Introduction to computational chemistry:
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Chichester [u.a.]
Wiley
2007
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Beschreibung für Leser Table of contents only Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke Includes bibliographical references and index |
| Physical Description: | XX, 599 S. Ill., graph. Darst. |
| ISBN: | 9780470011867 9780470011874 0470011866 0470011874 |
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| 100 | 1 | |a Jensen, Frank |d 1961- |e Verfasser |0 (DE-588)141010312 |4 aut | |
| 245 | 1 | 0 | |a Introduction to computational chemistry |c Frank Jensen |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Chichester [u.a.] |b Wiley |c 2007 | |
| 300 | |a XX, 599 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Chimie physique et théorique | |
| 650 | 4 | |a Chimie physique et théorique - Informatique | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Chemistry, Physical and theoretical |x Data processing | |
| 650 | 4 | |a Chemistry, Physical and theoretical |x Mathematics | |
| 650 | 0 | 7 | |a Computational chemistry |0 (DE-588)4290091-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Computersimulation |0 (DE-588)4148259-1 |2 gnd |9 rswk-swf |
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| 856 | 4 | |u http://www.loc.gov/catdir/toc/ecip0617/2006023998.html |3 Table of contents only | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014945664&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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| _version_ | 1804135579422556160 |
|---|---|
| adam_text | Contents
Preface
to the First Edition
xv
Preface to the Second Edition
xix
1
Introduction
1
1.1
Fundamental Issues
2
1.2
Describing the System
3
1.3
Fundamental Forces
4
1.4
The Dynamical Equation
5
1.5
Solving the Dynamical Equation
8
1.6
Separation of Variables
8
1.6.1
Separating space and time variables
10
1.6.2
Separating nuclear and electronic variables
10
1.6.3
Separating variables in general
11
1.7
Classical Mechanics
12
1.7.1
The Sun-Earth system
12
1.7.2
The solar system
13
1.8
Quantum Mechanics
14
1.8.1
A hydrogen-like atom
14
1.8.2
The helium atom
17
1.9
Chemistry
19
References
21
2
Force Field Methods
22
2.1
Introduction
22
2.2
The Force Field Energy
24
2.2.1
The stretch energy
25
2.2.2
The bending energy
27
2.2.3
The out-of-plane bending energy
30
2.2.4
The
torsionai
energy
30
2.2.5
The van
der Waals
energy
34
2.2.6
The electrostatic energy: charges and dipoles
40
2.2.7
The electrostatic energy: multipoles and polarizabilities
43
vi
CONTENTS
2.2.8
Cross
terms
47
2.2.9
Small rings and conjugated systems
48
2.2.10
Comparing energies of structurally different molecules
50
2.3
Force Field Parameterization
51
2.3.1
Parameter reductions in force fields
57
2.3.2
Force fields for metal coordination compounds
58
2.3.3
Universal force fields
62
2.4
Differences in Force Fields
62
2.5
Computational Considerations
65
2.6
Validation of Force Fields
67
2.7
Practical Considerations
69
2.8
Advantages and Limitations of Force Field Methods
69
2.9
Transition Structure Modelling
70
2.9.1
Modelling the TS as a minimum energy structure
70
2.9.2
Modelling the TS as a minimum energy structure on the reactant/
product energy seam
71
2.9.3
Modelling the reactive energy surface by interacting force
field functions or by geometry-dependent parameters
73
2.10
Hybrid Force Field Electronic Structure Methods
74
References
77
3
Electronic Structure Methods: Independent-Particle Models
80
3.1
The Adiabatic and Bom-Oppenheimer Approximations
82
3.2
Self-Consistent Field Theory
86
3.3
The Energy of a Slater Determinant
87
3.4
Koopmans Theorem
92
3.5
The Basis Set Approximation
93
3.6
An Alternative Formulation of the Variational Problem
98
3.7
Restricted and Unrestricted Hartree-Fock
99
3.8
SCF Techniques
100
3.8.1
SCF convergence
101
3.8.2
Use of symmetry
104
3.8.3
Ensuring that the HF energy is a minimum, and the
correct minimum
105
3.8.4
Initial guess
orbitais
107
3.8.5
Direct SCF
108
3.8.6
Reduced scaling techniques
110
3.9
Periodic Systems
113
3.10
Semi-Empirical Methods
115
3.10.1
Neglect of Diatomic Differential Overlap Approximation (NDDO)
116
3.10.2
Intermediate Neglect of Differential Overlap Approximation
(INDO)
117
3.10.3
Complete Neglect of Differential Overlap Approximation (CNDO)
117
3.11
Parameterization
118
3.11.1
Modified Intermediate Neglect of Differential Overlap (MINDO)
119
3.11.2
Modified NDDO models
119
3.11.3
Modified Neglect of Diatomic Overlap
(MND0)
121
3.11.4
Austin Model
1
(AMI)
121
3.11.5
Modified Neglect of Diatomic Overtap, Parametric Method Number
3
(PM3)
122
3.11.6
Parametric Method number
5
(PM5) and PDDG/PM3 methods
123
CONTENTS
vii
3.11.7
The MNDO/d and AMl/d methods
124
3.11.8
Semi Ab initio
Method
1 124
3.12
Performance of Semi-Empirical Methods
125
3.13
Hiickel Theory
127
3.13.1
Extended Hiickel theory
127
3.13.2
Simple Hiickel theory
128
3.14
Limitations and Advantages of Semi-Empirical Methods
129
References
131
4
Electron Correlation Methods
133
4.1
Excited Slater Determinants
135
4.2
Configuration Interaction
137
4.2.1
CI
Matrix elements
138
4.2.2
Size of the
CI
matrix
141
4.2.3
Truncated
CI
methods
143
4.2.4
Direct
CI
methods
144
4.3
Illustrating how
CI
Accounts for Electron Correlation, and the
RHF Dissociation Problem
145
4.4
The
UHF
Dissociation, and the Spin Contamination Problem
148
4.5
Size Consistency and Size Extensivity
153
4.6
Multi-Configuration Self-Consistent Field
153
4.7
Multi-Reference Configuration Interaction
158
4.8
Many-Body Perturbation Theory
159
4.8.1
Meller-Plesset perturbation theory
162
4.8.2
Unrestricted and projected
M0tter-Plesset
methods
168
4.9
Coupled Cluster
169
4.9.1
Truncated coupled cluster methods
172
4.10
Connections between Coupled Cluster, Configuration Interaction
and Perturbation Theory
174
4.10.1
Illustrating correlation methods for the beryllium atom
177
4.11
Methods Involving the Interelectronic Distance
178
4.12
Direct Methods
181
4.13
Localized Orbital Methods
182
4.14
Summary of Electron Correlation Methods
183
4.15
Excited States
186
4.16
Quantum Monte Carlo Methods
187
References
189
5
Basis Sets
192
5.1
Slater and Gaussian Type
Orbitals 192
5.2
Classification of Basis Sets
194
5.3
Even- and Well-Tempered Basis Sets
198
5.4
Contracted Basis Sets
200
5.4.1
Pople style basis sets
202
5.4.2
Dunning-Huzinaga basis sets
204
5.4.3
MINI, MIDI and
MAXI
basis sets
205
5.4.4
Ahlrichs type basis sets
205
5.4.5
Atomic natural orbital basis sets
205
5.4.6
Correlation consistent basis sets
206
viii CONTENTS
5.4.7
Polarization consistent basis sets
207
5.4.8
Basis set extrapolation
208
5.5
Plane Wave Basis Functions
211
5.6
Recent Developments and Computational Issues
212
5.7
Composite Extrapolation Procedures
213
5.8
Isogyric and Isodesmic Reactions
221
5.9
Effective Core Potentials
222
5.10
Basis Set Superposition Errors
225
5.11
Pseudospectral
Methods
227
References
229
6
Density Functional Methods
232
6.1
Orbital-Free Density Functional Theory
233
6.2
Kohn-Sham Theory
235
6.3
Reduced Density Matrix Methods
236
6.4
Exchange and Correlation Holes
240
6.5
Exchange-Correlation Functionals
243
6.5.1
Local Density Approximation
246
6.5.2
Gradient-corrected methods
248
6.5.3
Higher order gradient or meta-GGA methods
250
6.5.4
Hybrid or hyper-GGA methods
252
6.5.5
Generalized random phase methods
253
6.5.6
Functionals overview
254
6.6
Performance and Properties of Density Functional Methods
255
6.7
DFT Problems
258
6.8
Computational Considerations
260
6.9
Final Considerations
263
References
264
7
Valence Bond Methods
268
7.1
Classical Valence Bond Theory
269
7.2
Spirt-Coupled Valence Bond Theory
270
7.3
Generalized Valence Bond Theory
275
References
276
8
Relativist* Methods
277
8.1
The Dirac Equation
278
8.2
Connections Between the Dirac and
Schrödinger
Equations
280
8.2.1
Including electric potentials
280
8.2.2
Including both electric and magnetic potentials
282
8.3
Many-Particle Systems
284
8.4
Four-Component Calculations
287
8.5
Relativistic Effects
289
References
292
9
Wave Function Analysis
293
9.1
Population Analysis Based on Basis Functions
293
9.2
Population Analysis Based on the Electrostatic Potential
296
CONTENTS ix
9.3 Population
Analysis Based on the Electron Density
299
9.3.1
Atoms In Molecules
299
9.3.2
Voronoi, Hirshfeld and Stewart atomic charges
303
9.3.3
Generalized atomic polar tensor charges
304
9.4
Localized
Orbitals 304
9.4.1
Computational considerations
306
9.5
Natural
Orbitals 308
9.6
Natural Atomic Orbital and Natural Bond Orbital Analysis
309
9.7
Computational Considerations
311
9.8
Examples
312
References
313
10
Molecular Properties
315
316
316
318
318
319
319
321
321
324
325
329
329
329
329
331
332
333
333
334
334
338
10.8
Geometry Perturbations
339
10.9
Response and Propagator Methods
343
10.10
Property Basis Sets
348
References
349
11
Illustrating the Concepts
350
11.1
Geometry Convergence
350
11.1.1 Ab Initio
methods
350
11.1.2
Density functional methods
353
11.2
Total Energy Convergence
354
11.3 Dipole
Moment Convergence
356
11.3.1 Ab
Initio methods
356
11.3.2
Density functional methods
357
11.4
Vibrational Frequency Convergence
358
11.4.1 Ab
Initio methods
358
11.4.2
Density functional methods
360
10.1
Examples of Molecular Properties
10.1.1
External electric field
10.1.2
External magnetic field
10.1.3
Internal magnetic moments
10.1.4
Geometry change
10.1.5
Mixed derivatives
10.2
Perturbation Methods
10.3
Derivative Techniques
10.4
Lagrangian Techniques
10.5
Coupled
Perturbed Hartree-Fock
10.6
Electric
Field Perturbation
10.6.1
External electric field
10.6.2
Internal electric field
10.7
Magnetic Field Perturbation
10.7.1
External magnetic field
10.7.2
Nuclear spin
10.7.3
Electron spin
10.7.4
Classical terms
10.7.5
Relativistic terms
10.7.6
Magnetic properties
10.7.7
Gauge dependence of magnetic properties
x
CONTENTS
11.5
Bond Dissociation Curves
361
11.5.1
Basis set effect at the Hartree-Fock level
361
11.5.2
Performance of different types of wave function
363
11.5.3
Density functional methods
369
11.6
Angle Bending Curves
370
11.7
Problematic Systems 370
11.7.1
The geometry of FOOF
371
11.7.2
The
dipole
moment of CO
372
11.7.3
The vibrational frequencies of 03
373
11.8
Relative Energies of C4H6 Isomers
374
References
378
12
Optimization Techniques
380
12.1
Optimizing Quadratic Functions
381
12.2
Optimizing General Functions: Finding Minima
383
12.2.1
Steepest descent
383
12.2.2
Conjugate gradient methods
384
12.2.3
Newton-Raphson methods
385
12.2.4
Step control
386
12.2.5
Obtaining the Hessian
387
12.2.6
Storing and diagonalizing the Hessian
388
12.2.7
Extrapolations: the GDIIS method
389
12.3
Choice of Coordinates
390
12.4
Optimizing General Functions: Finding Saddle Points (Transition Structures)
394
12.4.1
One-structure interpolation methods: coordinate driving,
linear and quadratic synchronous transit, and sphere
optimization
394
12.4.2
Two-structure interpolation methods: saddle, line-then-
plane, ridge and step-and-slide optimizations
397
12.4.3
Multi-structure interpolation methods: chain, locally
updated planes, self-penalty walk, conjugate peak
refinement and nudged elastic band
398
12.4.4
Characteristics of interpolation methods
401
12.4.5
Local methods: gradient norm minimization
402
12.4.6
Local methods: Newton-Raphson
403
12.4.7
Local methods: the dimer method
405
12.4.8
Coordinates for TS searches
405
12.4.9
Characteristics of local methods
406
12.4.10
Dynamic methods
406
12.5
Constrained Optimization Problems
407
12.6
Conformational Sampling and the Global Minimum Problem
409
12.6.1
Stochastic and Monte
Carto
methods
411
12.6.2
Molecular dynamics
412
12.6.3
Simulated annealing
413
12.6.4
Genetic algorithms
413
12.6.5
Diffusion methods
414
12.6.6
Distance geometry methods
414
12.7
Molecular Docking
415
12.8
Intrinsic Reaction Coordinate Methods
416
References
419
CONTENTS xi
13
Statisticei
Mechanics and Transition State Theory
421
13.1
Transition State Theory
421
13.2
Rice-Ramsperger-Kassel-Marcus Theory
424
13.3
Dynamical Effects
425
13.4
Statistical Mechanics
426
13.5
The Ideal Gas, Rigid-Rotor Harmonic-Oscillator Approximation
429
13.5.1
Translational degrees of freedom
430
13.5.2
Rotational degrees of freedom
430
13.5.3
Vibrational degrees of freedom
431
13.5.4
Electronic degrees of freedom
433
13.5.5
Enthalpy and entropy contributions
433
13.6
Condensed Phases
439
References
443
14
Simulation Techniques
445
14.1
Monte Carlo Methods
448
14.1.1
Generating non-natural ensembles
450
14.2
Time-Dependent Methods
450
14.2.1
Molecular dynamics methods
451
14.2.2
Generating non-natural ensembles
454
14.2.3
Langevin
methods
455
14.2.4
Direct methods
455
14.2.5
Extended
Lagrange
techniques (Car-Parrinello methods)
457
14.2.6
Quantum methods using potential energy surfaces
459
14.2.7
Reaction path methods
460
14.2.8
Non-Born-Oppenheimer methods
463
14.2.9
Constrained sampling methods
463
14.3
Periodic Boundary Conditions
464
14.4
Extracting Information from Simulations
468
14.5
Free Energy Methods
472
14.5.1
Thermodynamic perturbation methods
472
14.5.2
Thermodynamic integration methods
473
14.6
Solvation Models
475
14.7
Continuum Solvation Models
476
14.7.1
Poisson-Boltzmann methods
478
14.7.2
Born/Onsager/Kirkwood models
480
14.7.3
Self-consistent reaction field models
481
References
484
15
Qualitative Theories
487
15.1
Frontier Molecular Orbital Theory
487
15.2
Concepts from Density Functional Theory
492
15.3
Qualitative Molecular Orbital Theory
494
15.4
Woodward-Hoffmann Rules
497
15.5
The Bell-Evans-Polanyi Principle/Hammond Postulate/Marcus Theory
506
15.6
More
O Ferrall-űencks
Diagrams
510
References
512
xii CONTENTS
16
Mathematical Methods
514
16.1
Numbers, Vectors, Matrices and Tensors
514
16.2
Change of Coordinate System
520
16.2.1
Examples of changing the coordinate system
525
16.2.2
Vibrational normal coordinates
526
16.2.3
Energy of a Slater determinant
528
16.2.4
Energy of
a CI
wave function
529
16.2.5
Computational Consideration
529
16.3
Coordinates, Functions, Functionals, Operators and
Superoperators
530
16.3.1
Differential operators
531
16.4
Normalization, Orthogonalization and Projection
532
16.5
Differential Equations
535
16.5.1
Simple first-order differential equations
535
16.5.2
Less simple first-order differential equations
536
16.5.3
Simple second-order differential equations
536
16.5.4
Less simple second-order differential equations
537
16.5.5
Second-order differential equations depending on the
function itself
537
16.6
Approximating Functions
538
16.6.1
Taylor expansion
539
16.6.2
Basis set expansion
541
16.7
Fourier and Laplace Transformations
541
16.8
Surfaces
543
References
546
17
Statistics and QSAR
547
17.1
Introduction
547
17.2
Elementary Statistical Measures
549
17.3
Correlation Between Two Sets of Data
550
17.4
Correlation between Many Sets of Data
553
17.4.1
Multiple-descriptor data sets and quality analysis
553
17.4.2
Multiple linear regression
555
17.4.3
Principal component and partial least squares analysis
556
17.4.4
Illustrative example
558
17.5
Quantitative Structure-Activity Relationships (QSAR)
559
References
561
18
Concluding Remarks
562
Appendix A
565
Notation
565
Appendix
В
570
B.I The Variationat Principle
570
B.2 The Hohenberg-Kohn Theorems
571
B.3 The Adiabatic Connection Formula
572
Reference
573
CONTENTS xiii
Appendix
С
574
Atomic Units
574
Appendix
D
575
Z-Matrix Construction
575
Index
583
|
| adam_txt |
Contents
Preface
to the First Edition
xv
Preface to the Second Edition
xix
1
Introduction
1
1.1
Fundamental Issues
2
1.2
Describing the System
3
1.3
Fundamental Forces
4
1.4
The Dynamical Equation
5
1.5
Solving the Dynamical Equation
8
1.6
Separation of Variables
8
1.6.1
Separating space and time variables
10
1.6.2
Separating nuclear and electronic variables
10
1.6.3
Separating variables in general
11
1.7
Classical Mechanics
12
1.7.1
The Sun-Earth system
12
1.7.2
The solar system
13
1.8
Quantum Mechanics
14
1.8.1
A hydrogen-like atom
14
1.8.2
The helium atom
17
1.9
Chemistry
19
References
21
2
Force Field Methods
22
2.1
Introduction
22
2.2
The Force Field Energy
24
2.2.1
The stretch energy
25
2.2.2
The bending energy
27
2.2.3
The out-of-plane bending energy
30
2.2.4
The
torsionai
energy
30
2.2.5
The van
der Waals
energy
34
2.2.6
The electrostatic energy: charges and dipoles
40
2.2.7
The electrostatic energy: multipoles and polarizabilities
43
vi
CONTENTS
2.2.8
Cross
terms
47
2.2.9
Small rings and conjugated systems
48
2.2.10
Comparing energies of structurally different molecules
50
2.3
Force Field Parameterization
51
2.3.1
Parameter reductions in force fields
57
2.3.2
Force fields for metal coordination compounds
58
2.3.3
Universal force fields
62
2.4
Differences in Force Fields
62
2.5
Computational Considerations
65
2.6
Validation of Force Fields
67
2.7
Practical Considerations
69
2.8
Advantages and Limitations of Force Field Methods
69
2.9
Transition Structure Modelling
70
2.9.1
Modelling the TS as a minimum energy structure
70
2.9.2
Modelling the TS as a minimum energy structure on the reactant/
product energy seam
71
2.9.3
Modelling the reactive energy surface by interacting force
field functions or by geometry-dependent parameters
73
2.10
Hybrid Force Field Electronic Structure Methods
74
References
77
3
Electronic Structure Methods: Independent-Particle Models
80
3.1
The Adiabatic and Bom-Oppenheimer Approximations
82
3.2
Self-Consistent Field Theory
86
3.3
The Energy of a Slater Determinant
87
3.4
Koopmans' Theorem
92
3.5
The Basis Set Approximation
93
3.6
An Alternative Formulation of the Variational Problem
98
3.7
Restricted and Unrestricted Hartree-Fock
99
3.8
SCF Techniques
100
3.8.1
SCF convergence
101
3.8.2
Use of symmetry
104
3.8.3
Ensuring that the HF energy is a minimum, and the
correct minimum
105
3.8.4
Initial guess
orbitais
107
3.8.5
Direct SCF
108
3.8.6
Reduced scaling techniques
110
3.9
Periodic Systems
113
3.10
Semi-Empirical Methods
115
3.10.1
Neglect of Diatomic Differential Overlap Approximation (NDDO)
116
3.10.2
Intermediate Neglect of Differential Overlap Approximation
(INDO)
117
3.10.3
Complete Neglect of Differential Overlap Approximation (CNDO)
117
3.11
Parameterization
118
3.11.1
Modified Intermediate Neglect of Differential Overlap (MINDO)
119
3.11.2
Modified NDDO models
119
3.11.3
Modified Neglect of Diatomic Overlap
(MND0)
121
3.11.4
Austin Model
1
(AMI)
121
3.11.5
Modified Neglect of Diatomic Overtap, Parametric Method Number
3
(PM3)
122
3.11.6
Parametric Method number
5
(PM5) and PDDG/PM3 methods
123
CONTENTS
vii
3.11.7
The MNDO/d and AMl/d methods
124
3.11.8
Semi Ab initio
Method
1 124
3.12
Performance of Semi-Empirical Methods
125
3.13
Hiickel Theory
127
3.13.1
Extended Hiickel theory
127
3.13.2
Simple Hiickel theory
128
3.14
Limitations and Advantages of Semi-Empirical Methods
129
References
131
4
Electron Correlation Methods
133
4.1
Excited Slater Determinants
135
4.2
Configuration Interaction
137
4.2.1
CI
Matrix elements
138
4.2.2
Size of the
CI
matrix
141
4.2.3
Truncated
CI
methods
143
4.2.4
Direct
CI
methods
144
4.3
Illustrating how
CI
Accounts for Electron Correlation, and the
RHF Dissociation Problem
145
4.4
The
UHF
Dissociation, and the Spin Contamination Problem
148
4.5
Size Consistency and Size Extensivity
153
4.6
Multi-Configuration Self-Consistent Field
153
4.7
Multi-Reference Configuration Interaction
158
4.8
Many-Body Perturbation Theory
159
4.8.1
Meller-Plesset perturbation theory
162
4.8.2
Unrestricted and projected
M0tter-Plesset
methods
168
4.9
Coupled Cluster
169
4.9.1
Truncated coupled cluster methods
172
4.10
Connections between Coupled Cluster, Configuration Interaction
and Perturbation Theory
174
4.10.1
Illustrating correlation methods for the beryllium atom
177
4.11
Methods Involving the Interelectronic Distance
178
4.12
Direct Methods
181
4.13
Localized Orbital Methods
182
4.14
Summary of Electron Correlation Methods
183
4.15
Excited States
186
4.16
Quantum Monte Carlo Methods
187
References
189
5
Basis Sets
192
5.1
Slater and Gaussian Type
Orbitals 192
5.2
Classification of Basis Sets
194
5.3
Even- and Well-Tempered Basis Sets
198
5.4
Contracted Basis Sets
200
5.4.1
Pople style basis sets
202
5.4.2
Dunning-Huzinaga basis sets
204
5.4.3
MINI, MIDI and
MAXI
basis sets
205
5.4.4
Ahlrichs type basis sets
205
5.4.5
Atomic natural orbital basis sets
205
5.4.6
Correlation consistent basis sets
206
viii CONTENTS
5.4.7
Polarization consistent basis sets
207
5.4.8
Basis set extrapolation
208
5.5
Plane Wave Basis Functions
211
5.6
Recent Developments and Computational Issues
212
5.7
Composite Extrapolation Procedures
213
5.8
Isogyric and Isodesmic Reactions
221
5.9
Effective Core Potentials
222
5.10
Basis Set Superposition Errors
225
5.11
Pseudospectral
Methods
227
References
229
6
Density Functional Methods
232
6.1
Orbital-Free Density Functional Theory
233
6.2
Kohn-Sham Theory
235
6.3
Reduced Density Matrix Methods
236
6.4
Exchange and Correlation Holes
240
6.5
Exchange-Correlation Functionals
243
6.5.1
Local Density Approximation
246
6.5.2
Gradient-corrected methods
248
6.5.3
Higher order gradient or meta-GGA methods
250
6.5.4
Hybrid or hyper-GGA methods
252
6.5.5
Generalized random phase methods
253
6.5.6
Functionals overview
254
6.6
Performance and Properties of Density Functional Methods
255
6.7
DFT Problems
258
6.8
Computational Considerations
260
6.9
Final Considerations
263
References
264
7
Valence Bond Methods
268
7.1
Classical Valence Bond Theory
269
7.2
Spirt-Coupled Valence Bond Theory
270
7.3
Generalized Valence Bond Theory
275
References
276
8
Relativist* Methods
277
8.1
The Dirac Equation
278
8.2
Connections Between the Dirac and
Schrödinger
Equations
280
8.2.1
Including electric potentials
280
8.2.2
Including both electric and magnetic potentials
282
8.3
Many-Particle Systems
284
8.4
Four-Component Calculations
287
8.5
Relativistic Effects
289
References
292
9
Wave Function Analysis
293
9.1
Population Analysis Based on Basis Functions
293
9.2
Population Analysis Based on the Electrostatic Potential
296
CONTENTS ix
9.3 Population
Analysis Based on the Electron Density
299
9.3.1
Atoms In Molecules
299
9.3.2
Voronoi, Hirshfeld and Stewart atomic charges
303
9.3.3
Generalized atomic polar tensor charges
304
9.4
Localized
Orbitals 304
9.4.1
Computational considerations
306
9.5
Natural
Orbitals 308
9.6
Natural Atomic Orbital and Natural Bond Orbital Analysis
309
9.7
Computational Considerations
311
9.8
Examples
312
References
313
10
Molecular Properties
315
316
316
318
318
319
319
321
321
324
325
329
329
329
329
331
332
333
333
334
334
338
10.8
Geometry Perturbations
339
10.9
Response and Propagator Methods
343
10.10
Property Basis Sets
348
References
349
11
Illustrating the Concepts
350
11.1
Geometry Convergence
350
11.1.1 Ab Initio
methods
350
11.1.2
Density functional methods
353
11.2
Total Energy Convergence
354
11.3 Dipole
Moment Convergence
356
11.3.1 Ab
Initio methods
356
11.3.2
Density functional methods
357
11.4
Vibrational Frequency Convergence
358
11.4.1 Ab
Initio methods
358
11.4.2
Density functional methods
360
10.1
Examples of Molecular Properties
10.1.1
External electric field
10.1.2
External magnetic field
10.1.3
Internal magnetic moments
10.1.4
Geometry change
10.1.5
Mixed derivatives
10.2
Perturbation Methods
10.3
Derivative Techniques
10.4
Lagrangian Techniques
10.5
Coupled
Perturbed Hartree-Fock
10.6
Electric
Field Perturbation
10.6.1
External electric field
10.6.2
Internal electric field
10.7
Magnetic Field Perturbation
10.7.1
External magnetic field
10.7.2
Nuclear spin
10.7.3
Electron spin
10.7.4
Classical terms
10.7.5
Relativistic terms
10.7.6
Magnetic properties
10.7.7
Gauge dependence of magnetic properties
x
CONTENTS
11.5
Bond Dissociation Curves
361
11.5.1
Basis set effect at the Hartree-Fock level
361
11.5.2
Performance of different types of wave function
363
11.5.3
Density functional methods
369
11.6
Angle Bending Curves
370
11.7
Problematic Systems 370
11.7.1
The geometry of FOOF
371
11.7.2
The
dipole
moment of CO
372
11.7.3
The vibrational frequencies of 03
373
11.8
Relative Energies of C4H6 Isomers
374
References
378
12
Optimization Techniques
380
12.1
Optimizing Quadratic Functions
381
12.2
Optimizing General Functions: Finding Minima
383
12.2.1
Steepest descent
383
12.2.2
Conjugate gradient methods
384
12.2.3
Newton-Raphson methods
385
12.2.4
Step control
386
12.2.5
Obtaining the Hessian
387
12.2.6
Storing and diagonalizing the Hessian
388
12.2.7
Extrapolations: the GDIIS method
389
12.3
Choice of Coordinates
390
12.4
Optimizing General Functions: Finding Saddle Points (Transition Structures)
394
12.4.1
One-structure interpolation methods: coordinate driving,
linear and quadratic synchronous transit, and sphere
optimization
394
12.4.2
Two-structure interpolation methods: saddle, line-then-
plane, ridge and step-and-slide optimizations
397
12.4.3
Multi-structure interpolation methods: chain, locally
updated planes, self-penalty walk, conjugate peak
refinement and nudged elastic band
398
12.4.4
Characteristics of interpolation methods
401
12.4.5
Local methods: gradient norm minimization
402
12.4.6
Local methods: Newton-Raphson
403
12.4.7
Local methods: the dimer method
405
12.4.8
Coordinates for TS searches
405
12.4.9
Characteristics of local methods
406
12.4.10
Dynamic methods
406
12.5
Constrained Optimization Problems
407
12.6
Conformational Sampling and the Global Minimum Problem
409
12.6.1
Stochastic and Monte
Carto
methods
411
12.6.2
Molecular dynamics
412
12.6.3
Simulated annealing
413
12.6.4
Genetic algorithms
413
12.6.5
Diffusion methods
414
12.6.6
Distance geometry methods
414
12.7
Molecular Docking
415
12.8
Intrinsic Reaction Coordinate Methods
416
References
419
CONTENTS xi
13
Statisticei
Mechanics and Transition State Theory
421
13.1
Transition State Theory
421
13.2
Rice-Ramsperger-Kassel-Marcus Theory
424
13.3
Dynamical Effects
425
13.4
Statistical Mechanics
426
13.5
The Ideal Gas, Rigid-Rotor Harmonic-Oscillator Approximation
429
13.5.1
Translational degrees of freedom
430
13.5.2
Rotational degrees of freedom
430
13.5.3
Vibrational degrees of freedom
431
13.5.4
Electronic degrees of freedom
433
13.5.5
Enthalpy and entropy contributions
433
13.6
Condensed Phases
439
References
443
14
Simulation Techniques
445
14.1
Monte Carlo Methods
448
14.1.1
Generating non-natural ensembles
450
14.2
Time-Dependent Methods
450
14.2.1
Molecular dynamics methods
451
14.2.2
Generating non-natural ensembles
454
14.2.3
Langevin
methods
455
14.2.4
Direct methods
455
14.2.5
Extended
Lagrange
techniques (Car-Parrinello methods)
457
14.2.6
Quantum methods using potential energy surfaces
459
14.2.7
Reaction path methods
460
14.2.8
Non-Born-Oppenheimer methods
463
14.2.9
Constrained sampling methods
463
14.3
Periodic Boundary Conditions
464
14.4
Extracting Information from Simulations
468
14.5
Free Energy Methods
472
14.5.1
Thermodynamic perturbation methods
472
14.5.2
Thermodynamic integration methods
473
14.6
Solvation Models
475
14.7
Continuum Solvation Models
476
14.7.1
Poisson-Boltzmann methods
478
14.7.2
Born/Onsager/Kirkwood models
480
14.7.3
Self-consistent reaction field models
481
References
484
15
Qualitative Theories
487
15.1
Frontier Molecular Orbital Theory
487
15.2
Concepts from Density Functional Theory
492
15.3
Qualitative Molecular Orbital Theory
494
15.4
Woodward-Hoffmann Rules
497
15.5
The Bell-Evans-Polanyi Principle/Hammond Postulate/Marcus Theory
506
15.6
More
O'Ferrall-űencks
Diagrams
510
References
512
xii CONTENTS
16
Mathematical Methods
514
16.1
Numbers, Vectors, Matrices and Tensors
514
16.2
Change of Coordinate System
520
16.2.1
Examples of changing the coordinate system
525
16.2.2
Vibrational normal coordinates
526
16.2.3
Energy of a Slater determinant
528
16.2.4
Energy of
a CI
wave function
529
16.2.5
Computational Consideration
529
16.3
Coordinates, Functions, Functionals, Operators and
Superoperators
530
16.3.1
Differential operators
531
16.4
Normalization, Orthogonalization and Projection
532
16.5
Differential Equations
535
16.5.1
Simple first-order differential equations
535
16.5.2
Less simple first-order differential equations
536
16.5.3
Simple second-order differential equations
536
16.5.4
Less simple second-order differential equations
537
16.5.5
Second-order differential equations depending on the
function itself
537
16.6
Approximating Functions
538
16.6.1
Taylor expansion
539
16.6.2
Basis set expansion
541
16.7
Fourier and Laplace Transformations
541
16.8
Surfaces
543
References
546
17
Statistics and QSAR
547
17.1
Introduction
547
17.2
Elementary Statistical Measures
549
17.3
Correlation Between Two Sets of Data
550
17.4
Correlation between Many Sets of Data
553
17.4.1
Multiple-descriptor data sets and quality analysis
553
17.4.2
Multiple linear regression
555
17.4.3
Principal component and partial least squares analysis
556
17.4.4
Illustrative example
558
17.5
Quantitative Structure-Activity Relationships (QSAR)
559
References
561
18
Concluding Remarks
562
Appendix A
565
Notation
565
Appendix
В
570
B.I The Variationat Principle
570
B.2 The Hohenberg-Kohn Theorems
571
B.3 The Adiabatic Connection Formula
572
Reference
573
CONTENTS xiii
Appendix
С
574
Atomic Units
574
Appendix
D
575
Z-Matrix Construction
575
Index
583 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Jensen, Frank 1961- |
| author_GND | (DE-588)141010312 |
| author_facet | Jensen, Frank 1961- |
| author_role | aut |
| author_sort | Jensen, Frank 1961- |
| author_variant | f j fj |
| building | Verbundindex |
| bvnumber | BV021732173 |
| callnumber-first | Q - Science |
| callnumber-label | QD455 |
| callnumber-raw | QD455.3.E4 |
| callnumber-search | QD455.3.E4 |
| callnumber-sort | QD 3455.3 E4 |
| callnumber-subject | QD - Chemistry |
| classification_rvk | VC 6100 |
| classification_tum | CHE 150f CHE 020f |
| ctrlnum | (OCoLC)70707839 (DE-599)BVBBV021732173 |
| dewey-full | 541.0285 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 541 - Physical chemistry |
| dewey-raw | 541.0285 |
| dewey-search | 541.0285 |
| dewey-sort | 3541.0285 |
| dewey-tens | 540 - Chemistry and allied sciences |
| discipline | Chemie / Pharmazie Physik Chemie |
| discipline_str_mv | Chemie / Pharmazie Physik Chemie |
| edition | 2. ed. |
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| genre_facet | Lehrbuch |
| id | DE-604.BV021732173 |
| illustrated | Illustrated |
| index_date | 2024-07-02T15:26:44Z |
| indexdate | 2024-07-09T20:42:45Z |
| institution | BVB |
| isbn | 9780470011867 9780470011874 0470011866 0470011874 |
| language | English |
| lccn | 2006023998 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014945664 |
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| physical | XX, 599 S. Ill., graph. Darst. |
| publishDate | 2007 |
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| publisher | Wiley |
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| spelling | Jensen, Frank 1961- Verfasser (DE-588)141010312 aut Introduction to computational chemistry Frank Jensen 2. ed. Chichester [u.a.] Wiley 2007 XX, 599 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Includes bibliographical references and index Chimie physique et théorique Chimie physique et théorique - Informatique Datenverarbeitung Mathematik Chemistry, Physical and theoretical Data processing Chemistry, Physical and theoretical Mathematics Computational chemistry (DE-588)4290091-8 gnd rswk-swf Computersimulation (DE-588)4148259-1 gnd rswk-swf Chemie (DE-588)4009816-3 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Computational chemistry (DE-588)4290091-8 s DE-604 Chemie (DE-588)4009816-3 s Computersimulation (DE-588)4148259-1 s 1\p DE-604 http://deposit.dnb.de/cgi-bin/dokserv?id=2711643&prov=M&dok_var=1&dok_ext=htm Beschreibung für Leser http://www.loc.gov/catdir/toc/ecip0617/2006023998.html Table of contents only Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014945664&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Jensen, Frank 1961- Introduction to computational chemistry Chimie physique et théorique Chimie physique et théorique - Informatique Datenverarbeitung Mathematik Chemistry, Physical and theoretical Data processing Chemistry, Physical and theoretical Mathematics Computational chemistry (DE-588)4290091-8 gnd Computersimulation (DE-588)4148259-1 gnd Chemie (DE-588)4009816-3 gnd |
| subject_GND | (DE-588)4290091-8 (DE-588)4148259-1 (DE-588)4009816-3 (DE-588)4123623-3 |
| title | Introduction to computational chemistry |
| title_auth | Introduction to computational chemistry |
| title_exact_search | Introduction to computational chemistry |
| title_exact_search_txtP | Introduction to computational chemistry |
| title_full | Introduction to computational chemistry Frank Jensen |
| title_fullStr | Introduction to computational chemistry Frank Jensen |
| title_full_unstemmed | Introduction to computational chemistry Frank Jensen |
| title_short | Introduction to computational chemistry |
| title_sort | introduction to computational chemistry |
| topic | Chimie physique et théorique Chimie physique et théorique - Informatique Datenverarbeitung Mathematik Chemistry, Physical and theoretical Data processing Chemistry, Physical and theoretical Mathematics Computational chemistry (DE-588)4290091-8 gnd Computersimulation (DE-588)4148259-1 gnd Chemie (DE-588)4009816-3 gnd |
| topic_facet | Chimie physique et théorique Chimie physique et théorique - Informatique Datenverarbeitung Mathematik Chemistry, Physical and theoretical Data processing Chemistry, Physical and theoretical Mathematics Computational chemistry Computersimulation Chemie Lehrbuch |
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