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This is to certify that the

dissertation entitled

THE ELECTRONIC AND GEOMETRIC STRUCTURES OF
VARIOUS SMALL MOLECULES CONTAINING EARLY
TRANSITION METALS

presented by
Jesse Edwards 111

has been accepted towards fulfillment
of the requirements for

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Date W777?

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THE ELECTRONIC AND GEOMETRIC STRUCTURES OF VARIOUS SMALL
MOLECULES CONTAINING EARLY TRANSITION NIETALS

By

Jesse Edwards III

A DISSERTATION

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

DOCTOR OF PHILOSOPHY
Department of Chemistry

1999

ABSTRACT

THE ELECTRONIC AND GEOMETRIC STRUCTURES OF VARIOUS SMALL
TRANSITION METAL CONTAINING MOLECULES

By

Jesse Edwards III

Earlier work on Scandium Nitride and Scandium Imide has prompted the study of
this unique class of compounds through ab-initio methods. Computationally, the
transition-metal nitrides have been studied in some detail. In these studies the ScN
molecule was found to possess a '2? ground state with a 32* state lying only about 7 kcal
higher in energy. The triplet state comes about by decoupling the weak sigma bond in

the singlet state, leaving a diradical with the two remaining 1: bonds ('Sc=N'). The

relative ordering of the low lying states predicted by Harrison and Kunze agrees

extremely will with experiment. Coupling two of the diradicals leads to an alternating
doubly-bonded dimer, 'Sc=N-Sc=N' with a lone electron found in the 0' symmetry

orbitals to the rear of the terminal Sc and N atoms. These lone electrons are left available
to form additional bonds. This work will cover the studies conducted investigating the
electronic structure of the scandium nitride dimer.

Ab-Initio studies of diatomic metal nitrides and phosphides provide a fundamental
tool in understanding the bonding between nitrogen and phosphorus atoms and metals.
The bond lengths, bond energies, dipole moments, and vibrational frequencies of the

ground and several low-lying states of the YN and YP molecules, calculated using GVB

(Generalized Valence Bond), GVB+1+2, MCSCF (Multiconfigurational Self-Consistent
Field), and MCSCF+1+2 techniques will be reported.

The basis sets used for the Y atom in the YN and YP calculations contained a
relativistic effective core potential (RECP) to account for the relativistic effects on Y.
There will be a comparison of the results of YP using two different all electron basis sets
on the phosphorus atom. The calculated ground states of YN, YP, and ScN 1' 2 and ScP5
are strongly bound ‘27 states at each level of theory. The calculated bond length of YN is
1.8147 angstroms. The experimental value was reported as 1.8148 angstroms“. The
ordering of states for the YN molecule was in agreement with experiment at each level of
theory.

The early transition metal methylidynes provide another unique class of
compounds to study. The electronic structure of ScCH, TiCH, VCH, and CrCH, as well
as, their positive cations will be presented for the ground and selected excited states. The
geometries, energies, and dipole moments, and electron distributions (populations) were
calculated using RHF, MCSCF, and MRCI techniques. Density Functional Theory was
used to calculate the vibrational frequencies, along with the other properties mentioned
on the ground and selected excited states.

Our results are also in good agreement with the few experimental results

available. The vibrational frequencies and bond lengths of TiCH in the 22+ ground state
are compared to experiment, along with the separation (energetically) between the 22*
and 2II states of the TiCH molecule. The vibrational frequencies and bond lengths of the

VCH molecule in the 3A state are also compared to our calculated results.

To Tyler and Anika

iv

ACKNOWLEDGEMENTS

First of all, I would like to thank Dr. James Harrison for his support. He has not
only provided me with guidance in my research, but with the many ‘life’ issues that have
arisen during my stay. I feel very fortunate to have had him as an advisor. I would also
like to thank the many members of my committee, new and old, Dr. Richard
Schwendeman, Dr. Mecouri Kanatzitdas, Dr.Michael Rathke, Dr. Gary Blanchard, Dr.
James Jackson, and Dr. Daniel Nocera. Although a few of these professors only served
on my committee for a short period their support, good nature and advice will always be
appreciated. I would like to offer a special thanks to Dr. Schwendeman who served as my
second reader. His dedication definitely helped to make this dissertation possible.

My gratitude also extends to the Harrison group members who have helped me in
so many ways. I would also like to thank the staff of the Chemistry Department, Dr.
Thomas Atkinson and Mr. Paul Reed in particular, and the staff of the College of Natural
Science for the many pep talks and assistance.

My parents, Jesse Edwards Jr. and Brenda E. Smith, deserve much more than a
thank you for their encouragement, help, and endurance through this entire process.
Finally, I would like to thank my friends and family, especially, my Aunt Reese and her

family, Aricka, LaVetta, Ken, and Phil. I can not thank you all enough.

TABLE OF CONTENTS

LIST OF TABLES .......................................................................... ix
LIST OF FIGURES ......................................................................... xiii
KEYS TO SYMBOLS AND ABBREVIATIONS .................................... xxv
CHAPTER I
INTRODUCTION ................................................................ 1
BIBLIOGRAPHY ....................................................... 12
CHAPTER H
THE ELECTRONIC STRUCTURE OF YN AND YP ..................... 15
BACKGROUND ......................................................... 15
METHODS ................................................................ 19
RESULTS .................................................................. 26
COMPARISON TO EXPERIMENT ................................. 46
CONCLUSIONS ......................................................... 50
FUTURE WORK ....................................................... 51
BIBLIOGRAPHY ....................................................... 52
CHAPTER III
AB-INI T10 STUDIES OF THE SCANDIUM ............................. 56
NITRIDE DIMER
WAVEFUNCTION CONSTRUCTION ............................ 57
RESULTS ................................................................. 58

vi

A. CHARGE DISTRIBUTION

AND POPULATION ANALYSIS ........................ 61
B. DISCUSSION ................................................ 68
l. DENSITY DIFFERENCE CONTOUR

RESULTS ................................................ 66

2. DENSITY DIFFERENCE MESH PLOT
RESULTS ................................................ 66
CONCLUSIONS .......................................................... 77
BIBLIOGRAPHY ........................................................ 79

CHAPTER IV
THE ELECTRONIC STRUCTURE AND VARIOUS
PROPERTIES OF EARLY TRANSITION METAL
METHYLIDYNES AND THEIR POSITIVE CATIONS

INTRODUCTION ........................................................ 82
BASIS SETS AND MOLECULAR CODES ........................ 85
MOLECULAR F RAGMENTS ....................................... 87
WAVEFUNCTIONS AND CONIPUTATIONAL
DETAILS .................................................................. 92
RESULTS AND DISCUSSION ........................................ 94
A. ScCH and ScCH+ ............................................. 96
B. TiCH and TiCH+ ............................................. 105
C. VCH and VCH+ ............................................... 124
D. CrCH and CrCH+ ............................................. 128
CONCLUSIONS ........................................................... 129
TABULATED RESULTS ................................................ 135
BIBLIOGRAPHY ......................................................... 149

vii

APPENDIX
LIST OF PUBLICATIONS ...................................................... 155

viii

LIST OF TABLES

Table Page
Chapter II
1. The relative energy (eV) of two states of the Y atom

relative to the 2D ground state. ......................................................... 21
2. A comparison of various states of the YH molecule.

The energy separation relative to the ground state YH

molecule and the equilibrium geometry is reported. ................................. 22
3. YN Mulliken Population Analysis (a.u.). .............................................. 34
4. Comparison of equilibrium internuclear separations and

vibrational frequencies for ScN and YN. ............................................. 35
5. Comparison of equilibrium internuclear separations

and vibrational frequencies for ScP and YP. ......................................... 36
5a. YN equilibrium internuclear separations, vibrational

frequencies and energies. ............................................................... 37
5b. YP equilibrium internuclear separations, vibrational

frequencies, and energies. ............................................................... 38
6. ScN Mulliken Population Analysis (GVB) (a.u.).

Taken from Harrison and Kunze reference 10). ...................................... 39
7. YP Mulliken Population Analysis (an) at the MCSCF level. . ................... 40
8. YP Mulliken Population Analysis (an) at the MCSCF+1+2 level. ............. 41
9. Dipole Moments (Debye) of YN. . .................................................. 47
IO. Dipole Moments (Debye) of YP. ................................................... 48
Chapter IV
1. The equilibrium metal-carbon and carbon hydrogen

ix

5a.

bond lengths, energy, and dipole moment of ScCH

in the ground 3II state using the AWACH basis at the

MRCI, MCSCF, DFT, and RHF levels (MRCIa

corresponds to a MRCI wavefunction with an extra

orbital of a1 symmetry in correlation of the MCSCFa reference) .................. 137

The equilibrium metal-carbon, RechC(A), and carbon

hydrogen, ReqCH(A), bond lengths, and energy of ScCH“

in the ground 2l‘l state using the AWACH basis at the MRCI,

MCSCF, DPT, and RHF levels (MRCIa corresponds to a MRCI

wavefunction with an extra orbital of a; symmetry in correlation

of the MCSCFa reference). .............................................................. 138

The Mulliken population analysis of ScCH in the ground

3T1 state using the AWACH basis at the MRCI and MCSCF

level (MRCIa corresponds to a MRCI wavefunction with an

extra orbital of a; symmetry in correlation of the

MCSCFa reference). . .................................................................... 139

The Mulliken population analysis of ScCH+ in the ground 211
state using the AWACH basis at the MRCI (MRCIa extra orbital
of al symmetry in correlation of the MCSCFa reference) ........................... 140

The equilibrium metal-carbon, ReqTiC(A), and carbon

hydrogen, ReqCH(A), bond lengths, energies, and dipole

moments of the ground state, 22’, and three excited states

of TiCH using the AMES, and AWACH basis at the MRCI,

and MCSCF level (extra orbital of a1 symmetry in correlation

of the MCSCF reference), DF'I‘, and experimental geometry

(ground state) and experimental separation between the

ground state and 21'! state. .............................................................. 141

The equilibrium metal-carbon, ReqTiC(A), and carbon

hydrogen, ReqCH(A), bond lengths, energies, and dipole

moments of the ground state, 22?, and three

excited states of TiCH using the AWACH

basis at the RHF level. .................................................................. 142

The equilibrium metal-carbon, ReqTiC(A), and
carbon hydrogen, ReqCH(A), bond lengths, and
energy of TiCW in the ground ’2’ state using the

AWACH basis at the MRCI, MCSCF, DFT, and
RHF levels. ............................................................................... 143

7. The vibrational frequencies, we, of several states of
ScCH, TiCH, VCH and CrCH using DFT, the AWACH
basis on metal and 6-3lG** basis on C and H. ....................................... 143

8. The charge distribution and vibrational frequencies, we,
of ScCH”, 2H, ground state using DFI‘, the AWACH basis
on metal and 6-3lG** basis on C and H. ............................................ 144

9. The Mulliken population analysis of TiCH in the
ground 227 state and three excited states using the
AMES and AWACH basis sets at the MRCI level
(MRCIa extra orbital of a, symmetry in correlation
of the MCSCFa reference). ............................................................ 145

10. The Mulliken population analysis condensed to basis
function type of TiCH+ in the ground ‘2‘.“ state using
the AWACH basis at the MRCI (MRCIa extra orbital
of a. symmetry in correlation of the MCSCF“ reference). ....................... 146

11. The equilibrium metal-carbon, RquC(A), and carbon
hydrogen, ReqCH(A), bond lengths, energy, and dipole
moment of the ground state, 3A, and an excited
state (DPT level) of VCH using the AWACH basis at
the MRCI and DFT level. The experimental bond length
for the ground state is also reported. ................................................ 147

12. The equilibrium metal-carbon, RquC(A), and carbon
hydrogen, ReqCH(A), bond lengths, energy, and
dipole moment of the ground state, 3A, and an
excited state (DFT level) of VCH using the AWACH
basis at the MRCI and DFT level. The experimental
bond length for the ground state is also reported. ................................... 147

13. The Mulliken population analysis of VCH in the
ground 3 A state and three excited states using the

xi

14.

15.

l6.

l7.

AWACH basis at the MRCI level. ..................................................... 148

The Mulliken population analysis condensed

to basis function type of VCH+ in the ground

2A state using the AWACH basis at the MRCI

and MCSCF level ........................................................................ 148

The equilibrium metal-carbon, RequC(A),

and carbon hydrogen, ReqCH(A), bond lengths,

and energy of the ground state, 42', of CrCH using

the AWACH basis at the MRCI, MCSCF, DFI‘ and

RHF levels. ............................................................................... 149

The equilibrium metal-carbon, RequC(A), and

carbon hydrogen, ReqCH(A), bond lengths, and

energy of CrCH+ in the ground 32' state using the

AWACH basis at the MRCI, MCSCF, DFT, and RHF

level. ........................................................................................ 149

The mulliken population analysis condensed to

basis function type of CrCH+ in the ground 32‘ state

using the AWACH basis at the MRCI level (extra orbital

of a; symmetry in correlation MCSCF) ................................................. 150

18. The mulliken population analysis condensed to basis

function type of CrCH, and CrCH+ in the ground ‘2' and
32’ states respectively, using the AWACH basis at the MCSCF level. ........... 150

xii

LIST OF FIGURES

Figure Page

Chapter H

1. Selected experimental promotion energies of high spin
States of the Sc and Y atoms averaged over values for
J states for each term. Values taken from Moore (Reference 21)
except for the calculated state shown
above. ..................... ..... . ..................................................... 24

2. Bonding schemes for some of the states of ScN and YN. ........................... 25

3. Potential energy curves of several electronic states of YN.
MCSCF calculations performed in this work. ......................................... 29

4. Potential energy curves of several electronic states of YN.
MCSCF+1+2 calculations performed in this work. .................................. 30

5. Potential energy curves of several electronic states of YP.
MCSCF calculations performed in this work. ......................................... 31

6. Potential energy curves of several electronic states of YN.
MCSCF+1+2 calculations performed in this work. .................................. 32

7a. Figure 7a shows population curves of selected sigma symmetry
orbitals taken from the natural orbitals of the YN molecule at the
MCSCF+1+2 level. .................................................................... 42

7b. Figure 7b shows population curves of selected pi symmetry
orbitals taken from the natural orbitals of the YN molecule at the
MCSCF+ 1+2 level. .................................................................... 43

7c. Figure 7c shows population curves of selected sigma symmetry
orbitals taken from the natural orbitals of the first excited state of
the YN molecule at the MCSCF+1+2 level .......................................... 44

7d. Figure 7c shows population curves of selected pi symmetry
orbitals taken from the natural orbitals of the first excited state of
the YN molecule at the MCSCF+1+2 level .......................................... 45

xiii

Chapter HI

1. The geometries of the monomer and dimer of ScN
in the triplet sigma plus state. The calculations were
performed by varying the sigma bond distance of the dimer
while maintaining a distance of 3.34 ao between the
monomers, the equilibrium separation of
the ScN molecule in the triplet sigma plus state. .................................... 58

2. The potential curve of the ScN dimer in
the 32‘.“ state constructed from MCSCF wavefunctions
at selected separations of N(2)-Sc(3). The single bond
of 0 symmetry was correlated in a GVB manner in order
to insure that the two ScN monomers separate to the
correct SCF products. The ch of the dimer is at about
4.0 au. ....................................................................................... 60

3. Charge distribution in atomic units condensed to orbitals
and summed on atoms from the MCSCF wavefunction. ............................. 62

4. Total valence population of selected atomic orbitals
of sigma and pi symmetry of Sc(l). .................................................... 63

5. Total valence population of selected atomic orbitals
of sigma and pi symmetry of N(2). .................................................... 64

6. Total valence population of selected atomic orbitals
of sigma and pi symmetry of Sc(3). ................................................... 65

7. Possible structure of the ScN dimer in the 32" state
after electron transfer and formation of an internal
dative bond between the internal N and external Sc atoms. ......................... 66

8. Figure 8a-8d show the electron density difference between
two non-interacting ScN monomers in the 32+ state and the
dimer in the same state at selected geometries. The broken
lines depict significant gains in electron density. The solid lines
depict significant losses in electron density.
The contours range from 0.5 to -0.5 electrons/a03 at separations
of 3.8 ao (stepsize of 0.1), 4.0 a0 (stepsize of 0.1), and 4.2 ao
(stepsize of 0.12). At 5.0 a0 the contour range is 0.05 to —0.05
with a step size of 0.01. All of the contour values and stepsizes
were chosen in order to improve resolution. The large red
balls denote the Sc atoms and the smaller balls denote the
N atoms. .................................................................................. 69

xiv

8b. Electron density difference contour plot at a selected geometry. ................. 70
8c. Electron density difference contour plot at a selected geometry. .................. 71
8d. Electron density difference contour plot at a selected geometry. .................. 72

9. Figure 9a—9d show mesh plots of the electron
density difference between two non-interacting ScN
monomers in the 32” state and dimer in the same state
at selected geometries. The regions lying in the
plane bisecting the two spiked regions constitute zero
change in electron density. The spikes above the plane
depict positive differences (gains) in electron density.
The spikes below the plane depict negative differences
(losses). The maximum and minimum values in
electrons/a03 for the density differences are as follows
(separation between the internal Sc and N): -0.500,
0.886 (5.080); -0.860, 1.116 (4.230); -O.599, 1.123 (4%,);

-0.818, 1.241 (3.8ao). ..................................................................... 73
9b. Electron density difference mesh plot at a selected geometry. ..................... 74
9c. Electron density difference mesh plot at a selected geometry. ..................... 75
9d. Electron density difference mesh plot at a selected geometry. ..................... 76

10. The proposed structure of the cyclic ScN dimer. The spin state
for this structure is expected to be a triplet. .......................................... 78

Chapter IV

1. Figures 1,2, and 3 are electron density contour plots
of natural orbitals seven, eight and nine of the ScCH
molecule in the ground 311 state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................ 98

2. Figures 1,2, and 3 are electron density contour plots
of natural orbitals seven, eight and nine of the ScCH
molecule in the ground 3l'I state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................ 98

XV

. Figures 1,2, and 3 are electron density contour plots

of natural orbitals seven, eight and nine of the ScCH

molecule in the ground 311 state. The occupation and the

mulliken population condensed to a basis function type are

reported for each orbital. ................................................................. 98

. Figures 4 and 5 are electron density contour plots

of natural orbitals 10 and 11 of the ScCH

molecule in the ground 311 state. The occupation and the

mulliken population condensed to a basis function type are

reported for each orbital. ................................................................. 99

. Figures 4 and 5 are electron density contour plots

of natural orbitals 10 and 11 of the ScCH

molecule in the ground 3I'I state. The occupation and the

mulliken population condensed to a basis function type are

reported for each orbital. ................................................................. 99

. Figures 6 and 7 are electron density contour plots

of natural orbitals 24 and 37 of the ScCH

molecule in the ground 31'] state. The occupation and the

mulliken population condensed to a basis function type are

reported for each orbital. ................................................................. 100

. Figures 6 and 7 are electron density contour plots

of natural orbitals 24 and 37 of the ScCH

molecule in the ground 3H state. The occupation and the

mulliken population condensed to a basis function type are

reported for each orbital. ................................................................. 100

. Figures 8 and 9 are electron density contour plots

of natural orbitals 7 and 38 of the ScCH

molecule in the ground 3H state. The occupation and the

mulliken population condensed to a basis function type are

reported for each orbital. ................................................................. 101

. Figures 8 and 9 are electron density contour plots
of natural orbitals 7 and 38 of the ScCH
molecule in the ground 311 state. The occupation and the

xvi

mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 101

10. Figures 10 and 11 are electron density contour plots
of natural orbitals 8 and 9 of the ScCH+
molecule in the ground 21'1 state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 102

11. Figures 10 and 11 are electron density contour plots
of natural orbitals 8 and 9 of the ScCH+
molecule in the ground 2H state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 102

12. Figures 12 and 13 are electron density contour plots
of natural orbitals 10 and 23 of the ScCH+
molecule in the ground 211 state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 103

13. Figures 12 and 13 are electron density contour plots
of natural orbitals 10 and 23 of the ScCH+
molecule in the ground 2H state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 103

14. Figures 14 and 15 are electron density contour plots
of natural orbitals 36 and 37 of the ScCH+
molecule in the ground 2l'I state. The occupation and the
mulliken population condensed to a basis function type are .
reported for each orbital. ................................................................. 104

15. Figures 14 and 15 are electron density contour plots
of natural orbitals 36 and 37 of the ScCH+
molecule in the ground 2I'I state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 104

xvii

16. Figures 16 and 17 are electron density contour plots
of natural orbitals 8 and 9 of the TiCH
molecule in the ground 22” state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 109

17. Figures 16 and 17 are electron density contour plots
of natural orbitals 8 and 9 of the TiCH
molecule in the ground 22‘? state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 109

18. Figures 18 and 19 are electron density contour plots
of natural orbitals 10 and 11 of the T iCH
molecule in the ground 22* state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 110

19. Figures 18 and 19 are electron density contour plots
of natural orbitals 10 and 11 of the TiCH
molecule in the ground 22‘ state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 110

20. Figures 20 and 21 are electron density contour plots
of natural orbitals 24 and 25 of the TiCH
molecule in the ground 22* state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 11 1

21. Figures 20 and 21 are electron density contour plots
of natural orbitals 24 and 25 of the TiCH
molecule in the ground 227 state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 1 ll

22. Figures 22 and 23 are electron density contour plots
of natural orbitals 38 and 39 of the TiCH

xviii

molecule in the ground state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 112

23. Figures 22 and 23 are electron density contour plots
of natural orbitals 38 and 39 of the TiCH
molecule in the ground state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 112

24. Figures 24 and 25 are electron density contour plots
of natural orbitals 8 and 9 of the TiCH+
molecule in the ground '2‘ state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 113

25. Figures 24 and 25 are electron density contour plots
of natural orbitals 8 and 9 of the TiCH”
molecule in the ground '2? state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 113

26. Figures 26 and 27 are electron density contour plots
of natural orbitals 39 and 40 of the TiCH
molecule in the 2H excited state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 114

27. Figures 26 and 27 are electron density contour plots
of natural orbitals 39 and 40 of the TiCH
molecule in the 2H excited state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 114

28. Figures 28 and 29 are electron density contour plots
of natural orbitals 23 and 24 of the TiCH+
molecule in the ground '2? state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 115

xix

29. Figures 28 and 29 are electron density contour plots
of natural orbitals 23 and 24 of the TiCH+
molecule in the ground '2’ state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 115

30. Figures 30 and 31 are electron density contour plots
of natural orbitals 37 and 38 of the TiCH+
molecule in the ground '2+ state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 116

31. Figures 30 and 31 are electron density contour plots
of natural orbitals 37 and 38 of the TiCH+
molecule in the ground '2? state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 116

32. Figures 32 and 33 are electron density contour plots
of natural orbitals 8 and 9 of the TiCH
molecule in the 2II state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 117

33. Figures 32 and 33 are electron density contour plots
of natural orbitals 8 and 9 of the TiCH
molecule in the 211 state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 117

34. Figures 34 and 35 are electron density contour plots
of natural orbitals 10 and 24 of the TiCH
molecule in the 211 state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 118

35. Figures 34 and 35 are electron density contour plots
of natural orbitals 10 and 24 of the TiCH

XX

molecule in the 2II state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 118

36. Figures 36 and 37 are electron density contour plots
of natural orbitals 25 and 26 of the TiCH
molecule in the 21'1 state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 119

37. Figures 36 and 37 are electron density contour plots
of natural orbitals 25 and 26 of the TiCH
molecule in the 2T1 state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 119

38. Figures 38 and 39 are electron density contour plots
of natural orbitals 39 and 40 of the TiCH '
molecule in the 2H state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 120

39. Figures 38 and 39 are electron density contour plots
of natural orbitals 39 and 40 of the TiCH
molecule in the 211 state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 120

40. Figures 40 and 41 are electron density contour plots
of natural orbitals 8 and 9 of the TiCH
molecule in the 2A state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 121

41. Figures 40 and 41 are electron density contour plots
of natural orbitals 8 and 9 of the TiCH
molecule in the 2A state. The occupation and the
mulliken population condensed to a basis function type are

xxi

reported for each orbital. . ................................................................ 121

42. Figures 42 and 43 are electron density contour plots
of natural orbitals 24 and 25 of the VCH
molecule in the 3 A ground state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 122

43. Figures 42 and 43 are electron density contour plots
of natural orbitals 24 and 25 of the VCH
molecule in the 3 A ground state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 122

44. Figures 44 and 45 are electron density contour plots
of natural orbitals 38 and 39 of the VCH
molecule in the 3 A ground state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 123

45. Figures 44 and 45 are electron density contour plots
of natural orbitals 38 and 39 of the VCH
molecule in the 3 A ground state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 123

46. Figures 46 and 47 are electron density contour plots
of natural orbitals 8 and 23 of the VCH+
molecule in the 2A ground state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 127

47. Figures 46 and 47 are electron density contour plots
of natural orbitals 8 and 23 of the VCH+
molecule in the 2A ground state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. . ................................................................ 127

xxii

48. Figures 48 and 49 are electron density contour plots
of natural orbitals 24 and 37 of the VCH+
molecule in the 2A ground state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 130

49. Figures 48 and 49 are electron density contour plots
of natural orbitals 24 and 37 of the VCH+
molecule in the 2A ground state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 130

50. Figures 50 are electron density contour plots
of natural orbital 10 of the VCH+
molecule in the 2A ground state. The occupation and the
mulliken population condensed to a basis function type is also
reported. . ................................................................................... 131

51. Figures 51 through 54 are electron density contour plots
of natural orbitals 25, 26, 40 and 39 of the CrCH
molecule in the 42." ground state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 132

52. Figures 51 through 54 are electron density contour plots
of natural orbitals 25, 26, 40 and 39 of the CrCH
molecule in the 42’ ground state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 132

53. Figures 51 through 54 are electron density contour plots
of natural orbitals 25, 26, 40 and 39 of the CrCH
molecule in the 42‘ ground state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 132

54. Figures 51 through 54 are electron density contour plots
of natural orbitals 25, 26, 40 and 39 of the CrCH
molecule in the 42' ground state. The occupation and the
mulliken population condensed to a basis function type are

xxiii

reported for each orbital. ................................................................. 132

55. Figures 55 and 56 are electron density contour plots
of natural orbitals 24 and 25 of the CrCH+
molecule in the 32’ ground state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 133

56. Figures 55 and 56 are electron density contour plots
of natural orbitals 24 and 25 of the CrCH+
molecule in the 32" ground state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 133

57. Figures 57 and 58 are electron density contour plots
of natural orbitals 38 and 39 of the CrCH”
molecule in the 32' ground state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 134

58. Figures 57 and 58 are electron density contour plots
of natural orbitals 38 and 39 of the CrCH+
molecule in the 32’ ground state. The occupation and the
mulliken population condensed to a basis function type are
reported for each orbital. ................................................................. 134

xxiv

KEY TO SYMBOLS AND ABBREVIATIONS

Symbol or
Abbreviation

\l’

H

SCF
RHF
MCSCF
CI
CASSCF
GVB

MCSCF+1+2

GVB+1+2

MRCI

DFT

¢/<l>

W.-

B3LYP

XXV

Wavefunction

Hamiltonian
Self-Consistent Field
Restricted Hatree-Fock
Multiconfigurational SCF
Configuration Interaction
Complete Active Space SCF
Generalized Valence Bond

Single and double excitations from
From a MCSCF reference space

Single and double excitations from
From a MCSCF reference space

Multireference CI

(Single and double excitations
out of a multireference space)
Density Functional Theory
Spin orbital/ space orbital

Kohn-Sham ith orbital

Laplace operator

Becke-Lee-Yang-Parr hybrid-
exchange correlation functional

ECP/RECP

xxvi

Effective Core
Potential/Relativistic
Effective Core Potential

Kohn-Sham Operator/Fock
Operator

Fock Matrix

Pseudo-orbital/Itth basis function
Effective Potential

Exchange operator/Exchange
integral

Coulombic operator/Coulombic
integral

Equilibrium distance
Configuration State Function

Natural Orbital

Chapter 1

METHODS SUMMARY

Introduction

The methods used in this dissertation are derived from the time independent
Schroedinger equation, H‘I’=E‘I’.3 These methods use the variation principle ' to
approach the exact wavefunction. This principle states that :

“Given a normalized wavefunction I ‘I’> that satisfies the appropriate boundary
conditions, then the expectation value of the Hamiltonian is an upper bound to the exact
ground state energy; i.e., <‘I’IHI‘P 2 E0 .”1 Therefore the energy calculated depends on
the wavefunction that is constructed. The wavefunction is a mathematical function that
depends on both spatial, and spin variables. The Hamiltonian is the operator for the
motion of the electrons and nuclei in the Coulomb field of the electrons and nuclei of the

system.

Hamiltonian

The Hamiltonian has the form,

 

       

H=-Ziv3- "' +2ii+iiZ”Z‘-22—*
2 k=12Mk i=1i>irij k=1p>k Rkp i=lk= 1 rik

Here ri denotes the coordinates of the ith electron, Rk the coordinates of the kth nucleus,

and 2;, the charge of the kth nucleus. The terms -l/2(Vi2) and (-1/2Mk)Vk2 represent the

kinetic energy of the ith electron and kth nucleus, respectively. The charges and masses are
in atomic units (au) with me: 1 au. The terms l/Iij, (Zka)/Rkp, and Zk/rik represent the
electron-electron, nuclear-nuclear, and electron-nuclear Coulomb interactions. The
Hamiltonian as written excludes relativistic effects that can be accounted for by using
relativistic effective core potentials, which will be discussed later.

A simplification of the Hamiltonian is obtained by using the Bom-Oppenheimer
(B.O.) approximation. In the 8.0. approximation the nuclei are assumed to move much
slower than the lighter electrons and one considers the electrons to be moving in the field

of the fixed nuclei. ‘3 The Hamiltonian then takes on the form,

a

{Jazz—+2»; vizi-

i=1 i>i .-,- k: lp>k i=1 k=l rik

The Hamiltonian can be divided into two parts, one being a one electron operator that

includes the kinetic energy of the electrons and the nuclear-electron attraction.

h(i') = EVE-7 5:5
Then,

HI = :Zlho')

The remaining part is

zz—+zz ,ng

i=1 [>1 "i,- k=1p>k

 

In this part, the first term describes the electron-electron repulsion of the system and the
second term describes the'nuclear-nuclear repulsion, which is a constant for a particular
nuclear configuration. Commonly the two body electron-electron interaction term is

written as g(1,2)=1/r12.

Wavefunction

Having specified the Hamiltonian, we can turn our attention to the wavefunction. There
are various methods used to construct wavefunctions of atomic and molecular systems.
All of the wavefunctions must follow the Pauli exclusion principle, which requires that a
wavefunction must be antisymmetric with respect to the interchange of the coordinates of

both space and spin of any two electrons,

‘I”(xl,xz,...xi,....xj,...xn)= -‘l’(xl,xz,...xj,....xi,...xn)

where x] represents the space and spin coordinates of the ith electron. While the
nonrelativistic Hamiltonian does not include a contribution from the electron spin, the
wavefunction often does, and this is usually accomplished by using spin orbitals.“9 The

spin orbital is a product of a spatial function, (1),, describing the space in which the

electron moves, and a spin function, with either spin up (or) or spin down ([3); e. g.,

¢,.(i) = ¢,(i)a(i).

One of the first wavefunctions to describe a system with this antisymmetric nature

was the Hartree-Fock wavefunction.l A Hartree-Fock wavefunction is described by a

1.9.10

Slater determinant of spin orbitals selected so as to minimize the energy of the

system.
AU) ¢2(l) ¢,.(1)
.1, =_1_¢.<2> 492(2) ¢,.<2)
HF J; I I .. ¢n(3)

 

¢r(n) (1)201) ¢,,(n)

 

The form of the orbitals is determined by varying the orbitals to minimize the energy

under the following constraints:

a. the set (1),, is orthonormal
b. and the variation in each orbital is orthogonal to variations in the other
orbitals.

This procedure leads to the Fock equation, 55¢, = 5,43,, where 3 is the Fock operator.

The Fock operator has the form,

where

h=—iV2 55—
2 k r,

and

J”.- = J¢‘.-<2>g<1,2>¢,<2>dr<2)

is the Coulomb operator and

1?. = M<2)g<1.2>ih¢.<2)dr(2)

is the exchange operator.

For a closed shell system the energy has the form,

E: if hi>+::(21,j —K,j)
i=1

i=1 j>l

where <hi> is the one electron energy of the ith electron, J ij is the coulombic repulsion

between electron i and j and Kij is the exchange energy between the two electrons.

Self-Consistent Field Procedure1

The unknown orbitals (spatial part) are expanded in a basis {xu} as

¢i = XCM'ZAI
p=1
where the C M. is the expansion coefficient of the um basis function 1". The basis

functions used in this work are of the Gaussian type. These functions are of a form that is

11.12.13

easy to use in calculating the integrals needed in the following procedures. Upon

substitution into the Schroedinger equation and variation of the C M. to minimize the

energy, the Roothaan equations3 are obtained as
FCi=8iS C}.
F: H“ore + G

where F is the canonical Fock matrix whose elements are
Fm, = JZLSZVdT;

S is the overlap matrix, whose elements are

S w, = I 1:11th and Ci, is a column vector of coefficients cm, and 6,. is the energy of an

electron in orbital i. The G term is the two electron part of the Fock matrix.

N/2

G... = Elm; <1)[21.<1> — K.<1>l¢.(1>

0

Here the 0 corresponds to the ath orbital.

The Roothaan equations are solved by an iterative procedure. First, the geometry
of the molecule is specified, a basis set is specified and the required integrals are
calculated. The overlap matrix is diagonalized and a transformation matrix is obtained to

transform the Fock matrix. One obtains a guess at the density matrix P

often from the eigenvectors of the one electron Hamiltonian in the selected basis. The G
matrix (obtained from the two electron intergrals) of the F matrix is calculated from the
density matrix and the two-electron integrals. The Hcm or H I matrix is called the core-
Hamiltonian. The transformed Fock matrix is calculated and diagonalized to obtain a new
coefficient vector, C’, and orbital energy, 8. The new coefficients are used to form a new
density matrix. This procedure is repeated until one obtains a solution that is consistent

within a specified criterion on the energy or density, thus the idea of self-consistency. The

field comes from the idea that there is an averaged field due to the electrons in the system.

Using this procedure it is possible to solve for a near Hartree-Fock wavefunction self-

consistently. With a complete basis set this solution is considered the Hartree-Fock limit.

Correlation

The Hartree-Fock description does not provide adequately for the correlated
motion of electrons in the system. 1’8 Therefore, this wavefunction description will not be
adequate for quantitative studies. Correlation energy is by definition the energy

difference between the exact energy and the Hartree-Fock energy.

Eexact-EHartree-Fock=Ecorrelation

This correlation energy may be (approximately) recovered by several methods
including Generalized Valence Bond (GVB) Theory, 6‘8' 9 Multiconfigurational Self-
Consistent Field (MCSCF)5‘7 and Configuration Interaction (CI)3'7 techniques. In general,

the exact wavefunction can be written as:

‘1’ = co‘l’o +cl‘lr’l -I-c2‘I’2 +---
where To is a single determinant wavefunction (possibly the Hartree-Fock solution), ‘1’.
consists of all determinants obtained as single excitations from ‘I’o, ‘Pz consists of all
determinants obtained as double excitations from ‘l’o, etc. Note that this is exact only
when the expansion basis {xu} is complete. In CI calculations only the coefficients are
permitted to vary; i.e., the orbitals {o} are fixed at the SCF level. Practical considerations

limit most calculations to single, ‘1’], and double, ‘1’; excitations and also to a finite or

incomplete basis {xu}. Under these circumstances, a better approximation is to vary the

coefficients of the basis functions themselves, as well as the coefficients of the selected
determinants. This is the MCSCF technique. In the MRCI or multi-reference
configuration interaction technique a MCSCF wavefunction is used as the reference space
from which excitations are made to describe the MRCI wavefunction. The GVB method
is just a special version of the MCSCF wavefunction. The MCSCF wavefunction is
constructed under the constraints of orthonorrnality between the orbitals being
constructed.

The final method to be discussed briefly is that of Density Functional Theory.7’l4
DFT is a development from the theory of Hohenberg and Kohn in 1963 which states that
all the ground-state properties of a system are functions of the charge density. The
Hohenberg-Kohn theorem thus enables us to write the total electronic energy as a

function of density:

 

V2 1 , '
Em) = 21w.- (.7)...» + JV.......p(r)dv +5fldvdv WW ) + E. [pm]

r—r’l

 

where ECO) is the energy as a function of the density, the first term is the kinetic
component of the energy, the second term is the nuclear attractive component of the
energy, the third term is the coulombic repulsive term, and the last term is the exchange-

correlation functional.

The ‘1’, are the Kohn-Sham orbitals,14c defined so that the [7(7) = 2 9’52 and obtained

-
—
—

from a Hartee-Fock like eigenvalue problem.

 

Unfortunately, Exc, the exchange correlation energy is unknown and one is forced to use
various approximate forms. We will use the Becke-Lee-Yang—Parr hybrid exchange-

correlation functional called B3LYP.

Relativistic Effective Core Potentials

The Hamiltonian described earlier did not include relativistic effects; however, for
atoms heavier than Al relativistic effects come into play. In the case of YN and YP
discussed in a later chapter the relativistic effects are accounted for by using Relativistic
Effective Core Potentials (RECP’s).‘5‘ '6

The Effective Core Potential, ECP is also used in computational studies to
provide computational savings. The number of integrals that need to be calculated in
these systems scale on the order of M4 where M is the number of basis functions. By
using effective core potentials the core electrons on individual atoms are represented by a

potential chfcctive or Veff and are eliminated. The potential takes the form:

10

l 2 I
z... _l(1+1)+(§V ’lem
r 2r2 1,

 

 

Mm=q+

Here, 8, is the atomic orbital energy, Z,“ is the effective nuclear charge due to screening,
and the third term represents the orbital kinetic energy. The last term consists of the

kinetic ener of the electron in the orbital, V4,, re resents the Coulomb and exchan e
gy P g

potentials due to the other valence electrons, and 2’: represents the pseudo-orbital

constructed from the Hartree-Fock orbitals that would see the potential due to the core

electrons. Each valence orbital, Zr , with a given angular momentum generates a unique
potential. This decreases the number of integral calculations significantly because fewer
basis functions are necessary to describe the system.

Relativistic Effective Core Potentials are generated in a similar manner, except the
Dirac-Fock relativistic equations are solved and new relativistic pseudo-orbitals are
generated with the relativistic effects already incorporated. These new pseudo-orbitals

will then have an I and j dependence.

ll

BIBLIOGRAPHY

12

BIBLIOGRAPHY

I. A. Szabo and NS. Ostlund, “Modern Quantum Chemistry: Introduction to Advanced
Electronic Structure Theory”, Macmillan Pub. Co., Inc., New York, N.Y., 1982.

2. H. F. Schaefer III, “The Electronic Structure of Atoms and Molecules”, Addison-
Wesley Pub. Co., Reading, Mass, 1972.

3. I. Shavitt, “The Method of Configuration Interaction” in “Methods of Electronic
Structure Theory”, edited by H. F. Schaefer H, Plenum Press, New York, 1977.

4. AC. Wahl and G. Das, “The Configuration Self Consistent Field Method” in
“Methods of Electronic Structure Theory”, edited by HE Schaefer III, Plenum Press,
New York, 1977.

5. a) R. Shepard, “Ab-Initio Methods In Quantum Chemistry II,” Advances in Chemical
Physics, edited by K. P. Lawley, Wiley, New York, 1987.

b) T. H. Dunning, Jr., “Multiconfigurational Wavefunctions for Molecules: Current
Approaches” in “Methods of Electronic Structure Theory”, edited by HR Schaefer
IH, Plenum Press, New York, 1977.

6. a) F.W. Bobrowicz and WA. Goddard I1], “ The Self Consistent Field Equations for
Generalized Valence Bond and Open-Shell Hartree -Fock Wavefunctions” in
“Methods of Electronic Structure Theory”, edited by H. F. Schaefer III, Plenum Press,
New York, 1977.

b) W. A. Goddard IH, T. H. Dunning, Jr., W. J. Hunt, P. J. Hay, Acc. Chem. Res., 6,
368, (1973)

c) W. A. Goddard III, L. B. Harding, Ann. Rev. Phys. Chem., 29, 363, (1978)

7. A. R. Leach, “Molecular Modeling: Principles and Applications”, edited by Addison
Wesley Longman Limited, Essex, England, 1996.

8. E. Merzbacher, “Quantum Mechanics”, 2nd. Ed., John Wiley and Sons, New York,
1970.

9. I. N. Levine, “Quantum Chemistry”, 2'“. Ed., Allyn and Bacon, Inc., Boston, 1974.

10. J. C. Slater, Phys. Rev. 34, 1293 (1929).

13

ll

12.

13.

14.

15.

16.

. S. F. Boys, Proc. Roy. Soc. (London), A200, 542, (1950).

a) T.H. Dunning, Jr., J. Chem. Phys., 53, 2823, (1970).

b) T.H. Dunning, Jr. and R]. Hay, “Guassian Basis Sets for Molecular Calculations”
in “Methods of Electronic Structure Theory”, edited by HP. Schaefer III, Plenum
Press, New York, 1977.

a) BB. Botch, T.H. Dunning, Jr. and J .F. Harrison, J. Chem. Phys., 75, 3466, (1981)
b) R]. Hay, J. Chem. Phys., 66, 4377, 1977.

a) J. A. Pople, P. M. W. Gill, and B.G. Johnson, Chemical Phys. Lett. 199, 557, 1992
b) P. Hohenberg and W. Kohn, Phys. Rev. B 136, 864, 1964.

c) W. Kohn and L. J. Sham, Phys. Rev. A 140, 1133, 1965.

Hay, P. J .; Wadt, W. R. J. Chem. Phys. 1986, 82, 5606.

Krauss, M.; Stevens, W. J ., Ann. Rev. Phys. Chem., 1994, 34, 357.

14

CHAPTER 2

THE ELECTRONIC STRUCTURE OF YN AND YP

This chapter contains a detailed study of the electronic structure and various
properties of YN and YP. Two of the central purposes of this work are to gain an
understanding of the nature of the bonding between transition metals and main group
elements and to characterize the effect of electronic structure on the properties of these
compounds. This knowledge is important in the areas of astrophysics, organometallics,
solid state chemistry, gas-phase spectroscopy, surface chemistry, and catalysis.

Yttrium nitride and phosphide have a variety of low-lying electronic states with an
assortment of bonding possibilities. As has been seen in various studies of metal-main
group diatomics, there are several bound single, double, and triply bonded states. It is our
intention to investigate seven of the low-lying states of YN and YP. We will compare
and contrast these two compounds and other first and second row transition metal

diatomics

Background

There have been numerous experimental3 and theoretical studies" 2 completed on
the first row transition metals bonded to main group elements. Harrison and Kunze
published ab-initio studies on several bound states of scandium nitride along with a
significant compilation of work on transition metals bonded to other main group

elements, including studies on TiN, VN, CrN and their mono and dipositive ions.l Other

15

researchers have produced work on the positive cations and also the dipositive ions of
some of these unique metal-main group element diatomicsz’ 3 Very little has been done
on the metal-phosphides. The ScN molecule was observed by Ram and Bemath by using
Fourier transform emission spectroscopy,4 and they found the ground state of ScN to be

'2? in keeping with the theoretical prediction. The experimental bond length of 1.654 A 4

is in reasonable agreement with a predicted bondlength of 1.768 A by Harrison and
Kunzem". Titanium nitride’s electronic emissions were analyzed by Dunn, Hanson, and
Rubinson and they observed a bondlength of 1.583 A for the lowest energy state.5
Harrison and Kunze reported the bond length to be 1.613 A, in reasonable agreementlm
Vanadium nitride was generated and observed by Dunn and Peter by way of
electronic emission studies and they determined that it had the shortest bond length
(1.566 A ) of any observed transition metal diatomic.6 Theoretical calculations have

predicted it be 1.588 Al“) The term symbols of the ground states of TiN and VN, 22+,

and 3 A, respectively, were the results found in both experiment and in theory. Theoretical
calculations predict the ground state of CrN to be a 42' with a bondlength of 1.597 Am)

The second row transition metal nitrides have been studied to a lesser extent
theoretically, although significant work has been compiled in the experimental regime.
Some of the earliest work was done on MoN and NbN in the 19605.7' 8 Since then there
has been Fourier transform emission spectroscopy on YN,“ ') electronic emission
spectroscopy on ZrN9 and vibrational absorption spectrum observations on tantulum
nitrideIO isolated in an argon matrix. Studies of MoN and Mo atoms in neon, argon, and

krypton matrices using a hollow cathode ion sputter source for electron spin resonance

16

experiments followed some of this earlier work.11 MoN has a ground state of 42'. Also,

the compound yttrium imide has been studied by using jet-cooled spectroscopy. '2
Theoretical studies have often provided valuable information relating experiment
to theory. Balasubramanian12 performed calculations on the yttrium imide molecule and

found that the ground state was 322‘, which Simard et at. were unable to confirm

experimentally.” Gingerich calculated the dissociation energy of YN, LaN, HfN, NbN,
TaN, MoN, WN, and several other first row transition metal nitrides using the
experimental results of ZrN and UN“) Gingerich and Shimzm performed calculations
on YN to aid in the understanding of the bonding of this gaseous compound studied
experimentally by Bemath and Ram.3r The molecule ZrN has also been examined

experimentally and theoretically.9' 2”" The experimental ground state detected was 22'.
In YN, the ground state has been found by Gingerich and ourselves to be the '2’“

statezm There are some differences in the bonding and other physical properties between
Gingerich’s results and ours. In the case of MoN the ground state was found theoretically
by Goddard to be of sigma symmetry with a triple bond.2i This coincides with the

2(a. b. c, i)

chromium nitride 42' ground state. The ScN ground state possesses a weak

sigma bond. Daoudi et. a1. calculated similar results for ScN using the CIPSI method,2n
however, they suggested that the ground state, '2‘: does not posses the weak sigma bond

as suggested by Harrisonzm'p)

Harrison and Kunze calculate that the ground state lies
only 7 kcal below that of the doubly bonded 32“ first excited state.” 2°'P This unique

situation perseveres in the YN ground state, as will be discussed. This brings us to the

significance of this work. As mentioned earlier, this work has import in areas of

17

catalysis, and organometallics and other areas where the question of bonding is
important. Mulliken population22 analysis and contour plots have been effective methods
of examining the character and visualizing the structure of the bonding in this work, as
has been noted by Goddard et al. in their examination of the electronic structure of
MON.2(3' b’ c“ i) The triple bonded species might form the bonds using pure atomic orbitals
on M0 or hybrid orbitals, which would affect the bond length, bond energy, dipole
moment, and an assortment of other physical properties.

The difference in the bond length affects the Coulombic interaction, electron
distribution, and in turn the entire physical nature of these diatomic molecules. Referring
back to MoN in the Goddard study and several triple-bonded metal nitride systems, the
character of the sigma bond changes between the extensive valence s orbital character and

the do character depending on the exchange energy and the ability of the orbital forming

the bond to hybridize. In the case of catalysis and vapor deposition the ability of the
metal nitride moieties to form stable bonds, affecting the surfaces in these systems, can be
determined by the characteristics that have been cited. In the yttrium imide molecule

12 IO

Simard13 and coworkers turned to theoretical calculations of Balasubramanian
interpret their results.

Another factor that this type of study aids in disclosing is the nature and location
of excited states and the relative ordering of these states. It is often difficult for a
spectroscopist to examine some of the excited states in these systems because of the small
1(h)

separations in energy found between the states. Harrison and Kunze examined sixteen

significant low-lying bound states relative to the separated ground state atoms. The

18

energy separations between states in these systems is sometimes as low as a few kcal/mo].

This would be difficult for some spectroscopic techniques to uncover.

Methods

The computational work was completed using the COLUMBUS suite of
programs.14 There were two types of wavefunctions generated as references to the MRCI
wavefunctions. Both sets of calculations were at the multiconfigurational self-consistent
field (MCSCF) level; one set used the generalized valence bond (GVB) perfect pairing
technique. The significance of near degeneracy in the Sc atom was noted by Harrison,
Dunning and Botch.l5 It was not accounted for in either of the reference wavefunctions
generated by these two techniques, but the single and double excitations out of the
reference spaces in the (CI) calculations included the effect. The importance of the near
degeneracy arises in that it affects the calculated dissociation energy. In the case of ScN
including near degeneracy in the MCSCF wavefunction of Harrison and Kunze drops the
ground state energy by 2-4 kcal/mol.”h)

The MCSCF wavefunctions of YN and YP are described below:

N=nitrogen or phosphorus py or p,,= 2p or 3p of N or P, respectively.

‘2‘ ~ [0(Y)6(N) + 6(N)6(Y)][ny(Y)1ty(N)+1ty(N)ny(Y)][nx(Y)1tx(N)+nx(N)nx(Y)l
32* ~ [fly(Y)1ty(N)+1ty(N)1ty(Y)l[nr(Y)1tr(N)+1tr(N)1tx(Y)l Y5s Npo

3Ii ~ [o(Y)o(N) + o(N)o(Y)][ rt(Y)1t(N)+1t(N)rt(Y)] Y5s pr

(a. 1!)

l9

311 ~ [ny(Y)1ry(N)+1ry(N )ny(Y)][nx(Y)nx(N)+nx(N)nx(Y)] Y5py N96

(n. n)

l” t... .t ~ 10(Y)6(N) + 6(N)O(Y)][ nx(Y)1tx(N)+1tx(N)nx(Y)] Y5py Npo (singlet COllpled)
3A ~ [Try(Y)TCy(N)+1ty(N)1ty(Y)l[nx(Y)1tx(N)+1tx(N)1rx(Y)l Y6+ Npo
‘A ~ [rty(Y)1t,(N)+rty(N)1ty(Y)][n.(Y)1tx(N)+rtx(N)1tx(Y)] Y8+ Npo (singlet coupled)

In the MCSCF wavefunction the electrons are correlated without the pairwise constraint.
Due to symmetry constraints the wavefunctions employed using the MCSCF and GVB
techniques will not be significantly different, but the small difference in applying the
perfect pairing has an effect on the manner in which the atoms separate. The GVB
technique does not allow for the atoms to separate to the correct atom states and only the
MCSCF and MCSCF+1+2 potential curves will be presented. However, the results of the
GVB and GVB+1+2 calculations on the YN and YP molecules are presented in Tables 5a
and 5b.

The calculations were performed using Hay and Wadt’s relativistic effective core
potentials (RECP’s) with accompanying basis functions on the yttrium atom.16 The
Dunning double-zeta basis set was used on N.‘7 The phosphorus basis set consisted of
(l6lep3d2f)/[655p3d2f].l7 The yttrium basis was augmented according to Bauschlicher
and Langhoff et. a1. with polarization functions and a set of three uncontracted f-
functions.18‘ ‘9 In order to test the reliability of the Y basis, a comparison was made with
the work of Bauschlicher and Langhoff et. al.18 on the Y atom and the YH molecule. The
Y atom was compared at the following levels of theory: RHF”, SCF“, single-reference

SDCIb‘C, coupled-pair functional“, and modified coupled-pair functional“. Table 1

20

displays the relative energy (eV) of three states of the Y atom relative to the 2D ground
state using the methods mentioned above, and compares them to the experimental results.
In comparing the 2P and the 4F states at the SCF level our results are 0.02 and 0.04 eV
lower in energy relative to the ground state of the atom. In the single-reference C1 the
difference increases to -0.05 and 0.08 eV for the two states. The differences can be
attributed to symmetry and equivalence constraints placed on the orbitals in the Y atom
by Langhoff et a1.18 Our calculations have no such constraints. Therefore, despite using
the same basis sets with the same contraction schemes the resulting energies are different.

SCF CI

MH LPB EH LPB EH
State Occupation RHF“ scr" scrc SDCI“ SDCI“ Expt.“

 

21) 5s24dl 0.00 0.00 0.00 0.00 0.00 0.00
2P 5s25p‘ 1.19 1.41 1.39 1.08 1.13 1.33
4F 4d25p‘ 0.75 0.69 0.65 1.36 1.44 1.36

aR. L. Martin and P.J. Hay, J. Chem. Phys. 75, 4539 (1981).
“S. R. Langhoff, L. G. M. Pettersson, and C. W. Bauschlicher, J. Chem. Phys. 86, 268 (1986).
“J. F. Harrison and J. Edwards, Department of Chemistry, Michigan State University.

Table l. The relative energy (eV) of two states of the Y atom relative to the
2D ground state.

Next, several states of the YH molecule were contrasted to continue our
verification of the Y basis set. The same basis was used for the Y atom. The hydrogen
basis set used was a duplicate of the hydrogen basis used by Langhoff and co-workers.19
The H basis set consisted of 7s and 4p functions contracted to 48 and 3p functions as

[4111/211], augmented with a diffuse function in an even-tempered manner.20 A (211)

21

contraction of a Slater 2p function with an exponent of 1.0 was used for the p functions

on the H atom.

Molecule State Level AE(eV) ch(a.u.)
YH ‘2” SDCI‘ 0.00 3.700
SDCI“ 0.00 3.700
CPF“ 0.00 3.706
MCPF‘ 0.00 3.706
YH ’11 SDCI' 0.78 3.843
s1:>c1b 0.86 3.842
CPF‘ 0.86 3.842
MCPF“ 0.86 3.843
YH 3r1 SDCI‘ 0.94 3.826
SDCI“ 1.01 3.824
CPF‘ 1.01 3.825
MCPF“ 1.01 3.825

3‘S. R. Langhoff, L. G. M. Pettersson, and C. W. Bauschlicher, J. Chem. Phys. 86, 268 (1986).
bJ. F. Harrison and J. Edwards, Department of Chemistry, Michigan State University.

Table 2. A comparison of various states of the YH molecule. The energy separation relative to the
ground state YH molecule and the equilibrium geometry is reported.

As can be seen from the data above our results at the SDCI agree extremely well with
those of Langhoff et. al. at the CPF and MCPF levels.18 It appears that the small
correlation energy difference evident in the atoms due to the symmetry and equivalence
constraints may be accounted for in the CPF and MCPF calculations.

The Y atom and the Sc atom are obvious places to begin our comparison of the

YN and ScN molecules. Figure 1 provides selected promotion energies of the Y

22

 

 

 

and Se atoms averaged over the J values of each state.21 The most striking difference in
the ordering of these states is ‘that the first excited states of each atom is different, yet
similar in energy relative to the 2D ground state. The 2P, in a 5825p1 configuration, is the
first excited state of the Y atom followed closely by the 4F , 3d24sl configuration. On the
other hand the Sc atom’s first excited state is the 4F , 4d25sl configuration. The
promotion energies of these three states are all within about 32 kcal/mol. The 4524pl
configuration in the 2P state for the Sc atom has not yet been observed experimentally. It
was calculated using the basis set shown in Figure l at the SCF+1+2 level. The
promotion energy puts it highest in energy amongst the states shown, about 8 kcal/mo]
higher than the 4G, 3d24pl configuration. The isoelectronic configuration for Y is also a
2P state and lies about 30 kcal/mole above the ground state of the Y atom. The only
similarity displayed in Figure 1 between the atomic states of Y and Se are the relative
separation of the 4F states corresponding to the configurations dzsl and dsp

configurations.

23

Promotion Energy (kcal/mol)

 

85.00

 

 

"—1 4d3 04F
80.004 4d25p1 246°
75.004 4.24,,1 2p __
70 00‘ Calculated relative to the ground state
. Sc atom using (t4sttp6d1554p3d) ‘
65.00‘ 3d24p1 24Gb __
60.00-
50.00~
45,00. 3614s‘4p1 24F0— ___4d15515p1 24,:
40,00.
35.00‘ :3d24s1 a4F — . __ 4d2531 a4F'
30 00. —" 5525p1 22P°
25.00~
Selected Experimental Promotion
20°004 Energies of High Spin States of
the Sc and Y atoms
15-00‘ (Averaged Over Values for 1 States for Each Term)
10.00.
500‘ 4s2‘3d1 20 5s24d1 20
0.00
So Y

' SCFetoz calculation periorrned on the Sc atom 4:241:11

Figure 1. Selected experimental promotion energies of high spin states of the Sc and

Y atoms averaged over values forJ states for each term. Values taken from
Moore (Reference 21) except for the calculated state shown above.

24

 

.’
43+:Sc/+ N ————-— ScEN 12+

11: 4 2P
7 .. __. sacs 332+

3,1! donblo bond.

2 0
45 .SC + N ————p- . sea 0 3H 0',“
3d1' 4s 21:,t

43 .s + N —————- obsc TN .0 3A

I. it double bonds

 

 

 

 

 

5s1
4 2 . - ____.
d 1|:\. Y + N Y __ N 12*
. 531 1,11: double bonds
4d“ —>: Y + N 3 53
TC . Y . 32+
1 2p°
. 4d,t 5
2 _._o 8
5’ °Y+ N .YZ‘N- “Hon:
2px
. 519,t
““121! ':Y+ N .Y:N° Hm
5P1! 2P0
5911:
. ' Ad 3
4d2nT° Y + N TY - A
2pc

n. x double bonds

Figure 2. Bonding Scheme of analogous states
of IN and Sen (Harrison and Kunze 1'2)

25

Results

Figure 2 presents the bonding scheme for the 12", 32*, 3A, 1A, 1I11“, and “Hm states

in the ScN and YN molecules and also the 31'1“,t state of the YN molecule which would

be analogous to those of YP with the difference being the atomic

configuration of the phosphorus atom. The 3TI and 311m states are doubly bonded pi

mt’
and double bonded sigma and pi bonded systems, respectively. Triplet coupled lone

electrons are on the Y and N atoms. In the 3IImt state the lone electron on the Y atom is

localized in a 5P1: orbital, whereas in the 3T1“O state the N atom possesses a 2P1: lone

electron while the Y atom has a lone 58 electron making up the triplet coupling. The

bonding in the 32* state of both of these molecules consists of pi double bonds with lone

electrons triplet coupled in an s orbital on the metal and in a 2pc orbital on N. In both

molecules the triplet del state has a lone electron in a d5... orbital on the metal and in a 2pc

orbital on the N.

Our MCSCF and MCSCF+1+2 wavefunctions provide the appropriate correlation
to examine the molecules in a detailed fashion. The potential curves of the 7 states of
interest are shown for YN and YP at both levels of theory in Figures 3, 4, 5, and 6. The

ground state, '2‘“, of YN lies about 17 mH below the 323+ at the MCSCF level. In

comparison, the ScN 12.“ ground state is about 12 mH lower in energy than the 323+ first

excited state at the MCSCF+1+2 level.lh The relative ordering of the ‘2“, 32+, 3IT and

no’

26

3 A states are the same in ScN at the MCSCF+1+21h and in YN (this work) at the MCSCF

and MCSCF+1+2 levels.

The singlet coupled A and IT states are in close proximity in energy relative to the ground

states for each of the systems examined. In contrast to the ScN systems studied, the YN

molecule separates to a 58'5p14dl valence configuration in the 3A state, while the ScN

molecule separates to a 3d3 configuration of Se with lone electrons in the 3dnx, 3d“, and

3d5_ at the CI levels. In all of the states at each level of theory for both molecules, N

separates to the 4S ground state valence configuration of 2822p3. At the MCSCF level the
3A state valence configuration of YN matches that of the 3117m. At the asymptotic limit
of the MCSCF+1+2 calculation the “firm state does not remain in the same configuration
as the 3 A state of YN; it falls to a lower energy configuration of 5s‘4d“. The GVB

calculations produce different results than those of the MCSCF. As mentioned earlier,
constraints on the GVB wavefunctions do not allow for the atoms to separate smoothly to
their proper limits. This can be corrected by modifying the GVB wavefunction as the
molecule begins to separate. Despite this, the relative ordering of the energy levels was
consistent with that of the MCSCF calculations. One significant difference arises in

comparing the YN and YP molecular states. Figure 6 shows that the first excited state of

the YP molecule is the “IIm state at each level of theory. In the analogous diagram for

YN this state lies slightly above the first excited state, 32". The 32" state lies several tenths

of an of an electron volt above the ground state in the YP case at each level of theory. In

the YN molecule at the CI level, the separation is slightly increased between the triplet

27

and singlet A and 1'10,“ states, which was not evident in the MCSCF+1+2 calculations, as

can be seen from Figure 4. The CI calculations for each of the MCSCF and GVB
reference spaces lower the overall separations of the states relative to the ground state, but

the overall ordering stays almost identical. The few exceptions arise in the ordering

between the excited states 3A, ‘A, and 31'1“. Despite this inconsistency, the lower lying

states of “2‘, 311m and III“ maintain a consistent order of separation of a little over 0.2

eV. Correlation introduced by the CI calculations accounts for these differences in
ordering.

As mentioned earlier, one of the major differences predicted between the YN and

YP molecules was the ordering between the 3Z7 and 311“ states. In the 37..“ state of YN

the two pi bonds are made from the N 2px and 2py orbitals and Y (1,,z and dyz orbitals. In

the case of the 3HM state of YP the bonds are made from more spatially extensive

orbitals of the P atom allowing for this state to be lower energetically than the 32‘ state.

28

YN 5p14d2

1A
3A

 

 

 

AE (eV)
1 1 1
X
/
./
:1
5)
:1
8'
.53
e.-

 

 

. 3an

-2 — ' MCSCF

3 ‘ 32+ YRECP(6s6p5d31)/[5s4p4d:3fj
‘ 12+ N(lOsSp3d)/[4s3p2d]

'4 ' 1 r T ' I ' 1 ' r ' l ' 1 r 1
2 3 4 5 6 7 8 9 1 D

Rtau)

Figure 3. Potential energy curves of several electronic states of YN. MCSCF calculations
performed in this work.

29

 

a - YN 13 581W
.1 ‘ 34
- 31'1 rt, it 5si4d2
27.—=5—

 

 

  
 

 

 

 

5 24d1
% 0d \\ S
E . 3
<1 4 q II 0,1: 11 0,1r
_2_‘ MCSCF+1+2
. YRECP(6s6p5 d31)/[5 s4p4 th]
'3 7 8 32+ N (1035p3d)/[4s3p2d]
« 12+
-4 I I ‘ l ' T ‘ l ' I ' l ' l ' l
2 3 4 5 6 7 8 9 10
Rla.u.)

Figure 4. Potential energy curves of several electronic states of YN. MCSCF+1+2
calculations performed in this work.

30

 

 

 

 

 

 

 

5pl4d2
3 _
2 ..
, .‘Ssl4d2
1 4 /———~
2 2 1
§ 0 _ __ 58 4d
El“ 7 / 11'! 0,1:
‘51 -1 — x
-2 _ m 0,1: MCSCF
- YRECP(6 s6p5 d3f)/[5 s4p4d3f]
‘3 ‘ P (1559p2dlfl/[Ss4p2d1fl
i
'4 I I I r I I r F I I 1 I
2 a 4 5 6 7 a 9 10
R(a.u.)

Figure 5. Potential energy curves of several electronic states of YP. MCSCF

calculations performed in this work.

31

 

 

   
 

 

 

1
4 A
3: :is14d2
2 - \ If;
1 ..
‘ 5 24d1
Eu” 3
<1 -1 j 11 0, rr
-2 ‘ MCSCF+1+2
3 . YRECP(6s6p5 d31)/[5 s4p4d31]
P (15 s9p2dlf)/[5 s4p2d1f]
'4 ' r ' l ' I ' 1 ' r ' I r f ' 1
2 3 4 5 6 r 8 9 10
R(a.u.)

Figure 6. Potential energy curves of several electronic states of YP. MCSCF+1+2
calculations performed in this work.

32

Population Analysis

From Tables 3, 7 and 8 it can be seen that the populations of selected atomic
orbitals for the YN and YP atoms are almost identical for each of the states shown. Figure
7a-7d show plots of the populations of selected atomic orbitals of YN versus the
internuclear separation. Comparison of these plots with plots of the same type shown for

ScN by Harrison and Kunze” shows that the '2' and 32' states of YN and ScN follow

similar bonding patterns. In each case there are large shifts of charge from n: and do

orbitals of the metal atoms to the corresponding symmetry orbitals of the nitrogen atom.
The shifts begin as the atoms approach the equilibrium bonding distances. Comparison
of the population analyses of YP in this work and of ScP from the work of Tientega5a and
Harrison shows that the populations at the equilibrium separation are very similar.

Bond lengths, bond energies, and vibrational frequencies are compared in Table 4
for YN and ScN and in Table 5 for YP and ScP. The data for the scandium diatomics,
ScN and ScP, come from the work of Harrison and Kunzelj and Tientega and Harrison,
5“ respectively. The bond lengths of the phosphides are consistently larger than the
nitrides, because of the larger phosphorus atom. The Sc atom being smaller than the Y
atom leads to shorter bond lengths for the Sc species of the metal nitrides and phosphides.
The vibrational frequencies are higher for the nitrides than the phosphides in keeping with
the shorter bond lengths. This was also the case when comparing the scandium nitride

and phosphide states with the corresponding states of

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mrwv

5.0
00.0
mmd
m0.0
m0.0

86
3w

000

00.0
00.0
mwd
00.0
m0.0

mod
am

.353 Q. can 3 05 5.. mod ,2 033 coca—smog 56¢ >
a

00.0
00.0
00.0
00.0
00.0

00.0
+03.

0N.0

am .0

0N0

wmd

3 .0

0m.0

mad
a

v0.0

2 .0
v0.0
N00
m _ .0
2 .0
N_ .0

3w
flag.

0N0 0_ ed
0: mwvd
0N.0 00v.m
m: .0 0_ UN

_0._ SYN

00.0 mafia
No.0 mth
m a

 

A95— N+~+h0m02 2: “a 03.3 Ema—«:4N noun—50.5 ESE—=2 m> .0 035,—.

41

Population (a.u.)

 

 

2.00

 

 

 

 

 

 

1.80- N28
1.60~
12+ YN MCSCF+1+2
1.40~
1.20-
N2po
1.00- F
0.80- ”3
Y4do
0.60‘
0.40~
l
0.20-
YSpo
0.00 l I I l l
2 3 4 5 6 7 8 9
R (a.u.)

Figure 7a shows population curves of selected sigma symmetry orbitals

10

taken from the natural orbitals of the YN molecule at the MCSCF+1+2 level.

42

Population (a.u.)

 

2.00

 

 

 

 

 

 

1'80‘ MCSCF+1+2 YN 12+
1.60-
1.40-
1.20. N am
1.00- .07
0.80‘ Y4¢hx
0.60-
0.40-
0.20-
Y5pnx
/—_\
0000 l l I I I I l I
1 2 3 4 5 6 7 8 9
R (a.u.)

Figure 7b. Population curves of selected pi symmetry orbitals taken from the
natural orbitals of the YN molecule at the MCSCF+I+2 level.

43

10

 

2.00

1.80-

1.60-

1.40~

Population (a.u.)
S
C?

p
00
9

.9
as
‘P

0.40-

0.20d

 

0.00

N23

32+ YN MCSCF+1+2

 

 

Y4do

Y5po

 

 

 

\0—4

10

Figure 7c shows selected sigma symmetry orbitals taken from the natural orbitals of the
first excited state of the YN molecule at the MCSCF+1+2 level.

44

 

 

 

 

 

 

 

2.00
1.80-
1.60- 32+ MCSCF+1+2
1.40:
A 1.20-
=3
5.1
:: 1.00-
.2
E
2. 0.80-
6
9..
0.6M
0.40-
0.20-
YSan
N
0.00 l l l I l l I
2 3 4 5 6 7 8 9 10
R(a.u.)

Figure 7d shows the population curves of selected pi symmetry orbitals fiom the natural
orbitals of the first excited state of YN at the MCSCF+1+2 level.

45

YN and YP. The bond energies of YP were consistently greater than those of the same
states of YN.

Another property that was examined was the dipole moment of the YP and YN
diatomics. The scandium nitride and phosphide and the yttrium nitride and phosphide
have similar valence structure, but the overall electronic structure does not translate to

'j'Zi'zn‘p'Sa Tables 9 and 10 report the dipole

definite similarities in dipole moments.
moments of YN and YP as calculated in this work, Table 9 also reports the dipole
moments of ScN from the work of Harrison and Kunze.lj Comparison of the values of the
dipole moments shows that the dipole moments of the various states of YP are 20-40%

larger than the dipole moments of the corresponding states of YN, with the exception that

the values of YN and YP are about the same for the ground state, '2‘“, and the dipole

moment of the 311mt state of Y? is about 50% larger than the corresponding state of YN.

Comparison to ijperiment

The next logical comparison would be between experiment and theory, but
unfortunately there are very few results to compare. Ram and Bemath have performed
Fourier transform emission spectroscopy on YN in the gas phase. The bond length of the
ground state, '27, derived by Ram and Bemath 2' (1.815 A) was good agreement with our
computed bond length (1.847A). The bond length calculated by Shim and Gingerich Zj

(1.746130 is in significant disagreement with these

46

.235va new

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38

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47

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48

results. In the work of Shim and Gingerich no effective core potentials were used and a
smaller basis set was used on the nitrogen atom. Also our results are those of a
multireference CI calculation, whereas their work is the result of calculations at the

CASSCF level.

49

Conclusions

There are several conclusions that can be made from the work presented. First,
the accuracy of the computational studies of the electronic structure of YN and YP
depends greatly on the ability of the techniques to provide the proper correlation to
describe the atomic states of the metal. The high level of correlation needed to discern
the energetically close states of YN and YP is crucial. In comparison with calculations on
ScN by Harrison et al.1 the excited states of YN can be described with the same degree of
precision at a lower level of theory than the MRCI.

Despite differences in the ordering of the low-lying states of Y and Sc, the nature of the
bonding, character of the bonding, and the ordering of the lower energy states in the
nitrides and phosphides of these two metals are the same. Also as seen in the metal
hydrides, SCN, YN, and YP exhibit weak sigma bonding with the metal possessing

largely do character. Finally, the properties examined, bond length, bond energy, and

dipole moment provide evidence of periodic trends, one of the goals of this work.

50

Future Work

The investigation of periodic trends in transition metal nitrides and phosphides is
one of the goals of our future work. Extension of the results of this work to comparisons
between VN and NbN, TiN and ZrN and the positive and dipositive ions of these
compounds is planned. Also, comparisons can be made by replacing the nitrogen in the
above diatomics with phosphorus. This would also result in an abundance of states and

properties for comparison.

51

BIBLIOGRAPHY

52

l.

BIBLIOGRAPHY

Publications in this series include: (a) Alvarado-Swaisgood, A. E.;
Allison, J.; Harrison, J. F. J. Phys. Chem. 1985, 89, 2517. (b) Alvarado-
Swaisgood, A. E.; Harrison, J. F. J. Phys. chem. 1985, 89, 5198. (c)
Harrison, J. F. J. Phys. chem. 1986, 90, 3313. (d) Mavridis, A.;
Alvarado-Swaisgood, A. E.; Harrison, J. F. J. Phys. Chem. 1986, 90,
2548. (e) Alvarado-swaisgood, A. 15.; Harrison, J. F. J. Phys. Chem.
1988, 92, 2757. (f) Alvarado-Swaisgood, A. 13.; Harrison, J. F. J. Phys.
Chem. 1988, 92, 5896. (g) Alvarado-Swaisgood, A. E.; Harrison, J. F.
1988, 46, 155. (h) Harrison, J. F.; Kunze, K. L. Journal of Physical
Chemistry 1989, 93, 2983.(I) Tientega, F.; Harrison, J. F. Chem. Phys.
Letters, 1994, 223, 202. (j) (i) Harrison, J. F.; Kunze, K. L.. “Gas Phase
Organomettaliic Chemistry”, Freiser, B; Ed.; Kluwer Academic
Publishers: Netherlands, 1995, Chapt. 2, 89-121.(j) Harrison, and Kunze,
J. Am. Chem. Soc. Vol. 112, No. 10, 1990.

. Publications of the theoretical groups: (a) Schilling, J. B.; Beauchamp, J. L.;

Goddard, W. A., III; J. Am. Chem. Soc. 1987, 109, 4470. (b) Schilling, J. B.;
Goddard, W. A., III; Beauchamp, J. L. J. Am. Chem. Soc. 1987, 109, 5573. (c)
Schilling, J. B.; Beauchamp, J. L.; Goddard, W. A., 111 J. Am. Chem. Soc. 1987,
109, 5565. ((1) Carter, E. A.; Goddard, W. A., 111 J. Am. Chem. Soc. 9186, 108,
2180, 4746. (e) Pettersson, L. G. M. ; Bauschlicher, Jr., C. W.; Langhoff, S. R.;
Partridge, H. J. Chem. Phys. 1987, 87, 481. (f) Blomberg, M. R. A.; Siegbahn, P.
E. M.; Backvall, J. E. J. Am. Chem. Soc. 1987, 109, 4450. (g) Siegbahn, P. E.;
Blomberg, M. R. Chem. Phys. 1984, 87, 189. (h) Bauschlicher, C. W. Chem. Phys.
Letters, 1983, 100, 515. (1) Allison, J. N.; Goddard, W. A. , III Chem. Phys. 1983,
81, 263. (j) Shim, I.; Gingerich, K. A. Int. J. Quant. Chem., 1993, 46, 145. (k)
Gingerich, K. A. J. Chem. Phys. 1968, 49, 19. (l) Musaev, (1. G.; Koga, N. ;
Morokuma, K. J. Phys. Chem. 1993, 97, 4064. (m) Blomberg, R. A.; Siegbahn, P.
E. M.; Svensson, Matts, Inorg. chem. 1993, 32, 4218. (n) Elkhattabi, S.; Daoudi,
A.; Berthier, G.; Flament, J. P. 1997 to be published. (0) Harrison, J .F., J. Phys.
Chem., 1996, 100, 3513.

Publications of experimental groups: (a) Elkind, J. L.; Armentrout, P. B. J. Chem.
Phys. 1987, 86, 1868. (b) Sunderlin, L. ; Aristov, N.; Armentrout, P. B. J. Chem.
Phys. 1987, 109, 78. (c) Aristov, N.; Armentrout,P. B. J. Phys. Chem. 1987, 91,
6178. (d) Reents, W. D.; Strobe], F.; Freas, R. B.; Wronka, J .; Ridge, D. P. J. Phys.
Chem. 1985, 89, 5666. (e) Hettich, R. L.; Freiser, B. S. J. Am. Chem. Soc, 1987,
109, 3543. (f) Radecki, B. D.; Allison, J. Organometallics 1986, S, 411. (g)
McElvany, S. W.; Allison, J. Organometallics 1986, 5, 1219. (h) Hanratty, M. A.;
Beauchamp, J. L.; Illies, A. J.; van Koppen, P.; Bowers, M. T. J. Am. Chem. Soc.
1988, 110, 1. (I) Schilling, J. L.; Beauchamp, J. L. J. Am. Chem. Soc. 1988, 110,

53

15. (i) Schilling, J. L.; Beauchamp, J. L. Organometallics 1988, 7, 194. (k) Tolbert,
M. A.; Mandich, M. L.; Halle, L. F.; Beauchamp, J. L. J. Am. Chem. Soc. 1986,
108, 5675. (l) Kang, H.; Beauchamp, J. L. J. Am. Chem. Soc. 1986, 108, 5663.
(m) Kang, H.; Beauchamp, J. L. J. Am. Chem. Soc. 1986, 108, 7502. (n) Lebrilla,
C. B.; Schulze, C.; Schwarz, H. J. Am. Chem. Soc. 1987, 109, 98. (0) Lebrilla, C.
B.; Drewello, T.; Schwarz, H. Int. J. Mass Spectrum. Ion Proc. 1987, 79, 287. (p)
Schulze, C.; Schwarz, H. J. Am. Chem. Soc. 1988, 110, 67. (q) Stepnowski, R.;
Allison, J. Organometallics, in press. ( r) Bemath, P. F.; Ram, R. S. J. Mol. Spect.
1994, 165, 97.

3. Bemath, P. F.; Ram, R. S. J. Chem. Phys. 1992, 96, 6344.

5. Dunn, T. M.; Hanson, L. K.; Rubinson, K. A. Can. J. Phys. 1970, 48, 1657.

5a. Tientega, F.; Harrison, J. F. Chem. Phys. Letters, 1994, 223, 202.

6. Peter, S. L.; Dunn, T. M. J. Chem. Phys. 1989, 90, 5333.

7. Howard, J. C.; Conway, J. G. J. Chem. Phys. 1965, 43, 3055.

8. Dunn, T. M.; Roa, K. M. Nature 1969, 222, 266.

9. Bates, J. K.; Dunn, T. M. Can. J. Phys. 1976, 54, 1216.

10. Bates, J. K.; Gruen, D. M. J. Chem. Phys. 1979, 70, 4428.

11. Knight, L. B., Jr.: Steadman, J. J. Chem. Phys. 1982, 76, 3378.
12. Balasubramanian, K.; Das, K. K. J. Chem. Phys. 1990, 93, 6671.

13. Simard, B.; Balfour, J .; Vasseur, M.; Hackett, P. A. J. Chem. Phys. 1990, 93,
4481.

14. Lischka, H.; Shepard, R.; Brown, F. B.; Shavitt, 1. Int. J. Quantum Chem.,
Quantum Chem. Symp. 1981, 15, 1991.

15. Botch, B. H.; Dunning, T. H.; Harrison, J. F.; J. Chem. Phys. 1981, 75, 3466.

16. a) Hay, P. J.; Wadt, W. R. J. Chem. Phys. 1986, 82, 5606.
b) Krauss, M.; Stevens, W. J., Ann. Rev. Phys. Chem., 1994, 34, 357.

17. Dunning, T. H. J. Chem. Phys. 1971, 55, 3958.

18. Langhoff, S. R.; Pettersson, L. G. M.; Bauschlicher, C. W. J. Chem. Phys.
1986, 86, 268.

54

19. Martin, R. L.; and Hay, P. J. J. Chem. Phys. 1981, 75, 4539.

20. Van Duijneveldt, F.B.; Research Report RJ 945, IBM, San Jose, California,
December 10, 1971.

21. Moore, C. B. Atomic Energy Levels; National Standard Reference Data
Series; National Bureau of Standards: Washington DC, 1971; Vol. I and
H, Circular 35.

22. Mulliken, R. S. J. Chem. Phys. 1955, 23, 1833.

55

CHAPTER 3

AB-INITIO STUDIES OF THE SCANDIUM NITRIDE DIMER
INTRODUCTION

Work on the synthesis of metallic-nitride polymers has prompted the study of this
unique class of compounds through ab-initio methods."2 Computationally, the
transition-metal nitrides have been studied in some detail.3'4" ”2 In these studies the ScN
molecule was found to possess a '2'." ground state with a 32* state lying only about 7 kcal
higher in energy. The triplet state comes about by decoupling the weak sigma bond in the
singlet state, leaving a diradical with the two remaining 1: bonds. The relative ordering of
the low lying states predicted by Harrison and Kunze agrees extremely well with
experiments“ Coupling two of the diradicals leads to an alternating doubly-bonded
dimer, with a lone electron found in the 6 symmetry orbitals to the rear of the terminal Sc
and N atoms. These lone electrons are left available to form additional bonds.

Ab-initio studies of transition-metal nitride dimers can serve as a tool to examine
the electronic structure and nature of the bonding in systems that may be of importance in
catalysis and surface chemistry. Also, these calculations can be used as a predictive tool

in unraveling the reactivity of compounds. Along with these advantages, these

56

computational studies can provide an impetus for research in the area of mass
spectroscopy, Fourier transform emission spectroscopy, and other areas of spectroscopy.5

Earlier work on the ScN molecule by Harrison and Kunze3 predicted a 12'.“ ground
state with a 32+ excited state, as mentioned above. The relative order of the low-lying

states of ScN were later supported through emission spectroscopy experiments conducted
by Bernath et al.5 The closeness of the ground and first excited states of the ScN

molecule suggests that the thermodynamically stable species, the 32+ state, is accessible
for chemistry. Daoudi er al also examined the 32* state for evidence of weak sigma
bonding between monomers.‘2 The ScN dimer was constructed by bringing two ScN
molecules in the 32* state together in a linear fashion, forming a sigma bond from two of

the lone electrons, leaving two lone electrons on the terminal Sc and N atoms to

propagate the linear chain, as shown in Figure 1.

WavefunctiLon Construction

The multiconfigurational self-consistent field (MCSCF) wavefunctions were
constructed by correlating the sigma and pi bonds of the dimer with orbitals of proper
symmetry. The sigma orbitals were correlated in (GVB) generalized valence bond
fashion in order to allow the two monomers to separate to the proper SCF products. The
wavefunction for the dimer was constructed with C2,, symmetry and there were a total of
37 configuration state functions. The ab-initio calculations on the ScN dimer were
performed on Silicon Graphics IRIS2 workstations in the Chemistry Department

Visualization Center using the Columbus package.6 The basis sets used were A. J. H.

57

Wachters’ (1481 lp6d)/[Ss4p3d] on Sc and the (9s4p0/[3s2p] Dunning double zeta basis
set (absent d-functions) on the N.7'8 The d-functions were omitted for computational

savings.

3.34au
1t

\_ 3
/SCTN\

2 z
SC=N a S<3=N-/:2:+

/ 3.34a,varyin9 3.34a_

4.

2

 

sigma
bond
4: distance

Figure l. The geometries of the monomer and dimer of ScN in the triplet sigma plus
state. The calculations were performed by varying the sigma bond distance of the
dimer while maintaining a distance of 3.34 a, between the monomers, the

equilibrium separation of the ScN molecule in the triple sigma plus state.

RESULTS

The potential energy curve for the scandium nitride dimer in the 322+ state

generated from the wavefunctions is shown in Figure (2). Upon analysis of this potential
curve there is evidence of two potential curves. At large separations, there is a sigma

bond between the internal scandium and nitrogen, while nearer to the minima at shorter

58

bond lengths there exists an ionic interaction between the internal Sc and N. The
calculations were performed by varying the intermonomer N-Sc distance shown in Figure
1, while maintaining the double 1: bond distances of the two monomers at the equilibrium
internuclear separation of 3.34 a() of the ScN molecule in the 323+ state. This bond length

serves as a good starting point for the separation between the terminal and internal Sc
and N atoms. The structure of the dimer with various double bond lengths can be

examined in later work.

59

-1628.25- 3
MCSCF ScN Dimer 2+

correlated a and 1: bonds

1”

-l628.30-

 

-l628.35-

 

Energy (Hartree)

-1628.40- U More Ionic Character in a bond

0 Less Ionic Character in a bond

All calculations were performed
w/(14s11p6d/954p)/[5s4p3d/382p]

 

'1628'45 I I I 1 I I I I

2 3 4 5 6 7 8 9 10
Internuclcar Separation (ScN-ScN) au

 

Figure2.'l‘he. potential curve of the ScN dimer in the 32‘." state
constructed from MCSCF wavefunctions at selected separations of
N(2)-Sc(3). The single bond of a symmetry was correlated in a GVB
manner in order to insure that the two ScN monomers separate to the
correct SCF products. The Req of the dimer is at about 4.0 au.

60

Charge Distribution and Population Analysis

In order to distinguish between the Sc and N atoms the individual atoms will be
labeled one through four from left to right along the linear chain ( i.e., Sc(l) N(2) Sc(3)
N (4)) or referred to as an internal or terminal Sc or N, accordingly. Mulliken population
analysis shows significant charge transfer, suggesting an electron transfer from the
internal Sc to the internal N in the dimer. Figure 3 shows the charge on each of the Sc
and N atoms at various sigma bond lengths on the potential curve shown in Figure 2. At
10 a0 of separation between the internal N and Sc the charge transfer is not apparent
between the two internal atoms. At 5.0 a0 separation between the monomers there is a -
0.74 charge on the internal N and +0.85 on the internal Sc atom. This signifies that a
charge transfer of one electron has begun. With a further change in bondlength of 0.4 ao
the charge on the N(2) becomes -O.94 au. . The charge on the internal Sc(3) atom is at
+0.88 atomic units at this point. This value decreases slightly as we go from 4.6 ao
separation between the monomers to 3.8 a0 separation in steps of 0.2 a0. The change in
the charge on the external Sc and N atoms is greatest going from 5.0 a0 separation to 4.6
ao between the two monomers. The Sc(l) atom has a large charge change of -0.09
atomic units between 5.0 and 10.0 a0 separation between the two ScN monomers. The
same atom experiences a charge change of positive 0.17 au. between 5 .0 a0 and 4.6 a0.

Figure (4 ) shows how the terminal Sc orbital populations decrease for the 3d,,z

and 3dyz orbitals, while the population remains relatively unchanged in the 4s orbital. As

required by symmetry, the population of the 3dyz orbital mirrors that of the 3d“ orbital.

The same thing occurs in the case of the py and px orbitals on N(2) and the d“ orbitals on

61

Sc(3). Therefore, only one of each pair will be displayed in the population plots that
follow. Figure 5 shows that the internal nitrogen 2pc orbital population increases from
about 0.89 to 1.4 au as the N(2)-Sc(3) internuclear separation decreases, while the 2px and

the 2py orbitals exhibit small changes in population.

(1) (2) (3) (4) (1) (2) (3) (4)
Sc_N [13.-.92 IScZN Sc:N|1-‘-?—'fil'—°-|Sc:N
q=+.45 -.4s +.45-.45 q=+.49 -.es «nae-.48
(1)_(2> <3) (4) (1) <2) (3) (4)
Sc_N [iii‘LISCIN Sc:N [Lass-.IScZN
q=+.36 -.74 +.85-.47 q=+.5o -_83 +.86'-‘3
(1) (2) (3) (4) (1) (2) (3) (4)
Sc_N [LE-i SCIN Sc:N [2.2.2.114 ScZN
q=+.53 -.94 +.88'-59 q=+.54 -.91 +.os-.48

Figure 3. Total charge in atomic units is condensed to orbitals and summed on atoms from
the valence electron population of the valence natural orbitals. Obtained from the MCSCF
wavefunction of the ScN dimer at selected bond lengths.

62

The 25 orbital of N(2) decreases in population from about 1.9 to 1.75 (at 4.0 a0) for the

same change in monomer separation as shown in Figure (5). The internal Sc, Sc(3), gains

population in the 3d,, , 3d)z and 3dyz orbitals.

Population Sc(l)N(2)-Sc(3)N(4) 32+ (Sc(l))

1 -
’5 man-6H
E 0.75-4
3 D Sc“) 43
0
V %
5 0-5e . \o 0 Se“) 3dslgma
‘5
'2 0 0 Se“) 3dxz
o 0.25d \
“- O'o-"o
o I T I F

 

 

o 2 4 6 8 1‘0
Internuclear Separation (N (2)-Sc(3)) au

Figure 4. Total valence population of selected atomic orbitals of o and a
symmetry of Sc(l). Obtained from the valence natural orbitals of the
MCSCF wavefunction. The Req is at about 4.0 an.

63

Sc(1)N(2).Sc(3)N<4 3:. (N(2))

 

 

 

Population
2T
Al.75-
m
=
g 1.5-
8
E 1.25“
g 1 a 0 N(2) 2px _
.5 u fit:
a -
8'
0.25~
0 I I I I I
0 2 4 6 8 10
Internuclear Separation (N(2)-Sc(3))au.

Figure 5. Total valence population of selected atomic orbitals of o and a
symmetry of N(2) Obtained from the valence natural orbitals of the
MCSCF wavefunction. The Rag of the dimer is at about 4.0 an.

However, there is a substantial decrease in the population of the 4s orbital of Sc(3) of
about 0.65 electrons as shown in Figure (6). This large loss reflects the charge transfer

coming from the 4s orbital. The terminal N atom, N(4), shows a variation in the charge

on the atom as seen in Figure (3).

Population Sc(l)N(2)-S¢(3)N(4) 32+ (Sc(3))
2T
1.75- n Sc(3) 4 s

1'5“ ° Sc(3) 3dslgrna

1.25- o

Sc(3) adxz

0.75-

Population (electrons)
T

0.5-

     

0.25 -' 0"‘°"'° ....... o

 

 

0 1 I I I I

o 2 4 6 (A 10
Internuclear Separation (N -Sc(3)) au

Figure 6'. Total valence population of selected atomic orbitals of sigma
and pi symmetry on Sc(3). Obtained from the valence natural orbitals
of the MCSCF wavefunction. The equilbrium separation between the
internal Sc and N atoms is about 4.0 au.

65

In all the population analysis shown, there exist sharp variations when the N(2)
and Sc(3) atoms are separated about 4.4 a0. This is the region of the potential curve,
Figure 2, at which the charge transfer occurs or a curve crossing, as we go from the sigma

bonded structure to the ionic species.

Discussion of Density Difference Contour and Mesh Plots

Density difference contours and mesh plots of the of the same density difference
provide further evidence of charge transfer and possibly the formation of an internal

dative sigma bond in the ScN monomer on the left. Figure 7 show this possible structure.

1 2
43\( l ( L +(3) (4)/2P3

-SC“"N Sc_N '
/\ \
1:, “x

dat 1v. 0’

Figure 7. Possible structure of the ScN dimer in the triplet sigma plus state
after electron transfer and formation of an internal dative bond between
the internal N and external Sc atoms.

The density difference contours and mesh plots are constructed by subtracting the density

of the two non-interacting ScN monomers in the 3}.”+ state from the density of the dimer in

the same state and appropriate geometry. Actually the plots and contours show where the
electron density is coming from and going to during formation of the dimer in the 321*

state from the two non-interacting monomers in the same state.
The contour plots seen in Figures 8a-8d show gains in the electron density in the

p, orbital of the internal, N(2) atom and to the rear of the Sc(l), external Sc atom. Also
the p41: system of the Sc(l) experiences some increase in population as we bring the two
ScN monomers together, whereas Sc(l) loses electron density in the drt system. It
appears that Sc(l) loses some electron density from the (11: bonds in order compensate for

the gain in the sigma region. This suggests the formation of an internal dative sigma
bond from N(2) to Sc(l). From Figures 5 and 6 it can be seen that the N(2) gains an
electron from the 4s orbital of Sc(3). Although it may not be obvious from the contours
presented, the most significant losses occur on the Sc(3) atom. The net differences that
occur on the N(4) center appear not to be significant, possibly due to shifts and
reorganization in the electron density due to polarization.

The density difference mesh plots seen in Figures 9a-9d show the same physical
picture with a slightly different perspective. The grey regions lying in the plane bisecting
the two spiked regions constitute zero change in the electron density. The spikes and
raised regions above the plane depict positive differences (gains) in the electron density.

The spikes below the plane and depressions display negative differences (losses) in

67

electron density. Inspection of the plots shows that there are more positive spikes than
negative spikes. Since one would expect equivalent losses and gains, this is an artifact of
large amounts of electron density lost from the diffuse 4s orbital of the internal Sc atom,
which is too expansive relative to the other orbitals to appear in the plot.

Just as in the case of the contours, there exist major gains in the pa orbital of the

internal N atom from the internal Sc atom. There also exist gains to the rear of the
terminal Sc atom. This is also evidence of a dative sigma bond being formed between the
terminal Sc and the internal N, as mentioned earlier. At 3.8 a0 the magnitude of the
positive difference increases between these same centers. There seems to be a slight
increase in the density to the rear of the terminal Sc atom as we squeeze the two
monomers even closer. Also the plots depict larger losses on the terminal Sc atom.
Indeed, at this geometry we have started back up the repulsive side of the potential well

seen in Figure 2. The terminal N remains relatively unchanged.

 

Figure 8a-8d show the electron density difference between two non-interacting ScN
monomers in the 32* state and the dimer in the same state at selected geometries.
The broken lines depict significant increases in electron density. The solid lines
depict significant losses in electron density. The contours range from 0.5 to -0.5
electrons/a.,3 at separations of 3.8 ao (stepsize of 0.1), 4.0 ao (stepsize of 0.1), and 4.2
ao (stepsize of 0.12). At 5.0 a(, the contour range is 0.05 to —0.05 with a step size of
0.01. All of the contour values and stepsizes were chosen in order to improve
resolution. The large red balls denote the Sc atoms and the smaller balls denote the

N atoms.

69

 

 

 

2

Figure 8b. Electron density difference contour plot at a selected geometry.

70

 

ScN Dimer Den

 

sity Diff. 4.2au

     

 

 

 

Figure 8c. Electron density difference contour plot at a selected geometry.

71

   

 

   

Figure 8d. Electron density difference contour plot at a selected geometry

72

ScN Dimer Density Diff. 3.8au

 

Figure 9a-9d show mesh plots of the electron density difference between two non-
interacting ScN monomers in the 32+ state and dimer in the same state at selected
geometries. The regions lying in the plane bisecting the two spiked regions
constitute zero change in electron density. The spikes above the plane depict
positive differences (gains) in electron density. The spikes below the plane depict
negative differences (losses). The maximum and minimum values in electrons/a03 for
the density differences are as follows (separation between the internal Sc and

N): -0.500, 0.886 (5.0ao); -0.860, 1.116 (4.2ao); -0.599, 1.123 (4.0ao); -0.818, 1.241
(3.8ao).

73

ScN Dimer Density Diff. 4.0au

 

Figure 9b. Electron density difference mesh plot at a selected geometry.

74

ScN Dimer Density Diff. 4.2au

 

Figure 9c. Electron density difference mesh plot at a selected geometry.

75

ScN Dimer Density Diff. 5.0au

 

SCN SCN

Figure 9d. Electron density difference mesh plot at a selected geometry.

At a separation of 4.0 a0, there exists a state which effectively has the geometry of
the 22‘.“ ground state of the ScN+ positive ion on the right experiencing an ionic interaction
with a 22+ state of ScN anion on the left seen in Figure 7. This suggests that the ground

state of the dimer may not be linear and might be indeed be cyclic.

Conclusions

Solid ScN has the same crystal structure as that of NaCl 5 and the cyclic structure
shown in Figure 10 may be the dimer prelude to this crystal structure. In fact, Andrews
has synthesized a dimer of ScN with a open rhombus structure.11 The structure of this
species is similar to that shown in Figure 10 with the open end of the rhombus possibly

being the electrostatically interacting ends of the dimer shown in Figure 7.

<11t electron

/”N
/

p“ electron

N'\

p1t electron

 

c1,t electron

Figure 10. The proposed structure of the cyclic ScN dimer. The spin
state for this structure is expected to be a triplet. The sigma bonds
depicted in this structure are not necessarily equivalent.

78

BIBLIOGRAPHY

79

10.

ll.

12.

BIBLIOGRAPHY

. C. M. Jones, M.E. Lerchen, C. J. Church, B. M. Schomber, and N. M. Doherty;

Inorganic Chemistry 29, 1679 (1990).
S. C. Critchlow, M. E. Lerchen, R. C. Smith, N. M. Doherty, Journal of American
Chemical Society 110, 8071 (1988).

J .F. Harrison, K.L. Kunze, Journal of Physical Chemistry 93, 2983 (1989).

. J. F. Harrison, K.L. Kunze, Michigan State University, Department of Chemistry and

Center of Fundamental Materials Research, to be published.

Bemath, P. F.; Ram, R. S.; J. Chemical Physics 1992, 9, 96.

R. Shepard, I. Shavitt, R. M. Pitzer, D. C. Comeau, M. Pepper, H. Lischka, P.G.
Szalay, R. Ahlrichs, F. B. Brown, J. G. Zhao, International. J. Quantum Chemistry,
1988, 822, 149.

A. J. H. Wachters; J. Chemical Physics, 1970, 52, 1033.

T. H. Dunning; J. Chemical Physics, 1970, 53, 2823.

SciAn, Scientific Animation Package Version 0.853, Florida State University: E.
Pepke, J. Murray, J. Lyons, and T ku., 1993.

AVS, Advanced Visualization Systems: Waltham, 1992.

Lester Andrews, Journal of Electronic Spectroscopy and Related Phenomena 97
(1998) 63-75.

A. Daoudi, and S. ElkHattabi Laboratoire de Chimie Theorique, Faculte des Sciences

Dhar Mehraz, BP.; G. Berthier, Laboratoire de Radioastronomie Millimetrique, Ecole

80

Normale Superieure, France; J. P. Flament, Lavoratoire de Dynamique Moleculaire et

Photonique, Universite USTL de Lille, France; submitted for publication.

81

CHAPTER 4

THE ELECTRONIC STRUCTURE AND VARIOUS PROPERTIES OF EARLY

TRANSITION METAL METHYLIDYNES AND THEIR POSITIVE CATIONS
INTRODUCTION

The lack of experimental data on the gas-phase, biomolecular reactions of

transition metals with main group elements has prompted a quantum chemical study of
the transition metal methylidynes. There have been fairly extensive quantum chemical
studies of the transition metal cations with various alkanes and other main group
elements." 2’ 3 The prior work was prompted by an interest in understanding the
chemistry of these transition metals bonding with main group elements as well as
explaining the results of experimental studies of the gas-phase, bimolecular reactions of
transition metal cations with alkanes and other main group elements. These studies have
received impetus from developments in organometallic chemistry, surface chemistry,
laser spectroscopy, and catalysis.3’ 4 In particular, reactions in which ions are involved
can be studied by use of sophisticated mass spectroscopic techniques such as ion
cyclotron resonance and guided ion beam mass spectrometry. The information obtained
from these experiments has led to some understanding of the kinetic and thermochemical
factors that allow these reactions to proceed. The neutral metal methylidynes have have

,4
(1,323

been experimently observe while the isoelectronic neutral metal nitrides, metal

nitride cations, and transition metals bonded to other main group elements have been

82

3n-o, 4—13.

studied previously. '8 They have also been studied thoroughly by theoretical
methods." 2 The work reported here provides data to compare the properties and energies
of these isoelectronic compounds.

Also, in the case of positive ions, the guided ion beam mass and the ion cyclotron
resonance spectroscopic methods are used to study endothermic, as well as exothermic,
reactions.”c The information gained can be applied to the analysis of the reactivity of C-
H bonded systems with transition metals, reaction mechanisms, and surface reactions.

It is often difficult to experimentally determine the electronic and geometric
structures of these species. This is the case for the positive ions, for while the data
provide information on bond energies and reaction mechanisms, very little if anything can
be said about the electronic and geometric structures. Mass spectrometers can only
provide the mass ratios (tn/z) of reactant and product ions.3f'g’q Most of the time, proposed
structures are based on the structure of reactants, reactivity information, and chemical
intuition about the reaction mechanism.” 24 The possibilities are numerous for structural
isomers, which increase with larger systems. By contrast, the necessary properties like
bond lengths, bond angles, electron distributions, character of the bonding, etc., can be
calculated through the use of ab-initio quantum mechanical techniques.”

Recent advances in the level of sophistication of electronic structure theory and its
implementation in modern programs and the substantial increase in speed and
accessibility of computers make it possible to study these important molecules
computationally. The large number of closely spaced energy levels, the near degeneracy

of ns-np shells, as well as other shells, and the importance of including or not including

particular core orbitals in the correlation when working with the early transition metals,

83

and the as yet poorly understood relativistic effects of heavy atoms raise the required level

8““ 93‘ '5 suggests that an adequate description of the

of theory significantly. Work to date
electronic structure of a first row transition element or a small molecule containing a
transition element can be constructed using a multiconfigurational self-Consistent field
(MCSCF) wavefunction. The MCSCF wavefunction often provides the proper
correlation necessary to describe the molecule or atom effectively, and higher levels of
theory that provide additional correlation, such as the configuration interaction technique,
can be used when necessary.

In this work we will also explore the use of density functional theory to calculate
the wavefunction for the ground and selected excited states. These wavefunctions are
then used to calculate vibrational frequencies of these species at the equilibrium
geometries. The density functional calculations used the Becke-3LYP functional, which
has been used in related work on transition metals bonded to CH2.28 This functional
should provide the proper correlation and exchange energies to give good geometry and
vibrational frequencies.

The calculations presented in this work contain a large number of configuration
state functions at the MCSCF level. Compared to the previous theoretical calculations
performed on the positive ions of the transition metal methylidyne or corresponding
methylidene, our MCSCF reference spaces are just as large as the Swaisgood and
Harrison 1" multireference configuration interaction spaces.

This work will permit a comparison between a neutral transition metal bonded to

CH and the positive ion of the same molecule. Also, the positive ion and neutral

molecule will be compared to the isoelectronic metal nitride cation and neutral metal

34

nitride, respectively. The effect of including the near degeneracy in these calculations will
be discussed, including the possible necessity of higher levels of theory than the MCSCF
level of theory. Along with these results, bond lengths, vibrational frequencies, energies,
dipole moments, the nature of the bonding and the populations will be discussed.
Descriptions of the wavefunctions, and possible transition metal-CH fragment bonding

will be provided .

BASIS SETS AND MOLECULAR CODES

The primary basis sets used for transition metal atoms in the (T M)-CH (Sc,Ti,V,
or Cr atom bonded to the CH) molecules are the Watchers’ basis sets modified under
scheme number 3, '5 using diffuse functions found in the work of Bauschlicher et. al in
their calculations of (TM)CH2+ (Sc,Ti,V, or Cr atom bonded to CH2+) using Becke-3LYP
density functional. However, we did not follow the same procedure for Sc and Ti in these
calculations. It was felt that the inner shell correlation provided by using the scandium
and titanium basis sets were not necessary because we were not going to be calculating
bond energies. Instead, we followed the scheme (shown below) of the later early
transition metals of vanadium and chromium in our Becke-3LYP calculations of these
(TM)—CH systems.
To the Watchers’ basis sets two diffuse p-functions were added; the exponents were those
optimized by Watchers multiplied by 1.5. The (1 space was contracted in a (311) fashion.

Then a diffuse (1 function19 and three term fit to a Slater type f polarization function were

85

added to each metal atom. The f exponents vary from 1.6 for SC to 4.8 for Cu in steps of
0.4 and are uncontracted. The f functions are constructed according to the paper by
Stewart.lgal The final basis sets of the metals had the contraction scheme:

(l4sl lp6d30/[8s6p4d2f]
because of the (3312) contraction of the p space maintained in all of the transition metal
atoms. These basis sets will be referred to as the AWACH basis sets.14 The C and H
atoms used a 6-31G** basis set 23 in the DFT calculations.

The RHF, MCSCF, and MCSCF+1+2, and DFT calculations used the same
AWACH basis set on the transition metal atoms. The C and H basis sets used in the
RHF, MCSCF, and MRCI calculations were the Dunning augmented valence contracted
quadruple-zeta basis sets with s, p, d-functions (on carbon atom). 33 However; the
change in basis on these two atoms should be negligible, between the DFT and the other
ab-initio methods used.

The DFT and frequency calculations were carried out using GAUSSIAN9429
while the restricted Hartree-Fock, multiconfigurational self-consistent field, and
multireference configuration interaction calculations used the MOLPRO9620 set of codes.
The calculations were performed on Silicon Graphics Indigo2 Workstations, supported by
the Michigan State University Chemistry Department.

Another basis was also used in calculating wavefunctions and properties of the

TiCH ound state, 22", and the two excited states 2A, 211nm, and 2l'l),,,m.17()° usin
gr 8

MCSCF and MRCI techniques. This basis set is referred to as the AMES basis set.3 ' It
was developed by Partridge et. al and consists of (20$12p9d70/[7s6p5d2f]. This basis

set is extremely large and proved to be computationally expensive.

86

MOLECULAR F RAGMENTS

Bond energies and separated fragments of the (TM)—CH and the positive ion were
not calculated. However, the possible combination of fragments for the particular state of
interest can be predicted by using spin and symmetry considerations and the bonding in
the resulting molecule. We will focus this discussion on the ground states of ScCH,
TiCH, VCH, and CrCH and their positive ions. Note that we label the 3d,(2.y2 and 3d,,y
orbitals on the TM as 5.. and 5- with the 3d}, 3d”, 3dyz represented as do, d,x. and dny,
respectively.

First, the ScCH molecule has a unique bonding structure that arises from the

4s'3d2 configuration on the Sc atom. The CH fragment could be in a 42’ state or a 211
state if the Sc atom is in the 2D or 4F state, respectively. The 3H state of the ScCH
molecule consists of a d'-px bond between the Sc and C atoms with a lone electron in a

hybrid orbital of the 43 of Sc and p and d sigma orbitals on Sc. The C atom forms a dative
sigma bond with Sc and another sigma bond with the hydrogen atom. The remaining

electron forms a one electron 1: bond significantly polarized toward carbon, suggesting

that the in situ state of CH is 2H.

87

  
     

. PF! H":

. dativebon =5 r

1%; ’35
W;

fkuv

one electron
drrx-pn:x dative pi
bond Sc to C

The positive ion, ScCH+ has a ground state of 2H . In this molecule the lone

electron in the Sc 45 orbital of ScCH is removed to make the cation. Once again, dative
sigma bonds and dative one electron pi bonds are made between the Sc and C, just as the

case of the neutral compound.

dative sigma bond +

 

 

bond

In the TiCH molecule the ground state is 22* which results from the 4s‘3d3

configuration on the Ti atom. The CH fragment would have to bond with titanium in a

88

42' state in order to form two pi bonds and one sigma bond; leaving a lone electron in the

4s orbital of titanium.

 

sigma bond

The TiCH+ molecule is formed in the 12" ground state by removing an electron
from the 4s orbital of the titanium atom, leaving the two It bonds and one sigma bond

between the Ti and C atoms intact.

 

 

sigma bond

The VCH molecule has a just slightly shorter separation between the metal and C atoms

than the TiCH molecule, and a structure that is similar to that of TiCH with vanadium’s

89

extra electron in a 8_ orbital forming a 3A ground state. This results in a molecule with a

triple bond between the vanadium and the C atoms.

 

The VCH+ molecule is the same structure as the VCH molecule absent the electron in the

4s orbital.

 

onfpnybond

    

 

dn;pnxbond

Note that both the electronic states of the VCH+ and TiCH+, 2A and '2‘”, correlate

with the transition metal ion in its ground electronic state. In these molecular states the

V+ atom is in (14 configuration and the Ti+ atom is in a sd2 configuration, respectively.7a

90

These configurations produce the atomic states 5D and 4F, respectively.7a The CH

fragment exists in situ in the excited 42- state.

The CrCH molecule consists of a Cr atom with a sld5 configuration and the CH

fragment once again in the 42' state. Chromium in the CrCH+ molecule exists in the (15

configuration bonded to the CH fragment.

   
   

dn;pnxbond

Shown above is the schematic representation of the CrCH molecule. The representation

of the CrCH+ molecule is shown below.

 

dn;pnxbond

91

The ground state configurations for the Cr atom and the Cr+ ion are the 7S and 6S,

respectively.8“' ‘5

Wavefunctions and Computational Details

The wavefunctions for all of these molecules were constructed in a similar
fashion. The restricted Hartree-Fock wavefunction was used as an initial guess for the
positive ion of the carbyne at the MCSCF level; on most occasions only the sigma and pi
bonds were correlated with orbitals of the corresponding symmetry. This was done in a
generalized valence bond fashion; one sigma bonding orbital at a time or pair of pi
bonding orbitals at a time. In this way the wavefunction was built up slowly until an
electron was added back into the wavefunction and the corresponding carbyne was
constructed. Later calculations added an additional orbital of a) symmetry to the
correlation in each of the MCSCF calculations. In this way some of the near degeneracy
was taken into account. Therefore, two sets of MCSCF calculations were used as
reference spaces for the multireference configuration interaction calculations that
followed. One set of calculations accounted for some of the near degeneracy in the

correlation and the other set neglected the additional orbital in the sigma space. The

92

following are the wavefunctions for the carbynes and the positive cations in the

generalized valence bond fashion:

CrCH 42' ~ [o(Cr)o(C)+o(C)o(Cr)] [rtx(Cr)1tx(C)+1tx(C)1tx(Cr)]

[1c,(Cr)rry(C)+1ry(C)1ty(Cr)]3d5_3d5+4s

VCH 3A ~ to<V)o(C>+o(C)o(V)1 [n.(V>n.<C)+n.<C)n.<V)1

[ny(V)1ty(C)+n,(C)rty(V)]3dg4s

TiCH 22" ~ [o(Ti)o(C)+o(C)o(Ti)] [nx(Cr)nx(C)+1tx(C)1tx(Cr)]

[ny(Ti)rcy(C)+1ty(C)1ty(Ti)]4s

ScCH 3r1 ~ [o(Sc)o(C)+o(C)o(Sc)] [ny(Sc)ny(C)+1ty(C)1ty(Sc)]1432pnx

CrCH+ 32' ~ [0(CI)G(C)+G(C)O(CI)] [fix(Cr)1tx(C)+1tx(C)Ttx(Cr)l

[1t,(Cr)1ry(C)+1t,(C)rty(Cr)]3dg3d,»

VCH* 2A ~ [0(V>o<C)+o(C>o(V)1 [n.(V)nx<C>+n.(C)n.(V)1

[1Cy(V)1ty(C)+1ty(C)1cy(V)]3d5_

93

TiCH+ '2‘? ~ [o(Ti)o(C)+c(C)o(Ti)] [nx(Ti)1tx(C)+1tx(C)1tx(Ti)]

[ny(Ti)ny(C)+1ty(C)1ty(Ti)]

ScCH+ 2r1 ~ [o(Sc)o(C)+o(C)o(Sc)] [n,(Sc)n,(C)+n,(C)n,(Sc)112pm.

Also presented are two excited states of TiCH, and two excited states of VCH. The

excited state wavefunctions are represented in the GVB fashion as such:

TiCH 2A ~ [G(Ti)G(C)+O'(C)O'(Ti)] [nx(Ti)1tx(C)+1tx(C)1cx(Ti)]

[1t,(Ti)ity(C)+1ty(C)1ty(Ti)]3dg

TiCH 2mm... ~ [6(Ti)6(C)+6(C)o(Ti)] [MTi)nx(C)+1cx(C)1tx(Ti)]

[n,(Ti)n,(C)+1ty(C)1ty(Ti)l4p.y

VCH 3%. ~ [0(V)o(C)+o(C)o(V)1 [n.<V)n.(C)+n.(C)n.(V)1

[ny(V)ny(C)+1ry(C)1cy(V)]3dg4px

VCH in ~ [0(V>o(C)+o(C)o(V)1 [n.(V)n.(C>+n.(C)n.(V)1

[ny(V)1ry(C)+1ty(C)1ry(V)]4s4pn

94

Results and Discussion

The following will provide structural information on the carbynes and their
cations and a comparison between the metal nitrides” and corresponding metal nitn'de
cations'h. Also, previous work by Alvarado-Swaisgood and Harrisonld will be compared.
This previous work consists of MCSCF, and MCSCF+1+2 calculations with fewer
configuration state functions and, therefore, smaller reference spaces than the present
calculations.

Contour plots27 of the electron density of selected natural orbitals will be
presented. 25' 26 The contour plots were constructed by using positive and negative
contour values of 0.02, 0.04, 0.08, 0.16, 0.32, and 0.64 au. The positive contours are
solid lines, while the negative contours are dashed lines. The nodes are depicted by
dotted lines. Occupations and populations condensed to basis function groups for the
each of the natural orbital (N O) contour plots are also presented. The occupations and
populations presented on the contour plots are calculated using the MSU properties
program developed by Harrison.26 The populations presented in the tables are from the
Mulliken population22 program of the MOLPRO96 20 suite of codes.

The following methods are listed in the tables: RHF, MCSCF, and Configuration
Interaction. The configuration interaction calculations refer to a MRCI calculation in
each case. The MCSCF wavefunctions refer to wavefunctions constructed in a GVB
fashion. Several of the tables will point out that an extra a) symmetry orbital was added to

the correlation of the MCSCF wavefunction.

95

ScCH and ScCH”

The first of the TM-CH series is ScCH, which has a 311 state. It offers a unique

structure and corresponding geometry. The Sc—C bondlength is 1.954 A at the
multireference configuration interaction level (MRCI) (Table 1). The relatively long
bond length is attributed to the double bond between the Sc and C atoms, rather than the
triple bond found in the other TM-CH molecules. The Sc-C bondlength obtained from a
DFT calculation is 1.892 A. The dipole moment from the DFT calculation is 2.79 Debye
(metal end positive), while that from the MRCI calculation is 2.18 Debye. The MCSCF
calculation predicts a much longer bondlength of 1.996 A with a dipole moment of 1.83
Debye (Table 1).

Removing a 43 electron from Se in ScCH produces the 211 state of ScCH“. The
2H state of ScCH+ has a shorter Sc-C bond than that of the 3H state of ScCH as shown in
Table 2. Also, the OH bond length shortens to a length of 1.089 A, comparable to the C-
H bondlengths in the other early TM-CH molecules. Swaisgood and Harrison 1" predicted
a Sc-C bondlength of 1.940 A and a CH bondlength of 1.082 A for the 211 state of
ScCH+ at the MRCI level.

The ScCH molecule is isoelectronic with ScN. The ScCH molecule in the ground
state has a much longer bondlength than the other early TM-CH molecules. This is also
the case for ScN when compared with the other transition metal nitrides. In fact, early

work suggests a weak sigma bond in the tn'ply bonded ScN U ; and the existence of a

96

doubly-bonded low-lying excited state. The calculated dipole moment of ScN is 6.04
Debyelj while that of ScCH is 2.18 (metal end positive).

ScCH+ is isoelectronic with ScN+. Comparing the 2H ground state of ScCH+ to
the ground state, 22.", of ScN+, the transition metal nitride cation is reported to have a
double bond and a lone electron in the sigma system of the Nitrogen atom.1h The ScCH+
molecule also has a double bond, but places the lone electron in the 1: system of the
carbon atom. The 22* state of ScN+ has a longer bond length of 1.804 A relative to the
Sc-C separation in the ScCH+.

The energies of the ScCH 3H state at the MCSCF level are reported for two

different wavefunctions in Table 1. The energy difference between the two
wavefunctions is about 8mH and the optimized geometries are almost identical. At the
MRCI level the differences are even smaller using these two wavefunctions as references.

The extra flexability provided by including another a) symmetry orbital in the
correlation is important in describing the separation of the ground and excited states of
TiCH described later in this chapter.

For ScCH, Tables 1 and 2 provide a comparison between the 3IT state of the

neutral molecule and the positive cation in the 2H state, with a energy difference of 213

mH. The MCSCF wavefunction (Table l and Table 2) have a difference in energy of 204
mH. The vibrational frequencies of the ScCH and ScCH” are given in Tables 7 and Table

8. The antisymmetric bending modes lend support to a lone electron in the 1cx system of

the C atom.

97

The contour plots of ScCH in the 3H state are in Figures 1-8. First the OH sigma

bonding natural orbital (NO) 7 shows a C s-p hybrid bonded to H s orbital (Figure 1).

This orbital contour plot of C-H is typical of all of the OH 0 bonds in the early TM-CH
molecules; therefore, this particular contour and that of ScCH+ NO 7 , Figure 8, will serve
as a reference to all of the other C-H bonding orbitals of this class of compounds. The
contour plot of NO 8 (Figure 2) shows a dative sigma bond between the Sciand C atoms.
The Sc spd hybrid follows in NO 9 (Figure 3) a sigma antibonding orbital. Natural
orbital 11 (Figure 5) is the Sc-C o antibonding orbital. Figure 6 shows a one electron
dative 1: bond between Sc => C. Swaisgood et alId also found a dative sigma bond and
one electron 1: bond in ScCH”. This is also shown in the ScCH+ contour plot of NO 23 in
Figure 13 from this work. The bonding 1t, orbitals of ScCH and ScCH+ are shown in

Figure 7 and Figure 14, respectively. The occupations are slightly different in these

natural

98

ScCH 3?! Natural Orbital Number 7

 

 

 

 

 

 

1 . - - - - T - - - - . -
. . ace-1.96
1 q
4 ‘ cs-1.23
’u':"’~s\ ‘ cp-0018
’ "'..:I“~ ~ 4
‘ I“) lie-0.55
i ':::‘ \‘I' '- ‘ ‘\\‘\‘\
| o- :‘i‘ :; .figxng :4
D‘ 4 \If' h I \ ',"o I:
' ‘ ‘ \ Q-a ’ I
s a’
U ‘\“: ‘-- o"”"
~a:;»’. Figure 1
J
4 .
-1 fl rrrrr I - - - - . v
-1 o a
zan-
ScCH3P1NatunlOrbttalNumbu'8 ScCH 3PlNdunlOrbttelNumba-9
1L.-L-,, -,- - 1-.v-c3r-c--f-

A A A L A
Y-Alll
A A 4 L A _A 4 A

A A

 

Y-Alil
JAAALA?

 

 

 

 

 

-1-1--v-

-1 v '

 

 

Dec-1.94 Ca-O.67 Cp-0.87 Dec-0.990 See-0.92
8:80.29 Sod-0.20 Sop-0.17 8cd=0.04

Figure 2 Figure 3

Figures 1, 2, and 3 are electron density contour plots of natural orbitals seven

3
eight and nine of the ScCH molecule in the ground l'I state. The occupation
and the mulliken population condensed to a basis function type are reported

for each orbital.

99

SoCHSPI WON“! Minter 10

 

ace-0.036
8c total-0.02
C total-0.02

 

 

 

 

Dec-0.023

8c total-0.00
c toteln 0.01
n total-0.01

 

 

 

 

Figure 4 and Figure 5

Figures 4 and 5 are the electron density contour plots of natural orbitals

3
10 and 11 of the ScCH molecule in the n ground state. The occupations
and the mulliken population condensed to a basis function type are reported

for each orbital.

100

ScCH 3P1 Natural Orbital Hunter 24

7 if V v—f '7 r r v f

 

Doc-0.975
Bed-0.12
Cp=0.81

XAfls

 

 

 

 

ScCH 3P1 Natural Orbital Number 37

 

Doc-1.830
Sod-0.67
Cp-1.07

Sc total-0.71
c total-1.09

Y-Alls

 

 

 

 

Figure 6 and Figure 7

Figures 6 and 7 are the electron density contour plots of natural orbitals

3
24 and 37 of the ScCH molecule in the F1 ground state. The occupations
and the mulliken population condensed to a basis function type are reported

for each orbital.

lOl

ScCH+ 2P1 Natural Orbital Number 7
1

 

 

 

 

vi v # - a I—' ‘ 'fi ' r
. ccag « Occ=1.96
. j j os=1.zo
”.f’.’ ’ ...... ~ 4 ”=0 . 2°
.. , ----- x
. x r\ xranurvk‘ 83:0 56
i . r tern-:«ssaxn °
I 04 i, A{-' F: ”L?" "Hd
D‘ i - “J i‘\ \ ‘ ~~~~ Ix”)
. \ L/ ~
‘ ...... a!”
\~ ----- i
. ‘\ ‘
. l
4 I’M;
-1 , ,‘ v v v v I ' ' ' fr
-1 0 7
2m

ScCH 391 Natural Orbital Nunber 38

1 - v

 

Dec-0.146
Bed-0.09
Cp-0.06

 

 

Y-Alk
(p A

 

 

 

 

Figure 8 and Figure 9
Figures 8 and 9 are the electron density contour plots of natural orbitals
3
7 and 38 of the ScCH molecule in the H ground state. The occupations

and the mulliken populationcondensed to a basis function type are reported

for each orbital.

102

ScCB+ 21’! Natural Orbital Number 8
I

 

ace-1.94
Scd=0.25
Cs-O.66
Cp-O.89
8830.23

(

1.4.1.
.i.?ii.i

A A

 

 

 

 

ScCH-r 2P1 Namnl Orbital Nulnber 9
1

 

Dec-0.04
Sc total-0.02
C total-0.02

i
J
i
i; J
9- .

 

 

-1

 

 

Figure 10 and Figure 11

Figure 10 and 11 are the electron density contzour plots of natural
orbitals 8 and 9 of the ScCH+ molecule' In the2 II ground -

state. The occupation and the mulliken population condensed to a
basis function type are reported fro each orbital.

103

ScCH-I- 2P1 Natural Orbital Nimber23

 

Dec-0.022
c total-0.01
H total=0.0

 

 

 

-1

 

1

 

Dec-0.972
Scd=0.15
€630.78

8c tota1=0.16
C tota1=0.79

 

 

-7

 

-1

 

Figures 12 and 13 are electron density contour plots of natural orbitals

10 and 23 of the ScCH+molecule in thezl‘l ground state. The occupations
and the mulliken population condensed to a basis function type are reported
for each orbital.

104

ScCH+ 2P1 Naturfl Orbital Nutter“

1 ..fiT‘-T--c-r-
.

 

Dec-1.79
Sod-0.82
Cp-0.91
Sc tota1=0.83
c total-0.93

 

 

 

 

ScCH+ 2?! Natural Orbital Number 37

7

 

« Dec-0.194
Sod-0.11
Cp-0.09
4 8c total-0.11
. C total=0.09

 

 

Y-Axh
‘ P

 

 

 

 

Figures 14 and 15 are electron density contour plots of natural orbitals

36 and 37 of the ScCH+molecule in the 21'! ground state. The occupations

and the mulliken population condensed to a basis fiinction type are reported
for each orbital.

105

orbitals with increases in the Sc drty population and decrease in C pay population going

from the 3 I1 state to the 211 state.

The ScN ground state has a do orbital participating strongly in the sigma bond.” 30

The ScCH molecule in the 311 state exists with a dative sigma bond. The charge on the

Sc atom in ScN is +0.59 au.” 3° The Secrr molecule also has a dative bond with a

charge transfer of +1.45, while the ScN+ molecule in the 211 state has a +1.49 charge

transferlj from Sc to the N atom.

TiCH and TiCH+

The bond lengths, energies, and dipole moments (dipole moments of positive
TiCH+ are not reported) for TiCH and TiCH+ are summarized in Tables 5 and 6,

respectively. The 22* ground state wavefunction has a Ti-C bondlength of 1.751 A using

the AWACH basis set. The wavefunction was constructed in a GVB fashion correlating
the bonding pairs with the antibonding counterpart. Also an additional orbital was
included in the active spave with a) symmetry. The TiC bond length using the same
framework for the wavefunction and the AMES basis set is 1.750 A. The C-H
separations were almost identical at 1.0887 and 1.0892 A, respectively. Dunning
augmented quadrupole zeta basis33 sets were used on both atoms.

The MCSCF calculations produced slightly longer Ti-C bond lengths than the

MRCI calculations for all of the states of TiCH (Table 5). The same can be said for the

106

TiCH+, 12+ state (Table 6). The C-H bondlength is predicted to be slightly shorter than
the MRCI predictions.

The DFT calculations predict much shorter Ti-C bondlengths and slightly loner C-
H bondlengths than the MRCI calculations. The DFT calculations predict a 22+-2Hnnw
separation of 59.5 mH. The experimental separation is around 62.8mH.32 These
experimental results along with others can be found in Table 7.32' 34

The experimental TiC bondlength is 1.728 A 32 compared to the CI values of
1.750 and 1.751 A for the AWACH and AMES basis on the Ti atom. We calculate the
separation between the Zzt-Znnm, states to be 64.3 mH with the AWACH basis on Ti and
65.1 mH with the AMES basis on Ti, using MRCI techniques with additional correlation
provided to the sigma system by adding an a) symmetry orbital to the correlation in the
reference space. The experimental separation between the two states is near 62.8 mH 32.

The 2H state in the experiment is thought to be bent.32 Our imaginary (negative valued)
vibrational frequency calculations on the inn"... state add support to the experimental
results. A single point calculation on the 211 state bent at an angle of 170 degrees using
the experimental geometry for the ground state yielded an energy 2mH higher than our
linear prediction. The experimental frequencies are shown in Table 7 32. These values are
in close agreement with our results also shown in Table 7.

To move the lone electron in the 4s orbital of the 22* state of TiCH to the d5_
orbital on Ti to make the 2A state takes 31mH, according to both MRCI calculations in

Table 5. However, DFT predicts a value of 20.5 mH as shown in Table 6.

107

The TiCH molecule can be ionized to TiCH+ by removing a lone electron of Ti.
The 22+ and 12+ energies differ by 0.221 hartree or 5.99 eV. The ionization potential of
Ti is 6.58 eV 2'. The energies are reported in Table 5 and Table 6, respectively.

Now, for a comparison of the electronic states of TiCH and TiCH+ with the
isoelectronic TiN, TiN+, and other positive ion results. The bondlength in TN U is much

shorter than the Ti-C separation at 1.602 A. The energy separation between the 22* and
the 2A states of TiN calculated by Harrison et. a1 is 0.95 eV or 34.9 mH U. The 2H state of

TiN is 73.9 mH above the ground state. Both of these values are very close to the same

electronic state separations relative to ground state for TiCH at the MRCI level.

108

Contour Plot TiCH

The contour plot of TiCH 22‘.“ N O 8 is shown in Figure 16. This contour shows a
Ti-C sigma bond consisting mainly of a carbon s-p hybrid bonded to a smaller
contribution of 0.35 an from the Ti do. The Ti 45 orbital is the primary contributor in NO
9 (Figure 17). Figure 19 shows the contour plot of the anti-bonding sigma orbital of the
OH fragment.

The TiCH+, 12+, N O contour plots, populations, and occupations are similar to those
of 221+ in TiCH. The contour plots of TiCH+ are shown in Figures 24-31 while the
populations of TiCH and TiCH+ are in Tables 7 and 8, respectively. The population of TiN
(22‘3”)1'”lj is also comparable to that of the TiCH ground state. The sigma bond is consists
mainly of N p, character bonded to Ti do, with the lone electron in the 45 of the Ti atom.
However, the N 2P0 contributes 1.20 au. 'j to the bond while the do contributes 0.78 to the

sigma bond. The lone electron in the TiN is calculated to be 0.79 'j 45 on Ti which is in
agreement with experiment 1". In the TiCH NO 9 (Figure 17) the lone electron is almost

completely the 4s orbital (1.11 au) on Ti with a small contribution from the 3d,, orbital on

Ti (0.091au). Figures 20 and Figure and 21 show

109

'IICH ZSIgmaplm Natural Orbital Number 8

7 v i

 

ace-1.93
Tia-0.35
Ce=0.56
Cp=0.87

Ti tota1=0.32
C tote1=1.40

 

 

 

-7 v
-7

 

7 v f v T V V ' v

 

Occ=0.99
T1881.12
rid-0.09
Ti tote1=1.31

Y-Aals

 

 

 

 

-11

Figures 16 and 17 are electron density contour plots of natural orbitals seven

8 and 9 of the TiCH molecule in the +ground state. The occupations
and the mulliken population condensed to a basis fimction type are reported
for each orbital.

110

THCHZngqmnPhhufl(hmmnDMmhulo
1

 

Dec-0.06
Tia-0.04
Cp-0.01

Ti total-0.04
C total-0.02

 

 

 

704

 

4

Dec-0.02
“-0 O 01
nI-0.01

c total-0.01

Y—Axir
P .

 

 

-7

 

 

Figure 18 and Figure 19

Figures 18 and 19 are electron density contour plots of natural orbitals

10 and 11 of the TiCH molecule in the 2laid-ground state. The occupations
and the mulliken population condensed to a basis function type are reported

for each orbital.

lll

11GB Emu: Natural Orbital Number 24

7

 

Doc-1.831
T1620.84
Cp-0.93

Ti total-0.87
c total-0.94

 

 

 

 

7 v ' v v v v I v v v v

 

Occ=0.15
Tia-0.08

 

 

 

-7..--r-,
-1 0

 

9

Figure 20 and Figure 21

Figures 20 and 21 are electron density contour plots of natural orbitals

24 and 25 of the TiCH molecule in the 22+ ground state. The occupations
and the mulliken population condensed to a basis function type are reported

or each orbital.

112

FCHWWOMMaS

 

Dec-1.83
Tid-0.84
Cp-0.93
Ti total-0.87
C total-0.94

 

 

 

 

 

’ rrrrrr ' ...... mc-o 01“
( . era-o .0a
4 ‘ ”.0 O 07

 

 

 

 

Figure 22 and Figure 23

Figures 22 and 23 are electron density contour plots of natural orbitals

38 and 39 of the TiCH molecule in the ground state. The occupations

and the mulliken population condensed to a basis function type are reported
for each orbital.

113

1Km+muflhMmflOflm0Mmmu7
1 - . -

 

Occ=1.96
Ce-1.26
Cp-0.15
3830.55

C tota1=1.43

 

 

 

 

7

 

 

Dec-1.92
Tid=0.38
Ce-0.45
Cp-O.93
3830.25

Y—Axis
- 9-

 

 

 

Figures 24 and 25 are the electron density contour plots of natural orbitals

8 and 9 of the TiCH +‘molecule in the 12‘. ground state. The occupations
and the mulliken population condensed to a basis firnction type are reported
for each orbital.

114

TiCH 2P1 Natural Orbital Number 39

 

Dec-1.82
Tia-0.91
Cp-o e 85

Ti total-0.93

 

 

 

 

 

TMCHHHHBhdunfl(1flfiufl40

 

. . Occ=0.16

, , Tia-0.08
Cp-0.08

Ti total-0.08
C total-0.07

 

 

 

 

 

-7 v 1' v v i 7 ji r r . r V v
-7 ' O 2
2 Axis

Figures 26 and 27 are the electron density contour plots of natural orbitals

39 and 40 of the TiCH molecule in the excited state. The occupations
and the mulliken population condensed to a basis function type are reported
for each orbital.

115

'l‘lCH-I- 1313])! Natural Orbital Number 23

 

Dec-1.821
Tia-0.95
Cp-O.82

Ti total=0.97
C totel=0.84

 

XAlla
I

 

 

 

 

 

. : Dec-0.16
d Tia-0 e 08
Cp-0.08

 

 

 

 

7 T I V I v *1

 

Figures 28 and 29 are the electron densig' contour plots of natural orbitals
23 and 24 of the TiCH molecule in the 2 ground state. The occupations

and the mulliken population condensed to a basis function type are reported
for each orbital.

116

TiCH-I- LSigpl Natural Orbital Number 37

7 . .

 

l " ' " ' " , ace-1.821
j i . Tid=0.95
& Cp=0.82

Ti total-0.97
C total-0.84

 

Y—Axis

 

 

 

-? .
-7

 

 

7 V ' V v v v 1

f

, Occ=0.16
Tia-0.08
Cp=0.08

Ti total-0.08
C tota1=0.08

 

 

 

 

 

-7 v j v v T

Figures 30 and 31 are electron density contpur plots of natural orbitals

37 and 38 of the TiCH molecule in the 12 ground state. The occupations
and the mulliken population condensed to a basis firnction type are reported
for each orbital.

117

'IlCH 2P1 Natural Orbital Number 8

 

 

 

 

 

 

. Dec-1.93
, Tid-O.31
. C8-0.53
i
i a
I
9" f
‘1.
i.
i \. i
-7 . . . . . . , . . . . IL-
-7 o 7
ZAds
'DCH 21’! Natural Orbital Number 9
A ace-0.05
. Tia-0.03

Ti total-0.03
C total-0.02

 

 

-7 -
-1

 

 

Figures 32 and 33 are the electron density contour plots of natural orbitals

8 and 9 of the TiCH molecule in the state. The occupations and the

mulliken population condensed to a basis function type are reported
for each orbital.

118

'DCH 2P1 Natural Orbital Number 10

7.r.

 

Occ=0.025
C tote1=0.02

A

A A

 

 

-7 .

 

 

 

Occ=1.85
TiCH 2P1 Natural Orbital Number-24 Tidal) . 79
1 - 4 - - - , , L , , , , . CPIO e 95
4 . Ti total-0.87
' . C total-0.96

 

 

 

 

 

Figures 34 and 35 are electron density 5.0an plots of natural orbitals

10 and 24 of the TiCH molecule in the II state. The occupations
and the mulliken population condensed to a basis function type are reported
for each orbital.

119

13C112Pihhmmnfl(1flflhflBhnnberzs

 

Dec-0.997
T1980.59
Tia-0.31

Ti total-0.89
C total-0.13

 

 

 

 

 

-? v f r v f v

1103 2P1 Natural Orbital Number 26

1....r.,...... Doc-0.11
4 . Tip-0.02
Till-0.04
Cp-0.04

 

 

XAais

 

 

 

 

-? v j V v v v l v '—

Figures 36 and 37 are the electron density contour plots of natural orbitals

25 and 26 of the TICH molecule in the 2n state. The occupations
and the mulliken population condensed to a basis function type are reported
for each orbital.

120

1108 2?! Natural Orbital Number 39

 

 

 

 

 

 

 

? - v
. Dec-1.82
. Tid-O.91
. Cp-0.85
Ti total-0.93
a
I; e
b-
i
J
-7 r r
-7
TMCEHflfiPfluunfl(Jflfihfl4m
? ' ' I r v v 1 fi
. . Dec-0.16
. . Tid-0.08
Cp-0.08

Ti total-0.08
C total-0.07

 

Y-Axis
I?

 

 

 

 

-7 ,,,.f.r-..
-? O
ZAIIS

Figures 38 and 39 are the electron density contour plots of natural orbitals
39 and 40 of the TlCH molecule in the 211 state. The occupations

and the mulliken population condensed to a basis function type are reported
finmmhmmml

121

1103 206 Natural Orbital Number 8

 

 

 

-7fi

I t v r v

 

Doc-1.93
Tia-0.23
Cs=0.46
Cp=0.84

 

 

-7

7

 

Y—Axis
P

 

Dec-0.048
Tia-0.03

Ti total-0.03
C total-0.02

 

 

 

Figures 40 and 41 are the electron depsity contour plots of natural orbitals
8 and 9 of the TiCH molecule in the A state. The occupations

and the mulliken population condensed to a basis fiinction type are reported
for each orbital.

122

VCH 3Del Natural Orbital Number 24

7 I ' "r V Y 1 V V " V ' T"
I
I

‘ ‘ Dec-1.80
- vet-o .eo

vp-o . 03

ep-o .93

 

 

 

 

-7 .
-7

 

 

 

1‘TF"""rvv'v ace-0.179
‘ Vd-0.11
cp-o.oa

 

XAxfi
I

 

 

 

 

'7 V I V V v V ' V V V V t—T'

-7 O 7

Figures 42 and 43 are the electron density contour plots of natural orbitals

24 and 25 of the VCH molecule in the 3A gromld state. The occupations
and the mulliken population condensed to a basis fimction type are reported
for each orbital.

123

 

VCH 3Del Natural Orbital Number 38

7 - 1

 

Occ=1.80
Vd=0.80
Cp-0.93
'v tota1=0.83
C total=0.94

1

 

Y—Aldl
1'?

 

 

 

 

VCH 3Del Natural Orbital Number 39

7 v fij V V V l f T

 

4 OCCIIO e 18
VH-O.11
Cp-0.07

4

 

Y-Alis
I?

 

 

 

 

-7 f

-1

t°€

Z

Figures 44 and 45 are the electron density contour plots of natural orbitals
38 and 39 of the VCH molecule in the 3A ground state. The occupations
and the mulliken population condensed to a basis filnction type are reported
for each orbital.

124

symmetric 1tx and try orbitals between Ti and carbon. The populations are slightly
different than those of TiN (0.05 Ti 41),, 0.75 Ti 30,9}j

The contours of the selected natural orbitals of two low-lying excited states of
TiCH are shown in Figures 32-41. The contour plot of NO 8, the Ti-C sigma bond in the

211 state, has almost identical occupations and populations to that of the ground state and
2A states NO 8 of the TiCH molecule. The 2IT NO 10, anti-bonding C—H sigma bond, is
slightly different in structure than that of the NO 10 of the 222+ state, However, the

bonding and the anti-bonding orbitals are almost identical in the 2IT and 222+ state(Figures
35, 36, 38, 39 and Figures 20-23), as well as, the 2A state.

Finally, the RHF energies and geometries are found in Table 5a, for the
wavefunctions that we were able to construct. The bondlengths are significantly shorter
than those of the MCSCF+1+2.

In the case of TiN and TiN-I- there is significant charge transfer before reaching
the equilibrium geometries; +0.50 and +0.43 au, respectively, on the Ti atom. In TiCH
and TiCH+ there is also some charge transfer shown in Tables 9 and 10. The amount of

the charge transfer is undoubtedly different due to electronegativity differences.

VCH and VCH+

The bond lengths, energies and dipole moments of VCH and VCH+ (dipole
moment not reported for VCH+) are also reported. The bond length of V-C in the VCH

molecule in the ground state 3 A state using the MRCI level of theory is 1.725 A (Table

125

 

11). The corresponding separation using DFT theory is 1.750 A while the CH bond
length was calculated to be 1.090 A.

The VCH molecule is constructed analogously to the CrCH molecule absent a
lone electron in the 3d15+ orbital on the V atom. The isoelectronic VN has a much shorter
triple bond. The experimental results for VCH in the ground 3 A state are given in Table
11.34 Our calculated vibrational frequencies are in good agreement with experiment. The
carbon-hydrogen bond length is in relatively good agreement with experiment. The
metal-carbon bond length calculated in this work is slightly longer than experiment
(1.705 A) at 1.750 A (DFT calculation) and 1.725 A (MRCI) (Shown in Table 11).

Going from VCH to VCH+, a lone electron in the 4s orbital of vanadium would be
removed to leave VCH+ in the 2A state. The VN+ state is predicted to have a triple bond
between the V and N atoms.lh Harrison and Swaisgood1d predict a triply bonded VCH+,
2A, ground state like the one reported in this work. Their bond lengths are V-C 1.745 and
OH 1.091 A while our results predict a V-C separation of 1.599A at the DFT level and a
CH separation of 1.083A at the DFT level. Using the more correlated MCSCF
wavefunction we calculated a V-C separation of 1.720 A and a CH separation of 1.088 A
(Table 12). There is evidence of a significant difference in the sigma system of VCH+
relative to the other TM-CH+ molecules. In VCH+ there is slight (dative) sigma bond
between vanadium and carbon. The carbon atom holds almost two electrons in the 2s

orbital, Figure 46, while forming a dative pi bond V=>C in Figure 47. Despite being in

effect a double bonded system, our results report a shorter V-C separation than the triply-

126

bonded V-CH molecule reported by Swaisgood et. al.1d The isoelectronic VN+ in the 2A
state exists with a much shorter triple bond.lh

The occupations shown on the contour plots of the 1t systems of VCH describe
more correlation with the If orbitals than the pi systems of TiCH and ScCH. The

populations are given in Figures 42-45. The populations of VCH and VCH+ in the
ground state and some excited states are given in Table 13 and 14, respectively.

An excited state of VCH, the 311 state, at the MCSCF level has 70,860
configuration state functions (CSF’s). The geometries and energies are given in Table 9.
Another excited state, the 3(1),",5+ state, is also reported. The 3CD“, energies, geometries and

frequencies are reported in Tables 11 and 7, respectively.

127

VCH+ Natural Orbital Nurrfl) er 8

 

ace-1.99
c.-a.os
Cp-0.13
C total-1.8

 

 

 

 

Dec-1.97
Via-3L5
Vd-O.21
Cp-O.17

 

Kills

 

 

 

 

Figure 46 and Figure 47

Figures 46 and 47 are the electron density contour plots of natural orbitals
8 and 23 of the VCl-I+ molecule in the 2A ground state. The occupations
and the mulliken populationcondensed to a basis function type are reported
finmmhmme

n8

 

CrCH and CrCH+

The CrCH molecule in the 42' ground state is analogous to VCH with another lone
electron in the Cr d8+ orbital. Tables 15 and 7provide the MCSCF, MRCI, and DFT
geometries, energies, dipole moments, frequencies and populations for CrCH in the 42'

state. The CrCH bond is much longer than the isoelectronic CrN at (1.619A) at all levels
of theory. The dipole moments are quite similar at 2.7 (this work) and 2.0 Debye (CrN).'j
CrN had a large charge transfer from the Cr to the N atom of +0.5 atomic untis.lj In

CrCH that charge transfer is half that at +25 au. (See Table 17) The geometry presented

in Table 16 for CrCH 42' using a MCSCF wavefunction included 71,213 CSF.
In CrCH+ an electron is removed from the 4s orbital of Cr in CrCH in the 42' state
to leave lone electrons in the 3d,? and 3d,» orbitals of Cr. The natural orbitals are shown

in Figures 54-57 show the highly correlated pi system of Cr relative to the other TM-CH
molecules. The bondlengths, energies, dipole moments, frequencies, and populations for

CrCH+ are displayed in Tables 16, 18, and 8.

129

Conclusions

The results reported for the TMCH were in fair agreement with experiment for
VCH and TiCH in terms of geometries at the MRCI level. The density functional theory
frequency calculations on the TiCH ground state were in good agreement with
experiment. The VCH vibrational frequencies calculated were slightly smaller for the V-
C stretch

All of the same ground electronic states for the TMCH and TMN molecules are
predicted and follow the same bonding patterns. Comparisons between the metal-nitrides
and TM-CH molecules suggest similar structures with much shorter bondlengths and
greater charge transfer in the nitrides than in the TM-CH molecules. In fact the character
of the bonding in the sigma systems were extremely close. Upon exarrrining the TM-CH+
molecules, all of the structures again remain similar in structure except for the case of the
VCH+ where our results are in slight disagreement with Swaisgood’s previous results.lg

Restricted Hartree-Fock calculations are also reported. These results can be found
in Tables 5, 6, 12, and 15. These resultant bondlengths are not in agreement with those of

the MRCI, and MCSCF results.

130

VCH+ Natural Orbital Number 24

 

 

 

 

 

 

 

7 f r .
Dec-0.02
' Vii-0.02
3?
fi 4
-7 T .
-7
VCH+ Natural Orbital Nimber 37
7 - a - - 1+ , , ,
ace-1.92
Vet-1.67

‘v total-1.86

 

Y-Aais

 

 

 

 

-7 v I v v v r

ZAxis

Figure 48 and Figure 49

Figure 48 and 49 are the electron density contour plots of natural orbitals

2481“} 37 0f VCH+ in the 2 A ground state. The occupation and mulliken
population condensed to a basis function type are reported for each orbital

131

 

'4‘

Y—Aais

Y-Ards

VCH+ Natural Orbital Number 24

 

 

 

-7 v ‘

Dec-0.02
vp=0.02

 

 

-7

 

VCH-I- Natural Orbital Ntmaber 37

 

 

 

-? v I v v v v I

 

Dec-1.92
va-1.67
‘V total-1.86

 

 

o
2.431.:

v v v v V

Figure 48 and Figure 49

Figure 48 and 49 are the electron density contour plots of natural orbitals

24and 37 of VCH+ in the 2 A

round state. The occupation and mulliken

population condensed to a bum function type are reported for each orbital

131

VCH+ Natural Orbital Number 10

 

7 v f V v r r I r v V v 1 v

Y-Axis
P

 

 

 

 

 

OCC-O . 007 Vl-O . 01

Figure 50

Figure 50 is the electron density contour plot of natural orbital 10 of VCH+
in the 2A ground state. The occupation and mulliken poupulatin condensed
to a basis function is also reported.

132

 

cumuapn-humumnuxunHNmmru
7

 

g . Cflmuflyunhuflmuflcflmanmuat
/ ‘ I l 1 .

 

   

 

 

 

 

 

 

-1 “rm-E”
2 u z u

Dec-1.68 era-0.04 Cp-o.80 Dec-0.300 era-0,16
Cr total-0.87 C total-0.81 Cr total-0.16 C total-0.14

O'Cll esp-l- Natlral Orb“ N-ber 40
OCH 48W Natural Orbital Number 39 1 . . -

7

 

 

 

 

 

 

 

 

 

 

 

-7

 

Dec-1.68 Crd-0.84 Cp-0.80 Ode-0.300 Crd-0.16

Cr total-0.87 C total-0.81 Cp-0.14 C total-0.14
Cr total-0.16

Figure 51, 52, 53. 54 (Clockwise)

Figures 51 through 54 are the electron density contour plots of natural
orbitals 25, 26, 40, and 39 of the CrCH molecule in the 42' ground state. The
occupations and the mulliken population condensed to a basis function type
are reported for each orbital.

133

(hCH+supnmumuNmmnHmmmuNmmurmt
Occ=1.70

Crd-1.04
Cry-0.02
Cp-0.63

 

 

 

 

 

CrCH+ 381mm: Natural Orbital Number 25

101 e . - - - - t . ~ - r . ' Dec-0.28
. era-0.12
‘ cp-o .16

 

 

 

 

 

Figure 55 and Figure 56

Figure 55 through 56 are the electron density contour plots of natural orbitals 24
and 25 of the CrCH+ molecule in the 32' ground state. The occupations and the
mulliken populations condensed to a basis function type are reported for each
orbital.

134

 

CrCB+ W Naturfl Orblal Mather”

 

7 vmr f ' I """ “0.1.7
/
. ‘x ere-1.03
. \\ j (21)-0.63
\ x rrrr . Cr total-1.06

-------- ‘ ‘ . C total-0.64

 

 

 

 

Occ0.28
era-0.1a

CrCB+ W Natural Orbitd Nunber 39 “'0 e 16

1-.- -, .....

 

Y-Aail

 

 

 

 

-7 . . --,-

Figure 57 and Figure 58

Figure 57 and 58 are the electron density contour plots of natural orbitals 38
and 39 of the CrCH+ molecule in the 32' ground state. The occupations and
the mulliken population condensed to a basis function type are reported for
each orbital.

135

 

Tabulated Results

Table 1. The equilibrium metal-carbon, RechC(A), and carbon hydrogen, ReqCH(A), bond
lengths, energy, and dipole moment of ScCH in the ground 3l'l state using the AWACH basis at
the MRCI, MCSCF, DFT, and RHF levels (MRCIa corresponds to a MRCI wavefunction with an
extra orbital of a) symmetry in correlation of the MCSCF“ reference).

 

 

 

State Level Basis RechC(A) RopCH(A) Enegymartrees) Dipole(Debye)
3l'l MRCI‘ AWACH 1.9541 1 1.09288 -798.27363 -2. 1857
3n MRCI AWACH 1.95570 1 .09252 -798.27204 -2. 1767
311 MCSCF AWACH 1.99972 1.10322 -798.14097 -l.8010
3n MCSCF‘ AWACH 1.99569 1.10430 -798. 14912 -l.83 14
311 DFT AWACH 1.89238 1.09588 -799.24958 -2.7912

 

136

Table 2. The equilibrium metal-carbon, RechC(A), and carbon hydrogen, ReqCH(A), bond
lengths, and energy of ScCH+ in the ground 211 state using the AWACH basis at the MRCI,
MCSCF, DFT, and RHF levels (MRCIa corresponds to a MRCI wavefunction with an extra
orbital of a) symmetry in correlation of the MCSCF‘I reference).

 

 

State Level Basis RechC(A) ReqCH(A) Energy(Hartrees)
2n MRCI AWACH 1.92960 1.08886 -798.05745
211 MCSCF AWACH 2.09038 1.08108 -797.85422
2l1 MRCI‘ AWACH 1.92813 1.08913 -798.05887
2n MCSCF‘ AWACH 1.96458 1.09889 -797.94483
2n DFT AWACH 1.86108 1.09419 49902300

 

 

137

Table 3. The mulliken population analysis of ScCH in the ground 3T1 state using the
AWACH basis at the MRCI and MCSCF level (MRCIa corresponds to a MRCI
wavefunction with an extra orbital of a1 symmetry in correlation of the MCSCF“
reference).

 

 

 

 

MRCI‘I Analysis by Basis Function Type

State Atom s p (1 Total Charge

3

11

Se 7.03910 12.24748 1.24790 20.56429 +0.43571
C 3.66683 2.83314 0.02900 6.52897 -0.52897
H 0.85269 0.05405 0.0000 0.90674 +0.09326

MRCI

3n
Sc 7.04266 12.26294 1.24566 20.57782 +0.42218
C 3.68906 2.83702 -0.00968 6.51639 -0.51639
H 0.87517 0.03062 0.00000 0.90578 +0.09422

MCSCF‘

3n
Sc 7.02360 12.26939 1.23059 20.54779 04522!
C 3.71419 2.83522 -0.00109 6.54832 -0.54832
H 0.87620 0.02679 0.00000 0.90389 +0.096l l

MCSCF

3n
Sc 7.02659 12.27048 1.23397 20.55485 +0.44515
C 3.71926 2.83325 -0.00604 6.54647 -0.54647
H 0.87093 0.02775 0.00000 0.89868 +0.10132

 

 

 

138

 

 

 

Table 4. The mulliken population analysis of ScCH+ in the ground 211 state using the
AWACH basis at the MRCI (MRCIa extra orbital of a1 symmetry in correlation of the

 

 

MCSCFal reference).
MRCI Level Analysis by Basis Function Type
State Level Atom 5 p (1 Total Charge
211 MRCI
Sc 6.07716 12.00787 1.43886 19.5469 +1.45315
3.76075 2.80089 0.01642 6.57806 -0.57806
0.82843 0.004665 0.00000 0.87508 +0.12492
2r] MRCI'
Sc 6.06521 12.01081 1.4451 1 19.54704 +1 .45296
3.75060 2.78928 0.04670 6.58657 -0.58657
0.80360 0.06279 0.00000 0.86639 +0.13361

 

 

 

 

 

 

139

 

 

 

Table 5. The equilibrium metal-carbon, ReqTiC(A), and carbon hydrogen, ReqCH(A), bond lengths,
energies, and dipole moments of the ground state, 22‘, and three excited states of TiCH using the AMES,
and AWACH basis at the MRCI, and MCSCFlevel (extra orbital of a1 symmetry in correlation of the

MCSCF reference), DFT, and experimental geometry (ground state) and experimental separation between

the ground state and 211 state.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

State Level Basis ReqTiC(A) ReqCH(A) Energy(Hartrees) Dipole(Debye)
22+ MRCI AMES 1.75024 1.08921 -887.01450 4.4490
2A MRCI AMES 1.79931 1.09566 886.98351 4.3121
2n.,,,.,_, MRCI AMES 1.72217 1.09202 88694941 -3.6733
annm" MRCI AMES 1.72217 1.09202' 886.94725 8.7013"
22* MRCI AWACH 1.75123 1.08865 886.97672 -1.8860
2A MRCI AWACH 1.80085 1.09503 -886.94619 -7.3964
znme MRCI AWACH 1.77341 1.09130 -886.91247 -3.8275
22* MCSCF AMES -----------------------------------------
2A MCSCF AMES 1.81461 1.10775 88682464 4.3361
L MCSCF AMES 1.72770 1.08500 88681038 -29747
’nmno" MCSCF AMES 1.72217' 109202" 88681104 -3.6346°
22* MCSCF AWACH 1.75479 1.10500 88684447 4.4142
2A MCSCF AWACH 1.81982 1.08427 88681271 -7.3674
211...... MCSCF AWACH 1.77240 1.07884 88678921 -3.1484
22* DFI‘ AWACH 1.69140 1.09490 88800013 -2.6910
2A on AWACH 1.74240 1.09570 887.97967 -6.1826
211.11.... DFT AWACH 1.72300 1.09310 887.94060 --------
22* Experiment 1.7277 1.085 X22221] ~62.8mH -------
Our DFI‘ Results xiv—Zn 59.5mH

 

140

 

Table 5a. The equilibrium metal-carbon, ReqTiC(A), and carbon hydrogen, ReqCH(A), bond lengths,
energies, and dipole moments of the ground state, 22‘, and three excited states of TiCH using the AWACH
basis at the RHF level.

 

 

 

 

State Level ‘ Basis ReqTiC(A) ReqCH(A) Energy(Hartrees) Dipole(Debye)
22+ RHF AWACH --------------------------------------------

2A RHF AWACH 1.73569 1.08239 -886.66760 -3.4093

21'1“,“ RHF AWACH 1.76599 1.08152 -886.631 19 -2.4709
’nmm" RHF AWACH 1.77217 1.09202 88663025 4.5001
(Applies to Table 5 and 5a.)

a. The zllbcmno" state bondlengths were not optimized. The bondlengths used were those of the
optimized 2111,,“ state.

b. The dipole moment reported corresponded to the z-component of the dipole moment. The y-
component calculated was -0.07227 debye. The TiCH molecule was constructed with the OH bond
bent in the yz plane while the TiC bond was along the z-axis.

c. The dipole moment reported corresponded to the z-component of the dipole moment. The y-

component calculated was -0.009446 debye. The TiCH molecule was constructed with the CH bond
bent in the yz plane while the TiC bond was along the z—axis.

141

 

Table 6. The equilibrium metal-carbon, ReqTiC(A), and carbon hydrogen, ReqCH(A),
bond lengths, and energy of TiCH+ in the ground '2‘.“ state using the AWACH basis at the
MRCI, MCSCF, DFT, and RHF levels.

 

 

State Level Basis ReqTiC(A) ReqCH(A) Energy(Hartrees)
'2‘ MRCI AWACH 1.73983 1.08999 88675643
'2’ MCSCF AWACH 1.73844 1.10157 88663855
'2‘ DFT AWACH 1.66905 1.09440 -887.74598
‘2’ RHF AWACH 1.67270 1.08051 88643718

 

Table 7. The vibrational frequencienes, (0c, of several states of ScCH, TiCH, VCH and
CrCH using DFT, the AWACH basis on metal and 6-3 lG** basis on C and H.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Molecule State to, (cm-1)
ScCH 3r1 487.2 513.5 802.1 3114.7
TiCH 22* 600.30 600.30 953.14 3119.2
Experiment 22* 578 578 855 ~3000
2A 49674 496.74 860.66 3098.7
2mm, 804.27 651.54 908.55 3139.0
“be?” ' " ' '
0
VCH 3A 577.28 577.28 693.95 3148.2
Experiment 3A 564 564 838 ~3000
30>”: ------ 631.95 776.79 3174.4
CrCH 4;: 545.74 545.74 640.39 3155.2
22* TiCI—I Experiment * TiCH Our DFT Results
xzrfin ~62.8mH xiv—2n 59.5mH

 

 

a. 3(1) w frequencies calculated using MCSCF equilibrium geometry

142

Table 8. The charge distribution and vibrational frequencienes, (06, of ScCH”, TiCH+,
VCH+, and CrCH” in their ground states using DFT, the AWACH basis on metal and 6-
31G** basis on C and H.

 

 

 

 

 

 

 

 

Molecule State 00e (cm-1)
ScCH” 211 552.84 605.21 815.09 3154.5
TiCH+ '2‘ 677.61 677.61 994.28 3156.3
VCH+ 2A 847.91 848.22 1064.1 3229.8
CrCH“ 32' 589.95 589.95 692.46 3179.0

 

 

 

 

 

 

 

 

143

Table 9. The mulliken population analysis of TiCH in the ground 22 state and three
excited states using the AMES and AWACH basis sets at the MRCI level (MRCIa extra

orbital of a1 symmetry in correlation of the MCSCF“ reference).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MRCI‘ AMES basis Analysis b Basis Function T
State Atom s p d Total Charge
22*
Ti 7.19463 12.39523 2.53457 22.16185 -0.16185
C 3.30996 2.71314 0.05006 6.07316 -0.07316
H 0.74872 0.01628 0.0000 0.7650 +0.2350
2
A
Ti 6.40492 12.2005 3.14550 21.77167 +0.22833
C 3.38170 2.94461 0.06773 6.39405 -0.39405
H 0.79626 0.03 802 0.00000 0.83428 +0. 16572
2
"111w
Ti 6.41862 12.71552 2.68921 21.85400 +0. 14600
C 3.37103 2.90426 0.08161 6.35689 0.35689
H 0.76191 0.02719 0.00000 0.78910 +0.21090
znbcntl700
Ti 6.93920 12.28476 2.67499 21 .92097 «1007903
C 3.35917 2.88907 0.03675 6.28499 -0.28499
H 0.76475 0.02929 0.00000 0.79404 +0.20596
MRCI’ AWACH basis
State
22"
Ti 7.16397 12.12480 2.44044 21.75934 +0.24066
C 3.57442 2.75750 0.02458 6.35650 -0.35650
H 0.85221 0.03195 0.00000 0.88416 +0.11584
2
A
Ti 6.14121 12.09255 3.10044 21.35628 0.64372
C 3.67550 2.94460 0.05251 6.67261 -0.67261
H 0.89372 0.07739 0.00000 0.97111 +0.02889
2
rllinear
Ti 6.07742 12.671 13 2.57873 21.35389 +0.6461 1
C 3.75619 2.98626 0.02418 6.76663 -0.76663
H 0.86770 0.01 178 0.00000 0.87948 +0. 12052
MRCI AWACH basis Analysis by Basis Function Type
State Atom s p d Total Charge
22”
Ti 6.94413 12.197613 2.69711 21.859557 +0. 140444
C 3.45601 2.74343 0.01524 6.259891 -0.214687
H 0.91 186 0.01390 0.00000 0.925757 +0.074243
2
A
Ti 6.28269 12.20102 3.27497 21.771917 +0.228082
C 3.44709 2.81591 0.01256 6.27554 -0.275540
H 0.93837 0.01418 0.00000 0.952541 +0.047458
ZI-Ilineai'
Ti 6.22478 12.77718 3.76464 21.829147 +0. 170853
C 3.45446 2.78006 0.01382 6.248332 -0.248332
H 0.90843 0.01 129 0.00000 0.922521 +0.077479

 

 

 

 

144

 

 

 

Table 10. The mulliken population analysis condensed to basis function type of TiCH+ in
the ground 12* state using the AWACH basis at the MRCI (MRCIa extra orbital of a1
symmetry in correlation of the MCSCF“a reference).

 

 

 

 

 

 

 

 

 

 

MRCI'I Level Analysis b Basis Function Type
State Atom 3 p (1 Total Charge
12+
Ti 6.00942 1 1.97325 2.59793 22.60728 +1 .39272
3.77514 2.73443 0.04343 6.55300 -0.55300
0.79754 0.04218 0.00000 0.83972 +0. 16028
MRCI Level
1,:
Ti 6.00893 1 1.96726 2.62095 20.61658 +1 .38342
C 3.77242 2.72439 0.01836 6.51517 -0.51517
0.83568 0.03257 0.00000 0.86825 +0.13175

 

 

 

145

 

 

 

 

Table 11. The equilibrium metal-carbon, RquC(A), and carbon hydrogen, ReqCH(A),
bond lengths, energy, and dipole moment of the ground state, 3A, and an excited state
(DFT level) of VCH using the AWACH basis at the MRCI and DFT level. The
experimental bond length for the ground state is also reported.

 

 

 

State Level Basis RquC(A) ReqCH(A) Energy(Hartrees) Dipole(Debye)
3A MRCI AWACH 1.72539 1.08954 -981.46786 -1.75693

3A MCSCF AWACH 1.74828 1.10044 -981.31299 -1.3349

3A DFT AWACH 1.69704 1.09301 -982.54778 -1.0039'
3(1),,» DFT AWACH 1.71391 1.08991 -982.36029 -1.3852‘

3A Experiment 1.702 1.080 ----------

3f] MCSCF AWACH 1.76573 1.09988 -981.25522 -1.6782

 

a. Dipole moment in atomic units

Table 12. The equilibrium metal-carbon, RquC(A), and carbon hydrogen, ReqCH(A),
bond lengths, and energy of VCH+ in the ground 2A state using the AWACH basis at the
MRCI, MCSCF, DFT, and RHF levels.

 

 

 

State Level Basis RquC(A) ReqCH(A) Bnegymartrees)
2A MRCI AWACH 1.72000 1.08852 981.23573
23 MCSCF AWACH 1.73289 1.09849 981.09832
213 DFT AWACH 1.59877 1.08329 -982.02962
2A RHF AWACH 1.64713 1.08003 980.86841

 

146

 

 

Table 13. The mulliken population analysis of VCH in the ground 3A state using the

AWACH basis at the MRCI level.

 

Analysis by Basis Function Type

 

State

 

 

Atom

 

7.17346
3.55884
0.86257

 

P

12.12899
2.73373
0.00705

 

d

3.53824
0.00149
0.00000

 

Total

22.85340
6.29108
0.85553

 

Charge

+0. 14660
-0.29108
+0. 14448

 

Table 14. The mulliken population analysis condensed to basis function type of VCH+ in

the ground 2A state using the AWACH basis at the MRCI and MCSCF level.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MRCI Level Analysis b Basis Function Type
State Atom s p d Total Charge
2A
4.99914 12.04193 3.70996 20.75104 +2.24896
5.58519 1.79378 -0.23210 8.14687 -1.l4687
0.43145 -0.32935 0.00000 0.10210 +0.29059
MCSCF
Level
2A
6.00942 12.00620 3.70600 21.73610 +1.26390
3.70986 2.69805 0.02298 6.43089 -0.43089
0.81742 0.01559 0.00000 0.83301 +0. 16699

 

147

 

 

Table 15. The equilibrium metal-carbon, RequC(A), and carbon hydrogen, ReqCH(A),
bond lengths, and energy of the ground state, 42', of CrCH using the AWACH basis at the

MRCI, MCSCF, DFT and RHF levels.

 

 

 

State Level Basis RequCat) ReqCH(A) EnergL(Hartrees) Dipole(Debye)
42' MRCI AWACH 1.74257 1.08754 -1081.9131 1 -2.3398
‘2'.“ MCSCF AWACH 1.77857 1.0981 1 -1081.71636 -2.0085
42." DFT AWACH 1.74670 1.09127 -1083.03970 -2.7418
427 RHF AWACH 1.91023 1.07540 - 1081 .42992 --------

 

Table 16. The equilibrium metal-carbon, RequC(A), and carbon hydrogen, ReqCH(A),
bond lengths, and energy of CrCH+ in the ground 32’ state using the AWACH basis at the
MRCI, MCSCF, DFT, and RHF level.

 

 

 

State Level Basis RequC (A) ReqCH (A) Energy(Hartrees)
3): MRCI AWACH 1.72025 1.08642 -1081.66315
32' MCSCF AWACH 1.74314 1.08442 4081.51000
3:: DFT AWACH 1.71720 1.09189 4082.76612
3: RHF AWACH 1.74314 1.07660 4081.44267

 

 

148

 

 

 

 

TlflOF.

 

Table 17. The mulliken population analysis condensed to basis function type of CrCH" in
the ground 32' state using the AWACH basis at the MRCI level (extra orbital of a1

symmetry in correlation of MCSCF).

 

Analysis b Basis Function Type

 

State
32-

 

 

Atom

Cr

 

6.33761
3.91776
0.72393

 

P

12.02527
2.61937
-0.01452

 

(1

4.34514
0.03973
0.00000

 

Total

22.71373
6.57686
0.70941

 

Charge

+1 .28627
-0.57686
+0.29059

 

Table 18. The mulliken population analysis condensed to basis function type of CrCH
and CrCH+ in their ground states using the AWACH basis at the MCSCF level (extra

orbital of at symmetry in correlation).

 

Analysis b Basis Function Type

 

 

 

 

 

 

 

 

 

 

 

State Atom 5 p d Total Charge

42-

Cr 6.93200 12.15021 4.65970 23.74754 +0.25246

C 3.63180 2.78929 0.021 17 6.44225 -0.44225

0.83284 -0.02263 0.00000 0.81021 +0. 18979
3):

Cr 6.33761 12.02527 4.34514 22.71373 +1 .28627

3.91776 2.61937 0.03973 6.57686 -0.57686

0.72393 -0.01452 0.00000 0.70941 +0.29059

 

 

149

 

 

BIBLIOGRAPHY

150

 

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152

 

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MOLPRO is a package of ab-initio programs written by H]. Werner and
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MSUPlot Program, J. F. Harrison, Michigan State University, Chemistry Department,
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MSUProp Program, J. F. Harrison, Michigan State University, Chemistry
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Plotmtv is a plotting program for the visualization of scientific data. It was developed
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Normale Superieure, France; J. P. Flament, Lavoratoire de Dynamique Moleculaire et
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153

 

33. Basis set was obtainedfrom the Extensible Computational Chemistry Environment
Basis Set Datatabase, Version 1.0, as developed and distributed by the Molecular
Science Computing Facility, Environmental and Molecular Sciences Laboratory,
which is part of the Pacific Northwest Laboratory, PO. Box 999, Richland,
Washington 99352, USA, and funded by the US. Department of Energy. The Pacific
Northwest Laboratory is a multi-program laboratory operated by Battelle Memorial
Institute for the U. S. Department of Energy under contract DE-AC06-76RLO 1830.
Contact David Feller, Karen Schuchardt, or Don Jones for further information.

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35. See Chapter 1 and references therein.

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APPENDIX

155

 

APPENDIX
LISTING OF PUBLICATIONS
1. “Ab-lnitio Studies of the Scandium Nitride Dimer” J. Edwards and J. F.
Harrison, Proceedings N OBCChE 95, 1995, 22, 122.

2. “Ab-Initio Studies of Several Low-Lying States of YN” J. Edwards
and J. F. Harrison, Proceedings NOBCChE 96, 1996.

3. “Electronic Structure of Early Transition Metal Carbynw” J. Edwards and J. F.
Harrison, to be submitted to Journal of Molecular Spectroscopy.

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