Cambridge University Press. 2003. - 238 p.
Valence bond theory is one of two commonly used methods in molecular quantum mechanics, the other is molecular orbital theory. This book focuses on the first of these methods, ab initio valence bond theory.
The book is split into two parts. Part I gives simple examples of two-electron calculations and the necessary theory to extend these to larger systems. Part II gives a series of case studies of related molecule sets designed to show the nature of the valence bond description of molecular structure. It also highlights the stability of this description to varying basis sets. There are references to the CRUNCH computer program for molecular structure calculations, which is currently available in the
public domain. Throughout the book there are suggestions for further study using CRUNCH to supplement discussions and questions raised in the text.
The book will be of primary interest to researchers and students working on molecular electronic theory and computation in chemistry and chemical physics.
Contents
Preface page
List of abbreviations
I Theory and two-electron systems
Introduction
History
Mathematical background
Schrodinger’s equation
The variation theorem
General variation functions
Linear variation functions
A2 ? 2 generalized eigenvalue problem
Weights of nonorthogonal functions
Weights without orthogonalization
Weights requiring orthogonalization
H2 and localized orbitals
The separation of spin and space variables
The spin functions
The spatial functions
The AO approximation
Accuracy of the Heitler–London function
Extensions to the simple Heitler–London treatment
Why is the H2 molecule stable?
Electrostatic interactions
Kinetic energy effects
Electron correlation
Gaussian AO bases
A full MCVB calculation
Two different AO bases
Effect of eliminating various structures
Accuracy of full MCVB calculation with 10 AOs
Accuracy of full MCVB calculation with 28 AOs
EGSO weights for 10 and 28 AO orthogonalized bases
H2 and delocalized orbitals
Orthogonalized AOs
Optimal delocalized orbitals
The method of Coulson and Fisher
Complementary orbitals
Unsymmetric orbitals
Three electrons in doublet states
Spin eigenfunctions
Requirements of spatial functions
Orbital approximation
Advanced methods for larger molecules
Permutations
Group algebras
Some general results for finite groups
Irreducible matrix representations
Bases for group algebras
Algebras of symmetric groups
The unitarity of permutations
Partitions
Young tableaux and N and P operators
Standard tableaux
The linear independence of NiPi and PiNi
Von Neumann’s theorem
Two Hermitian idempotents of the group algebra
A matrix basis for group algebras of symmetric groups
Sandwich representations
Group algebraic representation of the antisymmetrizer
Antisymmetric eigenfunctions of the spin
Two simple eigenfunctions of the spin
The ? function
The independent functions from an orbital product
Two simple sorts of VB functions
Transformations between standard tableaux and HLSP functions
Representing ?NPN? as a functional determinant
Spatial symmetry
The AO basis
Bases for spatial group algebras
Constellations and configurations
Example
1. H2O
Example
2. NH3
Example
3. The п system of benzene
Varieties of VB treatments
Local orbitals
Nonlocal orbitals
The physics of ionic structures
A silly two-electron example
Ionic structures and the electric moment of LiH
Covalent and ionic curve crossings in LiF
II Examples and interpretations
Selection of structures and arrangement of bases
The AO bases
Structure selection
N2 and an STO3G basis
N2 and a 6-31G basis
N2 and a 6-31G* basis
Planar aromatic and [i]п systems[/i]
Four simple three-electron systems
The allyl radical
MCVB treatment
Example of transformation to HLSP functions
SCVB treatment with corresponding orbitals
The He2+ ion
MCVB calculation
SCVB with corresponding orbitals
The valence orbitals of the BeH molecule
Full MCVB treatment
An SCVB treatment
The Li atom
SCVB treatment
MCVB treatment
Second row homonuclear diatomics
Atomic properties
Arrangement of bases and quantitative results
Qualitative discussion
B2
C2
N2
O2
F2
General conclusions
Second row heteronuclear diatomics
An STO3G AO basis
N2
CO
BF
BeNe
Quantitative results from a 6-31G* basis
Dipole moments of CO, BF, and BeNe
Results for 6-31G* basis
Difficulties with the STO3G basis
Methane, ethane and hybridization
CH, CH2, CH3, and CH4
STO3G basis
6-31G* basis
Ethane
Conclusions
Rings of hydrogen atoms
Basis set
Energy surfaces
Aromatic compounds
STO3G calculation
SCVB treatment of п system
Comparison with linear 1,3,5-hexatriene
The 6-31G* basis
Comparison with cyclobutadiene
The resonance energy of benzene
Naphthalene with an STO3G basis
MCVB treatment
The MOCI treatment
Conclusions
Interaction of molecular fragments
Methylene, ethylene, and cyclopropane
The methylene biradical
Ethylene
Cyclopropane with a 6-31G* basis
Cyclopropane with an STO-3G basis
Formaldehyde, H2CO
The least motion path
The true saddle point
Wave functions during separation
References
Index
Valence bond theory is one of two commonly used methods in molecular quantum mechanics, the other is molecular orbital theory. This book focuses on the first of these methods, ab initio valence bond theory.
The book is split into two parts. Part I gives simple examples of two-electron calculations and the necessary theory to extend these to larger systems. Part II gives a series of case studies of related molecule sets designed to show the nature of the valence bond description of molecular structure. It also highlights the stability of this description to varying basis sets. There are references to the CRUNCH computer program for molecular structure calculations, which is currently available in the
public domain. Throughout the book there are suggestions for further study using CRUNCH to supplement discussions and questions raised in the text.
The book will be of primary interest to researchers and students working on molecular electronic theory and computation in chemistry and chemical physics.
Contents
Preface page
List of abbreviations
I Theory and two-electron systems
Introduction
History
Mathematical background
Schrodinger’s equation
The variation theorem
General variation functions
Linear variation functions
A2 ? 2 generalized eigenvalue problem
Weights of nonorthogonal functions
Weights without orthogonalization
Weights requiring orthogonalization
H2 and localized orbitals
The separation of spin and space variables
The spin functions
The spatial functions
The AO approximation
Accuracy of the Heitler–London function
Extensions to the simple Heitler–London treatment
Why is the H2 molecule stable?
Electrostatic interactions
Kinetic energy effects
Electron correlation
Gaussian AO bases
A full MCVB calculation
Two different AO bases
Effect of eliminating various structures
Accuracy of full MCVB calculation with 10 AOs
Accuracy of full MCVB calculation with 28 AOs
EGSO weights for 10 and 28 AO orthogonalized bases
H2 and delocalized orbitals
Orthogonalized AOs
Optimal delocalized orbitals
The method of Coulson and Fisher
Complementary orbitals
Unsymmetric orbitals
Three electrons in doublet states
Spin eigenfunctions
Requirements of spatial functions
Orbital approximation
Advanced methods for larger molecules
Permutations
Group algebras
Some general results for finite groups
Irreducible matrix representations
Bases for group algebras
Algebras of symmetric groups
The unitarity of permutations
Partitions
Young tableaux and N and P operators
Standard tableaux
The linear independence of NiPi and PiNi
Von Neumann’s theorem
Two Hermitian idempotents of the group algebra
A matrix basis for group algebras of symmetric groups
Sandwich representations
Group algebraic representation of the antisymmetrizer
Antisymmetric eigenfunctions of the spin
Two simple eigenfunctions of the spin
The ? function
The independent functions from an orbital product
Two simple sorts of VB functions
Transformations between standard tableaux and HLSP functions
Representing ?NPN? as a functional determinant
Spatial symmetry
The AO basis
Bases for spatial group algebras
Constellations and configurations
Example
1. H2O
Example
2. NH3
Example
3. The п system of benzene
Varieties of VB treatments
Local orbitals
Nonlocal orbitals
The physics of ionic structures
A silly two-electron example
Ionic structures and the electric moment of LiH
Covalent and ionic curve crossings in LiF
II Examples and interpretations
Selection of structures and arrangement of bases
The AO bases
Structure selection
N2 and an STO3G basis
N2 and a 6-31G basis
N2 and a 6-31G* basis
Planar aromatic and [i]п systems[/i]
Four simple three-electron systems
The allyl radical
MCVB treatment
Example of transformation to HLSP functions
SCVB treatment with corresponding orbitals
The He2+ ion
MCVB calculation
SCVB with corresponding orbitals
The valence orbitals of the BeH molecule
Full MCVB treatment
An SCVB treatment
The Li atom
SCVB treatment
MCVB treatment
Second row homonuclear diatomics
Atomic properties
Arrangement of bases and quantitative results
Qualitative discussion
B2
C2
N2
O2
F2
General conclusions
Second row heteronuclear diatomics
An STO3G AO basis
N2
CO
BF
BeNe
Quantitative results from a 6-31G* basis
Dipole moments of CO, BF, and BeNe
Results for 6-31G* basis
Difficulties with the STO3G basis
Methane, ethane and hybridization
CH, CH2, CH3, and CH4
STO3G basis
6-31G* basis
Ethane
Conclusions
Rings of hydrogen atoms
Basis set
Energy surfaces
Aromatic compounds
STO3G calculation
SCVB treatment of п system
Comparison with linear 1,3,5-hexatriene
The 6-31G* basis
Comparison with cyclobutadiene
The resonance energy of benzene
Naphthalene with an STO3G basis
MCVB treatment
The MOCI treatment
Conclusions
Interaction of molecular fragments
Methylene, ethylene, and cyclopropane
The methylene biradical
Ethylene
Cyclopropane with a 6-31G* basis
Cyclopropane with an STO-3G basis
Formaldehyde, H2CO
The least motion path
The true saddle point
Wave functions during separation
References
Index