Helgaker T., Jorgensen P., Olsen J. — Molecular Electronic-Structure Theory. Part 2 :: Электронная библиотека попечительского совета мехмата МГУ

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Helgaker T., Jorgensen P., Olsen J. — Molecular Electronic-Structure Theory. Part 2

Helgaker T., Jorgensen P., Olsen J. — Molecular Electronic-Structure Theory. Part 2

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Название: Molecular Electronic-Structure Theory. Part 2

Авторы: Helgaker T., Jorgensen P., Olsen J.

Аннотация:

Ab initio quantum chemistry has emerged as an important tool in chemical research and is appliced to a wide variety of problems in chemistry and molecular physics. Recent developments of computational methods have enabled previously intractable chemical problems to be solved using rigorous quantum-mechanical methods.
This is the first comprehensive, up-to-date and technical work to cover all the important aspects of modern molecular electronic-structure theory. Topics covered in the book include:
* Second quantization with spin adaptation
* Gaussian basis sets and molecular-integral evaluation
* Hartree-Fock theory
* Configuration-interaction and multi-configurational self-consistent theory
* Coupled-cluster theory for ground and excited states
* Perturbation theory for single- and multi-configurational states
* Linear-scaling techniques and the fast multipole method
* Explicity correlated wave functions
* Basis-set convergence and extrapolation
* Calibration and benchmarking of computational methods, with applications to moelcular equilibrium structure, atomization energies and reaction enthalpies.
Molecular Electronic-Structure Theory makes extensive use of numerical examples, designed to illustrate the strengths and weaknesses of each method treated. In addition, statements about the usefulness and deficiencies of the various methods are supported by actual examples, not just model calculations. Problems and exercises are provided at the end of each chapter, complete with hints and solutions.
This book is a must for researchers in the field of quantum chemistry as well as for nonspecialists who wish to acquire a thorough understanding of ab initio molecular electronic-structure theory and its applications to problems in chemistry and physics. It is also highly recommended for the teaching of graduates and advanced undergraduates.

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Рубрика: Химия/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 2000

Количество страниц: 386

Добавлена в каталог: 21.02.2007

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Предметный указатель

Density functions and matrices, one-electron density matrix in spin-orbital basis      20
Density functions and matrices, permutational symmetries in orbital basis      62
Density functions and matrices, permutational symmetries in spin-orbital basis      22
Density functions and matrices, reduced density matrices      24 65 66
Density functions and matrices, relaxed coupled-cluster density matrix      677
Density functions and matrices, spin-density function      65
Density functions and matrices, spin-density matrix      64
Density functions and matrices, two-electron density matrix in orbital basis      62
Density functions and matrices, two-electron density matrix in spin-orbital basis      20 21
Density-based Hartree — Fock theory      465
Density-based Hartree — Fock theory, asymmetric BCH expansion of AO density matrix      469
Density-based Hartree — Fock theory, electronic gradient      474
Density-based Hartree — Fock theory, electronic Hessian      474 480
Density-based Hartree — Fock theory, idempotency of density matrix      467 468
Density-based Hartree — Fock theory, linear scaling in density-based Hartree — Fock theory      477
Density-based Hartree — Fock theory, Newton’s method      480
Density-based Hartree — Fock theory, optimization of orbital-energy function      477
Density-based Hartree — Fock theory, parametrization of AO density matrix      468
Density-based Hartree — Fock theory, properties of AO density matrix      468
Density-based Hartree — Fock theory, properties of MO density matrix      467
Density-based Hartree — Fock theory, purification of AO density matrix      470
Density-based Hartree — Fock theory, redundancy of density-matrix parametrization      469
Density-based Hartree — Fock theory, self-consistent field (SCF) method II      475
Density-based Hartree — Fock theory, trace of density matrix      467 468
Density-based Hartree — Fock theory, variational conditions      474
Density-functional theory      880
DIIS convergence acceleration in coupled-cluster theory      672
DIIS convergence acceleration in Hartree — Fock theory      460
DIIS convergence acceleration, DIIS equations      462
DIIS, direct inversion in the iterative subspace [method]      461
Dipole moments      836 (see also “Calibration of methods”)
Dipole moments, calculated dipole moments      837
Dipole moments, experimental and calculated dipole moments (table)      837
Dipole moments, experimental dipole moments      836
Dipole moments, predicted dipole moments      838
Dipole moments, statistical analysis of errors in calculated dipole moments      839
Dirac delta function      16
Direct CI methods      554
Direct CI methods, density-matrix construction      568
Direct CI methods, minimal operation-count (MOC) method for FCI      560
Direct CI methods, minimal operation-count (MOC) method for RAS      564
Direct CI methods, N-resolution method for FCI      558
Direct CI methods, naive approach      555
Direct CI methods, operation counts      560 563 564
Direct CI methods, separate treatments of occupied and virtual spaces      566
Direct CI methods, spin strings      550
Direct Hartree — Fock theory      463
Direct Hartree — Fock theory, Coulomb contribution      381 464
Direct Hartree — Fock theory, exchange contribution      464
Direct-product space      129 132 684
Disconnected cluster amplitudes      651
Dispersion energy      328
Dissociation energy      see also “Atomization energies”
Dissociation energy of $\matyrm{H_2O}$       175
Dissociation energy of $\matyrm{H_2}$       163 172 173
Dissociation energy of BH      303 333
Dissociation energy, basis-set convergence      324 333
Dissociation energy, fragment approach      173
Dissociation energy, supermolecule approach      172
Distributions, binomial probability distributions      539
Distributions, Gaussian (normal) probability distributions      539 821
Distributions, Gaussian charge distributions      361
Distributions, Gaussian overlap distributions      341
Double commutators      27
Double factorial function      220
Doublet operators      42 (see also “Spin tensor operators”)
Down rank      660 663
Dynamical correlation      162 165 278 526
DZ basis sets      228 300
DZ, double-zeta [basis]      295
DZP basis sets      300
DZP, DZ polarized [basis]      300
EA, electron affinity      455
Electron affinities      455(see also “Koopmans’ theorem”)
Electron correlation      158
Electron correlation in $\mathrm{H_2}$       154
Electron correlation, angular correlation      165
Electron correlation, dynamical correlation      162 165 278 526
Electron correlation, Fermi correlation      158 278
Electron correlation, left-right correlation      164
Electron correlation, long-range correlation      278
Electron correlation, near-degeneracy correlation      162
Electron correlation, nondynamical correlation      162
Electron correlation, radial correlation      165
Electron correlation, relation to Pauli antisymmetry principle      158
Electron correlation, short-range correlation      278
Electron correlation, static correlation      162 165 278 526
Electron-transfer recurrence relation      386
Electronic energies of sample molecules      841
Electronic energies of sample molecules, basis-set convergence      844
Electronic energies of sample molecules, basis-set extrapolation      842
Electronic energies of sample molecules, calculated electronic energies (table)      841
Electronic energies of sample molecules, CCSDT corrections      846
Electronic energies of sample molecules, contributions to the electronic energy      842
Electronic energies of sample molecules, relativistic corrections      849
Electronic gradient in CI theory (linear variation method)      113 542
Electronic gradient in density-based Hartree — Fock theory      474
Electronic gradient in MCSCF theory      603 608 639
Electronic gradient in MO-based Hartree — Fock theory      437 481 506
Electronic gradient in OCC theory      700
Electronic gradient, relation to singlet and triplet instabilities      498 499
Electronic Hessian in CI theory      113 542
Electronic Hessian in closed-shell canonical Hartree — Fock theory      488 512
Electronic Hessian in density-based Hartree — Fock theory      474 480
Electronic Hessian in MCSCF theory      603 604 609 616 639
Electronic Hessian in MO-based Hartree — Fock theory      437 485 488 512
Electronic Hessian, augmented MCSCF Hessian      616
Electronic Hessian, conditions on Hessian for ground and excited states      115
Electronic Hessian, linear transformations in AO-based Hartree — Fock theory      489
Electronic Hessian, linear transformations in density-based Hartree — Fock theory      480
Electronic Hessian, linear transformations in MO-based Hartree — Fock theory      488
Electronic Hessian, triplet Hartree — Fock Hessian      512
Elementary operators, annihilation operators      4 8
Elementary operators, creation operators      3 8
EOM-CC, equation-of-motion coupled-cluster [model]      678
Epstein — Nesbet zero-order Hamiltonian      739
Equation-of-motion coupled-cluster (EOM-CC) theory      677
Equation-of-motion coupled-cluster (EOM-CC) theory, biorthogonal basis      679
Equation-of-motion coupled-cluster (EOM-CC) theory, eigenvalue problem      679
Equation-of-motion coupled-cluster (EOM-CC) theory, energy expectation value      679
Equation-of-motion coupled-cluster (EOM-CC) theory, EOM-CC model      678
Equation-of-motion coupled-cluster (EOM-CC) theory, expansion of excited states      678
Equation-of-motion coupled-cluster (EOM-CC) theory, Hamiltonian matrix      680
Equation-of-motion coupled-cluster (EOM-CC) theory, Jacobian matrix      681
Equation-of-motion coupled-cluster (EOM-CC) theory, relation to CI theory      678
Equation-of-motion coupled-cluster (EOM-CC) theory, relation to response theory      684
Equation-of-motion coupled-cluster (EOM-CC) theory, right and left eigenvectors      681
Equation-of-motion coupled-cluster (EOM-CC) theory, similarity-transformed Hamiltonian      680
Equation-of-motion coupled-cluster (EOM-CC) theory, size-extensivity      683
Error function      369
Errors in calculations      819 (see also “Calibration of methods”)
Errors in calculations, apparent error      819
Errors in calculations, balanced level of description      820
Errors in calculations, basis-set error      819
Errors in calculations, intrinsic (TV-electron) error      820
Errors in calculations, N-electron error      820
Even-tempered basis sets      292
Exchange potential in Hartree — Fock theory      169 451
Excitation operators in coupled-cluster theory      186 649
Excitation operators in orbital basis      36 44
Excitation operators in spin-orbital basis      7 8
Excitation operators, commutators      26 46
Excitation operators, excitation rank      660 663
Excitation operators, singlet one-electron operator      36 44 686
Excitation operators, singlet two-electron operator      37 69 686
Excitation operators, triplet one-electron operator in Cartesian form      40 45
Excitation operators, vtriplet one-electron operator in spin-tensor form      41 44
Excitation-manifold basis in open-shell spin-restricted coupled-cluster theory      706 708
Excitation-manifold basis, double excitations in orbital basis      691 760
Excitation-manifold basis, double excitations in spin-orbital basis      188 649 655 740

Excitation-manifold basis, generic excitation operator      654
Excitation-manifold basis, linear dependence of triple excitations in orbital basis      761
Excitation-manifold basis, single excitations in orbital basis      691 760
Excitation-manifold basis, single excitations in spin-orbital basis      188 654 740
Excitation-manifold basis, triple excitations in orbital basis      760
Excitation-manifold basis, triple excitations in spin-orbital basis      740
Expectation values of kinetic and potential energies (virial theorem)      122
Expectation values of r for GTOs      234
Expectation values of r for hydrogenic functions      222
Expectation values of r for Laguerre functions      222
Expectation values of r for STOs      226
Expectation values of relativistic operators      853
Expectation values, coupled-cluster energy expectation values      652 653 679
Expectation values, coupled-cluster expectation values      675 714
Expectation values, density-matrix elements as expectation values      20 22 62
Expectation values, error in the energy expectation value      113
Expectation values, expectation value of triplet operators      63
Expectation values, Hellmann — Feynman theorem      119 675
Expectation values, second-quantization expectation values      19 62
Expectation values, total-spin expectation values in coupled-cluster theory      708
Expectation values, total-spin expectation values in UHF theory      172 174
Expectation values, vacuum expectation values      19
Experimental reference data, atomization energies      855 865
Experimental reference data, bond angles      833
Experimental reference data, bond distances      823
Experimental reference data, conformational energies      875 876 877
Experimental reference data, dipole moments      837
Experimental reference data, reaction enthalpies      866 874
Explicitly correlated methods      264 (see also “Helium atom”)
Explicitly correlated methods, correlating functions      265 280
Explicitly correlated methods, Hylleraas function      266
Explicitly correlated methods, R12 methods      265 267
Exponential ansatz in CCPT      749
Exponential ansatz in coupled-cluster theory      187 654
Exponential ansatz, relation to size-extensivity      132
Exponential matrix function for a general $2\times 2$ unitary matrix      96
Exponential matrix function for metric-conserving transformations      84 468
Exponential matrix function for orthogonal matrix      83
Exponential matrix function for special unitary matrix      82
Exponential matrix function for unitary matrix      81
Exponential matrix function, definition of      81
Exponential matrix function, evaluation of      83
Exponential matrix function, identities involving      81
Exponential unitary operator      86
Exponential unitary operator, applied to creation and annihilation operators      86 88
Exponential unitary operator, applied to electronic states      86 89
Exponential unitary operator, derivatives of      98
Exponential unitary operator, real singlet transformations in orbital basis      93 435 601
Exponential unitary operator, real transformations in spin-orbital basis      91
Exponential unitary operator, real triplet transformations in orbital basis      92
Exponential unitary operator, symmetry restrictions      89 497
Exponential unitary operator, transformation of a single state in configuration space      631
Exponential unitary operator, transformation of several states in configuration space      634
Extent of Gaussian      402 424
Extrapolation      see “Basis-set extrapolation”
Factorial function      220 525
Fast multipole method (FMM)      417 421 423 478
FCI, full CI [model      163 524
Fermi contact operator      63 66 499
Fermi correlation      see also “Electron correlation”
Fermi correlation in Hartree — Fock theory      169 443 451 464
Fermi correlation, relation to electron correlation      158 171 278
FF, far-field [box]      419
First quantization compared with second quantization      18
Fixed-point iteration      448
Floating orbitals      299
Floating-point operations      484
Fluctuation potential      192 453
Fluctuation potential in CCPT      750
Fluctuation potential in coupled-cluster theory      662 672
Fluctuation potential in Hartree — Fock theory      453
Fluctuation potential in MPPT      192 740 760 781
FMM, fast multipole method      422
Fock matrix      169 447 460 494
Fock matrix, $\mathbb{Q}$ matrix      483 622
Fock matrix, active Fock matrix      482 622 797
Fock matrix, CASSCF Fock matrix      797
Fock matrix, cost of evaluation      484
Fock matrix, Fock matrix in AO basis      460 464
Fock matrix, generalized Fock matrix      481 622
Fock matrix, high-spin Fock matrix      484
Fock matrix, inactive Fock matrix      482 494 622 688 797
Fock operator, CASSCF Fock operator      797
Fock operator, closed-shell Fock operator in orbital basis      444 450 491 494 760
Fock operator, Fock operator in spin-orbital basis      169 192 662 740 750
Fock potential      169 450
Fock space      1
Fock space, direct sum of subspaces      2
Fock space, inner product for nonorthogonal spin orbitals      27
Fock space, inner product for orthogonal spin orbitals      1 8
Force constants of harmonic potentials      203 230
Force constants of molecular force fields      847
Force constants, cubic force constants      849
Force constants, quadratic force constants      847
Force constants, quartic force constants      849
Front-door intruders      772
Frozen-core approximation      301 303
Full CI (FCI) theory      162 524
Full CI (FCI) theory, FCI benchmarks      163
Full CI (FCI) theory, ground state of $\mathrm{H_2O}$       165
Full CI (FCI) theory, ground state of $\mathrm{H_2}$       163
Full CI (FCI) theory, ground state of BH      302 326
Full CI (FCI) theory, number of determinants in FCI      163 525 551
Gamma function, Euler gamma function      220 368
Gamma function, incomplete gamma function      368
Gamma function, relation to Boys function      368
Gamma function, relation to factorial functions      220
Gamma function, relation to Pochhammer symbol      371
Gauge transformations      110
Gaussian (normal) probability distribution      539 821
Gaussian basis sets      287
Gaussian basis sets for correlated calculations      300
Gaussian basis sets, 3-21G basis set      297
Gaussian basis sets, 6-311G basis set      300
Gaussian basis sets, 6-31G basis set      297
Gaussian basis sets, 6-31G* basis set      300
Gaussian basis sets, 6-31G** basis set      300
Gaussian basis sets, atomic natural orbitals (ANOs)      301 304
Gaussian basis sets, aug-cc-pVXZ basis sets      312 314
Gaussian basis sets, basis-set convergence      315
Gaussian basis sets, cc-pCVXZ basis sets      312
Gaussian basis sets, cc-pVXZ basis sets      308
Gaussian basis sets, contracted GTOs      294
Gaussian basis sets, correlating orbitals      180 304
Gaussian basis sets, correlation-consistent basis sets      301 307
Gaussian basis sets, Dunning — Huzinaga basis sets      295
Gaussian basis sets, DZ basis sets      228 300
Gaussian basis sets, DZP basis sets      300
Gaussian basis sets, even-tempered basis sets      292
Gaussian basis sets, floating orbitals      299
Gaussian basis sets, Huzinaga basis sets      291
Gaussian basis sets, polarization functions      299
Gaussian basis sets, primitive GTOs      291 294
Gaussian basis sets, split-valence basis sets      297 300
Gaussian basis sets, STO-kG basis sets      288
Gaussian basis sets, TZ basis sets      300
Gaussian charge distributions      361
Gaussian charge distributions, electrostatics of spherical distributions      364
Gaussian charge distributions, extent of Gaussian      402 424
Gaussian charge distributions, Gaussian-type orbitals (GTOs)      232
Gaussian charge distributions, spherical charge distributions      361
Gaussian overlap distributions      341
Gaussian overlap distributions, derivatives      343
Gaussian overlap distributions, expansion in Cartesian Gaussians      343
Gaussian overlap distributions, expansion in Hermite Gaussians      353
Gaussian overlap distributions, factorization      342
Gaussian overlap distributions, recurrence relations      343
Gaussian product rule      238 341
Gaussian product rule, illustration      342
Gaussian product rule, pre-exponential factor      341

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