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Handbook of Computational Quantum Chemistry [Pehme köide]

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  • Formaat: Paperback / softback, 832 pages, kõrgus x laius x paksus: 215x39x137 mm, kaal: 843 g, Illustrations, unspecified
  • Sari: Dover Books on Chemistry
  • Ilmumisaeg: 29-Jul-2005
  • Kirjastus: Dover Publications Inc.
  • ISBN-10: 0486443078
  • ISBN-13: 9780486443072
Teised raamatud teemal:
Handbook of Computational Quantum ChemistrySuurem pilt
  • Formaat: Paperback / softback, 832 pages, kõrgus x laius x paksus: 215x39x137 mm, kaal: 843 g, Illustrations, unspecified
  • Sari: Dover Books on Chemistry
  • Ilmumisaeg: 29-Jul-2005
  • Kirjastus: Dover Publications Inc.
  • ISBN-10: 0486443078
  • ISBN-13: 9780486443072
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780486443072.html
Märksõnad:
This comprehensive text provides upper-level undergraduates and graduate students with an accessible introduction to the implementation of quantum ideas in molecular modeling, exploring practical applications alongside theoretical explanations. Topics include the Hartree-Fock method; matrix SCF equations; implementation of the closed-shell case; introduction to molecular integrals; and much more. 1998 edition.
Mechanics and molecules
1(36)
Introduction
1(4)
Time-independent Schrodinger equation
5(2)
The Born-Oppenheimer model
7(2)
The Pauli principle
9(2)
The orbital model
11(3)
The determinantal method
14(2)
Physical interpretation
16(2)
Non-determinantal forms
18(1)
The variation principle
19(4)
Summary
23(1)
Atomic units
24(3)
Standard Notation for Quantum Chemistry
27(10)
Introduction
27(1)
The Hamiltonian
28(1)
Many-electron wavefunctions
29(1)
Spin-orbitals
29(1)
Linear expansions for the spatial orbitals
30(1)
Primitive Gaussians
31(1)
Single determinant energy expression
32(1)
Notation for repulsion integrals
33(1)
Spatial orbital repulsion integrals
34(1)
Basis function repulsion integrals
35(2)
The Hartree-Fock Method
37(38)
Introduction
37(1)
The variational method
38(2)
The differential Hartree-Fock equation
40(7)
Canonical form
47(2)
Orbital energies
49(1)
Physical interpretation
50(1)
Direct parametric minimisation
51(2)
Summary
53(1)
Single-determinant energy expression
54(21)
Introduction
54(2)
The normalisation integral
56(5)
One-electron terms
61(4)
Two-electron terms
65(5)
Summary
70(5)
The matrix SCF equations
75(40)
Introduction
75(2)
Notation
77(1)
The expansion
78(2)
The energy expression
80(1)
The numerator: Hamiltonian mean value
81(3)
The denominator: normalisation condition
84(2)
The Hartree-Fock equation
86(1)
``Normalisation'': the Lagrangian
87(1)
Preliminary summary
88(1)
Some technical manipulations
89(3)
Canonical orbitals
92(3)
The total energy
95(1)
Summary
96(1)
Atomic orbitals
97(3)
Charge density
100(3)
Properties of the J and K matrices
103(5)
Mathematical properties
103(3)
Physical interpretation
106(1)
Supermatrices
107(1)
An artifact of expansion
108(2)
Lowest state of a given symmetry
108(2)
Single determinant: choice of orbitals
110(5)
Orthogonal invariance
110(2)
Koopmans' theorem
112(1)
Localised orbitals
113(1)
``Zeroth-order'' perturbed orbitals
113(2)
A special case: closed shells
115(8)
Introduction
115(1)
Notation for the closed-shell case
116(1)
Closed-shell expansion
116(1)
The closed-shell ``HF'' equation
117(4)
Closed-shell summary
121(2)
Implementation of the closed-shell case
123(76)
Preview
124(1)
Vectors, matrices and arrays
125(6)
The implementation: getting started
131(17)
The implementation: repulsion integral access
148(10)
Building a testbench: conventional SCF
158(7)
Another testbench: direct SCF
165(8)
Summary
173(1)
What next?
174(1)
Jacobi diagonalisation
175(9)
Introduction
175(1)
The problem
176(1)
The solution
177(2)
Implementation
179(3)
Other diagonalisation methods
182(2)
Orthogonalisation
184(6)
Introduction
184(2)
Functions of a matrix
186(1)
Implementation
187(3)
getint and data for H2O
190(4)
Coding the standard index loops
194(5)
Improvements: tools and methods
199(18)
Introduction
199(1)
Versions: conditional compilation
200(7)
Improved diagonalisation
207(3)
Simple interpolation
210(2)
Improving the formation of G(R)
212(3)
Summary
215(2)
Molecular integrals: an introduction
217(38)
Introduction
218(1)
Basis functions
219(2)
AOs and atom-centred-functions
221(1)
Multi-dimensional integral evaluation
222(1)
Molecular integrals over STOs
223(9)
Basis functions of convenience
232(2)
Gaussian basis functions
234(17)
The contraction technique
251(4)
Molecular integrals: implementation
255(42)
Introduction
256(1)
Data structures
256(4)
Normalisation
260(3)
Overview; the general structure
263(6)
Complex code management: the WEB system
269(7)
A working WEB
276(11)
Some comments on the WEB
287(1)
The full integral codes
288(1)
Source for the WEB of fmch
289(8)
Repulsion integral storage
297(14)
Introduction
297(1)
A storage algorithm
298(2)
Implementation: putint
300(7)
A partner for putint; getint
307(2)
Conclusion
309(2)
``Virtual orbitals''
311(20)
Introduction
311(1)
Virtual orbitals in practice
312(5)
The virtual space in LCAO
317(5)
Conclusions
322(1)
Perturbation theory
323(8)
Introduction
323(1)
Perturbation theory
324(5)
Perturbation theory for matrix equations
329(2)
Choice of tools
331(12)
Existing software
331(4)
Why ratfor?
335(2)
The Revision Control System: RCS
337(2)
RCS: version control
339(4)
Motivation
339(1)
Introduction
340(1)
Getting started with RCS
341(2)
Open shells: implementing UHF
343(56)
Introduction
344(1)
Choice of constraints
344(3)
Organising the basis
347(1)
Integrals over the spin-basis
348(2)
Implementation
350(1)
J and K for GUHF
351(6)
The GUHF testbench
357(3)
Interpreting the MO coefficients
360(3)
DODS or GUHF?
363(1)
Version 1 of the SCF code
363(5)
WEB output for function scf
368(8)
Comments
376(1)
WEB Source for the scf code
377(5)
Blocking the Hartree-Fock matrix
382(12)
The block form of the HF matrix
382(2)
Implementation
384(10)
The Aufbau principle
394(5)
Introduction
394(1)
The second variation
395(1)
Special case: a single excitation
396(3)
Population analysis
399(10)
Introduction
399(1)
Densities and spin-densities
400(1)
Basis representations: charges
401(3)
Basis-function analysis
404(2)
A cautionary note
406(1)
Multi-determinant forms
407(1)
Implementation
408(1)
The general MO functional
409(32)
A generalisation
409(1)
Shells of orbitals
410(2)
The variational method
412(4)
A single ``Hartree-Fock'' operator
416(3)
Non-orthogonal basis
419(1)
Choice of the arbitrary matrices
420(2)
Implementation: stacks of matrices
422(11)
Projection operators and SCF
433(8)
Introduction: optimum single determinant
433(2)
Alternative SCF conditions
435(1)
R matrices as projection operators
436(5)
Spin-restricted open shell
441(32)
Introduction
441(1)
The ROHF model
442(2)
Implementation
444(1)
A WEB for spin-restricted open shell
445(28)
Banana skins: unexpected disasters
473(6)
Symmetry restrictions
474(1)
Anions
475(2)
Aufbau exceptions
477(1)
Summary
478(1)
Molecular symmetry
479(26)
Introduction
479(1)
Symmetry and the HF method
480(3)
Permutational symmetry of the basis
483(5)
Implementation
488(16)
Permutation symmetry: summary
504(1)
Symmetry orbital transformations
505(10)
Introduction
505(4)
Symmetry-adapted basis
509(3)
Generation of symmetry orbitals
512(2)
Conclusions
514(1)
A symmetry-adapted SCF method
515(26)
Introduction
515(3)
Permutations only
518(10)
Full implementation; linear combinations
528(5)
Summary
533(1)
Kronecker product notation
534(7)
Basis transformations
534(1)
Basis-product transformations
535(1)
Density matrix transformations
536(1)
Transformations in the HF matrix
537(2)
Practice
539(2)
Linear multi-determinant methods
541(30)
Correlation and the Hartree-Fock model
541(2)
The configuration interaction method
543(1)
The valence bond method
544(1)
Restricted CI
545(5)
Symmetry-restricted CI
550(3)
More general CI
553(1)
Nesbet's method for large matrices
554(6)
``Direct'' CI
560(5)
Conclusions
565(1)
The ``orthogonal VB'' model
566(2)
DCI matrix elements
568(3)
The valence bond model
571(16)
Non-orthogonality in expansions
571(2)
Spins and spin functions
573(3)
Spin eigenfunctions and permutations
576(5)
Spin-free VB theory
581(4)
Summary
585(2)
Doubly-occupied MCSCF
587(18)
Introduction: natural orbitals
588(2)
Paired-excitation MCSCF
590(5)
Implementation
595(1)
Partial Paired-Excitations; GVB
596(3)
Details of GVB
599(5)
Implementation
604(1)
Interpreting the McWeenyan
605(6)
Introduction
605(2)
Stationary points
607(1)
Many shells
608(2)
Summary
610(1)
Core potentials
611(26)
Introduction
612(2)
Simple orthogonalization
614(1)
Transforming the Hartree-Fock equation
615(3)
The pseudopotential
618(3)
Arbitrariness in the pseudo-orbital
621(3)
Modelling atomic pseudopotentials
624(2)
Modelling atomic core potentials
626(3)
Several valence electrons
629(4)
Atomic cores in molecules
633(1)
Summary
634(3)
Practical core potentials
637(16)
Introduction
637(1)
Forms for the core potentials
638(3)
Core potential integrals
641(10)
Implementation
651(2)
SCF perturbation theory
653(16)
Introduction
654(1)
Two forms for the HF equations
654(3)
Self-consistent perturbation theory
657(2)
The method
659(8)
Conclusions
667(2)
Time-dependent perturbations: RPA
669(14)
Introduction
669(1)
Time-dependent Hartree-Fock theory
670(1)
Oscillatory time-dependent perturbations
671(4)
Self consistency
675(1)
Implementation
676(2)
``Random phase approximation''
678(2)
Time-dependent variation principle
680(3)
Transitions and stability
683(8)
Introduction
683(1)
Transitions
684(1)
The transition frequencies
685(1)
Finite perturbations; oscillations
686(2)
Stability; the time-independent case
688(1)
Implementation
689(2)
Two-electron transformations
691(32)
Orbital transformations
691(2)
Strategy
693(2)
Transformation without sorting
695(10)
Transformations with sorting
705(3)
Summary
708(1)
A bit of fun: MP2
709(14)
Derivation
709(3)
Implementation
712(11)
Geometry optimisation: derivatives
723(16)
Introduction
724(1)
Derivatives and perturbation theory
725(2)
Derivatives of variational solutions
727(2)
Parameter-dependent basis functions
729(1)
The derivative of the SCF energy
730(4)
Derivatives of molecular integrals
734(1)
Derivatives of non-variational energies
735(2)
Higher derivatives
737(1)
Summary
737(2)
The Semi-empirical approach
739(24)
Introduction
739(2)
Use of Coulomb's law
741(1)
Atomic data
742(2)
Simulation or calibration?
744(1)
General conclusions
745(3)
Introduction
748(2)
Hohenberg and Kohn's proofs
750(5)
Kohn-Sham equations: introduction
755(2)
Kohn-Sham equations
757(3)
Non-local operators in orbital theories
760(3)
Implementing the Kohn-Sham equations
763(16)
A precursor: The Hartree-Fock-Slater model
764(2)
Implementation of the Kohn-Sham method
766(5)
The kinetic energy density
771(1)
Gradients in the exchange-correlation energy
772(1)
Numerical integration of densities
773(3)
Summary
776(3)
Semi-numerical methods
779(12)
Non-variational expansions
779(3)
The pseudospectral methods
782(4)
The discrete variational method
786(5)
Additional reading and other material
791
Additional reading
791(3)
Additional material by ftp
794