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Handbook of Computational Quantum Chemistry [Kõva köide]

  • Formaat: Hardback, 766 pages, kõrgus x laius: 230x150 mm, kaal: 1280 g, 3 line figures
  • Ilmumisaeg: 01-Mar-1998
  • Kirjastus: Oxford University Press
  • ISBN-10: 0198501145
  • ISBN-13: 9780198501145
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Handbook of Computational Quantum ChemistrySuurem pilt
  • Formaat: Hardback, 766 pages, kõrgus x laius: 230x150 mm, kaal: 1280 g, 3 line figures
  • Ilmumisaeg: 01-Mar-1998
  • Kirjastus: Oxford University Press
  • ISBN-10: 0198501145
  • ISBN-13: 9780198501145
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780198501145.html
Märksõnad:
Quantum chemistry forms the basis of molecular modelling, a tool widely used to obtain important chemical information and visual images of molecular systems. Recent advances in computing have resulted in considerable developments in molecular modeling and these developments have led to significant achievements in the design and synthesis of drugs and catalysts. This up-to-date and comprehensive text provides an accessible introduction to the implementation of quantum ideas in molecular modeling, exploring practical applications alongside theoretical explanations. Written in a straightforward and accessible manner, Computational Quantum Chemistry provides a current account of a subject that has expanded enormously over the past decade.
1 Mechanics and molecules
1(33)
1.1 Introduction
1(3)
1.2 Time-independent Schrodinger equation
4(2)
1.3 The Born-Oppenheimer model
6(2)
1.4 The Pauli principle
8(2)
1.5 The orbital model
10(3)
1.6 The determinantal method
13(2)
1.7 Physical interpretation
15(2)
1.8 Non-determinantal forms
17(1)
1.9 The variation principle
18(3)
1.10 Summary
21(2)
1.A Atomic units
23(2)
1.B Standard Notation for Quantum Chemistry
25(9)
1.B.1 Introduction
25(1)
1.B.2 The Hamiltonian
25(1)
1.B.3 Many-electron wavefunctions
26(1)
1.B.4 Spin-orbitals
27(1)
1.B.5 Linear expansions for the spatial orbitals
27(1)
1.B.6 Primitive Gaussians
28(1)
1.B.7 Single determinant energy expression
29(2)
1.B.8 Notation for repulsion integrals
31(1)
1.B.9 Spatial orbital repulsion integrals
32(1)
1.B.10 Basis function repulsion integrals
32(2)
2 The Hartree-Fock Method
34(36)
2.1 Introduction
34(1)
2.2 The variational method
35(1)
2.3 The differential Hartree-Fock equation
36(8)
2.4 Canonical form
44(1)
2.5 Orbital energies
45(2)
2.6 Physical interpretation
47(1)
2.7 Direct parametric minimisation
48(1)
2.8 Summary
49(1)
2.A Single-determinant energy expression
50(20)
2.A.1 Introduction
50(2)
2.A.2 The normalisation integral
52(4)
2.A.3 One-electron terms
56(4)
2.A.4 Two-electron terms
60(5)
2.A.5 Summary
65(5)
3 The matrix SCF equations
70(38)
3.1 Introduction
70(2)
3.2 Notation
72(1)
3.3 The expansion
73(2)
3.4 The energy expression
75(1)
3.5 The numerator: Hamiltonian mean value
75(4)
3.6 The denominator: normalisation condition
79(1)
3.7 The Hartree-Fock equation
80(1)
3.8 "Normalisation": the Lagrangian
81(1)
3.9 Preliminary summary
82(1)
3.10 Some technical manipulations
83(4)
3.11 Canonical orbitals
87(2)
3.12 The total energy
89(1)
3.13 Summary
90(2)
3.A Atomic orbitals
92(2)
3.B Charge density
94(3)
3.C Properties of the J and K matrices
97(5)
3.C.1 Mathematical properties
97(2)
3.C.2 Physical interpretation
99(1)
3.C.3 Supermatrices
100(2)
3.D An artifact of expansion
102(2)
3.D.4 Lowest state of a given symmetry
102(2)
3.E Single determinant: choice of orbitals
104(4)
3.E.5 Orthogonal invariance
104(1)
3.E.6 Koopmans' theorem
105(1)
3.E.7 Localised orbitals
106(1)
3.E.8 "Zeroth-order" perturbed orbitals
107(1)
4 A special case: closed shells
108(6)
4.1 Introduction
108(1)
4.2 Notation for the closed-shell case
109(1)
4.3 Closed-shell expansion
109(1)
4.4 The closed-shell "HF" equation
110(3)
4.5 Closed-shell summary
113(1)
5 Implementation of the closed-shell case
114(71)
5.1 Preview
114(1)
5.2 Vectors, matrices and arrays
115(6)
5.3 The implementation: getting started
121(16)
5.4 The implementation: repulsion integral access
137(10)
5.5 Building a testbench: conventional SCF
147(7)
5.6 Another testbench: direct SCF
154(8)
5.7 Summary
162(1)
5.8 What next?
162(2)
5.A Jacobi diagonalisation
164(7)
5.A.1 Introduction
164(1)
5.A.2 The problem
165(1)
5.A.3 The solution
166(1)
5.A.4 Implementation
167(3)
5.A.5 Other diagonalisation methods
170(1)
5.B Orthogonalisation
171(6)
5.B.6 Introduction
171(2)
5.B.7 Functions of a matrix
173(1)
5.B.8 Implementation
174(3)
5.C getint and data for H(2)O
177(4)
5.D Coding the standard index loops
181(4)
6 Improvements: tools and methods
185(16)
6.1 Introduction
185(1)
6.2 Versions: conditional compilation
186(6)
6.3 Improved diagonalisation
192(3)
6.4 Simple interpolation
195(2)
6.5 Improving the formation of G(R)
197(2)
6.6 Summary
199(2)
7 Molecular integrals: an introduction
201(35)
7.1 Introduction
201(1)
7.2 Basis functions
202(1)
7.3 AOs and atom-centred-functions
203(2)
7.4 Multi-dimensional integral evaluation
205(1)
7.5 Molecular integrals over STOs
206(9)
7.6 Basis functions of convenience
215(1)
7.7 Gaussian basis functions
216(18)
7.8 The contraction technique
234(2)
8 Molecular integrals: implementation
236(38)
8.1 Introduction
236(1)
8.2 Data structures
237(3)
8.3 Normalisation
240(3)
8.4 Overview; the general structure
243(6)
8.5 Complex code management: the WEB system
249(7)
8.6 A working WEB
256(10)
8.7 Some comments on the WEB
266(1)
8.8 The full integral codes
267(1)
8.A Source for the WEB of fmch
268(6)
9 Repulsion integral storage
274(11)
9.1 Introduction
274(1)
9.2 A storage algorithm
274(2)
9.3 Implementation: putint
276(6)
9.4 A partner for putint; getint
282(2)
9.5 Conclusion
284(1)
10 "Virtual orbitals"
285(18)
10.1 Introduction
285(1)
10.2 Virtual orbitals in practice
286(5)
10.3 The virtual space in LCAO
291(4)
10.4 Conclusions
295(1)
10.A Perturbation theory
296(7)
10.A.1 Introduction
296(1)
10.A.2 Perturbation theory
296(5)
10.A.3 Perturbation theory for matrix equations
301(2)
11 Choice of tools
303(11)
11.1 Existing software
303(3)
11.2 Why ratfor?
306(2)
11.3 The Revision Control System: RCS
308(2)
11.A RCS: version control
310(4)
11.A.1 Motivation
310(1)
11.A.2 Introduction
310(1)
11.A.3 Getting started with RCS
311(3)
12 Open shells: implementing UHF
314(53)
12.1 Introduction
314(1)
12.2 Choice of constraints
315(2)
12.3 Organising the basis
317(1)
12.4 Integrals over the spin-basis
318(2)
12.5 Implementation
320(1)
12.6 J and K for GUHF
321(5)
12.7 The GUHF testbench
326(3)
12.8 Interpreting the MO coefficients
329(3)
12.9 DODS or GUHF?
332(1)
12.10 Version 1 of the SCF code
333(4)
12.11 WEB output for function scf
337(8)
12.12 Comments
345(1)
12.A WEB Source for the scf code
346(5)
12.B Blocking the Hartree-Fock matrix
351(12)
12.B.1 The block form of the HF matrix
351(1)
12.B.2 Implementation
352(11)
12.C The Aufbau principle
363(4)
12.C.3 Introduction
363(1)
12.C.4 The second variation
363(2)
12.C.5 Special case: a single excitation
365(2)
13 Population analysis
367(10)
13.1 Introduction
367(1)
13.2 Densities and spin-densities
368(1)
13.3 Basis representations: charges
369(3)
13.4 Basis-function analysis
372(2)
13.5 A cautionary note
374(1)
13.6 Multi-determinant forms
375(1)
13.7 Implementation
376(1)
14 The general MO functional
377(29)
14.1 A generalisation
377(1)
14.2 Shells of orbitals
378(2)
14.3 The variational method
380(3)
14.4 A single "Hartree-Fock" operator
383(3)
14.5 Non-orthogonal basis
386(2)
14.6 Choice of the arbitary matrices
388(2)
14.7 Implementation: stacks of matrices
390(10)
14.A Projection operators and SCF
400(6)
14.A.1 Introduction: optimum single determinant
400(2)
14.A.2 Alternative SCF conditions
402(1)
14.A.3 R matrices as projection operators
403(3)
15 Spin-restricted open shell
406(30)
15.1 Introduction
406(1)
15.2 The ROHF model
407(1)
15.3 Implementation
408(1)
15.4 A WEB for spin-restricted open shell
409(27)
16 Banana skins: unexpected disasters
436(6)
16.1 Symmetry restrictions
437(1)
16.2 Anions
438(1)
16.3 Aufbau exceptions
439(2)
16.4 Summary
441(1)
17 Molecular symmetry
442(25)
17.1 Introduction
442(1)
17.2 Symmetry and the HF method
443(2)
17.3 Permutational symmetry of the basis
445(5)
17.4 Implementation
450(16)
17.5 Permutation symmetry: summary
466(1)
18 Symmetry orbital transformations
467(10)
18.1 Introduction
467(3)
18.2 Symmetry-adapted basis
470(3)
18.3 Generation of symmetry orbitals
473(3)
18.4 Conclusions
476(1)
19 A symmetry-adapted SCF method
477(24)
19.1 Introduction
477(3)
19.2 Permutations only
480(9)
19.3 Full implementation; linear combinations
489(5)
19.4 Summary
494(1)
19.A Kronecker product notation
495(6)
19.A.1 Basis transformations
495(1)
19.A.2 Basis-product transformations
495(2)
19.A.3 Density matrix transformations
497(1)
19.A.4 Transformations in the HF matrix
498(2)
19.A.5 Practice
500(1)
20 Linear multi-determinant methods
501(29)
20.1 Correlation and the Hartee-Fock model
501(1)
20.2 The configuration interaction method
502(1)
20.3 The valence bond method
503(1)
20.4 Restricted CI
504(6)
20.5 Symmetry-restricted CI
510(2)
20.6 More general CI
512(1)
20.7 Nesbet's method for large matrices
513(6)
20.8 "Direct" CI
519(5)
20.9 Conclusions
524(1)
20.A The "orthogonal VB" model
525(2)
20.B DCI matrix elements
527(3)
21 The valence bond model
530(15)
21.1 Non-orthogonality in expansions
530(1)
21.2 Spins and spin functions
531(4)
21.3 Spin eigenfunctions and permutations
535(4)
21.4 Spin-free VB theory
539(5)
21.5 Summary
544(1)
22 Doubly-occupied MCSCF
545(17)
22.1 Introduction: natural orbitals
545(3)
22.2 Paired-excitation MCSCF
548(5)
22.3 Implementation
553(1)
22.4 Partial Paired-Excitations; GVB
553(3)
22.5 Details of GVB
556(5)
22.6 Implementation
561(1)
23 Interpreting the McWeenyan
562(5)
23.1 Introduction
562(1)
23.2 Stationary points
563(2)
23.3 Many shells
565(1)
23.4 Summary
566(1)
24 Core potentials
567(24)
24.1 Introduction
567(2)
24.2 Simple orthogonalization
569(1)
24.3 Transforming the Hartee-Fock equation
570(4)
24.4 The pseudopotential
574(2)
24.5 Arbitariness in the pseudo-orbital
576(3)
24.6 Modelling atomic pseudopotentials
579(2)
24.7 Modelling atomic core potentials
581(3)
24.8 Several valence electrons
584(4)
24.9 Atomic cores in molecules
588(1)
24.10 Summary
589(2)
25 Practical core potentials
591(14)
25.1 Introduction
591(1)
25.2 Forms for the core potentials
591(4)
25.3 Core potential integrals
595(9)
25.4 Implementation
604(1)
26 SCF perturbation theory
605(16)
26.1 Introduction
605(1)
26.2 Two forms for the HF equations
606(3)
26.3 Self-consistent perturbation theory
609(1)
26.4 The method
610(8)
26.5 Conclusions
618(3)
27 Time-dependent perturbations: RPA
621(12)
27.1 Introduction
621(1)
27.2 Time-dependent Hartee-Fock theory
621(2)
27.3 Oscillatory time-dependent perturbations
623(3)
27.4 Self consistency
626(1)
27.5 Implementation
627(2)
27.A "Random phase approximation"
629(2)
27.B Time-dependent variation principle
631(2)
28 Transitions and stability
633(7)
28.1 Introduction
633(1)
28.2 Transitions
634(1)
28.3 The transition frequencies
635(1)
28.4 Finite perturbations; oscillations
636(2)
28.5 Stability; the time-independent case
638(1)
28.6 Implementation
639(1)
29 Two-electron transformations
640(31)
29.1 Orbital transformations
640(1)
29.2 Strategy
641(2)
29.3 Transformation without sorting
643(11)
29.4 Transformations with sorting
654(2)
29.5 Summary
656(1)
29.A A bit of fun: MP2
657(14)
29.A.1 Derivation
657(3)
29.A.2 Implementation
660(11)
30 Geometry optimisation: derivatives
671(15)
30.1 Introduction
671(1)
30.2 Derivatives and perturbation theory
672(2)
30.3 Derivatives of variational solutions
674(2)
30.4 Parameter-dependent basis functions
676(1)
30.5 The derivative of the SCF energy
677(4)
30.6 Derivatives of molecular integrals
681(1)
30.7 Derivatives of non-variational energies
682(2)
30.8 Higher derivatives
684(1)
30.9 Summary
684(2)
31 The Semi-empirical approach
686(7)
31.1 Introduction
686(1)
31.2 Use of Coulomb's law
687(2)
31.3 Atomic data
689(1)
31.4 Simulation or calibration?
690(1)
31.5 General conclusions
691(2)
32 Density functional theory
693(15)
32.1 Introduction
693(2)
32.2 Hohenberg and Kohn's proofs
695(5)
32.3 Kohn-Sham equations: introduction
700(3)
32.4 Kohn-Sham equations
703(2)
32.5 Non-local operators in orbital theories
705(3)
33 Implementing the Kohn-Sham equations
708(14)
33.1 A precursor: The Hartree-Fock-Slater model
708(2)
33.2 Implementation of the Kohn-Sham method
710(5)
33.3 The kinetic energy density
715(2)
33.4 Gradients in the exchange-correlation energy
717(1)
33.5 Numerical integration of densities
717(3)
33.6 Summary
720(2)
34 Semi-numerical methods
722(10)
34.1 Non-variational expansions
722(2)
34.2 The pseudospectral method
724(5)
34.3 The discrete variational method
729(3)
35 Additional reading and other material
732
35.1 Additional reading
732(2)
35.2 Additional material by ftp
734