Electronic structure modeling connections between theory and software

Title:

Personal Author:

Trindle, Carl

Publication Information:

Boca Raton, FL : CRC, 2008

Physical Description:

1 CD-ROM ; 12 cm.

ISBN:

9780849384066

General Note:

Accompanies text of the same title : QC176.8.E4 T75 2008

Subject Term:

Electronic structure -- Mathematical models

Added Author:

Shillady, Donald

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010194577	CP 015955	Computer File Accompanies Open Access Book	Compact Disc Accompanies Open Access Book	Searching... Unknown

Computational chemistry, including electronic structure modeling, is a fast and accurate tool for treating large chemically meaningful systems. Unique among current quantum chemistry texts, Electronic Structure Modeling: Connections Between Theory and Software enables nonspecialists to employ computational methods in their own investigations.

The text illustrates theoretical methods with numerical detail and model calculations. It clarifies what these modeling programs can do, their known pathologies, which ones are suited for specific kinds of projects, and how to reproduce them using the accompanying PC-LOBE bundled software. While elucidating gradient-based molecular structure optimization, the text reviews notable successes and unsolved problems or failures in electronic structure modeling. It also describes the theory and computation of circular dichroism and optical rotation, including magnetically induced optical phenomena.

Offering an accessible introduction to computational methods, Electronic Structure Modeling permits users to practice modeling with a full understanding of the algorithms that support their calculations.

Author Notes

Trindle, Carl; Shillady, Donald

Preface	p. xiii
Authors	p. xvii
Chapter 1 One-Dimensional Quantum Mechanics: A Short Review
The Particle-in-a-Box	p. 3
Particle-on-a-Ring	p. 11
Operator Algebra in Quantum Mechanics	p. 15
Operator Commutation	p. 16
Commutation and Uncertainty	p. 17
The Harmonic Oscillator	p. 18
Summary	p. 20
References	p. 20
Chapter 2 Matrices, Representations, and Electronic Structure Modeling
Definition and Properties of Vectors and Matrices	p. 23
Response Matrices	p. 29
Symmetry Operations	p. 34
Conclusion	p. 35
References	p. 35
Chapter 3 Methods of Approximation and the SCF Method
The Variation Theorem	p. 37
The Variational Treatment of the H Atom	p. 38
Variational Treatment of the H Atom (Gaussian Trial Function)	p. 39
Variation Example with a Linear Combination of Basis Functions	p. 41
A Variational Calculation in One Dimension	p. 43
Determinantal Wave Functions and HF-SCF Theory	p. 45
Determinantal Integrals for One-Electron Operators	p. 48
Determinantal Matrix Elements for Two-Electron Operators	p. 49
Restricted Form of the Determinant	p. 52
Expansion of the RHF Energy in a Basis	p. 54
Roothaan-Hartree-Fock Self-Consistent Field Equation	p. 55
Koopmans' Theorem	p. 58
Brillouin's Theorem	p. 59
References	p. 59
Chapter 4 Gaussian-Lobe Basis Sets
Overlap (S[subscript AB])	p. 66
Kinetic Energy (T[subscript AB])	p. 67
Nuclear Potential (for Z Nuclear Charge Value, at r[subscript C])	p. 67
Electron Repulsion (Coulomb's Law for Two Charge Distributions)	p. 67
Dipole Moment	p. 68
Quadrupole Moment	p. 70
Angular Momentum (Imaginary Hermitian Operator)	p. 71
Spin-Orbit and Spin-Spin Interactions	p. 71
Frost FSGO Method	p. 72
Screened Coulomb Potential	p. 73
Electrostatic Potential Maps	p. 74
References	p. 75
Chapter 5 A Very Simple MO Program
Helium in SCF1s	p. 77
Beryllium Atom in SCF1s STOs	p. 81
Spherical Gaussian Contraction for Helium: 3G Expansion	p. 84
Molecular Hydrogen in SCF1s	p. 90
LiH-Frost Spherical Gaussian Pairs	p. 92
PCLOBE and Sample Output from RHF Calculations	p. 95
Li[subscript 2]	p. 95
N[subscript 2]	p. 102
N[subscript 2], CO, BF: An Isoelectronic Series	p. 108
The Value of Mulliken Charges and Mayer Bond Orders	p. 110
Bonding in C[subscript 2] and LiF by Natural Bond Order Analysis	p. 110
Summary and Conclusions	p. 114
References	p. 115
Chapter 6 Geometry Optimization and Vibrational Frequencies by SCF
Introduction	p. 117
The SCF-Roothaan Calculation in PCLOBE	p. 118
Geometry	p. 118
Basis	p. 119
Contraction and Weighting	p. 120
Lobe Representations of p Functions	p. 120
Symmetry and the Basis	p. 120
Overlap Matrix	p. 121
Solution of the SCF Equation: Dealing with the Overlapping Basis	p. 121
Construct the Core Matrix Representing the Kinetic Energy and Nuclear-Electron Attraction	p. 122
Approximate the Fock Matrix and Solve the Secular Equation	p. 122
Begin the Iterative Solution of the SCF Equation-Guess MOs	p. 123
Symmetry Labeling the MOs	p. 123
Evaluate the Density Matrix	p. 124
Repulsion Integrals	p. 124
Continue the Iteration	p. 126
Test for Convergence	p. 126
Inspect the Output: MOs and Energies	p. 127
Describe the Charge Distribution	p. 128
Molecular Structure Determination by Energy Minimization	p. 130
Derivative of the Hartree-Fock Energy	p. 130
Search Techniques Using the Gradient	p. 132
Geometry Optimization in PCLOBE	p. 133
Begin with the Steepest Descents Approach to a Minimum	p. 134
Second Derivatives of the Hartree-Fock Energy and Vibrational Spectra	p. 136
SCF Calculation Revisited: Alternatives and Points of Contention	p. 140
Impure Symmetry of Properties Computed in the Contracted Lobe Basis	p. 143
Completeness and Linear Dependence in the Lobe Basis	p. 143
Management of Two-Electron Integrals	p. 143
Assembly of the Fock Matrix	p. 144
Convergence of the Iterative Solution	p. 144
Reoptimization of Formaldehyde in an Extended Basis	p. 145
Historical Landmark: The Accomplishment of Boys	p. 153
References	p. 156
Chapter 7 Configuration Interaction and Potential Curves
Configuration Interaction in General	p. 159
Slater Determinant MO-CI	p. 160
CI Without Canonical Orbitals	p. 162
Pauling Valence Bond and CI	p. 162
Boys-Reeves CI (MOVB)	p. 165
Resolution of an MOVB-CI Wave Function into Leading Excitations	p. 165
Sydnone CI	p. 171
CI and Potential Curves	p. 172
Three Descriptions of Dissociation of the Hydrogen Molecule	p. 174
MOVB-CI for BH	p. 175
MOVB-CI of Formaldehyde Dissociation	p. 179
MCSCF and CASSCF: Achieving Proper Dissociation for Larger Systems	p. 181
Conclusions	p. 184
References	p. 185
Chapter 8 Perturbation Theory
First-Order Correction to a Nondegenerate Reference System	p. 187
Second-Order Correction-Nondegenerate Case	p. 189
The Morse Potential	p. 192
The Degenerate Case	p. 193
Perturbation Theory in Approximate MO Theory	p. 196
MP2 as Perturbation Theory	p. 198
Time-Dependent Perturbation Theory	p. 200
Hamiltonian for Matter in an Electromagnetic Field	p. 202
Time-Dependent Perturbation Theory for Charged Particles in the Electromagnetic Field	p. 203
Length-Velocity Relationship	p. 207
Response Theory	p. 209
References	p. 210
Chapter 9 Highly Accurate Methods: Coupled Cluster Calculations, Extrapolation to Chemical Accuracy, and Quantum Monte Carlo Methods
Aspiration to Chemical Accuracy	p. 211
An Aerial View of CC	p. 212
Theoretical Foundations	p. 213
A Notational Convenience: Creation and Annihilation Operators	p. 215
Specification of the T Operators	p. 216
The Size Consistency Issue in CC and CI	p. 217
Solving the CC Equations	p. 219
CC-Doubles Approximation	p. 219
Imminent Developments	p. 222
Beyond CCSD	p. 223
Performance of CCSD(T)	p. 224
Application to Isomer Energies	p. 232
Thermochemical Standards by Quantum Chemistry	p. 235
Aspiration to Exact Description: Quantum Monte Carlo Calculations	p. 240
Random (?) Numbers	p. 241
Anderson's Intuitive Application of Randomness	p. 242
An Early Example of Diffusion Quantum Monte Carlo Calculation	p. 244
Shortcuts: Pseudopotentials and the Sparse Algorithm	p. 248
Formaldehyde (Again) by QMC	p. 248
Conclusion	p. 250
References	p. 251
Chapter 10 Modeling the Coulomb Hole
The Fermi Hole and Exchange-Correlation	p. 256
Coulomb Correlation Hole	p. 256
Applying the Correlated-SCF Method to Hydroxylamine	p. 265
Summary	p. 267
References	p. 267
Chapter 11 Density Functional Theory
Introduction	p. 269
John Perdew's Ladder	p. 270
Early Forms of Density Functional Theory: Gill's History	p. 271
Thomas-Fermi-Dirac Theory	p. 271
The Hohenberg-Kohn Existence Theorem	p. 273
Kohn-Sham Procedure for Finding the Density	p. 274
DFT and SCF Calculations Have Common Features	p. 275
Search for the Functionals	p. 276
The Idea of the Hole	p. 277
Evaluating the DFT Energy Using Functionals (Slater)	p. 278
More on the Local Density Approximation's Hole	p. 279
Refinements to the VWN Exchange-Correlation Functionals	p. 280
Perdew Functionals	p. 280
Becke Functionals	p. 282
Lee-Yang-Parr Correlation	p. 283
The Adiabatic Connection and Hybrid Functionals	p. 284
Becke 1995-Impact of Imposing Constraints	p. 286
PBE Exchange-Correlation Functional	p. 288
Correlation Effects on Kinetic Energy	p. 293
TPSS Functional	p. 295
The Empirical Thread	p. 299
The Zhao-Truhlar M06-L DFT Functional	p. 300
M06-L Meta-GGA Correlation Functional	p. 301
Position-Dependent Exchange	p. 304
The Iterative Localized Local Hybrid Method, LLH	p. 308
Gridless!	p. 310
Resolution of the Identity	p. 310
A Gridless DFT Method Using Least-Squares Slater Exchange	p. 312
Slater-Roothaan SCF	p. 313
Two DFT-Focussed Programs	p. 315
The Amsterdam Density Functional Suite	p. 315
SAOP: A Fourth-Rung Exchange-Correlation Model for Excitations	p. 316
deMon2k	p. 319
Summary, Conclusions, and Overview	p. 330
Appendix: Technical Aspects of DFT Calculations	p. 333
Grid-Mesh Integration in DFT Programs	p. 333
Representation of the Density by Auxiliary Basis Functions	p. 335
Appendix References	p. 338
References	p. 339
Chapter 12 Calculation of Nuclear Magnetic Resonance Shielding/Shifts
Introduction	p. 343
Ramsey Theory	p. 344
Challenges to Use of Ramsey's Form	p. 345
Excitations	p. 345
Gauge Origin	p. 346
Semiempirical Adaptions of Ramsey's Formalism	p. 346
Ditchfield's Formalism	p. 347
Coupled Perturbed Hartree-Fock Method	p. 350
First Results of Calculations in Ditchfield's Formulation	p. 352
Ditchfield's Formulation in GAMESS	p. 353
Runtype	p. 354
Basis	p. 355
Already Familiar!	p. 359
Charge Analysis	p. 359
Timing	p. 360
NMR Report	p. 360
Ditchfield's Formulation in GAUSSIAN-03	p. 361
Use of Localized Orbitals in NMR-Shielding Calculations	p. 361
Individual Gauge for Local Orbitals	p. 362
RPAC Program (LORG)	p. 363
Subtleties of Orbital Localization	p. 367
Correlation Corrections and NMR Shielding: DFT	p. 368
GAUSSIAN-03 NMR Shifts: DFT-Based Values of Shielding	p. 369
CSGT Method (Continuous Set of Gauge Transformations)	p. 370
Practical Use of Calculated Chemical Shifts	p. 372
Chemical Shifts of Taxol	p. 374
Advances in DFT-Based NMR	p. 375
Keal and Tozer	p. 375
Arbuznikov et al.	p. 377
The Question of Coupling and Fine Structure	p. 380
Perturbative Correlation-Corrected Methods for Shielding	p. 381
ACES-II Coupled Cluster Calculation of NMR Properties	p. 382
Conclusion	p. 386
References	p. 386
Predicting Magnetic Properties with ChemDraw and Gaussian	p. 388
Chapter 13 The Representation of Electronically Excited States
Introduction	p. 389
CI-Singles	p. 389
Practical Use of the CIS Equations	p. 391
Singlet and Triplet State Energies for the 1G Model	p. 392
PCLOBE Illustration of CIS	p. 394
Structural Relaxation in the Excited State	p. 400
Case Study for Formaldehyde	p. 401
Correlation Corrections	p. 402
Time-Dependent Hartree-Fock Treatments of Excitations	p. 403
Formaldehyde Again	p. 404
A Case Study-Sulfur Dioxide	p. 405
Adaptation of the Time-Dependent Formalism to DFT	p. 407
Applications	p. 409
Sulfur Dioxide in TD-DFT	p. 409
Pyridine in TD-B3LYP	p. 410
Pyrrole in B3LYP-DFT	p. 411
Substituted Aniline	p. 412
CCSD-EOM Treatment of Excited States	p. 413
Conclusions	p. 414
References	p. 415
Chapter 14 Circular Dichroism and Optical Rotatory Dispersion
The Phenomenon of Optical Rotation	p. 417
PCLOBE Modeling of CD Spectra	p. 421
Examples of CD/ORD Computations with PCLOBE	p. 422
[alpha]-Pinene	p. 426
Ways to Improve CD and ORD Calculations	p. 433
Use GIAOs	p. 433
Use Linear Response Theory	p. 434
Use Correlation-Corrected Methods (Time-Dependent DFT, CCSD)	p. 435
Methyloxirane: A Hard Case	p. 435
Optical Rotatory Dispersion for Methyloxirane	p. 437
Experimental Data and Advanced Calculations for Methyloxirane	p. 439
A Brighter View	p. 442
Specific Examples	p. 443
The Phenomenon of Magnetic Circular Dichroism	p. 447
Theory of MCD	p. 448
PCLOBE Modeling of Rings	p. 450
Formaldehyde MCD	p. 451
CIS Output: Excited States	p. 456
MCD-A Challenge to Modern Theory	p. 465
Note on Units for Optical Activity	p. 468
Summary and Conclusions	p. 470
Acknowledgments	p. 470
References	p. 471
Index	p. 473

Available:*

On Order

Summary

Summary

Author Notes

Table of Contents