 

 

 

Calculate TAU(I) I , ' ,Calculate TAM(I)A
at TEM(I) at TEM(I)
let XEI 3: =1/T°K' "'" ', [let xx(1)=1/T°:K J
-1og TAU(I) »_ YY(I)= log TAI
Calculate Calculate
2x1 ; z XiYi . p 1 xxi {2211111111
'6 3 .1 ' . 2
:Yi ; 2 X5 .. ”.F- ZUfIEXXi
_ ...... N... at.
'68

 

 

Calculate lepe
and intercept_

l

1Print out '
ENG,FRE [ i

 

 

 

 

 

 

 

Calculate slepe
and intercept

Print out I
EN, FE

 

End

(W

('3

10
33

11

210

DDOGDAV NVDTAU

THI§ GIVES ENEQCY AN? FQFGUFNCY.HY INT QATIO ANU D¢A< qu
DIMENSION TAU(ICO).FR(ICO)oRA(lCC)oTNA(1C0).91C(ICC).R!SC(IOO)o
1895(1?3)1TFV(170)0PUVX(:n)QCUWV(:n)quHXV(:C)QQHMX?(TQ)0A(:3)0
?n(fin).CNC(?O).Cpcfufl).T5V(1CC)o=N(1”“)o::(In“).
FSUX(SC).SUY(53)oQUXY(=c).?Ux2(=n).
AX(§3)9Y(“C)o¥X(%C)oYY(=C)

FODMAT(12)
FOQMAT<6EI0.0)

ENG AND FRE ARE FRO“ INT QATIONHETHOD

L IS THE NUWGER CF SDECTQA TC DP CALCULATEH

DO 149 L=lol4

READ IQN

IF(N.LE.O)CO TO 100

DC 1C9 I=1¢N

TEMP IN CETIGQAUCo INTFNSITIES AP? DELATIV? LENCTH
SPE AND FR AR? IN CYCLFS

QEAD 2o TEY(I)97!G(I)0¢Hfi(I).?IGC(I).CDT(I).VP(l)
CONT I [\JUF
FORMAT (IQHBY INT RATIO. //)

Dr"INT 33

DO 11. I=1.N

RA(I)=(dIC(l)+JISG(I))/(2o*SMA(I))
TAU(I)=SCQTF(QA(I)+SSQTF(Q5(I)**2o-QA(!)))/
(3.1416%FD(I)*1o414?) '
FORVAT (*TAU(*I2*)=*~E3.;~‘X~*TEV(*IZ*)=*¢E”o?)
pQINT BQIQTAU(I)010T:7(13

X(I)=1./(TCM(I)+27?.?)

Y(I)=ALOGIC(T1J(!))

CONTIrufi?

LEAQR SQUASH APDLICWTICN

S'JV'X: 0 o

SUMYzo.

SUWXY=Oo

SUMX2=OO

DC 49 I=1¢N

QUMX=QUWX+X(I)

SUVY=GUVY+Y(I)

QUM<VtKMNIXY+X(I)’PV(I)

CWVX2=9UVX2+X(I)**2

FM:N

fl 1% TFE SLOW? EMU 9 TC T”? INTFCTDTIOW
A:(rw*cume-3w'xafwvv)/(rM%fin¥X?—fukxaap)
9=<$UWY*SUVX2-3UWXY*‘UV7)/(FW*°WVXE-SJVY**P)
EMQ(L)=2.3*1o°97*3
FQE(L)=S

FQRNAT (//*EYS(*12*)=%.?IC.7.:¥.*FQF(#IR*I=*oFIC.F.7//)
DRINT 59L.FHG(L)~LQFT’(LJ

H

211

C RY DEAK 9CD WCTHQD
99 FQQVQT (IPHCY PFAK SCP. //)
DQINT 09
DO 139 I=1oV
TAM(I)=1o/(l0314?*3014!Q*TOQTF(FQ(I)**?o-797(I)¥*2o))
Q FORMAT (*TAV(*I?*)=*0510.7.?X.*TCV(*I9*)=*o:1”o‘)

pRINT QQIOTAM(I)QIOTFM(I)
XX(I):lo/(TEV(I)+27302)
YY(I)=ALOG10(TAM(I))

l3 CONTINUE

c LEAST sauna APPLICATION
SUx=00
SUY=OO
suxvza.

CUX2=CQ
DO 60 1:19?“
qUX=QUX+XX(I)
CUY=§9Y+YY(I)
SUXY23UXY+XX(I)*YY(I)
5 SUXZSSUX2+XX(I)**2
FNN=N
C AAIS SLODEQBJ IS INTFCFPT
AA:(FNN*SUXY“;UX*SUY)/(FNN*SUX2~SUX**2)
38=(SQY*SUX2—CQX*SUXY)/(FNN*SUX2-SUX*%2)
EN(L)=203*10937*AA
FE(L)=?B
7 FOR 1AT (//*EN(*I?‘*)=*OF100305X9*F?(*‘I?*’)=*orlf‘o1o///)
pQINT 79Lqu(L)OL9:F(L)
14 CCNTINUF
ICC CONTINUE-
END
.QUNQIQjQfiOOl

 

IIIIIIIIIII