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Willi“ Will _. L

3129 006 343226

 

 

This is to certify that the

dissertation entitled

THE ELECTRONIC AND GEOMETRIC STRUCTURE OF
I. DILITHIOMETHANE, CH2 Li AND

II. VARIOUS SMALL CATIONS 2CONTAINING
SCANDIUM AND CHROMIUM

presented by
Aileen Evelyn Alvarado—Swaisgood
has been accepted towards fulfillment

of the requirements for

Ph 0 D 0 degree in Chemistry

 

 

 

Date 10-31—86

 

MS U is an Affirmative Action/Equal Opportunity Institution 0-12771

RETURNING MATERIALS:
Place in book drop to
remove this checkout from
your record. FINES will
be charged if book is
returned after the date
stamped below.

 
 

MSU

LIBRARIES

 
   

#—

 

THE ELECTRONIC AND GEOMETRIC STRUCTURE OF

I. DILITHIOMETHANE, CH2L1 AND

2!
II. VARIOUS SMALL CATIONS CONTAINING

SCANDIUM AND CHROMIUM
BY

Aileen Evelyn Alvarado—Swaisgood
A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements

for the degree of
DOCTOR OF PHILOSOPHY
Department of Chemistry

g 1986

 

ABSTRACT

THE ELECTRONIC AND GEOMETRIC STRUCTURE OF
I. DILITHIOMETHANE, CH2L12, AND
II. VARIOUS SMALL CATIONS CONTAINING

SCANDIUM AND CHROMIUM
BY

Aileen Evelyn Alvarado—Swaisgood

Dilithiomethane

The electronic structure of the lowest singlet and
triplet states of CH2Li2 has been studied with the goal of
understanding the bonding in this unusual molecule. Pre—
vious work placed the lowest triplet approximately 2 kcal/

mol above the lowest singlet with the calculated dipole mo—

 

ment of the singlet being +5.42 D and that of the triplet

 

being —O.76 D. We have constructed MCSCF functions at the
optimal SCF geometry and predict a similar shift in the di-
pole moment in going from the singlet to the triplet state.
In addition, these MCSCF calculations suggest an orbital
interpretation of the bonding consistent with the dipole
moments. Density difference plots, orbital contours, and a
population analysis of the various MCSCF functions are pre-

sented.

 

Small Cations Containing Scandium and Chromium
The electronic and geometric structure of the Cr

cations CrH+, CrCH3+, CrCH2+, CrCH+, and CrCl+, and of the

Sc cations ScH+, ScCH3+, ScCH2+, ScCH+, and ScH2+ have been

studied by ab initio MCSCF and CI (MCSCF+1+2) techniques.
The resulting bond energies, bond lengths, and electron
distribution suggest: Cr+ forms a single, double, and triple

bond with the ligands CH3, CH2, and CH, respectively, while

Sc+ forms a single, double, and double bond with the same
ligand series; the transition metal—carbon bonds become more
ionic and the bond lengths become shorter as the bond order
increases; the bonding in the low lying states of CrCl+ have

large ionic character due to the charge transfer from Cr to

Cl and the differences between the 52+ and 5n states of

CrCl+ are very subtle; the ground state of ScH2+ has a non—

linear structure and, based on the calculated energetics,

the reductive elimination of H2 from ScH2+ will be endother—

mic. An analysis of the exchange energy loss of the metal

 

ion upon bond formation suggests that there is an intrinsic

 

metal-carbon bond energy for these species given by the sum
of the exchange energy loss and the calculated bond ener—
gies. The calculated bond energies are compared with
available (ion beam) experimental values and a detailed
analysis of the role played by the metal ion 4s and ado
electrons in the bonding, as well as, the varying degrees of

charge transfer is presented.

 

 

 

TO THE "CONSTANT FACTOR IN MY LIFE"——

MY FAMILY

 

 

 

ACKNOWLEDGEMENTS

One may accomplish many mile stones in one's life
but those accomplishments are greatly possible by the love,
support, advice and encouragement of those fine individuals
we come across each day.

I wish to thank Dr. James Harrison for what seemed
like a boundless source of knowledge, guidance and
encouragement during the course of my graduate studies.

Also, I wish to extend my appreciation to the
members of my Guidance Committee (Dr. Schwendeman, Dr.
Allison, Dr. Rick, and Dr. Pinnavaia) for their valuable
suggestions. It is a pleasure to thank Drs. Paul and Kathy
Hunt, and Dr. Frederick Horne for the opportunity they have
given me to come to Michigan State University to pursue a
degree in Theoretical Chemistry.

A special acknowledgement to my family, in
particular to my parents, Hector I. Alvarado Rivera and
Carmen E. Santiago de Alvarado, and my dear husband, Mark,
for the love and moral support throughout the many stages of
my life.

Thanks are extended to Michigan State University
for financial support as a graduate assistant throughout the
course of this research. Finally, I would like to thank the

Department of Urban Affairs (MSU), the Dow Chemical Co., the

iii

 

College of Natural Science (MSU), and the Department of

Chemistry (MSU) for various academic fellowships.

 

 

 

 

TABLE OF CONTENTS

LIST OF TABLES ...................
LIST OF FIGURES ....... ...... ...
KEY TO SYMBOLS AND ABBREVIATIONS .................
CHAPTER I
INTRODUCTION ...............................
CHAPTER II
The Bonding, Dipole Moment, and Charge Distribution
in the Lowest Singlet and Triplet States of Dili-
thiomethane, CH2L12.
INTRODUCTION ...................... .......
A. Bonding of C with L12 ..... . ..............
ELECTRONIC STRUCTURE OF DILITHIOMETHANE, CH2L1

2 O 0
A. Orbital Description and Development

of Wavefunctions ........ ......... ......
B. Computational Details ....................
C. Results and Discussion .... ........ .......
1. Orbital Characterization ............

2. Charge Distribution and
Dipole Moment ... ..... . ............

3. 0n the Role of the Li p Orbitals ....

V

iIIIIIIIIIIIIt::_______________________________

 

ll

ll
16
16
20

28
35

 

 

Page
CONCLUSIONS .......... .. ..... ...... ...... ... ...... 36
REFERENCES ................. . ............ ... ...... 40
CHAPTER III

The Electronic and Geometric Structure of Various

Small Cations Containing Scandium and Chromium.
INTRODUCTION ..................................... 42
BASIS SETS AND MOLECULAR CODES ................ . 45
SIZE CONSISTENCY ................................. 46

NATURE OF THE FRAGMENTS: TRANSITION METAL IONS ... 48

BONDING OF Sc+ AND Cr+ WITH H, CH3, CH AND CH .. 51

 

2’
A. orH+ and CrCH3+ .......................... 56
B. ScH+ and ScCH3+ ...... . ................... 65
Comparison between ScH+ and ScH ........ 77
c CrCH2+ ............ . ...................... 83
D ScCH2+ ................................... 94
E CrCH+ . ...... . ............................ 101
+
F ScCH ................ . . .......... . ...... 108

Comparison between Cr-C and C—C Bonds .. ll4

BONDING or Sc+ WITH H2 . ....... ...... ...... .. ..... 115
Results and Discussion ....... ....... . ....... ll6
BONDING or or+ WITH Cl ............. . ....... . ..... 123

A. Wavefunctions and Computational Details .. 123
B. Energetics and Geometric Structure ....... l26

C. Potential Energy Curves and

Charge Distribution .......... .......... 126
D. Long Range Interactions .. ...... . ......... 135
vi

 

 

CONCLUSIONS: COMPARISON BETWEEN THE

Sc AND Cr COMPOUNDS .................... ... .....
REFERENCES ..... . .................................
APPENDIX A

Electronic Structure Theory: Techniques

INTRODUCTION .............. . .......... . ..... . .....
DEVELOPMENT OF WAVEFUNCTIONS ........ . ............
REFERENCES .......................................
APPENDIX B
Listing of Publications ..... . ......................
vii

 

LIST OF TABLES

 

Table Page
CHAPTER II
1. Comparison of Laidig and Schaefer (LS) Results
with Those of the Current Study ............. l8
2. The Principal Natural Orbitals of the Planar

Singlet and Their Contributions to the Dipole

 

Moment and Population Analysis ..... . ........ 29
3. The Principal Natural Orbitals of the Tetra-

hedral Singlet and Their Contributions to the

Dipole Moment and Population Analysis ....... 30
4. The Principal Natural Orbitals of the Planar

Triplet and Their Contributions to the Dipole

Moment and Population Analysis .............. 31
5. The Principal Natural Orbitals of the Tetra—

hedral Triplet and Their Contributions to the

Dipole Moment and Population Analysis ...... . 32

CHAPTER III

 

1. Experimental Bond Energies for Selected

Scandium, Chromium, and Vanadium Cations .... 53

viii

 

_

Table Page

2. Calculated Energies, Bond Strengths, and

Geometric Parameters for Various Chromium

Cations ............................ . ........ 54
3. Calculated Energies, Bond Strengths, and

Geometric Parameters for Various Scandium

Cations ........ . ............................ 55
4. Equilibrium Properties of SCH+ in the 2A, 2H,

and 22+ States Calculated with the spd and

spdf Basis Sets Using the MCSCF and MCSCF+1+2

Functions ... .............. ...... ............ 71

5. Equilibrium Properties of Neutral ScH in

 

Several Low-Lying Electronic States

Calculated with the spd Basis Set Using the

MCSCF+1+2 Functions .......................... 78
6. Equilibrium Properties of ScH2+ in the Ground

1A1 State Calculated with the spd and spdf

Basis Sets Using the MCSCF and MCSCF+1+2

Functions .......................... ......... 118

7. Equilibrium Properties of CrCl+ in the 52+ and

the 5n States Calculated Using the MCSCF and
MCSCF+1+2 Functions . ..... ....... ....... ..... 127

8. Long Range Interaction Energies of a Chlorine

Atom Approaching a Point Charge .......... ... 138

 

 

 

_—'—

Table Page
9. Comparison of the Transition Metal (TM)
Contribution to the a Bond, the Percentage
of 4s and ado Orbital Character, and the
Bond Lengths in Each of the Sc+—C and

Cr+—C Bonds ....... ... ............... ........ 142

 

e

 

LIST OF FIGURES

Figure

CHAPTER II

 

1. The Optimized SCF Geometries of Laidig and

Schaefer ............... ......... . ...........
2. The Contours of the (GVB) Valence Orbitals

in the Planar and Tetrahedral Singlets ......
3. The Contours of the 209 Orbital of L12+ .......
4. The Contours of the (GVB) Valence Orbitals

in the Planar and Tetrahedral Triplets ......
5. Density Difference Plots (molecule - atom)

in Several Planes for the Planar Singlet

and Triplet States of CH2Li2 .. ............. .

CHAPTER III

 

1. Flow chart for the QUEST-164 collection of

codes as implemented at MSU ........ ...... ...
N N+1
2. Comparison of experimental sd -d energy
separation with SCF and MCSCF results .......

3. Potential energy curve for the lowest 'E+
state of CrH+ ............ . ........... . ......
4. GVB orbitals for the Cr-H bond in 32+ CrH+ at

equilibrium geometry ............... . ........

xi

 

 

Page

17

21
23

25

27

47

49

57

59

 

Figure Page

5. Electron population of selected atomic orbitals

from the bonding natural orbitals of the 7

CSF MCSCF wavefunction of 92+ CrH+ .... ...... 60
6. Potential energy curve for the lowest 5A' state

of Crcng+ .............. ........... ......... . 63
7. Electron population of selected atomic orbitals

from the bonding natural orbitals of the 7

csr MCSCF wavefunction of BA' CrCH3+ ...... .. 64
8. GVB orbitals for the Cr-C bond in CrCH3+ at its

equilibrium geometry ...... . .......... .. ..... 65
9. Binding energy of ScH+ in the 2A state as a

function of R for the spd and spdf basis

sets in both the MCSCF and MCSCF+1+2

calculations . .......... . .............. . ..... 67
10. Binding energy of ScH+ in the 2n state as a

function of R for the spd and spdf basis

sets in both the MCSCF and MCSCF+1+2

calculations ..... . ..... . .................... 68
11. Binding energy of ScH+ in the 22+ state as a

function of R for the spd and spdf basis

sets in both the MCSCF and MCSCF+1+2

calculations ... ........................ ..... 70
12. Electron population of selected atomic orbitals

of a symmetry from the bonding natural

orbitals of the MCSCF wave function (spd

basis) of 2A SCH+ .................. ......... 73

Figure Page

13. Electron population of selected atomic orbitals

of a symmetry from the bonding natural

orbitals of the MCSCF wave function (spd

basis) of 2n SCH+ ....... . ................ ... 74
14. Electron population of selected atomic orbitals

of 0 symmetry from the bonding and nonbonding

natural orbitals of the MCSCF wave functions

(spd basis) of 22+ SCH+ ............... . ..... 75
15. Potential energy curve for the lowest 2A" state

of ScCH3+ ...................... . ..... . ...... 80
16. Electron population of selected atomic orbitals

from the bonding natural orbitals of the 4

CSF MCSCF wavefunction of 2A" ScCH3+ ........ 82
17. Potential energy curves for the 5B. (filled

circles) and 481 (open circles) states of

CrCHz+ ...................................... 85
18. Electron population of selected atomic orbitals

from the bonding sigma natural orbitals of

the 7 CSF MCSCF wavefunction of ‘Bl CrCHz+... 86
19. Electron population of selected atomic orbitals

from the bonding sigma natural orbitals of

the 34 CSF MCSCF wavefunction of 4B, CrCH2+.. 87
20. GVB orbitals for the Cr—C a bond and the singly

occupied n orbitals of “Bl CrCH2+ at its

equilibrium geometry .. .......... ..... ....... 88

xiii

Figure

21.

22.

23.

24.

25.

26.

27.

28.

29.

 

Page

GVB orbitals for the Cr—C a and n bonds of 4B;

CrCHz+ at its equilibrium geometry ..... ..... 89
Natural orbital occupation numbers for the

valence n orbitals of the MCSCF wavefunctions

of orcnz+ (4B,) and Crcn+ (32') .. ........ ... 92
Electron population of selected atomic orbitals

from the bonding n natural orbitals of the

MCSCF wavefunctions for CrCHz+ (4B,) and

orCH+ (32‘) ............ . .................... 93
Potential energy curves for the lowest 1A1

state of ScCHz+ ............ . ................. 95
Potential energy curves for the lowest 3A1

state of ScCH2+ ........................ ..... 97
Electron population of selected atomic orbitals

from the bonding o and n natural orbitals of

the 10 CSF MCSCF wavefunction of 1A1 ScCH2+.. 98
Electron population of selected atomic orbitals

from the bonding sigma natural orbitals of

the 7 CSF MCSCF wavefunction of 3A, ScCH2+... 99
Potential energy curves for the lowest 32—

states of CrCH+ .......... . ..... . ..... . ...... 103
Electron population of selected atomic orbitals

from the bonding a natural orbitals of the

126 CSF MCSCF wavefunction of 3:" Crcn+ ..... 104

xiv

 

 

 

Figure

30.

31.

32.

33.

34.

35.

36 Potential energy curves for the lowest 32

37.

38.

Page

GVB orbitals for the Cr—C o and n bonds of

3:" CrCH+ ......................... ... ....... 106
Potential energy curves for the lowest 2n state

of ScoH+ ................ .................... 109
Electron population of selected atomic orbitals

from the bonding a natural orbitals of the 17

CSF MCSCF wavefunction of 2H ScCH+ ........ .. 110
Bond energy and Sc—C bond lengths of various

states of ScCH+ which dissociate to Sc(3D)

+ CH(42") ........................ . .......... 113
Correlation of predicted (Cr-R)+ bond lengths

with standard R—R bond lengths .............. 115
Computed dissociation energies of various

combinations of Sc+ and two H atoms relative

to the separated ground state atoms ......... 122

and 7n states of CrCl+ ............ .......... 128
Electron population of selected atomic orbitals

from the bonding natural orbitals of the 7

CSF MCSCF wavefunction of 82+ orc1+ .. ....... 129
Electron population of selected atomic orbitals

from the bonding natural orbitals of the 14

CSF MCSCF wavefunction of 5“ CrCl+ .......... 130

XV

Figure Page
39. Comparison of the calculated bond energies and

geometric parameters for various Sc and Cr

 

compounds ................................... 140
APPENDIX A
1. Spin Eigenfunction Branching Diagram .......... 168

xvi

   

Symbol and/or
Abbreviation

SCF
GVB
MCSCF
SOGVB

CI

SCF+1+2

MCSCF+1+2

b b

l’ r
Y Y
LS

AE

PS
PT
TS

TT

KEY TO SYMBOLS AND ABBREVIATIONS

Meaning
Self—Consistent-Field
Generalized Valence Bond
Multiconfiguration SCF
Spin Optimized GVB
Configuration Interaction

Single and double excitations
from SCF reference space (CI)

Single and double excitations
from MCSCF reference space
(CI)

Bonding Orbitals

Lobe Orbitals

Laidig and Schaefer

Relative Energies

Dipole Moment

(GVB) Orbital Overlap

Planar Singlet (CH2L12)

Planar Triplet ( " )

Tetrahedral Singlet (CH2L12)

Tetrahedral Triplet ( " )

With Li p Orbitals

xvii

 

Symbol and/or
Abbreviation

NO-P

AD

”(e)

(N)

TM
ICR
m/z

or R
eq e

au
mH

2X2 MCSCF

3d
a

3d

3d

3d

 

 

Meaning
Without Li p Orbitals

Density Difference

( p - p )

molecule atom

Electronic Contribution to
the Dipole Moment

Nuclear Contribution to the
Dipole Moment

Transition Metal

Ion Cyclotron Resonance
Mass Ratio

Equilibrium (Bond) Distance

Dissociation Energy

( ER=Q - ER=eq )
Atomic units:
for Energies ... hartree
for Distance ... bohrs
Millihartree

Two Configuration MCSCF
m=0; 3d22 Orbital

a orbital (02v symm.)

|m|=1; adxz Orbital

b orbital (02v symm.)

|m|=1; 3d Orbital

YZ
b2 orbital (C2v symm.)
|m|=2; 3d 2 2 Orbital
X -Y

a orbital (C2v symm.)

xviii

 

 

Symbol and/or
Abbreviation

3d6

C(w) .BW)
(GB-Ba)

000...

CSF

d8

a8
F ,F

F018

Meaning
|m|=2; 3dXY Orbital
a2 orbital (C2v symm.)

Orthogonal Spin Functions

Singlet-Coupled Spin
Functions

High-Spin-Coupled Spin
Functions

Configuration State
Functions

Equilibrium Vibrational
Frequency

Polarizability Tensor
Quadrapole Moment Tensor
Electric Field

Electric Field Gradient

Total Wavefunction of the
System

Hamiltonian (Energy) Operator

Laplacian Operatgfi Associa—
ted with the 1 particle

Mass Ratio between nucleus A
and an electron

Atomic Number

Distance between 1th electron
and nucleus A

Distance between two electrons
Distance between two nuclei
Braket Notation for an Integral

One-electron Functions

xix

 

Symbol and/or
Abbreviation

94

[¢1(g1) ¢2(g2)

¢(f)

x“

oij
<Y|H|Y>
<111>
<ij|ij>
<ij|ji>

f‘fi)

 

Meaning
Antisymmetrization Operator

Electronic Configuration

One—electron Spatial
Function

Atomic Basis Functions
Kronecker Delta

Expectation Value of the Energy
One-electron Integral

Coulomb Two—electron Integral
Exchange Two-electron Integral
Fock Operator

Fock Matrix

One—electron Energy

Localized (GVB) Orbitals

XX

 

 

 

CHAPTER I

INTRODUCTION

The main objective of this dissertation is to
determine a) the electronic structure of dilithiomethane,
CH2L12, and b) the electronic and geometric structure of
various small cations containing scandium (Sc) and chromium
(Cr). Electronic Structure Theory has developed into a
useful technique for elucidating the factors which dictate
the electronic and geometric structure of molecules and
understanding the role of these factors in the observed
chemistry. In the past, ab initio calculations were limited
to small systems containing few electrons while the study of
larger systems involved higher levels of approximation
(e.g., Huckel Theory). However, increased computer power
and highly optimized computer codes have allowed for the
investigation of a whole new array of molecules.

In Chapter II, the electronic structure of the low
lying states of dilithiomethane, CHZLiz, is evaluated using
ab initio MCSCF and CI techniques with the goal of under-
standing the bonding in this unusual molecule. Dilithiome-
thane falls into the group of interesting compounds where

the carbon central atom, most commonly found in the "tetra-

1

__¥__

 

 

2

hedral" form when bound to four substituents, may also exist
in a low energy planar form. A study of this system contri—
butes to the understanding of the effect of substituents on
the stability of the planar tetracoordinate carbon.

The electronic and geometric structure of various
cations containing scandium and chromium, obtained by the
use of ab initio MCSCF and CI techniques, is discussed in
Chapter III. This study complements efforts made through
the use of mass spectroscopic techniques, in understanding
the nature of the chemical bond between the transition metal
cation and different ligands which, in turn, provides us
with the necessary information to understand the observed
chemical reaction processes.

A general discussion of the techniques used to
characterize the electronic structure of the various mole—
cular systems described in this dissertation, is found in
Appendix A. Special emphasis is given to the development of
wavefunctions (MCSCF: GVB, SOGVB; CI: MCSCF+1+2) used in the
calculations, though specific applications are discussed in
the main text (Chapters II and III). A Key to Symbols and
Appreviations was included (found prior to Chapter I) for
quick reference to the many "common" symbols and acronyms
used in this dissertation.

A listing of publications resulting from this

dissertation can be found in Appendix B.

 

 

 

CHAPTER II

THE BONDING, DIPOLE MOMENT, AND CHARGE DISTRIBUTION
IN THE LOWEST SINGLET AND TRIPLET STATES OF

DILITHIOMETHANE, CH L12

2
INTRODUCTION

Experimental determination of the structure of
organolithium compounds is difficult primarily because they
tend to aggregate in the solid and are highly solvated in
solutionl. Since ab initio calculations have been able to
provide useful structural information2 from molecules
containing main group elements, which is comparable to that
obtained experimentally, we anticipate similar calculations
on CH2Li2 will shed light on the bonding structure of this
molecule (not yet characterized by experiment).

Dilithiomethane, CH2L12' falls into the group of
interesting compounds where the carbon central atom, most
commonly found in the tetrahedral form when bound to four
substituents, may also exist in a low energy planar form.
As suggested by Hoffmanna, the stabilization of tetra-
coordinate carbon depends on the nature of the substituents.
For example, if the hydrogens in methane were substituted by

electron-withdrawing groups, the energy difference between

3

...-I--____

 

 

 

4

the planar form of the molecule and that of the nonplanar
"tetrahedral" would be reduced. C(CN)4 results in a planar-
tetrahedral energy difference of 78 kcal/mol compared to 150
kcal/mol needed to make methane planar. This lowering in
energy is due to the delocalization of the lone pair of the
planar tetracoordinate carbon among the cyano groups.
Substitution of hydrogen by less electronegative groups also
lower the planar-tetrahedral energy difference. In

C(SiHa) Si serves as both a a donor and n acceptor by

4.
inclusion of 3d orbitals resulting in an energy difference
of 67 kcal/mol.

Lithium atoms are very electropositive species and
play an important role in stabilizing the planar form of
CHzLiz. According to Collins et al.4, CHZLi2 has a planar—
tetrahedral energy difference of 10.35 kcal/mol based on a
RHF (4-316) ab initio calculation with the tetrahedral being
lower. The dissociation energy of LiC-Li is around 20
kcal/mol5 and that of C-Li is about 50 kcal/mol5 leading us
to believe that CH2L12 would rather take the planar form
than dissociate by breaking a C-Li bond.

6

Laidig and Schaefer (LS) have also studied the

lowest singlet and triplet electronic states of CH2L1 and,

2
on the basis of the calculated dipole moments, suggested a
C-Li+ polarity for both planar and tetrahedral singlet

states while the same molecule has reversed polarity C+Li-

in both triplet states. Unfortunately no interpretaton of

this remarkable observation was attempted.

 

 

 

 

5

We are interested in using the MCSCF and CI ab
initio techniques to understand the bonding in the low lying
states of CHZLi2 and to relate the structure of Li—C—Li in
CH2L12 with that in free C-Li25 (which has been studied by
our group). A study of these systems could shed light into
the understanding of the stability of planar tetracoordinate
carbon. In addition, CHzLi2 serves as a model for metal-

carbene interactions.

A. Bonding of C with Liz;

Before presenting the results of our calculations

on the structure of CH Li a review of studies done on

2 2'
small organo—lithium systems would be beneficial. Organo-
lithium compounds, R—Li, have gained a reputation as being
very useful synthetically, approaching the importance that
Grignard reagentsY, R-MgX (X = Cl, Br, I), have in organic
chemistry and other related fields. The carbon-metal
ligand bond has been described to be of high ionic character

(more like a hybrid between R—M and R—M+)5'7'8.

Since
lithium is more electropositive than the MgX ligand, C—Li
bonds are more "ionic" than C—Mg bonds and, thus,
organolithium compounds are more reactive than Grignard
reagents.

In spite of their importance and interest, little
has been done to study the electronic structure of lithium-

containing organic moleculess. Lithium is a three electron

system, making simple C—Li systems excellent models in the

6

study of organometallic compounds.

,8

Throughout the years, our group5 and others(see
for example: refs.4,6,9) have developed a keen interest in
the study of lithium-substituted carbynes, carbenes and
other lithiated hydrocarbons. Mavridis and Harrison5
reported the results obtained from the study of the
electronic structure of the carbyne C—Li and the carbene
CLi2. The ab initio techniques used were SCF, GVB, and CI
(see Appendix A) with a C (65,4p,1d), Li (3s,1p) contracted
basis sets. They noted that C-Li has a 42- ground state
with an excited state, 2nr, about 34 kcal/mol higher in

energy. In contrast, C-H has a 2": ground state and a

‘Z_ excited state 17 kcal/mol higher in energy. Also, in C-
Li, a zni state was found to be 49 kcal/mol higher than the.
42- ground state. The GVB representations of the 42-, 2"r’

and 2H1 states of CLi5 are as follows:

 

l 1

| Z > a | (core) (brb + b hr) onxnygaaac >

   

 

6

study of organometallic compounds.

Throughout the years, our groups'8 and others(see
for example: refs.4,6,9) have developed a keen interest in
the study of lithium-substituted carbynes, carbenes and
other lithiated hydrocarbons. Mavridis and Harrison5
reported the results obtained from the study of the
electronic structure of the carbyne C-Li and the carbene
CLiz. The ab initio techniques used were SCF, GVB, and CI
(see Appendix A) with a C (65,4p,1d), Li (33,1p) contracted
basis sets. They noted that C-Li has a 42- ground state

with an excited state, 2hr, about 34 kcal/mol higher in

energy. In contrast, C—H has a zflr ground state and a

‘2- excited state 17 kcal/mol higher in energy. Also, in C-
Li, a zni state was found to be 49 kcal/mol higher than the.
42- ground state. The GVB representations of the 42-, 2hr,

and 2H1 states of CLi5 are as follows:

 

 

| 2 > z | (core) (brbl + blbr) onxnygaaac >

 

 

 

 

| n > = 1 (core) (brb1 + blbr) (1Y1? + lyly) aBuano >

CLi (zni)

   

 

 

n > = core 1 l + l l n n +
l i |( )(YY YY)(YI‘Y1

nylnyr) nchaBa >

where terms in parenthesis represent bonding orbitals on the

right (r) and left (1) atom with the exception of ly,lY
which represent the singlet coupled lobe orbitals (result of

correlated carbon 28 orbital).

‘2’, 2nr, and 2n

The states were optimized at the

i
SCF+1+2 level and the results5 from the three states agree
in one aspect: the C-Li bond has high ionic character due to

considerable electron transfer from Li to C.

 

 

 

 

 

pa
9 j 25

00¢ 5

4

The Z- and 2

Hr states are composed of ground state frag-

2

ments while the n state is composed of a ground state

i
carbon and an excited state (2P) lithium atom.

In a study of the multiplicity of substituted
acyclic carbenes, Harrison et al.8 concluded that acyclic
carbenes with very electropositive substituents favor a
triplet ground state. Consistent with this we find that in
CLi there are three triplets before the first singlet

2
states:

32' R= 3.717 a.
9
3119(3) R= 3.507 a.
3A2 R= 3.815 a.; = 88.1’

The GVB description of how the linear 32; state of

CLi2 is formed shows two ground state (28) lithium atoms

bonding to both lobe orbitals in C(3P). Calculations at the

SCF+1+2 level5 suggest that this state is a carbon—centered

3

"carbene state". Bonding in the linear CLi "9(3) state is

2
similar to the bonding scheme in the C-Li 2111(3) state but

the second lithium (28) atom binds to the opposite lobe

orbital.

 

 

 

 

 

 

 

9

., e4
3ng(3)
LNZS) C(BP) Li(2P)

The results obtained for this state5 suggest that the lobe
orbital bonded to the Li(28) atom is more 2s-like and

essentially doubly occupied (due to the ionic character of a

C-Li bond).

The 3A2 state is obtained when the Y-component of

the 3119(3) state is bent in the X2 plane with x as the 02

axis. Self—consistently optimized orbitals5 lead to a Li

2
separation of 5.374 a. which lies between the Li; separation
10 and the experimental L12 separationll. As a result the

3A2 state is described5 as resulting from valence electrons

from the Li2 2og orbital being donated to an empty po

orbital on C.

 

Before discussing the importance of this conclusion, it is

32- state

useful to comment on the relative energies of the g

and that of the 3A2 state. At the SCF+1+2 level of

calculations, 32; is the ground state and 3A is an excited

2
state 6.2 kcal/mol higher in energy. By including

 

 

10

corrections for unlinked clusters5 the role switches, i.e.,
3

the A2 is the ground state while the 32; state is 0.2
kcal/mol higher. What we see are two low lying states,
nearly degenerate but with very different geometries. At
this level of calculation the ground state cannot be
distinguished.

Generally, carbon compounds have tetrahedral,
planar, or linear carbon centers depending on whether or not
the carbon atom is singly, doubly, or triply bonded. Usual-
ly the energy difference between a planar and tetrahedral
form of a tetracoordinate carbon is quite large; for exam-
ple, for methane it is ~150 kcal/mol. By appropriate

substitution1’4'6

this energy difference can be lowered.
The simplest candidate for planar tetracoordinate carbon is
dilithiomethane, CH2L12. Research to date suggests that

there are three main factorsl'4'6

leading to the
stabilization of a planar tetracoordinate carbon:
1) delocalization of the lone pair electrons of the
planar carbon into the vacant n orbitals of
the substituents.
2) o electron donation from substituent to carbon
atom.

3) angle reduction if the carbon atom is embodied

into small rings.

 

11
ELECTRONIC STRUCTURE OF DILITHIOMETHANE, Cfizgizg
A. Orbital Description and Development of Wavefunctions
Understanding how carbon can find itself in a
relatively stable tetracoordinate form would require some

study of the orbitals involved in such a molecule. In

CH4,each bond can be described as:
B=(sa) +(S)
p c H

Depending on equilibrium geometries, nonplanar CH2L12 bonds

can be thought of as:
B = Ms 3) + (s)
i P i ” i

in which A and u would be determined by the variational
principle. CH2L12 has 8 valence (bonding) electrons.
I By constructing symmetry orbitals (in C2v) from

each bond orbital, 81' we would obtain

1 2 1
"’82 34 Li B1 - 82 -o b2 (node in LiCLi
I

”/,c ——+z plane)
lf‘r' B + B 4 a
81‘1 33LJ 3 ‘ 1

x B3 - B4 4 b1 (node in HCH
plane)

Now

 

_ 3 3

B3 + B4 - A(sp )3 + p53 + A(sp )4 + us4
but

(5 3) ~ 5 + +

p 3 p2 px
3

(Sp )4 ~ 8 + p2 - px
Therefore,

B3 + B4 % A(s+pz) + ”(53+s4) e a1
and

33 - B4 e A(px) + ”(83.84) 4 b1

So the symmetry orbitals involved in the bonding of C with
the two Li atoms in the nonplanar CH2Li2 can be visualized

as follows:

.. .. 9/6
/
QC *2 I] —02
X 1 1
l
X

Keeping the hydrogens fixed and "twisting" the

lithiums so they also lie on the YZ plane,

1
\c
/

Ll Li

/—oy
H \\\\H

would give the cis—planar form for CH2L12. The trans-planar

 

 

13

form is higher in energy and will not be considered. The

symmetry orbitals, a and b1 in the nonplanar form, must

1
also conform to the change in the geometry. The al orbital
retains a1 symmetry in the planar form, but the two parts of

the b1 orbital have different symmetry in the planar form.

A(px) e b (nonbonding: node in the
molecular plane)
p(ss—s4) 4 b2 (antibonding: node between

the Li ligands)

Having two electrons in a b1 orbital, where px on carbon is
a n nonbonding orbital, is the preferred choice. This would

involve backbonding to the Li H system.
1

The planar A1 state of CH2L12 is characterized by
the configuration
2 2 2 2 2 2 2
1a12a11b23a12b24a11b1 (1)

The 1a1 orbital is the carbon is function, the 2a1 and 1b2

are the symmetric and antisymmetric combinations of the Li

ls orbitals, and the 2b2 and 3a orbitals represent the two

1

C-H bonds. The remaining two orbitals, 4a1 and 1b1,

the four electrons which must be responsible for binding the

host

two Li atoms to C.
Since we are interested in the bonding between C

and the two lithium atoms, the C-H bonding orbitals were

 

14

"fixed" at the SCF level. The remaining 4 valence electrons
in the SCF wavefunction (1) are correlated as in the
following example for the 1A1 case:

2 2 2
core (1a 2a 1b23a12b2)

HNHM

valence (4a 1b ) SCF

(5a 1b§)W
(3b ibi)

2
(2b 1b1)

 

(1a lb?) $ Diagonal Double

(4a Gai) Excitations
2

(4a 4b2)
2
(4a 3bl)

(4a

HNHNHNHNNNHNNNHNHNHN

 

2
2a2))

Here, the 4a: pair is excited into the 5a1, 2b1, 3b2, and
1a2 orbitals and the 1b? pair is excited into the Gal, 3b1,
4b2, and 2a2 orbitals. Thus, the MCSCF function for the 1A1
state of CH Li consists of nine configurations. The CI

2 2

function was a full four electron CI over the MCSCF orbital

reference space consisting of a total of 153 configurations.

The nonplanar 1A1 state of CH2Li2 is characterized

by the configuration

2
1

2 2 2 2 2 2
1a12a11b13a 1b24a12b1

This SCF wavefunction was then correlated, as in the planar

 

 

15

form, to give a MCSCF funtion consisting of 9 configurations
and a CI function of 153 configurations.

If the {1bi} electron pair were "split" to give

1, this would lead us to the 38 state:

{1b15a 1

l

| 3B > a (core)2 4ai1b15a

1 dado SCF

1
Keeping the orbitals involved with the core (including the
C-H bond orbitals) frozen, the remaining four electrons were
correlated in the following way:

For example,

 

3B1 planar
2 2 2 2 2
core (1a12a11b23a12b2)
2
valence (4a11b15a1) SCF
2 1
(6a11b15a1)’
(2bi1b15a1) ) Diagonal Double
2 .
(3b21b15a1) Exc1tations
2
(1a21b15a1)J
(4ai3b17a1) Off—diagonal Double
2
(4a14b22a2) Excitations
(maintaining overall
symmetry)
The MCSCF function for the 331 state of CH2Li2 consists of

seven configurations and a full four—electron CI function
from the MCSCF valence orbital reference space consists of
316 configurations. The wave functions for the nonplanar

381 were also constructed in a similar fashion.

 

 

 

16

B. Computationalfgetails

All wave functions used in this study were
constructed with the ALIS12 collection of codes as
implemented on the MSU CYBER 750. The basis sets for carbon
and lithium are the Duijneveldtla 1136p and 98 augmented
with a set of d functions (a= 0.75) on carbon and a set of
four p functions on each lithium14. The hydrogen basis is
the Huzinaga15 4s augmented with a set p functions (a=
1.00). The basis set was contracted following Raffenetti16
to 482p1d on carbon, 3s2p on lithium, and 2s1p on hydrogen.

All calculations were done at the optimal (SCF)

geometries reported by Laidig and Schaefer6 (L8) as seen in

Figure 1.

C. Results gnd Discussion

Relative energies (AE) and dipole moments (u) were
calculated for each of the low lying states of CH2L12. Our
results, which are compared to those reported by Laidig and
Schaefer6 (LS), appear in Table 1. The CI wavefunction used
was not as extensive as that used by LS (7000 to 9000
configurations) but could adequately track the previously
reported energy differences and dipole moments. We believe
the wavefunction we have chosen is sufficiently accurate so
as to capture the essential characteristics of the
electronic structure of CHzLiz. In other words, the MCSCF

wave functions and its corresponding CI functions used in

 

 

17

3—2.48—>LIT
L' TLi4—2.86—5Li
736°
IO|7
2.069>C/H'-115 "6 T>C.\/‘:|844
H/.’>Bl\ /|Al

TLi<—3.44—>Li
2128\/:4 2/I.72 0985:'\2:/l.981

”1
I””
4»

 

 

 

 

3Ea /VAl

Figure 1. The Optimized SCF Geometries of Laidig end
Schaefer. All distances are in angstroms.

 

 

 

18

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19

this study include those configurations needed to
essentially describe the bonding in CH2Li2 with special
emphasis in the C—Li2 moiety.

We have included two sets of calculations in Table
1: one using the basis described previously (P) and another
(NO-P) where the lithium p orbitals were deleted from the
basis. Our intention is to understand the effect these p
functions have in the overall bonding of CHzLiz. These
effects will be discussed at a later time. For now, we will
concern ourselves with those results where the lithium p
functions were included.

The tetrahedral (nonplanar) singlet (1A1) state is
the lowest lying state at the CI level followed by the
planar singlet 1.1 kcal/mol higher in energy. The 331
states are higher in energy relative to the singlet states.
The tetrahedral 3B1 and the planar 3B1 states are 3.5 and
3.8 kcal/mol, respectively, higher than the tetrahedral
singlet. The difference in energy between the tetrahedral
and planar structures among the spin states are very low.

As mentioned before, for the singlet states the tetrahedral—
planar energy difference is 1.1 kcal/mol and that for the
triplet states is 0.3 kcal/mol.

The dipole moments calculated at the CI level show
positive values for the singlet states and small negative
values for the triplet states. These results suggest a

C—Li+ polarity for the singlet states and a C+Li_ polarity

for the triplet states (also observed by LS). Note that

 

20
this is a consequence of the difference in the electronic
states (3B1 vs. 1A1) and not because of the symmetry of the
geometric structure (planar vs. nonplanar).
While these results compare favorably with those
found in the literature1’4'6, many questions remain
unanswered and we believe a more detailed analysis of the

charge distribution and orbital characteristics of the

predicted structures of CH2Li2 is useful.

1. Orbital Characterization
The three most important terms in the CI function

for both the tetrahedral and planar 1A1 states are:

2 2 17
4a11b1 SCF
Sailbi correlating a1 pair
2 2 n '
4a12b1 b1 pair

Using the relative weights of these configurations, we
defined the GVB (generalized valence bond) bonding pairs
from the two a1 and the two b1 orbitals, and these are

contoured in Figure 2. The plotted coordinate system is as

follows:

 

 

21

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x . A.
a M7. W ....... s X ......... X I .I I
. ..\. _ © .a . x x ...I ...\
.. .. . . .. _. ...HH . .\.I. a
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H Li ,
\C / _. z "”0, /L'
/ C

\\\\ __*z
H LI H’ \
I I Li
y x
Planar (molecule in Nonplanar (CLi2
YZ plane) in X2 plane and

CH2 in Y2 plane)

The calculated overlaps (S) of the GVB pairs are
around 0.7 and 0.8. These values attest to the inadequacy
of the SCF function (which does not allow the correlation of
1,b1 electrons; S=1) to describe these states.

Also, we note from the contours the "ionic" characteristic

the valence a

of the GVB n orbitals which are largely centered on the
carbon. The GVB 0 orbitals are more "covalent", where one
orbital (centered on carbon) looks like an sp2 orbital while
the other resembles the Li2+ 20g orbital. For comparison we
contoured the 209 bonding orbital of Li2+ at the Li—Li

separation in CH2Li and show the results in Figure 3.

2.
The interaction of C with L12 is similar in the "0"
system for both singlet states and the main difference in
the "n" system lies on the symmetry of the carbon px orbital
relative to the Li—C—Li molecular plane. In the planar
state, the pK orbital on carbon can only interact with the

px orbitals on the lithium atoms (out—of—plane) while in the

nonplanar state, it can interact with both the s and p

 

 

 

 

23

 

eeeee

 

 

 

Figure 3. The Contours of the 20g Orbital of Liz+.

 

IIIIIhIIIlIIIIIIIIIIIIIIIIIIIIiiIIIIIIIIIIIIIlllllIn----_._______

24

orbitals on the Li atoms (in-plane).

The most important terms in the CI function for

both the tetrahedral and planar 381 states are:

4a 1b15a SCF17

1

and 6a correlating a

HNI-‘N

1b15a pair

1 1

Using the relative weights of these configurations, we
constructed the GVB 0-bonding pair and these, as well as the
5a1 and 1b1 orbitals, are contoured in Figure 4.

The 0—bonding pair in the triplet states are very
similar to those of the singlet states (and essentially
identical to each other) yet have more carbon character than
the singlet states. This is due to the presence of the 5a1
orbital in the triplet states. The 5a1 orbital is rather
remarkable in that it is, in large measure, localized on the

side of the Li2 away from the carbon atom.

The 5a orbital has a node between the C and L12

1
group; in the 3B1 states this accounts for the increased C—
Li separation as compared to the 1A states (planar: 1.16A

2 1
4 1.66A; nonplanar: 0.986A 4 1.72A). The change in the
nonplanar form is the most dramatic. Also the 5a1 orbital
increases the Li2 bond strength, thus, decreasing the Li2
separation (planar: 2.86A 4 2.48A; nonplanar: 3.44A 4
2.51A). In both triplet states, the b1 orbital is centered

around carbon.

 

 

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qufinmmo muzmq<> m>o

 

 

26

The differences in energy between the tetrahedral
and planar structures among the spin states are very low:
1.1 kcal/mol between the singlet states and 0.3 kcal/mol
between the triplet states. From the orbital contours we
could see that the change from planar to tetrahedral in the
singlet states is more noticeable than for the triplet
states. This is due to the doubly occupied b1 orbitals and
its change in character (with its accompanied influence on
L12) between the two geometric structures. In the triplet
states, the larger C—Li2 separation appears to lead to an
indifference of the C p1T orbital to the L12 orientation, an
effect that lowers the energy difference between the two
geometric structures. Therefore, the rotation of L12 about
the 02 axis of CH2 is essentially barrier—free.

A useful interpretative tool is the electron
density difference plots for the planar 1A1 and 3B1 states
which appear in Figure 5. In these plots the electron
density of the molecule is compared to that of the separated
atoms. The solid lines represent an increase in electron
density over the separated atom values and the dotted lines
represent a decrease. These plots were also contoured in
several different planes: first, in the molecular plane;
second, along a C-Li bond in a plane perpendicular to the
molecular plane; and third, along the Li—Li bond in a plane
also perpendicular to the molecular plane. While the C-H
bonds are clearly visible as an enhanced electron density

along the line connecting the C and H nuclei, the

W7

27

ELECTRON DENSITY DIFFERENCE PLOTS

Bl planar

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 5. Density Difference Plots (molecule - atom) in
Several Planes for the Planar Singlet and Triplet States of
CH L12. The carbon atom for the singlet difference plot was
tagen as

2 2 1 2 1 2
1s (sp )8! (sp ),,2 p"

where (sp2)H is an sp2 hybrid orbital directed toward an H
atom and p is a 2p orbital perpendicular to the molecular
plane. Fog the triplet difference plot the carbon
configuration was

2 2 1 2 1 2 1 1
1s (sp )H‘ (89 Inz (Sp ) 911
Where the unsubscripted sp2 orbital is directed toward the
midpoint of the Li2 group.

 

28

enhancement in the density between C and Li2 seems
delocalized over a significant region between them and is
consistent with the carbon po bonding with the L12 20g
orbital (i.e., a three center bond). In the triplet state,

the presence of the delocalized 5a orbital is apparent with

1

the increase in electron density behind Li away from the

2

CH2 group. The plane perpendicular to the molecule plane

and containing the Li nuclei the strong Li-Li bonding

interaction in the 1A state while there is less enhancement

1
of electron density between the two Li nuclei in the 3B1
state. Much of the differential enhancement in the 1A1

state seems to be due to the n electrons delocalized onto
L12 from C. This is considerably reduced in the triplet
state because, as noted above, the Li2 group is much further

away from the C pTT orbital, preventing a significant

delocalization.

2. Charge Distribution and Dipole Moment

In the previous section we were able to obtain a
feeling for the spatial extension of those valence orbitals
crucial in the bonding of C with the two Li atoms. To
further aid our understanding of the electronic structure of
these states, we gathered the contribution of the most
prominent natural orbitals to the population analysis and
dipole moments for each of the states of CH2L12 and are
collected in Tables 2-5.

The dipole moment ”2 is the sum of an electronic

 

 

 

 

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33

contribution, ”ée)’ and a nuclear contribution, péN), with
the z axis being the C2 axis:
u = ”(e)+ ”(N)= —E n (Y |z|Y > + (62 + 22 )
z z 2 i=1 i i i Li H

In this expresion zLi and 2H are the z coordinates of the

nuclei, Ti is a natural orbital of the appropriate wave

function, n is the corresponding occupation number, and the

1

sum is over all the natural orbitals of the system.

For both 1A1 states, péN) > lpée)| and the total

dipole moment is positive, suggesting a shift of electrons

from Li2 to CH2. This is consistent with the charge

distribution of both states where 40.6 electrons shifts to

CH2 from Liz.
In forming the 381 state, the 1b? pair was split

placing an electron in the 5a1 orbital. This 5a1 orbital is

diffuse and localized to the side of the L12 away from the

CH group. This spatially extended orbital dominates the

2
valence electron contribution to uée)

and results in the
electronic contribution outweighing the nuclear and produces
a negative dipole moment.

As a schematic example, the overall charge
distribution and the 0," components of the planar 1A1 state

is shown as follows:

 

 

 

34

up an on

.an
@0668 Q HI,” 5.29’ésL'
... ’l
C - ;C\
(I; (9 H Li
TOTAL 0
and that of the planar 3B1 state:
oz) 093 an
Hl” 572 ‘sL'
: ”tact?

   

Note the similarities in the overall charge distribution
even though the dipole moments have different signs. When a

b electron from the 1A state is placed in the 5a orbital

1 1 1
(defining the 3B1 state), 0.26 electron is removed from the
pTr orbital on each Li atom and replaced with 0.31 electron

in the Li "0" orbitals. At the same time, lithium's
contribution to the 0 bond (4a1 orbital) is reduced.
Therefore, the 0 and 0 components of the charge distribution
for the two spin states are quite different but the

similarity lies on the net charge. This is also observed

for the nonplanar molecules.

 

“mm” '

35

3. On the Role of the Li p Orbitals

The data in Table 1. suggest that the Li p orbitals
are crucial for a balanced description of either the singlet
or the triplet states. In particular, one sees that the
energy separation between the planar and tetrahedral singlet
is far more sensitive to the presence of Li p orbitals than
to the level (SCF, MCSCF, or CI) of calculation. In
addition, the dipole moment of the planar singlet increases
in both the SCF and CI approximations by more than 3 debyes

when the p orbitals are removed, reflecting the lost

 

opportunity for back donation via the Li pTT orbitals. Note
that the tetrahedral singlet does not suffer so because the
carbon p1T can donate electrons to Li via the 0u orbitals on
L12. The triplet states respond differently than the
singlets to the absence of Li p orbitals. In this case they
have little effect on the energy separation between planar

and tetrahedral forms but result in an increase of ~3 debyes

in the dipole moment of both conformations. This is clearly

 

a result of the ability to properly polarize the 5a1 orbital

(see Figure 4) without the Li p orbitals.

36

CONCLUSIONS

 

While there are eight valence electrons in CH2L12,

four are involved in C—H bonds leaving the remaining four to
bind the two lithium atoms to carbon. How these four

electrons are distributed among the C-Li moiety will

2
determine the essential characteristics of each of the low-
lying states of CH2L12. A qualitative model of the bonding
in CH2Li2 which is consistent with the charge distribution,

low barrier of rotation (tetrahedral 4 planar), dipole

 

moment, and the geometric changes which accompany the
planar-tetrahedral rotations in either the singlet or

triplet states can be abstracted from these calculations.
1

For the planar A1 state, the four "CLiz" valence
electrons are in the 4a1 and 1b1 orbitals. The 4a1 orbital
seems to be a combination of a pa orbital on CH2 and the 209

bonding orbital on Li while the 1b1 orbital is a mixture of

2

the p on CH and the Li p orbitals. The resulting bonding
n n

2
structure, relative to the free CH2 (1A1) and Li2 (12+)
fragments, shows an electron donation from the Li2 20g
bonding orbital to the formally empty pa orbital on CH2 with

a concurrent delocalization of the CH electrons into the

2 p"
Li p1T orbitals.

 

 

37

H
\c +
H/

 

If the L12 group is rotated 90’ the 0 bond remains
intact while the n bond changes. Specifically, the ability
of the CH2 9" to donate electrons into the formally empty Li
pTT orbitals is lost. However, the Li2 20u orbital has the

correct symmetry to interact with the doubly occupied CH

9-9
H \ H III/[III

C +

“/ H/O—G

This results in significant increase in the Li—Li distance

2
p" orbital.

(2.86 A planar 4 3.44 A nonplanar) while the C-Li2

separation decreases (1.16 A 4 0.99 A) permitting a stronger

overlap between the CH p1T and Li2 Ou orbitals. Note that

2

while this interaction is antibonding from the L12

perspective, it enhances the bonding of C to Liz. This

picture of the tetrahedral 1A1 is, of course, equivalent to

the conventional model involving a substituted sp3 carbon

atom (except for the suggestion of a Li-Li bond).

When one forms the planar 381 from the planar 1A1

 

Iva-”mm

38

an electron is removed from the CH orbital (lbl) and

2 p"

placed in the antibonding companion to the 4a bonding

1
orbital.

5a 20

u
m
y
U
I

This orbital adds a node between the C and Li2 as observed

in the increased C—Li2 separation and the additional 20

contributes to the decrease in the Li-Li separation.
Detailed examination of the relevant orbitals (GVB orbital
plots) indicate a significant amount of pz orbital character

(in the 20g Li2 orbital) has been added to the o orbital

hosting the unpaired electron (Sal). Most of this electron

seems to be confined to the region behind the Li2 nuclei

away from the CH group. Due to the direction of the

2

orbital extension, it is the single electron in this orbital
that is, in large measure, responsible for the dramatic

shift in the dipole moment in going from the 1A1 planar
(+4.32 debyes) to the 381 planar (-1.34 debyes). This

change in dipole moment is not due to a change in polarity
(HZC+Liz—) since the overall electron distribution of both
the singlet and triplet states show a net charge transfer

from L12 to CH2 corresponding to a HZC-Liz+ polarity.

3

If one forms the nonplanar B1 by rotating the L12

group by 90‘ the a bond remains intact (including the effect

of the 5a1 orbital) and the pTr orbital on CH2 interacts with

the ou orbital on L12 as in the tetrahedral 1A1 state. Due

39

to the effect of the 5a1 orbital in the a system the C—Li

separation changes little upon rotation (planar to

2

nonplanar), thus, the symmetry transformation that the b1
orbital undergoes is essentially unnoticed.
After this work was completed we learned of a

similar study by Bachrach and Streitweiser18

in which they
arrived at similar conclusions but with a far less reliable
theoretical treatment. In addition we disagree on the

usefulness of the population analysis as an interpretative

tool.

.77 "fl. 1| n

 

 

LI ST OF REFERENCES

10.

11.

12.

13..

14.

 

 

 

LIST OF REFERENCES

T.H. Maugh II, Science, 1 4, 413 (1976).

H.F. Schaefer III, "The Electronic Structure of Atoms and

Molecules", Addison-Wesley, Reading, Mass., 1972.

R. Hoffmann, R.C. Alder, and C.F. Wilcox, Jr., J. Am.

Chem. Soc., 92, 4992 (1970).

J.B. Collins, J.D. Dill, E.D. Jemmis, Y. Apeloig, P.v.R.

Schleyer, R. Seeger, and J.A. Pople, J. Am. Chem. Soc.,
Eé. 5419 (1976).

A. Mavridis and J.F. Harrison, J. Am. Chem. Soc., 1 4,

3827 (1982).

W.D. Laidig and H.F. Schaefer III, J. Am. Chem. Soc.,

100, 5972 (1978); Erratum: J. Am. Chem. Soc., 101, 3706
(1979).

rd

edition, Allyn and Bacon, Inc., Boston, Mass., 1973,
pg.840.

R.T. Morrison and R.N. Boyd, "Organic Chemistry", 3

J.F. Harrison, R.C. Liedtke, and J.F. Liebman, J. Am.

Chem. Soc., 101, 7162 (1979).

M.A. Vincent and H.F. Schaefer III, J. Chem. Phys., 11,

6103 (1982); E.W. Nilssen and A. Skancke, J. Org. Chem.,
116, 251 (1976).

G.A. Henderson, W.T. Zemke and A.C. Wahe, J. Chem.
Phys., §§. 2654 (1973).

F.W. Loomis and R.E. Nusbaum, Phys. Rev., gg, 1447
(1931).

K. Rudenberg, L.M. Cheung, and, S.T. Elbert, Int. J.
Quantum Chem., lg, 1069 (1979).

F.B. Duijneveldt, "IBM Technical Research Report
No.RJ-945", IBM Research Laboratory, San Jose, CA,
1971.

J.E. Williams, Jr. and A. Streitwieser, Jr., Chem. Phys.
Lett., 25, 507 (1974).

40

41

S.J. Huzinaga, J. Chem. Phys., _g, 1293 (1965); T.H.
53, 2823 (1970).

15.
Dunning, Jr., J. Chem. Phys.,
4452 (1973).

 

16. R.C. Raffenetti, J. Chem. Phys., 58,
states, the SCF function

For the tetrahedral 1A and SB
In the singlet state, the

17.
has a 2b orbital occfipied.
doubly oécupied 2b orbital electrons are correlated
into 3b orbital (among the most important terms in
the CI function).
18. S.M. Bachrach and A. Streitwieser, Jr., J. Am. Chem.
5818 (1984).

Soc., 106,

 

 

 

CHAPTER III

THE ELECTRONIC AND GEOMETRIC STRUCTURE OF VARIOUS

SMALL CATIONS CONTAINING SCANDIUM AND CHROMIUM

INTRODUCTION

Experimental studies of the gas-phase, bimolecular
reactions of transition metal (TM) cations with alkanesl'a'5
have prompted an interest in understanding the chemistry of
these small systems. Such studies have immediate impact in
organometallic chemistry, surface chemistry, and catalysisz.
Reactions, where ions are involved, can be studied by use of
state-of-the—art mass spectroscopic techniques, such as Ion
Cyclotron Resonancea'4 and Guided Ion Beam Mass Spectrome-
try3'5, and the information collected from these studies has
led to some understanding of the kinetic and thermochemical
factors that allows a reaction to proceed. One of the
advantages of the Guided Ion Beam experiment relative to the
ICIR experiment is being able to study endothermic, as well
as exothermic, reactionss. These experiments address
Various questions: activation of C-H and C—C bonds,

reactivity of different transition metal ions, reaction

mecrhanisms, exothermic vs. endothermic reactions, bond

erlergies , etc .
42

¥

 

-_——-——-——’

43

While the experiments to date provide information
on bond energies and reaction mechanisms they say nothing
about the electronic and geometric structure of these
species. Mass spectrometers can only provide the mass
ratios (m/z) of reactant and product ionss. Usually,
proposed product structures are based on the structure of
the reactants, subsequent reactivity information, and
3,6

"plausible considerations" of the reaction process This

can be difficult since structural possibilities increase
with larger systems. For example, if the mass ratio of a
product suggests a TM—CH3+ structure, other isomers
(HZTM-CH+, H—TM—CH2+) should be considered. The necessary
structural information, such as bond lengths, bond angles,
bond energies, electron distributions, spin multiplicities,
among others, can be obtained through the use of ab initio
molecular structure techniques7

Theoretical studies of transition metal systems
have lagged the experiments for several reasons. First-row
transition metals and their ions are not well represented by
the single determinent self consistent field (SCF)
functions8 which have been so useful in understanding the
electronic structure of main group elements and compounds.
Ir: particular, the large number of closely spaced energy
1ew1els, the changing character of the 35,3p orbitals (from
SENni—core to core) as one goes from Sc to Cu, and the as yet
Pcuarly understood relativistic effects raise the required
8,9

level of theory significantly. Work to date suggests

44
that a usefully accurate description of the electronic
structure of a first row transition element or a small
molecule containing such an element is possible if one
starts with a multiconfiguration SCF (MCSCF) wavefunction
which recognizes the differential electron correlation in
the relevant low lying states of both the transition metal
and organic fragment. Additional levels of theory
(configuration interaction) can then be applied as the
problem and goal warrant.

The electronic and geometric structure of various
transition metal cations containing scandium and chromium,
obtained by the use of ab initio MCSCF and CI techniques,
will be discussed in this chapter. We are especially
interested in the nature of the chemical bond between the
transition metal cation and the ligand, and the effect of
the low lying states of the fragments on the bonding
structure of the overall ground state of the molecule. The
systems of interest are divided into three sections: the

bonding of Sc+ and Cr+ with the organic fragments CH CH

3' 2'

+ and the

2 ;
bonding in CrCl+. In addition to this discussion we will

and CH, as well as with H; the bonding in ScH

consider the possible consequences of this study.

45

BASIS SETS AND MOLECULAR CODES

 

The basis set used for Sc and Cr consists of

14s,11p,6d functions constructed by augmenting Wachters'10

14s,9p,5d basis with two additional diffuse p functions11
(to represent the 4p orbital) and an extra d function as
recommended by Haylz. The exponents used for the two p
functions are a=0.18975 and a=0.03103 for scandium, and
a=0.1207 and a=0.03861 for chromium. The extra d function
has an exponent of a=0.05880 (Sc) and a=0.0912 (Cr). This
basis was contracted to 53,4p,3d following Raffenetti's13
contraction scheme. The basis for carbon was a 95,5p,1d set
consisting of Duijneveldt's14 95,5p basis augmented by a d
set with the exponent a=0.85. The hydrogen basis was a
4s,1p set consisting of Huzinaga's15 48 basis augmented by a
p set with an exponent of 1.0. The C and H basis sets were
contracted to 38,2p,1d and 2s,1p, respectively, as
recommended by Raffenettila. The basis for Cl was a
12s,10p,2d set consisting of Huzinaga's16 12s,9p basis
augmented by a p set with exponent a=0.0436306 and by 2 d
sets with exponents of a=0.6 and a=0.2. The C1 functions
were contracted to 4s,4p,2d as recommended by Raffenettila.
The contracted basis set described in the previous
paragraph for Sc and H, [554p3d/2sip], is referred to as spd
in the text. A second set was formed by augmenting the spd
set with a single f function (a= 1.0) for Sc, contracting

Huzinaga's 43 hydrogen set to three components, and by

replacing the single p function on hydrogen with two p

 

46

functions (a= 1.73 and 0.43). This [554p3d1f/3s2p]
contracted basis is referred to as spdf in the text.
All calculations were done on a Floating Point
Systems FPS—164 computer, jointly supported by the Michigan
State University Chemistry Department and the Office of the
Provost, by using the Argonne National Laboratory collection
of QUEST-164 codes. In particular, the integrals were
17

calculated with the program ARGOS written by Pitzer the

SCF and MCSCF calculations used the 6V8164 program by Bair18
and the UEXP program and related utility codes written by
Shepardlg. The configuration interaction calculations were
done with the program UCI (and its related utility codes)
written by Lischka, Shepard, Brown, and Shavittzo. The
logical flow of the QUEST—164 system, as implemented at MSU,

is shown in Figure 1.

SIZE CONSISTENCY

Every calculation reported is size consistent,
i.e., the energy of the molecule when the fragments are far
apart is also the sum of the energies of the individual
fragments, not only at the MCSCF level but also at the
MCSCF+1+2 level. This is an important characteristic of
these calculations and suggests that the De's calculated

from the MCSCF+1+2 wave functions are lower bounds.

 

47

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48

NATURE OF THE FRAGMENTS: TRANSITION METAL IONS

 

Before we discuss the bonding in the various tran—
sition metal-containing (cationic) molecular systems, it is
useful to discuss the nature of the individual fragments.
Since we are interested in bond energies, we must insure
that the structure of the fragments, as well as the
molecules, are properly represented. For now we will
concentrate on the transition metal monopositive ions while
the "companion ligands" will be discussed in subsequent
sections.

In Figure 2 we observe the comparison of the expe-
rimental st-dN+1 energy separation21 with those calculated
using SCF and MCSCF (d-d radial correlation) techniques. It
is worth noting that an SCF wavefunction incorrectly
predicts a (sda) 5F ground state for V+ rather than the
experimentally observed 5D ground state. This illustrates
the need of a multiconfiguration wavefunction to better
approximate the low lying states of transition metal ions8

We have choosen Sc+ and Cr+ as representatives of
the first half of the first—row transition metal series for
CH CH

our studies of [TM-R]+ systems (R = H, H CH, and

2' 3’ 2’
C1). One of the advantages of studying monopositive TM ions
is that $2 correlations (mainly a near degeneracy effect
4s2-o4p2)8 of a 452 pair (low energy state in neutrals) will
not be necessary since a state with a 4s2 pair is very high
in energy. As in neutral atomsa, we should include d2

radial correlations,

 

49

 

 

 

3F<d2)\
MCSCF \
\ \
\ ‘\
EXP. ‘\ \
\\ ‘ \
05- n‘ ,f \
\\\ ‘F(d3) \
\
\\ \ 50w“)
\ “ I
\‘ \\ I‘
o.o- 30(sd) ‘F<sd2)\\ 5F(sd3) I ‘msw
Sc+ Ti+ \\ W I cw
\ I
g \\ 50(d“) I
9. ‘——~. |
Lu \__.I I
l
<1 Ig‘.
~05- "I I
(a I
I
I
I I
(I
'x
i .
I
I
I
I
I
I
I
4.5- I—EXP
“sum

Figure 2. Comparison of experimental st—dN+1
Separation with SCF and MCSCF results.

energy

¥

 

50

for improving the SCF model. Due to computational diffi-
culties core—core and core—valence correlations are not
included in our calculations.

The ground state21 of Cr+ is a 68 state arising
from a 3d5 configuration while the first excited configura-
tion, 4s3d4, gives rise to a 6D state. The Cr+ (ds—sd4)
splitting (expt = 35.1 kcal/mol)21 is calculated to be 23.8
kcal/mol at the SCF level and 36.9 kcal/mol at the MCSCF
(radially correlated) level. The ground state of Sc+ is of

3D symmetry and arises from the 483d configurationzl. The

companion 1D state is 0.302 eV (6.96 kcal/mol) above the 3D
with the lowest state arising from the 3d2 configuration (3F
symmetry) being 0.596 eV (13.7 kcal/mol) above the ground
state. The Sc+ (sd—dz) splitting (expt = 13.7 kcal/mol)21
is calculated to be 21.2 kcal/mol at the SCF level and 17.3
kcal/mol at the SCF+1+2 (CI) level. The smaller energy
difference between the relative st and dN+1 states in the
Sc+ as compared to the Cr+ ion will also be of concern when
We observe the contribution of these atomic states to the

1

molecular systems.

 

 

 

51

BONDING or Sc+ AND or+ WITH g, CH3, CH2, AND CH

Recent experimental studies of gas-phase, bimole—
cular reactions of transition metal (TM) cations with
organic molecules are providing significant insightsl'a'22
into the mechanism of important organometallic reactions.

In addition, the thermochemical data extracted from the
experiments1 allows for the collection of an invaluable data
base which will permit the systemization of the observed
chemistry, prediction of possible new chemistries (which
happens to be one of the major strengths of Organic Chemis—
try) and provide bench marks for theoretical studies

To date, these experiments have not been able to
provide structural information on the various reaction pro-
ducts. The purpose of this study is to provide such struc—
tural information via a uniformly accurate theoretical study
of the electronic and geometric structures of the titled
molecules. We are interested in the nature of the chemical
bond between transition metal monopositive cations, such as
chromium and scandium, and various simple organic ligands

(CH3, CH2, and CH), as well as, with H. In particular, we
are concerned with the extent to which these fragments form
single, double, and triple bonds. We have been motivated to
investigate the possibility of CH forming a triple bond with
Cr+ by the recent theoretical prediction of Carter and
GOddard9 that the ground state of CrCHz+ has a double bond
between CH2 and Cr+, and by the recent experimental work of

1e

Aristov and Armentrout suggesting that V+ forms single.

 

52

double, and triple bonds with CH3, CH2, and CH, respective-
ly (Table 1). We anticipate that this study will result in
our understanding the nature of the transition metal—main
group element bond sufficiently well so as to permit a
qualitatively correct prediction of the bonding in more
complex transition metal-containing system.

The absolute energies, calculated and experimental
bond energies for the various molecules to be discussed are

collected in Tables 1-3.

 

 

 

53

TABLE 1. Experimental Bond Energies for Selected Scandium,
. . a
Chromium, and Vanadium Cations .

 

 

 

 

Sc+-R Cr+—R V+—R
R ref1d reflg ref1b ref1g ref1e
H 54:4 55:2 35:4 27:2 50:2
CH3 65:5 59:5 37:7 26:2 50.5:3
CH2 97 65:7 <65 80:8
CH 115:5

 

aAll values are in kcal/mol.

54

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56

A. CrH+ and CrCH3+

~~~~~~~~~~~~~~~

We may imagine a hydrogen atom bonding to a dO
orbital in the 6S state or to a 45 orbital in the m=0

component of the 6D state of Cr+. In both cases the

symmetry of the resulting molecular state is 52+. Apart

from the Cr+ core the wavefunction would have the schematic

(GVB)23 form

1 1 1 1
( oh + ho ) 3dTr 3d1T 3d° 3d6
x y + -

( aB-Ba )aaaa

where at large distances 0 is a 3dO orbital on Cr+ and h is
a hydrogen is function. A CrH+ wavefunction of this form
which dissociates to the correct Hartree-Fock products
[Cr+(6S) + H(2S)] consists of seven configuration state
functions (CSF's) and will be referred to as the MCSCF
function. From the analysis described in Appendix A, one
recognizes that this seven configuration MCSCF (SOGVB)
function consists of a 2x2 MCSCF function (GVB) which
properly dissociates the Cr-H bond, augmented by five spin
eigenfunctions to completely describe six electrons being
coupled into an overall quintet state. The energy of this
wave function as a function of internuclear separation is
shown in Figure 3. Also shown is the CI function formed by
allowing all single and double excitations from the valence
orbitals in this 7 CSF MCSCF reference space. -In this and

all subsequent CI calculations no excitations from the Ar

57

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58

core of Cr+ were permitted; i.e., the core is determined
variationally in the molecular environment and kept at that
(SCF) level in the CI's. This CI function is referred to as
the MCSCF+1+2 function and dissociates to the 65 Cr+ in
which the d electrons are correlated essentially at the
SCF+1+2 level. The binding energy predicted by this
function is 25 kcal/mol, which is in excellent agreement
with the more recent experimental value of 27 kcal/mol1g and
is 71% of the earlier experimental value of 35 kcal/mollb.
As the CrH bond forms, the composition of the
bonding orbitals (o and h) evolve and we show in Figure 4
the contours of the GVB bond orbitals at equilibrium24.
Clearly, a substantial amount of 45 character has mixed with
the originally pure 3do orbital. A striking representation
of this mixing is shown in Figure 5 where we plot the
occupation of the Cr+ (3do, 4pc, and 4s) and h (ls) atomic
orbitals as a function of internuclear distance. These
occupations have been obtained from a Mulliken25 analysis of
the natural orbitals of the MCSCF calculation. As the H
atom approaches Cr+, there is a slight shift of electrons
from H to the Cr ado, and the originally empty 4pc and 4s
Orbitals until the nuclear separation reaches 4.00au at
which time the do occupancy plummets and the Cr 4s becomes
the dominant Cr component of the bond orbital. Soon after,
the occupancy of the Cr 43 orbital drops and that of the Cr
3do increases until at equilibrium the Cr component of the

b°rui is 61% sp and 39% do' The bond is essentially covalent

_¥

59

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60

Cr H*(’£*)

......O...’." 0 9 C 0'0"' 0l0~"
. O I a... I.

   

. .0 .
(D
I

0.7 '-

I
a-

0.6

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0.4)-

0.3 I- .15.;
“- Crs

I

0.2

 

0.! *-

 

 

l 1 I l

I 2 3 4 5 6 7 a 9 IO
RICr-HXou)

 

Figure 5. Electron population of selected atomic orbitals
from the bonding natural orbitals of the 7 CSF MCSCF
wavefunction of 5): CrH . R q designates the calculated

(equilibrium) bond length.

61
(48% H and 52% Cr). Also the Cr sp component of the bond is
essentially all 4s. The abrupt change in the o orbital from
ado to a 3d0,4s mixture is due to the 52+ root associated
with the 453d4 configuration of Cr+ crossing that with the
3d5 configuration (note the slight "kink" in the MCSCF
potential energy curve).

When CH3 approaches a Cr+ ion it can bond via its

singly occupied a orbital

to the 6D or 68 state of Cr+ to form a state of 5A1 (02v if

just considering the unpaired d electrons; 5A' in Cs )
symmetry. As in CrH+ the dominant form of the wave function

will be

1 1 1 1
( a o + o o ) 3d 3d 3d 3d ( a8-8a )aaaa
Cr CH3 CH3 Cr fix fly 0+ 0_

and at very large Cr-C separations the aCr orbital will be a

CH will be essentially a pure p orbital per-
a
25

pendicular to the CH3 plane (assuming free OR: is planar ).

3dO and the 0

Rather than optimizing the CH, geometry at each Cr-C
separation we have constructed a potential curve with the
CH3 geometry constrained to be "tetrahedral" and then

optimized the angles and Cr-C bond lengths around the

 

 

62

resulting (approximate) equilibrium Cr—C separation. As
with CrH+ this MCSCF function consisted of seven OSF's and
the subsequent CI calculation consisted of all single and
double excitations from these seven CSF's with the
constraint that there are no excitations from the Ar core,
the 18 on carbon, and the three C-H bonds. The resulting
potential energy curves are shown in Figure 6. The kink in
these curves around R= 4.50au correlates precisely with the
abrupt change in the occupancy of the Cr dO and the Cr 45
orbitals as shown in Figure 7. The MCSCF+1+2 optimized
CrCH3+ geometry corresponds to a Cr-C separation of 2.14A
and a HCH angle of 113.3° ( at a fixed C—H distance of
1.07OA). The MCSCF+1+2 bond energy was calculated directly
relative to the energy of CrCH3+ at a Cr-C separation of
20au and with the OH; group planar. The resulting energy,
18.0 kcal/mol, is less than that calculated for CrH+ and
considerably less than either of the two experimentallb’lg
values of 26 or 37 kcal/ mol. We believe that part of the
error in our calculated De is a consequence of our CI
function correlating only the CH3 electrons participating in
the 0 bond with Cr+. This leaves the six electrons in the
C-H bonds at the SCF level with the consequence that the
"in-situ" polarizability of CH3 is not well represented.

The Cr-C bond is essentially covalent (47% Cr, 53% C), and
the detailed character is only slightly different from Cr-

H+, with the Cr contribution being 54% sp and 46% do' Con-

tours of the valence GVB24 orbitals are shown in Figure 8.

 

63

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08- E
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a . I:
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05/}
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Req
A 3"! 1 I . I 1*
O I 2 3 4 5 6 7 8 9 IO

R(C-CrH0u)

Figure 7. Electron population of selected atomic orbitals
from the bonding natural orbitals of the 7 CSF MCSCF
wavefunction of sA’ CrCH;

 

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my. pm +nmouo :. econ o-uo may no. mflmufinuo m>0 .m canvas

 

 

65

 

 

 

 

 

 

 

 

 

66

B. ScH+ and ScCH3+

~~~~~~~~~~~~~~~

As a 28 H atom approaches Sc+ in the 30 state, we

may form doublet and quartet states of 2+, n and A symmetry.
If the Sc+ is in the 3F state, the molecular states are of
2—, n, A and 0 symmetry. We anticipate the ground state
will be a doublet of either 2+, H, or A symmetry.

Consider first a 2n or 2

A state of ScH+. Suppress-
ing the argon core, either state could be represented by a

function of the form

(oh+ho) d6 or " (oB-Ba)a

where at large separation, 0 is a Sc+ 4s orbital (or 3do for
the excited states of 2n and 2A) and h is a hydrogen is
function. The d orbital carries the angular momentum and is
either d‘5 or d". If one represents these states by an MCSCF
function consisting of all CSF's of either A or H symmetry
arising from two valence orbitals of sigma symmetry and one
of 0 or n symmetry, one has, in C2v' 9 CSF's. These
functions separate to the correct SCF asymptotes. The

2A state calculated with this

binding energy of ScH+ in the
ansatz, in both the spd and spdf basis, is shown as a

function of R in Figure 9 and for the 2“ state in Figure 10.
Keeping the Ar core at the SCF level, we then allowed single

and double excitations from the 9-configuration reference

Space. The bond energy vs. R calculated from these

 

67

 

  
  
  

O
-IO-I
-20«
ScH‘IzA)
E -40-
E
‘I ’50‘ MCSCF(sod)
b nMCSCF-‘Hvzhpw
£13 '60-
o .
c3 MCSCFIsde
-701
‘80“ MCSCF’I'ZISDdf)
_90-

 

 

 

5:00 I ' I000
R(Sc-H)(0u)

Figure 9. Binding energy of SCH+ in the 2A state as a
function of R for the spd and spdf basis sets in both the
MCSCF and MCSCF+1+2 calculations.

68

 

   
   

 

 

 

O
-lOd
-20.-
ScH“ (277)

-30...
A “40"
E MCSCFIspd)
E: -50... MCSCF’I’ZIIDG)
I:
I
a ’60“ MCSCFISDGU
‘7:-
C)

-70.

MCSCF+I+2I300II
'80‘
-90.-
I T I 1 I j I T T I
500 I000

R(Sc-H) (cu)

Figure 10. Binding energy of ScH+ in the 2n state as a
function of R for the spd and spdf basis sets in both the
MCSCF and MCSCF+1+2 calculations.

69

MCSCF+1+2 (CI) functions is shown in Figures 9 and 10.

The 22+ state is unique in that the 3F asymptote of
Sc+ does not contribute to this symmetry and the Sc+ ion has
the electronic configuration 453da, i.e., both the 4s and
3dO orbitals have the correct symmetry to bond to the

incoming H atom. We could represent this state with the

wave function

22+ ~ ( oh + ho ) o' ( 08-80 )0

where at large distances 0 is a Sc+ 4s orbital and 0' is the
companion ado. As Sc+ and H approach each other we expect 0
and 0' to become intimate mixtures of 4s and ado. To allow
for this mixing we represented this state with a MCSCF
function which permitted all excitations and spin couplings
among the three 0 orbitals involved and which also separated
to the correct SCF limit. The energy calculated with this
function for both the spd and spdf basis is shown in Figure
11 along with the MCSCF+1+2 configuration interaction
results.

The total energy, bond length, dissociation energy,
and vibrational frequency calculated for each state of ScH+
with both basis sets for the MCSCF and CI wave functions are
collected in Table 4.

From Table 4 we conclude that the ground state of

ScH+ is of 2A symmetry with the 2n lying 4.8 kcal/mol higher

2 2

and the 2+ being 1.1 kcal/mol above the H. While these

 

7O

 

 

   
  
  

 

 

 

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o.o-I
-20:
ScH’I22D

-30.-
‘I‘ -40. MCSCFIspd)
E
:1 MCSCFHvZIst)
I -507
b MCSCF (spdf)
‘3 -so«

‘70‘ MCSCF+I+2 (:00!)

-801

-9o-I

I I I I T I T
5.00 0.00

RISc-HIIOUI

Figure 11. Binding energy of ScH+ in the 22+ state as a
function of R for the spd and spdf basis sets in both the
MCSCF and MCSCF+1+2 calculations.

7I

 

 

 

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72
energy separations are from the spdf—CI calculation the
ordering and approximate separations are the same for either
basis at either the MCSCF or CI level. Furthermore, since
the vibrational frequencies are similar, the zero point
energy will not introduce a differential effect and the D°'s
will follow the same order. Correcting De for zero point
energy results in a D’ of 52.7 kcal/mol which is in good
agreement with the Tolbert and Beauchamp1d value of 54:4
kcal/mol and the Armentrout et a1.1g value of 55:2 kcal/mol.

The bond lengths of the 2A and 2n states are comparable, but

the bond length of the 22+ is substantially shorter. To
determine the "atomic" orbital composition of the bonding
orbitals we carried out a population analysis of the natural
orbitals of the MCSCF (spd basis) wave function for each
state as a function of internuclear separation. The results
are shown in Figures 12—14.

Consider first the 2A results in Figure 12. At
large separation (loau) we have one electron in both the H
ls orbital and the Sc+ 4s orbital. As the distance between
them decreases the Sc 45 character drops while the 3do and
4pc occupations increase until, at equilibrium, we have 1.10
electrons "on" H with the remaining 0.9 valence o electrons
on Sc distributed as 48°“', adoo-Z’, and 4p00-15.
Schilling and Goddard27 predicts a bond energy for the 2A
state of 56 kcal/mol and a hybridization of the Sc bonding
orbital of 41% 3d and 59% 4s and 4p. While our bond energy

18 in substantial agreement with this, our charge distri—

73

 

 

 

 

 

I
I
I
I
I
I
Sc4s
I . r"
Loo-I . ...——
I Hs
I
I
I
I
I
I
I
I
I
I
C I
.9 I
E I
3 I ScI-mzm
o I
0- 0.50- g
I
I
I
I
'5.300“,
I
I
Scncszo'!
. I
Real; .\.
I i I I I T 1 I I
5.00 I0.00
RISc-HIIOUI

Figure 12. Electron population of selected atomic orbitals
of 0 symmetry from the bonding natural orbitals of the MCSCF
wave function (spd basis) of 2A ScH .

74

 

LOO“

 

Population

0.50“

 

 

 

 

 

R (Sc-H)(0u)

Figure 13. Electron population of selected atomic orbitals
of 0 symmetry from the bonding natural orbitals of the MCSCF

wave function (spd basis) of 2n ScH .

75

 

Hs I bond)
I.oo- M

   
 
   
 

Sc 6,,» (NBI-L'r, Sc 4sIbond)

:
.9
:§ 2
3 + 0
$c4s(NB) . ScH ( 2 )
8 L/ -
CI. 0.50“ ‘
Sc 0, (bond)

  

 

 

 

 

Sc (bond)
90 L—a-I-' . . _’_~-
Rog—1,; - _ L'Sc4SINB)
' ' 'sfoo' ' ' 10.00
R(Sc-H)(ou)

Figure 14. Electron population of selected atomic orbitals
of 0 symmetry from the bonding and nonbonding natural
orbitals of the MCSCF wave functions (spd basis) of 22
SCH .

 

76
bution suggests the bond is 32% ado and 68% sp. The
population of the atomic orbitals in the 2“ state have a
similar distance dependence (as presented in Figure 13) and
the equilibrium electron distribution is given by 430-52,
3d00-24, and 4p00-ls with 1.08 electrons on H. The 22+
results are shown in Figure 14. Since all of the valence
electrons in this state are of 0 symmetry, we have three
electrons to keep track of. The two associated with the Sc—
H bond are labeled "bond" while the remaining electron is
"nonbonding" or "NB". The behavior of the bond populations
is similar to those in 2A and 2n states and results in the
equilibrium distribution 430-49, 3d00-39, and 4p00-lz with
1.00 electrons on H. The bond in this state is charac—
terized by the largest 3dO population and the shortest bond
length of the three studied. The ”nonbonding" electron has

the equilibrium distribution 450-35 and 3d00-53.

 

———I'—'

77

Comparison between ScH+ and ScH

Bauschlicher and Walch28 showed that the ground
state of ScH is of 12+ symmetry and is characterized by a
bond with a large do component. The bond in the low-lying
excited states had considerably reduced do character and
seemed to be more sp hybridized and consequently resulted in
larger bond lengths. Because Bauschlicher and Walch did not
calculate De's or we's we constructed wave functions for the
six lowest states of ScH using the spd basis. Since for the
neutral molecule one must be careful to take into account

the near degeneracy28 of the 482 pair on Sc, our MCSCF

 

calculations included all excitations and spin couplings of
the four valence electrons among the 4s,3d,4p, and H is
orbitals. Our CI calculations were then single and double
excitations from this MCSCF valence orbital reference space.
The MCSCF+1+2 (CI) results are collected in Table 5. Also
included are the first-order (F0) CI results from Bauschli-

cher and Walchza. The spd-CI results in Table 5 suggest

that if one ionizes either the 3A or 1A states of ScH to

2

form the A state of ScH+, the bond length will decrease by

~0.01A, the vibrational frequency will increase by ~188cm-1.
and the bond energy will increase from 41.2(3A) or 35.7(1A)

to 50.7 kcal/mol (2A). A similar pattern emerges if one

ionizes 3n or 1n to form the 2n state, i.e., Re decreases by

~0.01A, we increases by 157 cm-1, and the bond energy

increases from 36.3 or 30.4 to 45.6 kcal/mol. Unlike the

3A,1A and 3n,1n pairs, the 12* (4823d) and 32+ (4s3d4p)

 

78

 

.mu non Eonmo

 

 

882....- 88087 88.2....- 8. . ......- ~8887 8.8.87 2. ....
.N.. N... e... a... e... «N.. ..cu...
4.... 2.. ...8 08 a; ...? 85.3.. ..o
.....N .... ...... 8.. < ...z
8.... 8.... N2... .8. 8.... ...... < ....
=. +N. 6. Z. d. 4H.

. ”CO fl U Danna“

~+a+homoz may moans pom mammm 000 any nu“: 00u0~0oamo unusum cacouuooau
usaSAIzoq Hwn0>0m as now ammuaoz no mofiuuononm aaaunumasum .0 Danna

 

79

states do not arise from the same configuration and since

either could be ionized to form the 22+ state of ScH+, each

must be considered individually. The 32+ follows the above
pattern but with larger changes: ARe ~ 0.16A, Awe ~ 207
cm—1, and an increase in the bond energy from 30.7 (32+) to
44.6 (22+). These changes are consistent with an increase
in the number of do electrons in the ScH+ bond relative to
the ScH bond. However, since the 12+ state of ScH is
essentially a d bonded state there is a decrease in the dO
character of the bond in going to ScH+ and the bond length

increases while the dissociation energy and vibrational

frequency both decrease.

 

When CH3 approaches Sc+ it can bond via its singly
occupied p0 orbital and the resulting molecular state will
have 2A" (Cs) symmetry with the odd electron being hosted by

the (essentially) dO orbital on Sc+. An MCSCF function
2 -

(similiar to the A ScH+) was constructed as a function of
the Sc-C separation and the resulting potential curve is
shown in Figure 15 along with the MCSCF+1+2 result. As one
would expect, the De for SCCH3+ (46 kcal/mol) is similar to
that computed for ScH+ (51 kcal/mol). The experimental

d and 59:51g kcal/mol

values (Table 1) for D° are 65:51
suggesting that the OH: group is more strongly bound than H.
Given the demonstrated sensitivity of De to basis set size

and the probability that our basis set underestimates the

80

R(Sc-CH3) o.u.

 

 

 

2.0 4.0 6.0 8.0 - IO+O
/
20 -
E 40 . MCSCF
’2, MCSCF+I+2
I -—
‘3
£0": 60 — ScCHg FA")
00 _ Fixed CH3 Geometry
80 -
IOO L

Figure 15. Potential energy curve for the lowest 2A" state
of ScCH3 . The CH3 geometry is constrained to be
tetrahedral with a C—H bond length of 1.070A.

81

polarizability of CH3, it is not unreasonable that we
disagree with the experimental order. The MCSCF+1+2
optimized geometry for ScCH3+ corresponds to a Sc-C distance
of 2.25A and a HCH angle of 108.9° (at a fixed C-H distance
of 1.07A). The population of the various bonding orbitals
as a function of the Sc-C bond length is presented in Figure
16. The Sc—C bond is slightly ionic with Sc hosting 0.8
electrons and OR; the remaining 1.2 electrons; the
distribution of the 0.8 electrons on Sc is 480-42 3d00-23
4p00-03 and is remarkably similar to the distribution in

ScH+.

82

   
 

 

 

I
l
I
- I
ID I
I
- I
I
I
0.8 - I
I
22 I
C_) - I
I
E o. I
E ' - ScCH; (ZA')
8 . E Fixed CH3 Geometry
0.4 -
0.2-
I- SC pa/Z‘ _ 4
1 l 1 1 V

 

R (Sc-CH3) 0.u.

Figure 16. Electron population of selected atomic orbitals
from the bonding natural orbitals of the 4 CSF MCSCF
wavefunction of 2A" ScCH;

83

~~~~~~

approaches Cr+ it can use its pa orbital to form a bond to a

Cr+ o orbital resulting in the 681 stateg'29

6 1

1 1
B1 ~ ( 0pc + poo ) 3d" 3d" ado
x y +

1 1
ad‘s-p1T ( 08 80 )aaaaa

Alternatively, we can use both the pa and pTT orbitals on OH;

to form a double bond9 to Cr+ resulting in the ‘81 state

4
B ~ ( up + p o ) ( 3d p + p 3d )
1 o o "x fix "x "x

1 1
3d 3
fly 6+

3d; ( 08-80 ) ( 08-80 ) 000

MCSCF and MCSCF+1+2 functions were constructed for both
these options as a function of Cr-C separation (the CH2
geometryao was frozen at C-H R= 1.075A and a HCH angle of
128.8“). As usual, no excitations were permitted from the

Ar core of Cr+, the carbon is orbital, and the C-H bonding

84

orbitals. The resulting potential energy curves shown in
Figure 17 support the suggestion of Carter and Goddard9 that
the doubly bonded structure is more stable. The orbital
occupancies in the bonding 0 natural orbitals are plotted in
Figures 18 and 19. In Figures 20 and 21 we compare the
contours of the relevant GVB orbitals for the two states.
From Figure 18 we see that the outer minimum in the MCSCF
curve for the 681 state corresponds to Cr using a ado
orbital to bond the incoming methylene, while the inner
minimum results from the Cr using a mixture of 4s and ado.
If one constructs the 681 MCSCF solution as a function of R
by converging the calculation at R= 20au (separated atoms)
and uses this as an initial estimate for the subsequent 681
calculations at smaller internuclear separations one traces
the solid curve in Figure 17. If, however, one takes the
converged solution at R= 4.25au and uses this as an initial
estimate at R= 4.50au, one converges o a solution which has
a character similar to that at R= 4.25au and has an energy
which is higher than that obtained using the separated atoms
(R= 20au) as an initial estimate. Other points obtained in
this way ( and the associated CI) are connected by a dashed
line in Figure 17. If the molecule followed the "character—
conserving" curve rather than the adiabatic curve it would
separate to a Cr+ in the 453d4 configuration. A slight kink
is present in the 481 state and Figure 19 shows the

anticipated abrupt bond character change occurs between 4.5

and 4.25au. The frozen HCH angle used to construct Figure

85

RICr-CH2)(0u)

  
  
    
 
 

GBJMCSCF)
L—w

SBIIMCSCFIIIZ)
" CrCHZ’

(HXED CHZGEOMETRY)

 

’1‘ ‘9.(Mcscr)
E w
x '30—
t N
I
u
I
I.
8
w -40—
o
4
-50- B.(MC$CF9I02)
-60 I.

Figure 17. Potential energy curves for the SB, (filled
Circles) and 48, (open circles) states of CrCHz . The OH;
group is constrained to have a C-H bond length of 1.075A and
an HCH angle of 128.8°.

86

 

 

 

 

 

I2L
H‘
Crda)
I.O _ .................................................
0.9 - \
CfCHz' (68' )
08 " C90,”)
\_/————
07'
2:
S2 (36
[a .
_J
a? 05' '
g ' ewe-...
[/3
0.4 - "
Q3“
‘8
IS
,. /
O.I " Crpfi/I
Req \\
I I 1 . - 1 4
O I 2 3 4 5 6 7 8 9 IO

R(Cr-C)(ou)

Figure 18. Electron population of selected atomic orbitals
from the bonding sigma natural orbitals of the 7 CSF MCSCF
wavefunction of GB, CrCHz

08-

(16’

05'

POPULATION

0.3 '

 

87

chH2* (‘9, I

 

- Crda?
Cpav:
I \_____,___._E°_"l
. I
Crdq EI
I
Cr4s I
Cs—m,
R Cr4p

    

I23'356789Io
R(Cr-C)(0u)

Figure 19. Electron population of selected atomic orbitals
from the bonding sigma natural orbitals of the 34 CSF MCSCF
wavefunction of 4B, CrCHz

Y

+

‘ H

6 /
c —c

B' r ‘H

5
I S-O.747 I

 

 

 

   

 

 

 

 

 

 

-5 . .
-3 O 7 -3 0 7
5

 

 

 

 

 

 

 

-5 v
-3 O 7
30. Orbital 40l Orbital

Figure 20. GVB orbitals for the r—C 0 bond and the singly
occupied n orbitals of SB, CrCHz at its equilibrium
geometry.

89

 

 

Y
+
4 /I'I
Bl Cr —C\
E
5
8- 0.839

 

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 21. GVB orbitals for the Cr—C o and n bonds of 4B,
CrCHz at its equilibrium geometry.

90
17 is essentially optimal for those points to the right of
the Cr—C separation where the bond character changes but not
for those to the left. It seems that when the Cr+
contribution to the bond character changes from essentially
pure 3do to a strong mixture of ado and 43, there is a
significant shift of electrons from Cr into the CH2 po
orbital reflecting the lower ionization potential of the 45
vs. the ado electron. This has the anticipated effect of
reducing the HCH angle from the 381 value to 116‘, much
closer to the 1A1 value30 of 103°, observed when the po
orbital is doubly occupied.

The a bond in both molecules is essentially
covalent being 57% C and 43% Cr for both the 681 and 4Bl
states. In spite of this equal covalency, the character of
the Cr contribution in the two states is significantly
different, being 63% sp and 37% do in the high spin state
and, 36% sp and 64% do in the low spin state. The higher do
composition of the a bond in the low spin state correlates
with the shorter bond length in this state. Optimizing the
Cr-C distance and HCH angle (keeping the CH bond length at
1.075A) results in the MCSCF+1+2 values of 2.06A/117.3° for
the 681 state and 1.92A/116.7° for the 481 state. These
numbers are in excellent agreement with the Carter and
Goddard9 values of 2.07A/118.3° and 1.91A/117.6°,
respectively. Using these optimized equilibrium geometries
and the energies of the respective states at a Cr-C distance

of 20au, we calculated the bond energies 21.0 (681) and 38.7

91

kcal/mol (4B1) which are consistent with the Carter and
Goddard9 values of 25.0 and 44.0 kcal/mol but which fall
short of the experimental1b bond energy of 65:7 kcal/mol.
The 4B1—6B1 separation of Carter and Goddard is 19.0
kcal/mol while we calculated 17.7 kcal/mol.

The n bond between Cr+ and CH2 in the 4B1 state is
rather unusual. If one were to monitor the occupation of
the natural orbitals (NO's) associated with the n bond in
H2C=CH2 as a function of the separation between the triplet
OH; groups one would find that when the groups are separated
the two natural orbitals would both have unit occupation
numbers. As the groups approached, the n-bonding NO would
become more occupied than its antibonding companion until at
equilibrium it would dominate and have an occupancy close to
2.0. The occupancy of the natural orbitals associated with
the n bond in CrCH2+ are plotted in Figure 22. At the
equilibrium separation of 1.92A the n NO's have occupation
numbers of 1.48 and 0.52 which would characterize a very
"long" bond between the main group elements. This
observation, coupled with the small overlap (S= 0.366) of
the GVB n orbitals in Figure 21 and the relatively small

4

energy loss (17.7 kcal/mol) incurred in going from the B1

to the 681 states, suggests a relatively weak double band.
In addition, the atomic orbital occupations of the n natural
orbitals associated with the bond, plotted in Figure 23,

suggest that very little charge transfer has occurred

through the n system.

 

92

I

2.0

I.8 '- \
I.69 ---------------
|.6- \

IABP -------------- --

L4 -
3bl

I2 *-

 

I

0.8
4bI

OCCUPATION NUMBER

0.6 '

0.52 ----------------- --
0.4- /

0.3I --------------- 7

0.2 "

“(CI'CH.) Re (OCHz'I)

O I 2 3 4 5 6 7 8 9
RICF’CHou)

 

 

 

 

Figure 22. Natural orbital occupation numbers for the
valence n orbitals of the MCSCF wavefunctions of CrCHz
(481) and CrCH (32 ).

93

 

 

    

 

 

   
 

 

 

I2"
I | ;‘_.WCrd1(CrCHI)
c-deCrCH'zt)’ ""3-'-'.:::-;-..,..,
Lo- I :
Cpr(CrCH2T) :
0.9 - E ‘L-CpVICICHt)
z 0.8— I
Q I
,_ :
E 0.7- I
D :
U E
8 0.6- I
_J E
,3 0.5- I
53 I
L: I
o 0.4- :
E I
0.3- I
0.2 - 5
I I Re(CrCH*)
Crp-rICrCHz’.) I
0"" Crp-rICICH‘IE I RflchHg)

L. .

l 1 I l 1 1 l g l

0 | 2 3 4 5 6 7 8 9 I0

R(Cr-C)(au)

Figure 23. Electron population of selected atomic orbitals
from the bonding n natural orbitals of he MCSCF
wavefunctions for CrCHz (4B,) and CrCH (32 ).

94
D. ScCHz+
The doubly bonded state of this molecule arises
when the two valence electrons on Sc+ (3D) couple to the two
valence electrons on CH2(381). The wave function has the

schematic form

A ” [ OCH2 0Sc + 08c °CH2’ [ "CH2"Sc + "Sc"CH2]

( ae-Ba ) ( aB-Ba )

where at large separation OCH2 and "CH2 are the Po and p1T

orbitals of free CH2(3Bl) while 08c and "Sc are the 4s and
3dTr orbitals of Sc(3D). An MCSCF function which separates
to the correct SCF products consists of 10 CSF's while the
singles and doubles CI (MCSCF+1+2) from this reference space
consists of 3,660 CSF's. The energy as a function of Sc—C
separation is shown in Figure 24 for both wavefunctions.
The Sc-C bond length changes from 2.004 A at the MCSCF to
1.998A at the CI level while the HCH angle remains at 112°
in both calculations. The primary effect of the CI is to
increase the calculated De by 15 kcal/mol to 68 kcal/mol.
This is to be compared with the experimental value of 97
kcal/mol from Armentrout gt allg. There are no experimental
data on the geometric parameters with which to compare.

The lowest triplet state which correlates to the

ground state products maintains a bond in the a system and

triplet couples the n electrons. It is schematically

95

 

  
 

R (Sc-C) o.u.
O I 2:0 4.0 6.0 8.0 [0.0
20 '-
I 40 -
E MCSCF
7“ I-
I: + I
(.1) 60 _ SCCHZ ( Ag)
U
£9
m _
o
80 -
_ ”Mcscn H 2
IOO -

 

Figure 21. Potential energy curves for the lowest 1A, state
of ScCHZ . The CH2 group is constrained to have a C—H bond
length of 1.075A and an HCH angle of 128.8°.

96

represented as

a 1 1
A1” ‘ °cn2°3c + oSc °CH21 "CH2 "Sc ( “8‘8“ ) a“

An MCSCF function of this form which separates to the SCF
products consists of 7 CSF's while the corresponding singles

and doubles CI from this reference space contains 4,683

CSF's. The energy of this 3A state as a function of Sc—C
1

separation is shown in Figure 25. The optimized Sc—C bond
length changes from 2.287A at the MCSCF level to 2.264A at
the CI level with the HCH angle going from 112.4° to 113.4“.

The increased bond length of this state relative to the 1A1

state is consistent with the loss of the U component of the

ScC double bond. The calculated De for the 3A1 state is 42

kcal/mol which is 26 kcal/mol less than the 1A1 De reflect-

ing the strength of the ScC n bond.

The electron distribution in selected valence
orbitals is plotted as a function of internuclear separation
in Figures 26 and 27. Although these plots correspond to
the HCH angle of 128.8° they faithfully track the overall
distance dependence of the orbital occupancies. At the
optimal HCH angle the Sc orbitals have the occupancies

1

490-22 4p00-04 3d00-43 in the A1 state and 480'3' 4p00-‘1

3d00-21 in the 3A1 state. The corresponding carbon
occupancies are 280-31 2p00-es and 280-42 2p00-‘9.
Interestingly, the total Sc and carbon 0 populations in both

states are essentially identical although the electron

97

 

  
 

R(Sc-C)o.u.
o 21.0 1 4&0 . 6:0 . 81.0 . Q0
20-
I 40- flMCSCF+|+2
E
N '- +
5 ScCH2(3A.)
L» 60-
92
q; -
o
80-
I00»

 

Figure 2;. Potential energy curves for the lowest 3A, state
of ScCHz .

 

 

 

 

 

 

98
l
I
: Sc d7;
LO " . 9.. ‘_
. ‘..’1‘i7r' ‘Cka
J/Z—c
0.8 - p" - 4:
2
E 0'6 ’ 48c 45
<1 SOC“; ('AI)
_J t—
D
g n
0. (I4 :'
I
" l
AK1L432$
0.2 ' A
. ' e -
. : “Sc d,
l
L 1 ”(Reqh \SCR.’ at l— 4
5.00 I0.00
R(Sc-C) o.u.

JFigure 26. Electron population of selected atomic orbitals
from the bonding o and w natural orbitals of the 10 CSF
MCSCF wavefunction of 1A1 ScCHz

99

 

 

 

 

 

 

 

' I
I A .
l.O- I - , r
I
I
" I
I Cp
0.8- : a : c—
I
z I
9 I I
I- I
f, 0.6- E
a I ch 4s ScCH{(3A.)
O _ l
o.
0.4- I
V I
.- I
I
-o.‘2»- ' ”C25 . s.
. I “Sea.
SC|q,—’1v I
1 I 1 II‘ReLq \ 4 1
5.00 I0.00
R(Sc-C)o.u.

Figure 27. Electron population of selected atomic orbitals
from the bonding sigma natural orbitals of the 7 CSF MCSCF
wavefunction of 3A, ScCHz

100

distibutiton among the valence orbitals differs between the
two states. Since the n distribution in both states has one
electron on Sc and one on carbon, there has been a net loss
of 0.3 electrons from Sc to carbon in both states. This
transfer of electrons from Sc to the carbene p0 orbital is
consistent with the calculated in-situ HCH bond angle being

less than free 381 but greater than CH2(1A1).

 

IO]

~~~~~

Given the predicted stability of the double bonded
(low spin) CrCI-Iz+ molecule, we restricted our CrCH+ study to
that function which could represent a triple bond between
Cr+ and CH. Since this required three unpaired electrons on
CH, our asymptote for this fragment is the 42- state,

schematically represented by

42’

Q_H

 

3

An appropriate function for the 2. state of CrCH+ would be

3 ..
2 ~ ( op + p o ) ( d p + p d ) ( d p + p d )
o o "x “X "x "x fly ‘ITY fly fly

3d; ( aB-Ba )( aB-aa )( aB-ea ) ca
+ -

1
3d°

The MCSCF function of this form which separates to the SCF

4)2.) consists of 126 CSF's (in 02v symmetry)

products (68 +
and was constructed as a function of the Cr-C separation (at
a fixed C-H distance31 of 1.082A). The MCSCF+1+2 (no
excitations from the Ar core of Cr+, the C ls orbital, and

the C-H bond) calculation from the 126 CSF valence orbital

102

reference space consists of 249,208 configurations and was
too large for our computational facilities. The computation
can be brought within more manageable limits by restricting
the MCSCF+1+2 configurations to always have the two triplet
coupled d electrons singly occupied. This, in effect,
correlates the six electrons involved in the "triple bond"
and keeps the two singly occupied d orbitals at the SCF
level. The resulting number of configurations is then
reduced to 107,216. This "bond only" CI is designated by
(MCSCF+1+2): in the various figures and Table 2. The
resulting potential energy curves are shown in Figure 28,
the atomic population of the a N0's in Figure 29, the n N0
occupation numbers in Figure 22, and the atomic population
of the n N0's in Figure 23. The CI calculations predict a
Cr-C separation of 1.77A and a bond energy of 70.8 kcal/mol
making CrECH+ the most strongly bound of the Cr molecules in

this study. Since the 32- state of CrCH+ separates to Cr

4

+

in the ground 6S state and CH in the excited 2- state, we

must reduce the calculated De by the 2n-‘2- excitation
energy (17.1 kcal/mol) before comparing to experimental data
obtained via thermochemically interpreted experiments. This
results in a calculated bond energy of 53.7 kcal/mol for
CrCH+.

The atomic populations shown in Figure 29 suggest
that this Cr-C a bond is also the most polar of those
studied, being 64% C and 36% Cr. In addition, the Cr 0

contribution is 70% d and 303 sp, reflecting the short Cr-C

103

RICr-CH)(ou)

3.0 4.0 5.0 6:0 7.0 8.0 9.0 I00

I I l I

 

v

I

N

O
I

new

32-

 

 

 

De (Cr - CH‘IImH)

 

1’1~
MCSCF+H 2

U

-I00

-II0I-

 

Figure 8. Potential energy curves for the lowest 32_ states
Of CrCH . The CH distance is taken as 1.082A.

104

L2“

CrCH*(32’)

T

Crdcfl

(19*

(18*

  
 

(17L

0.6 I.
Cpc

POPULATION

(15*

  

 

(14

I

025

 
 

()2.

0J-

 

 

o I 2 3 4 5 6 7 a 9 I0
RICr-C)(ou)

Figure 29. Electron population of selected atomic orbitals
from the bonding c_natural orbitals of the 126 CSF MCSCF
wavefunction of 3: CrCH .

105

bond. This dO dominance is evident in contours of the GVB
bonding orbitals shown in Figure 30 where the a bond overlap
(S= 0.850) is greater than the a bond overlap (S= 0.747) in
CrCHz+. The "x and fly bonds are similar to that found in
Cr=CH2+; the n N0 occupation numbers (Figure 22) are both
significant and the total charge transfer in the n system is
small. More remarkably, on the scale of Figure 22, the
distance dependence of the occupation numbers for the n

4 3

orbitals in the B1 state of CrCHz+ and the

CrCI-I+ is indistinguishable.

2. state of

From Figure 29 we see that when the CH group is
separated from Cr+ the singly occupied a bonding orbital is
52% 0 pa, 41% C 2s, and 7% H (not shown). As this
(essentially) sp-hybridized orbital approaches Cr+, the 23
character initially decreases, the 2pc character increases,
and the Cr dO orbital remains singly occupied. This
situation continues until the Cr-C separation is less than
5au, at which point there is an abrupt transfer of electrons
in the a system from Cr+ to CH. This charge transfer is
associated with a sharp drop in the potential energy curve
(Figure 28). At a Cr—C separation of 4.00au the electron
distribution in the carbon orbitals has increased to 1.24
(0.60 in the C 2s and 0.64 in the C 2pc), while the electron
distribution in the Cr a valence orbitals has dropped to
0.70 (0.30 in both the Cr 3do and 4s orbitals and 0.10 in
the Cr 4pc). As the molecule approaches the equilibrium Cr-

C separation the occupancy of the chromium 4s,4p and the

 

106

Y
32’ (Cr CH )+ I z

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 30. GVB orbitals for the Cr-C o and n bonds of 3Z-
CrCH .

107

carbon 23 orbitals drop while the chromium 3do and carbon
2pc occupation increases. This behavior suggests that the
Cr 45 orbital attracts the CH group and "pulls it in" to a
distance where the Cr ado and 3d1T orbitals can form a bond.
A similar interpretation can be obtained for the interaction

of Cr+ with CH2 and CH3.

108

If the Sc+(3D) forms a double bond with the CH
group, we anticipate the unpaired electron will be in a w

orbital localized primarily on carbon

2p
S,<:=C.3H+

”x

(2m

Suppressing the Ar core on Sc, the carbon 18 orbital and the
CH bond orbital, the primary component of the wavefunction

would have the form

2n ~

x I OCH °8c + 0

+ n w ]

a J [ n n
5° C“ You ySc YSc You

"x ( ae-Ba I ( aB-Ba I a
CH

Asymptotically, the 08¢ would be a 4s orbital, the

ny(Sc) a 3dY2 orbital, (sp hybrid on C) and nx(CH)

°ca a po
a pn orbital on C. The MCSCF function which separates to
the SCF products (30 + 42.) consists of 17 CSF's while the
corresponding CI (MCSCF+1+2) contains 12099 CSF's. The
distance dependence of energy of the 2n state of ScCH+ is
shown for both functions in Figure 31 while the electron
population of various orbitals is shown in Figure 32. The

calculated dissociation energy is 96.3 kcal/mol and the bond

length is 1.940A. If we reference this De to the ground 2n

109

 

 

R (Sc-C) o.u.
2.0 4.0 6.0 8.0 loo
0 1 l I f l j I __________.._-—~
20 L
n- 0
4o -
- MCSCF
so -
saw“ (an)
I b
E
I .
80 - .. o
“i WMCSCF+ I +2
93
O)
0

I00 -

I20 *-

 

I4O *

 

Figure 31. Potential energy curves for the lowest 2n state
of ScCH . The CH distance is taken as 1.082A.

0.9

0.8

0.7

0.6

0.5

POPULATION

0.4
0.3
0.2

0.!

 

110

”SCBd‘W

 

 

 

 

c . (II—Sc4s

E CZPV
P I

ScCI-I"(2r1)
” C25 a
I— 3 ——-O"
“Sc4s

I
.. : ”503(10-
“ I R \"Scpa

Ir eq‘. . _ . . .

4 5 6 7 8 9 IO

R(Sc-C) cu.

Figure 32. Electron population of selected atomic orbitals
from the bonding a natural orbitals of the 17 CSF MCSCF

wavefunction of 2n ScCH .

111

state of CH using our calculated 2“ - 42— separation of 10

kcal/mol, we predict a D8 of 86 kcal/mol. This double bond
is substantially stronger and somewhat shorter than that in
ScCHz+(1A1) (68 kcal/mol and 1.998A).

If one breaks the n bond in this 2n state by

triplet coupling the n electrons

fl ~ [ o + n ( aB-Ba ) and

o o o J n H
CH Sc Sc CH yCH YSc xCH

the resulting state is bound by 69.4 kcal/mol and has a bond
length of 2.177A. Breaking the n bond costs 27 kcal/mol and
increases the bond length by 0.24A. Recall that breaking
the n bond in ScCHz+ costs 26 kcal/mol and increases the
bond length by 0.17 A. The larger bond energy in the
carbyne relative to the carbene is therefore due to the 0
bond. Looking at the electron distribution in Figures 26
and 32, we see that the carbyne p0 orbital hosts ~1.5
electrons and is essentially 50% 28 while the carbene pa
orbital contains ~1.3 electrons and is 25% 28. The stronger
bond is the more ionic and the one in which the carbon
bonding orbital is essentially an sp hybrid.

There are several other low lying states associated

3

with the D + 4Z— asymptote. For example, if we keep the a

bond intact but singlet couple the Sc 3d orbital to the

6
carbyne p1T orbital we have a 2A state. Alternatively, we
may singlet couple the Sc ado electron to the carbyne pfl

orbital and obtain a 22’ state. We optimized the geometry

112

for these states and the corresponding quartets and the
results are summarized in Figure 33. When we go from a 2n
to a 4H the energy increases but in going from a 2A to a 4A
or a 22- to a 4Z— the energy decreases. This is because the
higher multiplicity in the E state can be achieved only at
the expense of a chemical bond between orbitals of the same
symmetry (there is also a substantial increase in the bond
length). In the A and 2. cases the higher multiplicity is
lower in energy because the bond is between orbitals of
different symmetry (and, therefore, very weak) and one
recovers an exchange interaction which more than compensates
for the lost bond energy. Consistent with this, we note
that the bond lengths in the A and E- symmetries are
considerably less sensitive, than the H, to the multipli—

city.

113

Sc*(3D)+ CHI4Z') ——+ ScCH+

 

 

 

 

48 44. 75 69

 

‘III69/2I77)

I

(‘III44/ 2185’ 22"(75/2064) I0

,22‘I48/2I0I) 6 II J
- 4 -
142(50/203) 6 2 2 (79/2038)
1, A(8I/2.l35) g

I JIL“A(84/2.I20)
‘AI58/2I26) I5

 

 

 

 

 

 

 

(D-h

a...

2(3056/2150

h——-ay+-

 

I‘—

211(67/l973) I21'1(96/l.940)
MCSCF ' MCSCF+ I +2

Figure 33. Bon energy and Sc-C bond lengths of various
States of ScCH which dissociate to Sc(3D) + CH(4Z ).

114

Comparison between Cr-C and C-0 bonds

The structural predictions resulting from the
various calculations on the different Cr-C bonded molecules,
described in this study, are summarized in Table 2. We have
included the results of the "bond only" CI calculation,
(MCSCF+1+2)‘ for CrH+, CrCH3+, and Crcaz+ to calibrate the
effect of not correlating the triplet coupled electrons in
CrCH+. The data suggest that this omission results in the
Cr-C bond being longer than the "fully" correlated calcu-
lation would predict. Figure 34 shows the calculated Cr-C
bond lengths plotted vs. standard C-C single, double, and
triple bond lengths. It seems likely that this remarkable
correlation is somewhat fortuitous since we anticipate a
slight reduction in the Cr-C bond length for CrCH+ when the
two open shell electrons are correlated at the same level as
the bonding electrons. Nevertheless, the data support the
characterizaton of CrCH3+, CrCH2+ (481), and CrCH+ (32-) as
having a single, double, and triple bond between the metal
and the carbon atoms. It is interesting and consistent that
CrCHz+ (681) has a metal-carbon bond length less than the
spa single bond in CrCH3+ but greater than the sp2 double
bond in CrCHz+ (431). This sp2 single bond should correlate

*
with the bond length in the (n-n )3 state of CHZCHZ.

115

  

 

 

15.
1.4
13.
ID:
N
O
B
E ..................... ... 2.
L i
G
W
Q. I,
\lal \unllzp \H. .\l 4
..M 6W6 48 he 52
_3 _ .2 _ _ _ . _ _ . _ I.
.J 2 I
H 2 H o Hm 8 H 7. H 6.
C C 2 C I C I I
QEIG

CH3CH3

CHzCHz
c- RIII)

CHCH
Figure 34. Correlation of predicted (Cr—R)+ bond lengths

with standard R-R bond lengths.

116

BONDING 0F Sc+ WITH H2

Recently, the results of guided ion beam experi-

ments have provided estimates of the ScH+ bond energies (D‘)

1d

of 54:2 and 55:219 kcal/mol and estimated that the D' for

the process

ScH2+ (1A

1) » ScH+ (2A) + H (23)

is either 250 kcal/mol1d or equal to 64:5 kcal/mollg. Both
experiments suggest that the second ScH bond is comparable
in strength to the first and because the sum is greater than
104 kcal/mol predict that the reductive elimination of H;
from ScH;+ will be endothermic.

We are especially interested in these results since
a study of the electronic and geometric structure of ScH;+
would be a logical extension to our study of ScH+, discussed
in the previous section. Understanding the nature of the
bonding structure in ScH;+ would allow us to gain some
insight into multiple ligands bonded to one transition metal
center and, thus, into the structure of possible isomers
which could play a role in the chemistry of transition metal
ions. The reported experimental results can be used as

basis for comparison.

Results and Discussion
ScH;+ has four valence electrons and, if both

hydrogens are independently bonded to Sc+ (two ScH bonds as

117

opposed to a Sc-Hz bond), the molecule must be a closed
shell singlet. If we constrain ScH;+ to have C2v symmetry
and put it in the YZ plane with Sc at the origin and the Y
axis as the C axis, then the Ar core has the following

2

representation

2 _ 2 2 2 2 2 2 2 2 2
(core) — 1a1 2a1 3a1 4a1 5a1 1b2 2b2 1b1 2b1
and the SCF configuration would be
| 1A1 > ~ (core)2 6a? 3b: aBaB

We represent the 1A state of ScHz+ with an MCSCF function

1
consisting of all 1A1 CSF's which can be formed from the
four valence electrons and four orbitals 6a1, 7a1, 3b2, and

4b thus, building in the ability to separate smoothly to

2;

the [Sc+(1D) + H2(123)] or [ScH+ 2 +

( 2 ) + H(ZS)] products. We
Optimized the geometry of ScHz+ at this MCSCF level in both
the spd and spdf basis sets. These results are collected in
Table 6 along with our estimates of the harmonic vibrational
frequencies. The harmonic frequencies were obtained by
Iusing force constants extracted from a least—squares fit of
‘the ScHz+ energy to the bond length and bond angle. The
sgrid was sparce, consisting of nine points encompassing the
:minimum with a AR and A9 of 0.1au and 5°. We believe that
the ScH2+ frequencies are high, perhaps by 10%.

A population analysis of the MCSCF wave function at

118

Table 6. Equilibrium Properties of ScHz+ in the Ground IA]
State Calculated with the spd and spdf Basis Sets Using the
MCSCF and MCSCF+1+2 Functions.

 

 

 

 

 

 

SCH2+('AI)
MCSCF MCSCF+1+2
smi sufl an qflf

E, au -76065948 -76066406 46068426 -760.69935
R.. A 1.780 1.768 1.757 1.746
9. deg 103.4 104.8 103.6 106.7
PM“. cm-l 478 491 460 489
75,cm-' 1561 1712 1714 1734

7,. cm" 1568 1722- 1723 1745

119

the calculated equilibrium geometry allocates the four

valence electrons as follows:

0.47 0.05 0.23 0.15 0.79 1
4s 4py ado/6+ 4pz sayz 1 2

Given the known deficiencies of the Mulliken population
analysis25 one should not make too much of the quantitative
details of this distribution. The qualitative message.
however, is clear. The bonding in ScHz+ is primarily due to

the Sc 48 and 3dYz orbitals hybridizing as

0:19
+/ \-

. Q9
,. 4.

 

 

 

 

 

and then bonding to the incoming hydrogen atoms. This
picture is consistent with the calculated valence angle of
106.7° and the large "d character" in the bond (a total of
1.02 3d electrons or 0.51 3d electron/bond) is consistent
with the bond length in ScH;+ (1.745A) being shorter than

any in the calculated states of ScH+. The sdpf-CI function

120
predicts that ScHz+ is bound (De) by 106.4 kcal/mol relative
to Sc+ (3D) and 2H (28). Since the ScH+ (2A) De was
calculated to be 54.7 kcal/mol, we conclude the De for the

process

ScH2+ (1A

1I 4 ScH+ (2A) + H (28)
is 51.7 kcal/mol. Using the calculated vibrational fre-
quencies of ScH;+ and ScH+, this De translates into a D° of
48.3 kcal/mol. Even if our calculated vibrational fre-
quencies for ScH;+ were too high by 10% this 0’ would be
increased by only 0.5 kcal/mol. There are two experimental
values available for this dissociation energy: Tolbert and
Beauchamp1d report D°2 50 kcal/mol while Armentrout et

a1.lg

measure D°= 64:5 kcal/mol. In light of our success
with the ScH+ bond energy, the large discrepancy (~25%)
between the calculated value of 48.3 kcal/mol and the
measured value of 64 kcal/mol is disappointing.

In an attempt to understand the source of this
discrepancy we carried out several additional calculations
at the predicted equilibrium geometry. In particular we
increased the number of active orbitals in the MCSCF (we
used 6a1, 7a1, 8a1, 3b2, 2, 1,

correlation perpendicular to the molecular plane and

4b 3b 1a2) to allow for
increased flexibility in the "a" system. While the
resulting MCSCF energy was lowered by 6 milihartrees the

MCSCF+1+2 was essentially unchanged from that reported in

 

121
Table 6.

From the summary of the calculated energetics shown
in Figure 35 we anticipate that the reductive elimination of
H2 from ScHz+ will be endothermic. While the calculated
endothermicity is only 2 kcal/mol we do expect our
differential correlation error to favor the 1A1 state of
ScHz+, and thus, increase this calculated endothermicity.
Since this calculated endothermicity is with respect to the

spin forbidden process

the spin—allowed process (in which Sc+ is in the 1D

state)would be endothermic by at least 9 kcal/mol.

122

5c*(301+2HI251

20-

 

30t-

 

40 ' \ 103.0

 

 

 

 

 

I023
70 _ \ I064

D (kcal/ mol) ‘

I?

I
I
I
I
I
I
I
I
I
I
I I
60r- I was I
I 1
I
I
I
I
I
I

 

 

 

 

......... \---.----.
I) ____J ‘—'—_ v

"° " 5“”30““: "2°" ScHz*I'A.)

 

QOr

Figure 35. Computed dissociation energies of various
Combinations of Sc and two H atoms relative to the
separated ground state atoms. The dotted horizontal lines
(D°) are the D 's corrected for zero-point vibrational

energy.

123

BONDING 0r 0r+ WITH 01.

It has been shown that various first-row transition
metal cations react exothermically with small alkanes while
others do not. For example, Cr+ does not react exothermi-

cally with small alkanes but Fe+ doesa'32

Recently,
reactions of chloro-substituted Cr+ with small hydrocarbons

were found to be exothermic32

+ +
CrCl + /\/—--> ClCrC4H8 + H2

This is an example of the chemical activation of an unreac-

tive transition metal ion32’33.

Another interesting aspect
of these reactions is the fact that 01 remains "adhered" to
Cr+ throughout the reaction leading to the thought that Cl
plays an active role in the overall exothermicity of this
reaction.

In this study we are interested in the electronic
and geometric structure of the low lying states of CrCl+.
Through the analysis of the molecular wavefunction we wish
to develop a qualitative understanding of the nature of the

chemical bond and gain insight into the role Cl plays in

activating Cr+.

A. Wavefunctions and Computational Details

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

C1 in the 2P ground state has only one unpaired

electron. If this electron approaches either a do orbital

124

in the 6S state or a 4s orbital in the m=0 component of the

+
6D state of Cr+ then the resulting molecular state is a 52 .

 

This is analogous to the bonding involved in CrH+
Suppressing the argon core of Cr and all but the 3p
electrons on Cl, the 52+ state of CrCl+ can be represented

by the schematic (GVB)23 functional form

I a pa + pa 0 J pnx pny dnx dny 6+ _

where at large separation o is a do orbital from the 6S

state of Cr+ and pa is a 3pz orbital from C1. All singly
OCCupied d orbitals have 0 spin and the two electrons in the
°rPo «orbital pair, as well as the doubly occupied pn
Orbitals, are singlet coupled. A CrCl+ wave function of
this form, which dissociates to the correct Hartree—Fock
produt:ts [Cr+(63) + Cl(2P)], consists of 7 configuration
State functions (CSF's)20 and will be referred to as
MCSCF(7). The CI wave function, consisting of all single
and double excitations from the 7 CSF reference space,
Contains 92,256 CSF's. This wave function is referred to as

MCSCF(7)+1+2.

 

125

If instead a doubly occupied p orbital from Cl
approached either a dO or a 43 orbital on Cr+ then the
resulting molecular state is a 5n. This leaves the unpaired

electron perpendicular to the "sigma" system available for

pi—bonding with Cr+.

 

 

Whether this state is bound or not will depend to a large
extent on the interaction of the three electrons in the

sigma system and the extent of overlap of the pi "bonding"

orbitals.

5

The wave function for the n state of CrCl+ has

the asymptotic functional form

in which all singly occupied d orbitals have a spin and the

two electrons in the dny’pfly

doubly occupied pO fl orbitals, are singlet coupled. In

orbital pair, as well as the

addition to all of the obvious spin couplings, all
distributions of 3 electrons among both pa and do orbitals

are also included. The resulting wave function for the 5n

 

 

 

126
state contains 14 CSF's (MCSCF(14)) and dissociates to the
correct (Cr+(68) + 01(2P)] Hartree-Fock products. The

corresponding CI wave function, MCSCF(14)+1+2, consists of

139,579 CSF's.

B. Energetics and Geometric Structure
The calculated dissociation energies and other
geometric parameters obtained from the MCSCF and MCSCF+1+2

5 + 5

functions of the 2 and H states of CrCl+ are collected in

Table 7. At equilibrium, the difference in energy between

the 52+ and the 5

n states of CrCl+ is 8.2 kcal/mol at the
MCSCF level and 5.4 kcal/mol at the MCSCF+1+2 level. The
bond lengths of both states are essentially identical; in -
comparing with CrH+, the bond length of CrH+ is shorter by

~0.6A while the bond in CrCl+ is almost twice as strong.

C. Potential Energy Curves and Charge Distribution.

An analysis of the interaction of Cr... with Cl is
necessary for the interpretation of the overall chemistry of
the two low lying states of CrCl+. The calculated potential
energy curves for the 52+ and 5n states at the MCSCF and
MCSCF+1+2 levels are shown in Figure 36. In Figures 37 and
38, we show the electron distribution of the valence orbi-

tals more involved in bonding, as a function of internu-

clear distance for both states of CrCl+. The occupations of

 

 

 

 

 

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www.mmfi sfi www.mm a
flaw new one one
7 m.Hv «.mu m.s¢ v.vm
2
1 ha.m cm.“ mH.~ H~.~
N+H+momoz homo: N+H+momoz homo:
em +wm

:0 .m
mtmmo

0

Eu . 3

HI.

fioE o
\fiwox . o
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= may cam

m

+m

w way as +Hopo no mmauumaoum ssaunfifiassm .s mam<a

128

 

     
  

R(Cr-C|)o.u. , ,
\" I
rueo
l
SCF 71r/‘/" g
K10-
20.0-
% 300_ MCSCF(I4)5H
C 5 +
U 400‘ ,xz/MCSCF (7) 2
Q
a) 50.0-
C)
60.0- MCSCF (I4)+I+2 5n
70.0: rumcscrwnuz 52*
sum

 

Figure 36. Potential energy curves for the lowest 52+, 5n,
and 7n states of CrCl .

 

129

2.0 I ;
| y
I
.. I
I
I
I

s“
\
\

I
I
I
l \
I
I

 

 

I.5 "
I \\
'- I
2? I \lb’CIDU
Q ’ : I
F— I
<[ : II
..J ' ' |
0 IO - Cr d1r /' I‘M —
. : cr (3' I 2 )
I
- I
I
I
- : “U do
_ I
I
I
05” :
I
- I
I I
I 5
. Cr 5 "17““-
I
Cr dcr M "II I“
b : ,—~\’V Cr pcr
Req 14:1 ‘\

 

2.0 4.0 6.0 8.0 IOO
R(Cr-C|) o. u.

Figure 37. Electron population of selected atomic orbitals
from the bonding n tural+orbitals of the 7 CSF MCSCF
waVefunction of 52 CrCl .

 

I30

 

 

 

 

 

2(3- I
I 1‘
I/
' CI p”)! ‘ZnI’
II
in , I
Cl 590%.
I I
I5 - I I
I I
~ I I
I I
. E 341AClpwy
Z - g I
9 : E
F’ - l I
§ '0 C' “P?- ..... I .......
E3 . : ?,77
CL ’ I CrCIIISI'I)
'- I
E
” I
I
I
p I
I
0.5 " I art—Cr dry
I
" I
I
I
I. I
I
I
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.. I.--'
.1
I” [Kc/Crs
N bub- 4 4
8L) K10

 

RICr-C|)o.u.

Iigure 38. Electron population of selected atomic orbitals
from the bonding natural orbitals of the 14 CSF MCSCF
wavefunction of 'n CrCl .

I31
the valence orbitals were obtained from a Mulliken
analysis25 of the natural orbitals of the MCSCF
calculations.

By comparing Figures 36 and 3 (CrH+), we can
observe that for the 52+ state of CrCl+, the interaction of
the atomic fragments is initially repulsive but at around
6.00 au the energy drops, resulting in a De of 34.4/47.3
kcal/mol (MCSCF/MCSCF+1+2) relative to the asymptotic
products. On the other hand, the initial interaction of Cr+
and H is attractive but at ~4.00 au, the drop in energy is
also abrupt leading to a dissociation energy of 18.5/25.1
kcal/mol (MCSCF/MCSCF+1+2).

The character of these potential energy curves can
be understood by following the occupation of the valence
orbitals found in Figures 37 and 5 for the 52+ states of
CrCl+ and CrH+. At large internuclear separation, the dU
orbital from Cr+ and the pa orbital from Cl are singly
occupied, and the pfly from Cl is doubly occupied. At less
than 6.00 au, there is an abrupt change in the occupancy of
the do and 4s orbitals on Cr+. This sudden exchange of
"occupancy" (sharp decrease in do and increase in 45) is
observed in CrH+ and is due to the mixing of the 63 and the
6D states of Cr+. This dU/4s exchange represents the
initial reason for the observed discontinuity in the
potential energy curves. In CrH+ the do occupancy proceeds
to increase again while the 4s decreases until an almost 50—

50 mixture of do/4s at equilibrium. In CrCl+, however,

 

 

I32

after the initial 4s,da occupation exchange, the 4s
occupancy drops, the do remains essentially constant while
pa on Cl increases from the asymptotic occupancy of 1.0 to
the equilibrium value of 1.55. This is the main difference
between CrCl+ and CrH+ -——the charge transfer from the Cr+
4s orbital to Cl. In the CrCl+ case, this charge transfer
glgg contributes to the discontinuity observed. From the
population analysis, we infer that this charge transfer is a
consequence of a higher 52+ state with the asymptotic

++5

products (Cr ( D) + Cl-(1$)] intersecting the ground 5

2+
state with the lower energy asymptotic products [Cr+(SS) +

01(2P)1. There is also an indication of "backbonding" (Cl ~

Cr) through the n orbitals. Therefore, at equilibrium, the
5

overall charge distribution in the 2+ state is as follows;

 

vvhere the net charge transfer from Cr+ to Cl is ~0.5
(electrons.

In the 5n state of CrCl+, as Cr... and Cl approach
Geach other (Figure 36) the interaction is initially

5

attractive. However, as in the 2+ case, this initial curve

(solid curve) undergoes a sharp change in slope at ~5.00 au

133

resulting in a minimum of 26.2/41.9 kcal/mol (MCSCF/
MCSCF+1+2). The solid curve represents the minimum energy
solution for the 5n state where the converged calculation at
R=20.0 au is used as an initial estimate for subsequent
calculations at smaller internuclear distances.

However, if one takes the converged solution of the
5n state at R=4.75 au as an initial estimate for R=5.00 au,
one converges to a solution (dashed line with opened circles

++5
r

in Figure 37) leading to the asymptotic products (C ( D)
+ C1_(IS)J. This interpretation is based on the population
analysis shown in Figure 38.

In Figure 38, we can see that, at ~5.00 au, there
is an abrupt transfer of 0.88 electrons from Cr+ to Cl

through the n orbitals (Cr dn and Cl pfly) giving the mole—

Y
cule considerable Cr++,C1— character at this point. Subse-
quently, there is a shift of electrons back to Cr through
the n system (~0.1) and through the a system. In the a
system there is a larger amount of backbonding (compared to
52+) from the "spa" orbital in C1 to the 4s orbital in Cr+
With little participation from the dO in Cr+, i.e., very
little 4s/do mixing through the same mechanism seen in the
52+. Another way of thinking about this is that, in this
case, the 48 has an alternate source of electrons other than
do and the three electrons in the "a system" are distri—

buted to avoid a greater repulsive interaction. Therefore,

at equilibrium, the overall charge distribution in the 5N

State is as follows:

I34

 

where the net charge transfer (Cr 4 01) for the lower energy
minimum is ~0.5 electrons.

5n state of CrCl+, we

In order to form Cl- in the
must have electron transfer from the d17 orbital of Cr+ to
the Cl pfl orbital. If the two electrons in the d,p-nY
orbitals of the 5n state were instead triplet coupled, we
‘would then have the 7n state of CrCl+. An SCF calculation
‘was done for this state and its corresponding potential
energy curve appears in Figure 37. The dissociation energy
of this state is only 8.2 kcal/mol relative to the (Cr+(68)
‘+ Cl(2P)J fragments. This much reduced De' relative to the
5" state, is a measure of the importance of the charge
transfer in the 5n state which is now prohibited in the 7n
State by the Pauli Principle. It is worth noting the
s1milarities of this potential energy curve with that of the
5" state at distances greater than 5.00 an where no charge
transfer has taken place in either state. .

The large Cr++,Cl- character in both the 52+ and 5n
atates suggests that the relative energies of these states

may be interpreted with a ligand field model. Since the

I35

Cr++ ion is a d4 configuration and, therefore, a 5D state we

would expect the three components of the 5D ( 52+, 5n, and

5A ) state to be split by the ligand field of C1. in the

order 52+ < 5n < 5A which is as observed for the 52+ and 5n

states of CrCl+. We have not calculated the 5A state of
CrCl+ but anticipate it will be somewhat higher in energy

than the 5n state.

D. Long Range Interactions.

~~~~~~~~~~~~~~~~~~~~~~~

5

Both the 2+ and 5

fl states of CrCl+ dissociate to
the (Cr+(68) + 01(2P)] products but, as Cr+ approaches Cl,
the interaction is quite different at long range. At very
large distances, Cl views Cr+ as a point charge. The energy
of interaction was calculated for Cl in two ways. One, we
Isill call the "2 System" where the singly occupied valence
orbital of Cl lies on the internuclear axis pointing towards

the point charge.

 

a“ .Q.

point charge .

The other system is the "n System" where a doubly occupied

oI‘bital is now in the direction of the point charge while

I36

the singly occupied orbital is perpendicular to this.

 

e—
point charge

 

In general, the energy of interaction of an atom

with a point charge can be express34 as

E a 2° - a F F -

1 I
d8 a B 3 9&8 Fm8

NIH

where “as is the polarizability tensor, eaB

pole moment tensor of the system, and Fa,F

is the quadru-

B and Fae are the

electric field and the electric field gradient components

generated by the point charge34. Considering the symmetry
Of the chlorine atom approaching a point charge, the energy

exPression is then

 

a: or n 92 or n
A = 3(c1 R) - 2(01 0) = - ——55— + ‘2
E: or n ' ' 2R4 R3

where the first term on the far right is the charge-induced
d1Pele interaction and the second term is the charge-
quadrupole interaction.

The polarizability of the 2 system was calculated

I37

to be aiz=10.7 a.u. and the quadrupole moment as eiz=1.78

H

a.u. For the n system, dnz=10.9 a.u. and ezz=—0.89 a.u.

z
The results for the charge-induced dipole interaction
energy, the charge—quadrupole interaction energy, the
combined interaction energy (AF.z and AER) and the calculated
ab initio large distance energies (for CrCl+) are assembled
in Table 8.

The A2 values are comparable to the calcu-

Z or H

5 + 5 +
lated AE values for the Z and the n states of CrCl at
large distances, with a 7—12% deviation at ~R=6.0 bohrs. As
the chlorine atom approaches the point charge from large
separations, the interaction energy becomes slightly repul—
sive for the "2 System" (as in the 52+ state of CrCl+) while
the "n System" is quite attractive (as in the 5n state of

CrCl+). This is a consequence of the change in sign of the

quadrupole moment of Cl in the "n System".

 

I38

TABLE 8. Long Range Interaction Energies of a Chlorine Atom
approaching a Point Charge.

 

 

 

"X"—System:
R an -or/2R4 mH e/R3 mH AE mH AE mH
I I I El calcl
10.0 -0.54 1.78 1.24 1.24
8.0 -1.30 3.47 2.17 2.14
6.0 -4.13 8.23 4.10 3.65
"fl"—System:
10.0 —0.54 —O.89 —1.43 -1.46
8.0 -1.33 -1.74 —3.07 —3.17

6.0 -4.21 -4.11 -8.32 -8.94

I39

CONCLUSIONS:

COMPARISON BETWEEN THE SC AND Cr COMPOUNDS

 

A. Transition Metal—Single Ligand Bonds
1. Bond Lengths and Orbital Composition

The preceding discussion suggests that CH3, CH2,
and CH form single, double, and triple bonds, respectively,
with Cr+, and single, double, and double bonds with Sc+.

The calculated Cr—C and Sc-C bond lengths are consistent
with this observation. The Sc+ ion has only two valence
electrons available for bonding, which explains the inabi—
lity of ScCH+ to host a triple bond. The correlation of the
Cr-C bond lengths with the standard C-C bond lengths (Figure
34) is also consistent with the molecules containing a
single, double, and triple bonds. In Figure 39, we summa—
rize the structural and energetic results discussed for both
Sc and Cr sets of compounds. The Sc—ligand bond lengths and
bond energies are always larger than the corresponding Cr
compounds. The large Sc—ligand bond length is a reflection
of the larger ionic radius of Sc+. Of course, the metal—CH
bond is longer in ScCH+ than in CrCH+ because the former is
a double bond while the latter is a triple bond.

Throughout our study of Cr+ and Sc+ compounds, we
note the importance of the 4s,do mixture in characterizing
the electronic structure of transition metal—single ligand
bonds. The ground state of the Cr+ ion has a 3d5 electronic
configuration while the ground state of Sc+ has a 453d

configuration. The Cr+ 4s3d4 excited state is ~ 35

 

 

I40

50.7(54) 25. '. (59)
(2A) 'SciH (52") :6er
I834 .3. [63,8
40.I(43) ..H H l8.O(52)\\H
(2N) -Sc-C‘Z (5N) :Cr_C°AH o
2:2531;2{\{F:*\IC”3° E21:;2{!F:‘II3
68( 7|) /H 4 38.7(99) /H
('A.) SciCQ “2° ( B.) 'Cr; C\) ||7°
l.998 ZI H L92 5.
42(45) 2I.0(55)
(3A0 Sc - 03 lll° (68.) :CV 6:) II7°
2.264 3 H 2.06 K H
96.3 (99I 70.8(I48)
(2n) Sch-H (32‘) ICrEC-H
. I" .
I.94A L77A

Figure 39. Comparison of the calculated bond energies and
QEOmetric parameters for various Sc and Cr compounds. Bond
energies adjusted by the exchange energy loss in forming the
TM-R bonds are in parenthesis.

V

141

kcal/mol21 above the d5 ground state and the Sc+ 3d2 excited
state is ~14 kcal/mol21 above the sd ground state. At large
internuclear separations from the incoming ligands, the o
electron in Cr+ is essentially a pure do orbital and, in
Sc+, a 45 orbital. As the metal approaches the ligand, we
observed (by use of the potential energy curves and the
population plots) how a higher root of the same molecular
symmetry becomes lower in energy, to the point which, at
equilibrium, a mixture of the "asymptotic" ground and
excited molecular states is preferred. The effect of this
interplay of low lying states differs for the two metals
since Sc+ has 3dO being mixed in with the 4s orbital and Cr+
has the 45 mixed "into" the ado, but we can see that these
mixtures are more "gradual" when the ligand approaches Sc+
than approaching Cr+. The 45 orbital has a larger spatial
extension than the 3d orbitals and, thus, is the first to
feel the presence of the substituent. A mixture of the 4s,
ado, and 4pc orbitals allows for proper polarization of the
localized molecular orbital on the metal towards the ligand.
In Table 9 we summarize, for both Sc+ and Cr+, the
percentage of metal contribution to the a bond and the
percentage of 4s and 3dO character for comparison with the
Calculated bond lengths of the TM-H+, TM—CH3+, TM—CH2+, and
TM—CH+ sequence. The percentage of the Cr do orbital in the
0 bond increases, the 45 character decreases, and the Cr—C
bonds become more ionic as the bond order increases. Also,

as the dO character increases the bond length becomes

142

 

 

 

us.a mm on mm so.“ 06 an mu moI+za
um.H mu so as oo.m am No no NmoI+za
4H.~ we ow av on.“ «m om mm nmon+zs
I O I D
«.o 29m m« x o a :9 x <.o 29m me x o a so a
+po +om +29

 

.momom on no new on om may no sumo ca
mnuocmq ocom on» com .pmquumno kufinao om saw me mo wUMuzmoumm may .ocom
0 9.3. Cu Gofiufiflwhvcoo ASH; 2“..va GOfipHmGwhH 9.3. MO Gomfihwmfioo .m mgmfih

143
shorter. A similar pattern emerges for the Sc analogs, but
‘when the ligand changes from GE; to OH, the bond order does
not increase but the extent of charge transfer does and the
proportionalities of the 4s/do mixture is adjusted
accordingly. ScCH+ is more ionic than CrCH+ since the extra
n backbonding is not possible.

The mechanism in which the excited sd4 state of Cr+
comes into play is, first, a previously pure d0 orbital
becomes an approximate 50/50 mixture of 4s and 6.0 and,
second, as the bond order increases, the Cr 4s decreases not
only by a transfer "back" to the d0 orbital but, also, by a
(charge) transfer to the substituent (extent of which also
increases as the bond order increases) making the relative
Xdo larger. This mechanism is not obvious from the electron
distribution diagrams directly since the 4s,do mixture
occurs simultaneously with the charge transfer through the o
and n system.

From the discussion of the energetics and the
population analysis of the low lying 52+ and 5n states of
CrCl+, the bonding in both states has large ionic character
due to the charge transfer from Cr+ to Cl. Also in both
states, there are varying degrees of backbonding leading to
an overall charge transfer of ~0.5 electrons. The 52+ and
5n roots, with the asymptotic products of [Cr++ (d4) + Cl-

(15)], are low in energy (more so than any associated with

+ ..
[Cr+ + C ]) and we are able to observe a more direct

influence of these roots on the nature of the bond. These

144

"ionic" excited states seem to be in strong competition with

the 52+ and 5

fl states stemming from the excited state of Cr+
(6D,sd4), as well as the states from the ground state
products. In all TM+-C systems discussed, we observed the
usual 4s/do mixture but, even during charge transfer, there
is a decrease in the amount of 4s and an increase in do
(extent of which varied). In the 52+ state of CrCl+, we can

.4.

see an increase in 43 and a decrease in dO (Cr sd4 state

mixing in) followed by a decrease in 45 while the ado
remains constant (not observed in Cr+-C or Sc+-C). The 52+
"ionic" root took over the readjustment of the 4s/do
mixture. There is a charge transfer from the 4s orbital on
Or to Cl until the 4s occupancy reached the same as that of
3do. In this case, the 4s/d0 becomes about 50/50, but the
total number of electrons (in the 0 bond) is much less than
that of the Cr-C bonds. The total charge transfer is a
combination of o-donation (CraCl) and n—backbonding (CleCr).

In the 5H state of CrCl+, the incoming pO orbital
on C1 is already doubly occupied, therefore, charge transfer
will not occur from Cr»Cl through the 0 but through the n
system. As for 4s/do, the amount of 4s contributing to the
0 bond is about the same as in the 52+ state but the "source
of electrons" is not the do electrons, rather, the pO
orbital from Cl. The dc occupancy remains constant during
this (C14Cr backbonding) charge transfer (as in the 52+

state).

The previous analysis was possible by the use of

145

electron distribution diagrams (population plots) where the
the atomic orbital components of the o (and n) molecular
orbitals are monitored as a function of internuclear
distance (from large to around equilibrium separations).
Besides the disadvantages of not relying on the quantitative
details25 (exact values) of the occupations, an excellent
qualitative picture is possible by examining the changes
involved in the formation of the molecular system. Further

comments on the 4s/do mixture will be made by use of the

exchange energy loss concept.

2. Exchange Energy Loss

It is interesting that although the Cr compounds
have the shorter bonds they have the smaller bond energies.
This is quite different from the familiar structure/energy
systematics of molecules composed entirely of main group
elements and reflects the importance of the Exchange Energy
Eggs concept in transition metal systems.

The exchange energy associated with the d electrons

in the free Cr+ ion (d5 configuration) is given by

6 5
K ( S) = Z Kij
i>j
i.e., the sum of 10 interactions between the five singly
occupied d orbitals (do' dnx’ dny' d6+’ and d°_). If we

estimate a Cr+ d-d exchange integral as 17 kcal/mol, the

exchange energy loss in forming one, two or three bonds is

146

approximately 34, 60 and 77 kcal/mol. This is interpreted
as the amount of energy Cr+ must use to randomize the spins
of its high spin coupled electrons in anticipation of
forming one, two or three bonds using only d orbitals. The
Sc+ ion in the 3D state requires 3 kcal/mol to prepare for
either a single or double bond.

When the calculated De's are augmented by the
estimated exchange energy loss, the numbers in parenthesis
in Figure 39 are obtained. These very simple "corrections"
result in "derived" bond energies which are more in line
with conventional bond length/bond strength expectations.

In particular, the CrECH+ derived bond strength is ~3 times

 

as large as that of Cr-CH;+ and suitably larger than that of
Sc=CH+. While this simple model brings some order to the
calculated bond strengths, it must be emphasized that the
calculated, and not the "derived" bond energies, should be
compared with experiments. Furthermore, the model is based
on SCF concepts and presumes that the ground electronic
configuration of the transition metal ion is dominant not
only asymptotically, but also at Re’ This, clearly, is not
the case as the various population analysis plots demon-
strate. Nonetheless, we believe the model accounts in large
measure for why the positive ions of the early transition
series elements have such different De's for the same
ligandas.

An extension to the exchange energy model was

presented by Carter and Goddard9 to explain the relative

147

amount of the 4s/do mixture in the a bond of CrCHz+ (4B ).

1
We previously estimated the exchange energy loss in forming
a double bond, is approximately 60 kcal/mol, if we only
consider the Cr+ (d5) ion. If the exchange energy loss were
calculated for the Cr+ (sd4) ion, it would take ~37 kcal/mol
to form a double bond. The Cr+ (sd4) ion appears to be 23
kcal/mol more favorable towards forming a double bond, but
the Cr+ (sd4) ion is approximately 24 kcal/mol (SCF) higher
in energy than the ground state ion, thus, explaining the
near 50/50 mixture of 4s,do in the 0 bond. A similar
analysis can be performed for the triple bond, as well as
the single bond. The exchange energy loss, incremented by
the d5—sd4 excitation energy, needed in forming one, two,
and three bonds is approximately 34, 61, and 79 kcal/mol.
Under these terms, the Cr+ (sd4) ion is O, 1, and 2 kcal/mol
higher in energy than the Cr+ (d5) ion. For completion, one
should include the relative Cr++ (d4/sd3) "excitation
energies", keeping in mind that the actual amount of Cr++
character depends on the electronegativity of the

substituent.

B. Transition Metal—Double Ligand Bonds

One of the motives that led us to study ScH;+ was
to calculate the differential energy of removing one -H bond
from ScHz+ and compare with our calculated values for ScH+.
We calculate that the second bond in SCH2+ is almost as

strong as the first (a D8 of 51.7 vs. 54.7 kcal/mol) though

148
not as strong as experiment suggests (D'Z 501d or equal to
651g kcal/mol). The equilibrium structure of the ground 1A1
state of ScH2+ is nonlinear (S= 106.7°) with a bond length
of 1.75A. This bond length is shorter than in any of the
three ScH+ states studied and reflects the larger d
character in the ScH;+ bonds. Sc contributes to the bonds
in ScH2+ via the 4si3dY2 hybrids which is consistent with
the optimized H-Sc—H bond angle.

Through our analysis of the calculated energies we
anticipate that the reductive elimination of H2 from ScH2+
will be endothermic by ~9 kcal/mol. Preliminary results on
the 482 state of CrH;+ at the MCSCF level show that the bond
strength of the second bond is ~7 kcal/mol, about 12.5
kcal/mol (MCSCF) weaker than the first CrH+ bond.

Therefore, the reductive elimination of H; from Cer+ would
exothermic by ~75 kcal/mol.

Further studies are necessary to show the effect of
multiple ligands on the bond strengths of the individual
bonds. We have shown the case of two ligands of the same
kind. An interesting system to pursue would be the bonds in
CrClH+ and CrCle+. As mentioned before, Cr+ does not react
exothermically with small alkanes* but CrCl+ does*. If we
were to compare (theoretically) the reactions of Cr+ and
CrCl+ reacting with H2 or CH4, we would need to study the
bond strengths of multiple—ligand systems in order to
understand the effect Cl has on Cr+ and/or its participation

in the reaction mechanism so that the reaction would proceed

exothermically.

149

 

LI ST OF REFERENCES

b)

C)

d)

e)

f)

9)

b)

C)

CH

e)

f)

LIST OF REFERENCES

R.R. Corderman and J.L. Beauchamp, J. Am. Chem. Soc.,

2Q. 3998 (1976)

P.B. Armentrout, L.F. Halle, and J.L. Beauchamp, J.

Am. Chem. Soc., 103, 6501 (1981)

 

L.F. Halle, P.B. Armentrout, and J.L. Beauchamp, J.

Am. Chem. Soc., 103, 962 (1981)

M.A. Tolbert and J.L. Beauchamp, J. Am. Chem. Soc.,

N.

106, 8117 (1984)

Aristov and P.B. Armentrout, J. Am. Chem. Soc.,
106, 4065 (1984)

S.K. Huang and J. Allison, Organometallics, g, 883

(1933)

J.L. Elkind, N. Aristov, R. Georgiadis, L. Sunderlin,

H.F. Schaefer III, Acc.

and P.B. Armentrout, private communication.

Chem. Res., 19, 287 (1977) and
references therein -

G.A. Somorjai, Chemical Society Reviews, 19, 321

(1984)

6.0. Bond, "Catalysis by Metals", Academic Press, New

York, 1962

Sinfelt, Advan. Catalysis, g9, 91 (1973); Prog. in
Solid State Chem., 19, 55 (1975)

Biloen and W.M.H. Sachtler, Adv. in Catalysis, 99,
165 (1981)

Murad, W. Swinder, S.W. Benson, Nature (London),
289, 273 (1981); E. Murad, J. Geophys. Res., 99,
5525 (1978)

3- .J. Allison, "The Gas Phase Chemistry of Transition Metal
Ions with Organic Molecules", to appear in Progress in
Inorganic Chemistry, Vol. 34, 1984 and references
therein

4. T.A. Lehman and M.M. Bursey, "Ion Cyclotron Resonance

150

 

10.

11.

12.

13.

14.

15.

16.

17

e

151

Spectroscopy", John Wiley and Sons, Inc., New York, 1976

a) P.B. Armentrout, and J.L. Beauchamp, J. Am. Chem.
Soc., 102, 1936 (1980)

b) P.B. Armentrout, L.F. Halle, and J.L. Beauchamp, J.
Chem. Phys., 99, 2449 (1982)

c) R.V. Hodges, P.B. Armentrout, and J.L. Beauchamp, Int.
J. Mass Spectrom. Ion Phys., 99, 375 (1979)

J. Muller, Angew. Chemie, 11, 653 (1972)

See Appendix A and references therein.

B.H. Botch, T.H. Dunning, Jr., and J.F. Harrison, J.
Chem. Phys., 19, 3466 (1981); S.P. Walch and C.W.
Bauschlicher, Jr., J. Chem. Phys., 19, 4597 (1983)

E.A. Carter and W.A. Goddard III, J. Phys. Chem., 99,
1485 (1984)

A.J.H. Wachters, J. Chem. Phys., 99, 1033 (1970)
T.H. Dunning, Jr., private communication.
P.J. Hay, J. Chem. Phys., 99, 4377 (1977)
R.C. Raffenetti, J. Chem. Phys., 99, 4452 (1973)

F.B. Duijneveldt, IBM Research Laboratory, San Jose, CA,
1971, IBM Technical Research Report No. RJ-945.

S. Huzinaga, J. Chem. Phys., 19, 1293 (1965)

S. Huzinaga, "Approximate Atomic Functions II", Research
Report, Division of Theoretical Chemistry, Department of
Chemistry, The University of Alberta, 1971

The ARGOS integral program was developed by R.M. Pitzer
(Ohio State University).

The GVBl64 program was written by R. Bair (Argonne
National Laboratory).

A description of the UEXP program is given in: R.
Shepard, J. Simons, I. Shavitt, J. Chem. Phys., 19, 543
(1982)

H. Lischka, R. Shepard, F.B. Brown, and I. Shavitt,
Int. J. Quant. Chem. Symp., 19, 91 (1981)

C.E. Moore, Natl. Stand. Ref. Data Ser., Natl. Bur.
Stand. No. 35.

22.

23.

24.

25.

26.

27.

28.

29.

30.

533.

E34.

152

J. Allison and D.P. Ridge, J. Am. Chem. Soc., 99, 7445
(1976)

a) W.A. Goddard,III, T.H. Dunning, Jr., w.J Hunt, P.J.
Hay, Acc. Chem. Res., 9, 368 (1973)

b) W.A. Goddard,III and L.B. Harding, Annu. Rev. Phys.
Chem.. 22, 363 (1978)

The GVB bond orbitals were extracted from the MCSCF
calculation by truncating the MCSCF expansion to the
perfect pairing configurations, renormalizing, and using
the MCSCF orbitals.

R.S. Mulliken, J. Chem. Phys., 99, 1833, 1841, 2338, and
2343 (1955). For a critique, see J.O. Noell, Inorg.
Chem., 91, 11 (1982)

J. Pacansky, J. Phys. Chem., 99, 485 (1982)

B.J. Schilling, W.A. Goddard III, and J.L. Beauchamp, J.
Am. Chem. Soc., 108, 582 (1986)

C.W. Bauschlicher, Jr., and S.P. Walch, J. Chem. Phys.,
19, 4560 (1982)

M.A. Vincent, Y. Yoshioka, and H.F. Schaefer III, J.
Phys. Chem., 99, 3905 (1982)

C.W. Bauschlicher, Jr., H.F. Schaefer III, and P.S.
Bagus, J. Am. Chem. Soc., 99, 7106 (1977). This CH2
(3B,) geometry is not optimal (see, for example, C.W.
Bauschlicher, Jr., Chem. Phys. Lett., 19, 273 (1980))
but the energ tic consequences of its use in construct—
ing the CrCHz potential energy curves is negligible.

This CH d1stance was obtained by optimizing the energy
of the 42 state at the SC level by using the C and H
basis set used in the CrCH calculation.

M.L. Mandich, M.L. Steigerwald and W.D. Reents, private
communication.

J. Allison, private communication.

a) J.F. Harrison, "Chemistry 991 Lecture Notes", Depart—
ment of Chemistry, Michigan State University
b) A.D. Buckingham, Adv. Chem. Phys., 19, 107 (1967)

This analysis was also used for the tr nsition metal
cation series which included Ti and V bonding to CH.
See Appendix B.

 

APPENDIX A

APPENDIX A

ELECTRONIC STRUCTURE THEORY:

TECHNIQUES

INTRODUCTION

This appendix will include a general discussion of
the techniques used to characterize the electronic structure
of the various molecular systems described in this disser—
tation. Special emphasis will be given to the development
of wavefunctions used in the calculations.

To study the electronic structure of molecules is
to study the interaction of atoms brought close enough
together to form a lower energy system, resulting in changes
in the electron distribution (compared to that of separated
atoms) due to the proximity of the nuclei in a molecule. To

date, the fundamental equation that describes a system of

this type is the time-independent Schroedinger equation,

Where H is the Hamiltonian operator (in atomic units).

153

 

 

N 1 2 M 1 2 N M ZA
H="3§VI‘Z 251—VA '2 2";-
1=1 A=1 A i=1 A=1 1A
N N M M Z 2
+2 2+ +2 z-—§-§—
i=1 j>i ij =1 B>A AB

(MA is the mass ratio between nucleus A and an electron), Y
is the wavefunction, and E is the total energy of the
system” The solution to this equation has only been found
exactly for atomic and molecular ensembles containing one
electron. Therefore. one must rely on approximate

solutions.

First of all, in the case of molecular systems, the

Born—Oppenheimer approximationl'z

allows the wavefunction,
Y, to be separated into its nuclear and electronic
components. This is based on the idea that nuclei are much
heavier than electrons, so they move more slowly. At fixed

nuclear positions one can then solve for the electronic

Schroedinger equation,

 

N N M2 N N
He=-£%v§ —£ 2 I,“ +2 {-31,- (1)
1=1 i=1 A=1 iA 1:1 j>i ij

we is the electronic wavefunction which describes the motion

of the electrons but is dependent of the position of the

 

 

 

155
nuclei, as well as, those of the electrons. Ee is the
electronic energy (also dependent on the position of the
nuclei). What this means is that Ye and Ee are different
functions and values, respectively, at different spatial
arrangements of the nucleil.
The total energy of the system, where the nuclear

coordinates are fixed, is

M M ZAZB
e —R_ <2)
A=1 B>A AB

which includes the electronic energy and a constant nuclear
repulsion. Since the total energy. E, is a function of R

AB'
this function can define a potential surface as shown below:

 

I'll

 

RAB
As mentioned before, one can now concentrate on the
solution to the electronic Schroedinger equation, i.e, Ye
for a given He' The electronic Hamiltonian in Eq.(1)
depends only on the spatial coordinates of the electrons and
not on its spin. Therefore, we are using a non-relativistic
flamiltonian. Even though spin variables are not included in

the Hamiltonian, the electronic wavefunction must meet the

following requirement:

 

156

"A many-electron wavefunction must be antisymmetric

with respect to interchange of the coordinate

x (both space and spin) of any two electrons,

Y(x1,.....xi,....,xj,....,xN) =
-Y(x1,. .,xj,....,xi,....,xN).
This is knOWn as the Pauli Exclusion Principle. The
subcript "e" is to be implied when discussing the electronic
wavefunction.

There has been intense theoretical research in the
construction of electronic wavefunctions to describe the
energetic and spatial distribution of electrons in atoms and
molecules. The most reliable techniques of approximation
are the non—empirical or ab initio methods1—7, i.e.,
empirical data is not used in the calculation. Most of

these techniques are based on the Variational Principle:

"Given a normalized wavefunction |Y> that satifies
the appropriate boundary conditions (usually
Y(w)=0), then the expectation value of the
Hamiltonian is an upper bound to the exact
ground state energy. i.e.,

<~r|H|v>2 E0 1

The reliability of the solution depends on the choices made

in the construction of Y which should not be oversimplified.

 

 

 

 

157
DEVELOPMENT OF WAVEFUNCTIONS
An arbitrary function can be expanded in terms of
known functions that form a complete set. For example, the
wavefunction Y for a one electron system can be expanded in'

a linear combination of the one—electron functions, oi

(weighed by the coefficients C1) where these oi's form a

i=1'

For a many-electron function,

complete set: (oi) and are linearly independent.

Y(gllgzl'°°lgN) =

Z Z ...Z C.C ...C o (q I ¢.(q ) ...¢ (q )

i=1 j=1 n=1 1 j n i ~1 J ~2 n ~N
where for each term we have a product of one-electron
functions. This function must satisfy the Pauli Principle.

To see this, let us consider the two—electron case:

Y‘91'92) =izj Cicj °1‘91’ ¢j(92)

I

Since the wavefunction is antisymmetric with respect to

electron interchange, we may write:

158

_ —1/2
Y(g1.g2) -1zj 2 3133 E ¢i(g1) ¢j(g2)

— oiIgzI ¢j(gl) 1
This can be rewritten as a determinant:

Y(g1.g2) = 2 2‘“2 B

oi(g2) ¢j(g2)

=ifj BiBj :74 [ 41(g1) 43(g2) l
where :74 is an antisymmetrization operator2 which insures
that the one—electron function product in the brackets,
"[1", will be expressed in a Slater determinant (as the one
shown previously) which in turn insures that the overall
wavefunction, V, will be antisymmetric with respect to
electron interchange. This analysis is easily extended to
N-electron systems.

In the Hartree—Fock (HF) approximation for a

molecular system, the wavefunction Y is expressed as

Y(g1,g2,....gN) = :7! [ °1(§1)°2(92""°N(9N) l (3)

where oi's are molecular (spin-) orbitals occupied by the

1th electron. There are no sums in this expression, i.e.

I

this wavefunction is based on one configuration (one

"product" arrangement of one orbital per electron). This is

159
called a Hartree product. When a configuration (single
determinent) is expressed in brackets, only those orbitals
that are occupied will be included; the rest of the
orbitals, oj, in the complete set will be excluded (these
are then known as virtual orbitals).

Before we get into the choices of 01's which will
be a part of the configuration, we should realize that an
orbital is a wavefunction that describes a single particle;
in this case, an electron. Since an electron has an
intrinsic spin, the wavefunction to describe the electron
must include a component that will take the spin into

account. This would give us a spinorbital:

4(5) an»)
4(9) = or
9(5) 8(w)

where r are the spatial coordinates and, o(w) and B(w) are
two orthogonal spin functions, i.e., spin up or spin down.
When we are concerned with molecular orbitals, the nature of
the functions 6(3) is dependent on the molecular
environment. A general technique in constructing molecular
orbitals is to expand them in terms of known basis functions

which are characteristic of the atoms in the molecule:

4 (r) = E C x (r)
1.. ”=1uip-

160
For the equality to hold, these known basis functions, x”,
should form a complete set. To avoid computational
difficulties, Gaussian Basis Sets3 are generally used in
calculations of molecular systems. This technique (using
atomic basis functions) is the Linear Combination of Atomic
Orbitals (LCAO). In summary, the electrons in a molecule
occupy the molecular orbitals which are composed of
combinations of atomic orbitals.

Returning to the Hartree-Fock approximation, the
Hartree—Fock wavefunction, YHF’ is the best single deter—
minent wave function composed of orbitals, mi, in Eq. (3),
which gives the lowest possible value for the expectation
value of the energy (Variational Principle)2. This energy
is the Hartree—Fock energy, EHF' It is unlikely that the
orbital functions, oi, can be practically expressed by a
complete set of basis functions. By use of a finite set of
basis functions, the best single determinant wavefunction

(where the coefficients Cu 's are optimally determined) is

i
the Self-Consistent-Field (SCF) wavefunctionz. As the
expansion length reaches infinity (complete set), the SCF
energy and wavefunction approaches the Hartree—Fock limit.
To further understand how an SCF wave function is
obtined, let us reacquaint ourselves with the Variational

Principle. The spin orbitals in a Slater determinent are

usually taken to be orthogonal to each other,

 

161
< o | o > = o = o if ixj
1 3 ij 1 if i=3
since this allows the energy expression of a single
determinent (1—D) wavefunction to be written in the
following simple way:

N Z

 

1 2 M A
E _ = <? _ | H | Y _ > = I <6 | — — V — z |¢ >
1 D 1 D 1 D 1_1 i 2 i A=1 riA i
N 1 1
+ E E <¢.¢.l -—- l9 0 > - <0 4.! ——- l¢ 4 > ]
i<1 1 J r:13 i j i J rij j i

by use of the non—relativistic Hamiltonian described in Eq.
(1). The integrals, < | | >, are divided into one-electron
integrals and two-electron integrals. The two—electron

integrals have implied a specific electron, ( ), order:

<¢1¢JI "‘ I¢i¢j> * <¢1(1)oj(2)| "' 101(1)¢j(2)>

Through this convention only the orbital indices are needed
and the electron order is understood. The following is a

simplified notation of the previous energy equation:

a = z < 1 I i > + z E < 11 | 13 > — < ij I 31 > 3
1 i<j

The first two—electron integral is known as a Coulomb

integral, < 13 l ij >. The second is an Exchange integral,

< 13 | ji >, because this integral shows the effect of the

IIIIIIl-nn..___________i

162

interchange of two electrons in orbitals oi and °3 (a
consequence of the wave function satisfying the Pauli
Principle).

To obtain a Self—Consistent-Field (SCF) wave
function, a single determinant of 1—electron orbitals is

optimized so as to minimize the total energy,

8E
.Cui

where the coefficients are variationally determined via the
Roothaan eguations1 which simplifies the spatial integro—

differential equation,
fIfl) Y1(f1) = s1 Y1‘51) '

(f is the Hartree Fock operator) to a single matrix equation

which, in turn, can be solved by standard matrix techniques.
In the past two decades many electronic structure
calculations were successful with the use of an SCF wave

functionl'z.

The systems studied were mainly composed of
main-group elements. As molecules of interest became more
complicated (for example, transition metal—containing sys—

tems where correlation effects had not been addressed ),

solutions of more than one determinant were needed. We have

   

..-...

163

seen before that the overall molecular wavefunction, Y, can
be expanded by a linear combination of all possible arrange—
ments of 5's (configurations), but for practical purposes,
this too, must be limited to a finite expansion. The best
possible solution (lowest energy) under these conditions is
obtained by optimally determining the coefficients of each
configuration. The selection of which configurations are
included in this finite expansion merits extreme care.
There are two types of expansions which will be discussed
here: Multi—Configuration-SCF (MCSCF) and Configuration
Interaction (CI) wavefunctions. Variations of each of these
wavefunctions will also be considered.

A complete expansion for an N—electron system in

terms of Slater determinants has the form:

”I = g nay”... 74 I M91) °J<92> 0.39m”

and the individual one—electron orbitals have the expansion:

41(5) = E Ci” x”(§)

This is approximate because the expansion is finite. When
only the coefficients of the configurations are optimized
variationally then we have a Configuration Interaction (CI)
wavefunction‘. If both the coefficients of the configura-
tions and the orbitals are optimized, we have a Multi—

Configuration—SCF (MCSCF) wavefunction5. The determination

164

of these optimized functions is an immense task. Since
large expansions of each of these wavefunctions can lead to
computational difficulties, one attempts to choose only
those configurations and basis functions expected to be of
importance to the overall structure of the system.

The above molecular wave function is often written

as,

Y:

v Cv°v where 4v = :7! [¢i¢j...on]

"M:

O

i.e., Y is a linear combination of Slater determinants, 4v.

 

Go is taken as the SCF function and higher order Ov's are
configurations which represent electron excitations (single
excitations, double excitations, ..., etc.) from the SCF
configuration.

One of the main disadvantages of using an SCF
wavefunction is its inability to properly describe the
dissociation process of a molecule into its atomic
fragments. In a diatomic molecule with a simple single
bond, the dissociation into the homolytic components is not
possible with this wavefunction, leading to large errors in
calculated dissociation energies. This is an example where
additional correlation is needed. Take a hypothetical
diatomic system with only a single bond, A—B. A single bond
is commonly described by a doubly occupied molecular

orbital, e.g. 092, while other electrons in thesystem are

165
placed in what we will consider as core orbitals. 9999
orbitals are usually considered as doubly occupied ("inner—
shell") orbitals not involved in the overall chemistry of
the molecular system. Designations of types of orbitals
vary according to what is sought in a molecular study. For

example, in our study of dilithiomethane, CH2Li we are

2.
interested in the interaction of carbon with the two lithium
atoms and the C—H bonding orbitals were taken as core
orbitals.

According to the SCF description, as the distance
between atoms A and B increases (R e a), the doubly occupied
a: (which was shared among A and B at the equilibrium
B)2 ) can then be centered on atom A
(a: 4 oi), on atom B (a: e 0;), and on both A and B (a; a

distance, 02 e (o + o
g A

voB). If the proper description of the fragments requires
an equal splitting of the two electrons among atoms A and B
(with no ionic terms), then the SCF energy will be too high.
Suppose we included another configuration where the two
electrons in o are "excited" in an orthogonal antibonding

orbital, e.g. cu.
Y e C :>J | (core) 20 2dB >
MCSCF 0 9

2 2
+ 01 :74 | (core) on as >

The coefficients, 01's, and all orbitals are optimized in

this 2X2 MCSCF wavefunction and when rewritten as follows:

the extent by which the two configurations "mix" is
monitored by the parameter A. Orbitals cg and on can be

combined to form two localized orbitals:

 

 

 

 

 

 

_ 1 + S ' I 1 - S I
(+ — J-——§-—- | cg > + 2 1 cu >
_‘1+s‘ J1-s‘
(_ - J-—-§-— | 09 > —-—§——- 1 cu >
_ _ 1 - A
where S - < (+l {_> _ 1 A

These localized (+,(_ orbitals are known as Generalized

 

Valence Bond (GVB)6 orbitals. They are non—orthogonal to

 

each other but the orbitals as a pair are orthogonal to
other orbitals in the system. Since {+ and {_ are non—
orthogonal to each other, the integral < (+ l {_ > is non-
zero and the resulting value, S, is called the overlap of
these two orbitals. Note the transformation between the

(natural) molecular orbitals and the localized GVB orbitals:

2 2 _
( og — A on ) dB ———> ( {+{_ + {_{+) (68 Ba)

Note the similarities of the GVB expression to what we know

as the Valence Bond model. The GVB orbitals as a pair are

167

optimized as are the rest of the orbitals. One observation
to keep in mind: A monitors the "need" for the extra
configuration in the wavefunction, i.e., if at the molecular
level, on plays a small role, A is small; if at R=w, on is
equally important, then A=+1.

The GVB (2X2 MCSCF) wavefunction behaves properly
at all distances if the spin states of the individual
fragments lead to doublet states. For example, H2 separates
correctly to a 28 spin state for each hydrogen atom. This
is not the case for fragments with open shell electrons
having a total spin more than 1/2 (doublet state). The GVB

(2X2 MCSCF) wavefunction can not satisfactorily separate,

 

e.g. a C-H (2H) radical to the low energy3 P carbon and2 S
hydrogen atoms. To insure that the separated fragments have
the proper spin states, extra configurations are added (spin
eigenfunctions) resulting in a Spin-Optimized GVB (SOGVB)
wavefunction.

In Figure 1, we have an example of a Spin Eigen-
function Branching Diagram where the number of linearly
independent spin eigenfunctions is determined by the number
Of unpaired electrons and the overall multiplicity of the
molecular system. Beyond the 2-configuration MCSCF (GVB)
wavefunction needed to break the bond, we need to include 2
mOre configurations for a wavefunction (SOGVB) that can
Partition the C-H molecule in a 2n state to the correct 3?
carbon and 28 hydrogen spin states (two unpaired electrons

°n C and one unpaired electron on H gives a total of 3

7/2

5/2

3/2

1/2

Figure 1. Spin Eigenfunction Branching Diagram

168

 

 

 

 

6 _____

 

 

 

14 —————

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

iii.

Number of Electrons

 

Octet

Septet

Sextet

Quintet

Quartet

Triplet

Doublet

Singlet

Number of linearly independent spin eigenfunctions
one can form from a given allotment of electrons.

S is the total spin and the corresponding multipli-
city is on the right hand side.

169

unpaired electrons for the separated system which needs to
be coupled for an overall doublet state). The SOGVB wave—
function adjusts spin recouplings upon fragment separation.

All molecular systems under study in this
dissertation were done by the use of an MCSCF (SOGVB) wave
function. This function is then used as an initial estimate
for further extensive CI studies. The analysis for the
construction of a wavefunction describing multiple bonding
follows the same procedure (and requirements) as the single
bonded systems which, in addition to higher levels of
correlation beyond those addressed here, will be discussed
in the main text.

As mentioned before, only the coefficients of the
configuration expansion are optimized in a CI function; not
the coefficients for the basis functions used for defining
the orbitals. Generally, the procedure for constructing CI
functions is by using an optimized SCF orbital set and
expand the function with configurations which represent all
possible excitations from the valence orbitals of this set.

This is considered a Full (Valence Electron) CI. Excita-

 

tions from the core orbitals are not considered (i.e., kept
"frozen").

Of the many levels of excitations (single, double,
triple, ..., etc.), single and double excitations account
for ~90% of the correlation needed to improve the SCF
wavefunction for many molecular systems. A CI wavefunction

consisting of single and double excitations from an SCF

170
valence reference space is called an SCF+1+2 wavefunction.
The electrons in the optimized (SCF) orbitals are excited
into unoccupied virtual orbitals. Calculations done by this
method are far better (lower energy) than a simple SCF
wavefunction‘, but unfortunately this wavefunction is still
not size consistentl, i.e., the energy of the molecule when
the fragments are far apart is not the sum of the energies
of the individual fragments.

An appropriate extension to this SCF+1+2 (CI)
wavefunction is a wavefunction based on single and double
excitations from an optimized MCSCF valence orbital ~
reference space: MCSCF+1+2. As discussed previously, the
MCSCF function by which this CI function is based on, allows
for proper dissociation of the system (with the proper spin
characteristics). This type of wavefunction is used in our
studies and has the important characteristic of being,

essentially, size consistent.

 

 

LIST OF REFERENCES

LIST OF REFERENCES

A. Szabo and N.S. Ostlund, "Modern Quantum Chemistry:
Introduction to Advanced Electronic Structure Theory",
Macmillan Pub. Co., Inc., New York, N.Y., 1982.

H.F. Schaefer III, "The Electronic Structure of Atoms and
Molecules", Addison—Wesley Pub. Co., Reading, Mass.,
1972.

T.H. Dunning, Jr. and P.J. Hay, "Gaussian Basis Sets for
Molecular Calculations" in "Methods of Electronic
Structure Theory", edited by H.F. Schaefer III, Plenum
Press, New York, 1977, p.1.

I. Shavitt, "The Method of Configuration Interaction" in
"Methods of Electronic Structure Theory", edited by
H.F. Schaefer III, Plenum Press, New York, 1977, p.189.

a) A.C. Wahl and G. Das, "The Configuration Self—
Consistent Field Method“ in "Methods of Electronic
Structure Theory", edited by H.F. Schaefer III,
Plenum Press, New York, 1977, p.51.

b) R. Shepard, "The MCSCF Method“ to appear in Advances
in Chemical Physics, "Ab Initio Methods in Quantum
Chemistry", edited by K. Lawley, 1986.

c) T.H. Dunning, Jr., "Multiconfiguration Wavefunction
for Molecules: Current Approaches" in "Advanced
Theories and Computational Approaches to the
Electronic Structure of Molecules", edited by C.E.
Dykstra, Reidel Pub. Co., 1984, p.67.

a) F.w. Bobrowicz and W.A. Goddard III, "The Self-
Consistent Field Equations for Generalized Valence
Bond and Open—Shell Hartree-Fock Wave Functions" in
in "Methods of Electronic Structure Theory", edited
by H.F. Schaefer III, Plenum Press, New York, 1977,
p.79.

b) W.A. Goddard III, T.H.Dunning, Jr., W.J. Hunt, P.J.
Hay, J. Acc. Chem. Res., 9, 368 (1973).

c) W.A. Goddard III and L.B. Harding, Ann. Rev. Phys.
Chem., 22. 363 (1978).

Discussions with J.F. Harrison.
171

APPENDIX B

 

 

APPENDIX B

LISTING OF PUBLICATIONS

Included here is a listing of the publications resulting

from this dissertation:

1. "The Bonding, Dipole Moment, and Charge Distribution

in the Lowest Singlet and Triplet States of CHzLiz."

Aileen E. Alvarado-Swaisgood and James F. Harrison,

 

J. Phys. Chem., 1985, 99, 62.

2. "Electronic and Geometric Structures of the Chromium
Cations CrH+, CrCH3+, CrCH2+, and CrCH+."
Aileen E. Alvarado-Swaisgood, John Allison, and

James F. Harrison, J. Phys. Chem., 1985, 99, 2517.

3. "Electronic and Geometric Structures of ScH+ and
ScH2+." Aileen E. Alvarado-Swaisgood and James F.

Harrison, J. Phys. Chem., 1985, 99, 5198.

4. "The Electronic and Geometric Structures of the
Transition-Metal Carbyne Cations ScCH+, TiCH+, VCH+,
and CrCH+." A. Mavridis, A.E. Alvarado-Swaisgood and

J.F. Harrison, J. Phys. Chem., 1986, 99, 2584.

172

173

"Electronic and Geometric Structures of the Scandium
Cations ScH+, ScCH3+, ScCH2+, and ScCH+."
Aileen E. Alvarado-Swaisgood and James F. Harrison,

Submitted to J. Phys. Chem.

"The Electronic and Geometric Structure of the Lowest

5+ 5

2 and fl States of CrCl+." Aileen E. Alvarado-

Swaisgood and James F. Harrison, Submitted to J.

Phys. Chem.

 

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