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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.


Язык: en

Рубрика: Химия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 386

Добавлена в каталог: 21.02.2007

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Molecular integral evaluation, pre-exponential factor      341
Molecular integral evaluation, reduced exponent      341 364
Molecular integral evaluation, Rys quadrature      387
Molecular integrals      336
Molecular integrals, $\mathrm{H_2}$ minimal STO basis (table)      149
Molecular integrals, molecular integral evaluation      336
Molecular integrals, one-electron integrals      9 10 14 29 38 336 451
Molecular integrals, one-index transformations      67 488 510 511 624
Molecular integrals, T1-transformed integrals      690
Molecular integrals, two-electron integrals      11 13 14 29 38 336 451 464
Molecular orbitals (MOs)      144
Molecular orbitals (MOs), active orbitals      178 434 526 599
Molecular orbitals (MOs), canonical orbitals      169 444
Molecular orbitals (MOs), core orbitals      301
Molecular orbitals (MOs), inactive orbitals      178 434 526 599
Molecular orbitals (MOs), natural orbitals      21 63
Molecular orbitals (MOs), numerical orbitals      201 223 264 291 296 307 318 319
Molecular orbitals (MOs), secondary orbitals      178 434 526 599
Molecular orbitals (MOs), spin orbitals      1 35
Molecular orbitals (MOs), valence orbitals      301
Molecular orbitals (MOs), virtual orbitals      178 301 304 434 451 455 629 818
Molecular-orbital energy-level diagram for $\mathrm{H_2O}$      166
Molecular-orbital energy-level diagram for $\mathrm{H_2}$      147
Momentum integrals      348 (see also “Molecular integral evaluation”)
MP4(SDQ), MP4 singles-doubles-and-quadruples [perturbation theory]      769
MPn, nth-order Muller — Plesset [perturbation theory]      193 747
MPPT, Muller — Plesset perturbation theory      192 724 739
MRCI, multireference CI [model]      183
MRSDCI, multireference singles-and-doubles CI [model]      183 526
Muller — Plesset perturbation theory (MPPT)      192 739
Muller — Plesset perturbation theory (MPPT), convergence of MPPT series      193 195 778 802
Muller — Plesset perturbation theory (MPPT), dissociation of $\mathrm{H_2O}$      194
Muller — Plesset perturbation theory (MPPT), dissociation of $\mathrm{H_2}$      195
Muller — Plesset perturbation theory (MPPT), factorization of disconnected quadruples      744
Muller — Plesset perturbation theory (MPPT), fluctuation potential      192 740 760 781
Muller — Plesset perturbation theory (MPPT), hybrid methods      191 789 793 795
Muller — Plesset perturbation theory (MPPT), introduction      192
Muller — Plesset perturbation theory (MPPT), MP1 wave function      741 746
Muller — Plesset perturbation theory (MPPT), MP2 energies (table)      841
Muller — Plesset perturbation theory (MPPT), MP2 energy      193 745 746 766
Muller — Plesset perturbation theory (MPPT), MP2 wave function      742
Muller — Plesset perturbation theory (MPPT), MP3 energy      193 745 767
Muller — Plesset perturbation theory (MPPT), MP4 energy      193 768
Muller — Plesset perturbation theory (MPPT), MP4(SDQ) energy      769
Muller — Plesset perturbation theory (MPPT), numerical exercise      806
Muller — Plesset perturbation theory (MPPT), oscillations of bond distances      822 825 831
Muller — Plesset perturbation theory (MPPT), partitioning of Hamiltonian      740
Muller — Plesset perturbation theory (MPPT), size-extensivity      747
Muller — Plesset perturbation theory (MPPT), termwise separability      749
Muller — Plesset perturbation theory (MPPT), zero-order system      740
Multiconfigurational perturbation theory      196 796
Multiconfigurational perturbation theory, CASPT      796
Multiconfigurational perturbation theory, CASPT1 wave function      800
Multiconfigurational perturbation theory, CASPT2 energy      801
Multiconfigurational perturbation theory, CASSCF Fock matrix      797
Multiconfigurational perturbation theory, CASSCF Fock operator      797
Multiconfigurational perturbation theory, convergence of CASPT series      802
Multiconfigurational perturbation theory, internal contraction of wave function      800
Multiconfigurational perturbation theory, numerical example      801
Multiconfigurational perturbation theory, size-extensivity      798
Multiconfigurational perturbation theory, zero-order Hamiltonian      796 798
Multiconfigurational SCF (MCSCF) theory      598
Multiconfigurational SCF (MCSCF) theory, augmented electronic Hessian      616
Multiconfigurational SCF (MCSCF) theory, augmented-Hessian method      620
Multiconfigurational SCF (MCSCF) theory, CASSCF      178 599
Multiconfigurational SCF (MCSCF) theory, complete active space (CAS)      178 526 599
Multiconfigurational SCF (MCSCF) theory, configuration space (selection of)      177 178
Multiconfigurational SCF (MCSCF) theory, configuration trial vector      626
Multiconfigurational SCF (MCSCF) theory, construction of electronic gradient      622
Multiconfigurational SCF (MCSCF) theory, electronic gradient      602 603 608 639
Multiconfigurational SCF (MCSCF) theory, electronic Hessian      602 603 604 609 639
Multiconfigurational SCF (MCSCF) theory, exponential parametrization for a single reference state      631
Multiconfigurational SCF (MCSCF) theory, exponential parametrization for several reference states      634
Multiconfigurational SCF (MCSCF) theory, exponential parametrization of configuration space      630
Multiconfigurational SCF (MCSCF) theory, generalized Brillouin theorem (GBT)      608
Multiconfigurational SCF (MCSCF) theory, generalized Fock matrix      481 622
Multiconfigurational SCF (MCSCF) theory, ground state of $\mathrm{H_2O}$      178
Multiconfigurational SCF (MCSCF) theory, ground state of $\mathrm{H_2}$      177
Multiconfigurational SCF (MCSCF) theory, Hessian transformations      623
Multiconfigurational SCF (MCSCF) theory, inactive energy      623
Multiconfigurational SCF (MCSCF) theory, introduction      176
Multiconfigurational SCF (MCSCF) theory, MCSCF energy function      177 601
Multiconfigurational SCF (MCSCF) theory, MCSCF second-order Lagrangian      617
Multiconfigurational SCF (MCSCF) theory, Newton eigenvector method      616 617
Multiconfigurational SCF (MCSCF) theory, Newton trust-region method      610
Multiconfigurational SCF (MCSCF) theory, norm extended optimization (NEO)      619 628
Multiconfigurational SCF (MCSCF) theory, numerical examples of optimization      628
Multiconfigurational SCF (MCSCF) theory, one-index transformations      67 488 624
Multiconfigurational SCF (MCSCF) theory, orbital trial vector      626
Multiconfigurational SCF (MCSCF) theory, parametrization of MCSCF wave function      600
Multiconfigurational SCF (MCSCF) theory, rank-1 contributions to electronic Hessian      604
Multiconfigurational SCF (MCSCF) theory, RASSCF      599
Multiconfigurational SCF (MCSCF) theory, redundancy of CI expansion      601
Multiconfigurational SCF (MCSCF) theory, redundant CASSCF and RASSCF rotations      607 643
Multiconfigurational SCF (MCSCF) theory, redundant orbital rotations      605
Multiconfigurational SCF (MCSCF) theory, redundant parameters representation of orthogonal complement      633 637
Multiconfigurational SCF (MCSCF) theory, restricted active space (RAS)      526 599
Multiconfigurational SCF (MCSCF) theory, root flipping      610
Multiconfigurational SCF (MCSCF) theory, state-averaged MCSCF theory      638
Multiconfigurational SCF (MCSCF) theory, structure of electronic Hessian (numerical example)      626
Multiconfigurational SCF (MCSCF) theory, transition density matrix      624
Multiconfigurational SCF (MCSCF) theory, trust-region method      610
Multiple solutions in Hartree — Fock theory      174 502 504
Multiple solutions in MCSCF theory      629
Multipole method for Coulomb integrals      405
Multipole method for Coulomb integrals, complex bipolar multipole expansion      407 408
Multipole method for Coulomb integrals, complex interaction matrix      408
Multipole method for Coulomb integrals, complex multipole moments      408
Multipole method for Coulomb integrals, complex translation matrix      411
Multipole method for Coulomb integrals, convergence of multipole expansion      409
Multipole method for Coulomb integrals, multipole method for contracted integrals      409
Multipole method for Coulomb integrals, multipole method for primitive integrals      405
Multipole method for Coulomb integrals, real bipolar multipole expansion      415
Multipole method for Coulomb integrals, real interaction matrix      414
Multipole method for Coulomb integrals, real multipole moments      412
Multipole method for Coulomb integrals, real translation matrix      413
Multipole method for Coulomb integrals, translation of multipole moments      410
Multipole method for Coulomb integrals, zero-order multipole expansion      408 428
Multipole method for large systems      417
Multipole method for large systems, box      417
Multipole method for large systems, branch      424
Multipole method for large systems, child box      420
Multipole method for large systems, continuous FMM (CFMM)      423
Multipole method for large systems, far-field (FF) boxes      419
Multipole method for large systems, far-field (FF) contributions      419
Multipole method for large systems, far-field (FF) vector      419
Multipole method for large systems, fast multipole method (FMM)      421
Multipole method for large systems, linear scaling of the number of boxes in FMM      422
Multipole method for large systems, local FF (LFF) boxes      421
Multipole method for large systems, naive multipole method      417
Multipole method for large systems, near-field (NF) boxes      419
Multipole method for large systems, near-field (NF) contributions      418
Multipole method for large systems, near-field (NF) width parameter      423 424
Multipole method for large systems, nearest neighbours      418
Multipole method for large systems, parent box      420
Multipole method for large systems, remote FF (RFF) boxes      421
Multipole method for large systems, two-level multipole method      420
Multipole method for large systems, well separated boxes      418
Multipole moments of charge distributions, complex multipole moments      408
Multipole moments of charge distributions, real multipole moments      412
Multipole-moment integrals      see also “Molecular integral evaluation”
Multipole-moment integrals, Gauss — Hermite quadrature      361
Multipole-moment integrals, McMurchie — Davidson method      356
Multipole-moment integrals, Obara — Saika method      346
Multireference CI theory      183 526 599
N-electron error      819 (see also “Errors in calculations”)
N-resolution method      558 (see also “Direct CI methods”)
Natural orbitals      21 63
Natural orbitals in MCSCF optimization (as initial orbitals)      628
Natural orbitals in orbital basis      63 304
Natural orbitals in spin-orbital basis      21
Natural orbitals, atomic natural orbitals (ANOs)      304
Natural-orbital occupation numbers for orbitals      63
Natural-orbital occupation numbers for spin orbitals      21
Natural-orbital occupation numbers of $\mathrm{H_2O}$      168
Natural-orbital occupation numbers of $\mathrm{H_2}$      164
Natural-orbital occupation numbers of carbon atom      305
Natural-orbital occupation numbers of sample molecules      818
Natural-orbital occupation numbers, atomic natural orbitals (ANOs)      304
NEO, norm-extended optimization      619
Nested commutators      27
Newton eigenvector method      616
Newton’s method      see also “Second-order optimization”
Newton’s method, convergence rate of Newton’s method      545
Newton’s method, Newton’s method in CI theory      543
Newton’s method, Newton’s method in coupled-cluster theory      671
Newton’s method, Newton’s method in Hartree — Fock theory      478 511
Newton’s method, Newton’s method in MCSCF theory      610
NF, near-field [box]      418
NN, nearest neighbour [box]      418
Nondifferentiability of electronic wave function      259 261
Nonorthogonal spin orbitals      27
Norm-extended optimization (NEO)      619 628
Normal distribution      821 (see also “Distributions”)
Number operator      7 8 108
Number-conserving operator      7
Numerical quadrature      see “Gauss quadrature”
Obara — Saika method      344 381
Obara — Saika method, angular-momentum integrals      348
Obara — Saika method, computational considerations for Coulomb integrals      386
Obara — Saika method, differential-operator integrals      347
Obara — Saika method, kinetic-energy integrals      348
Obara — Saika method, momentum integrals      348
Obara — Saika method, multipole-moment integrals      346
Obara — Saika method, one-electron Coulomb integrals      382
Obara — Saika method, OS1, OS2, OS4 schemes      386 387 398
Obara — Saika method, overlap integrals      345
Obara — Saika method, recurrence relations for differential-operator integrals      348
Obara — Saika method, recurrence relations for kinetic-energy integrals      349
Obara — Saika method, recurrence relations for multipole-moment integrals      347
Obara — Saika method, recurrence relations for one-electron Coulomb integrals      382
Obara — Saika method, recurrence relations for overlap integrals      345
Obara — Saika method, recurrence relations for two-electron Coulomb integrals      385
Obara — Saika method, translational recurrence relations      345 346
Obara — Saika method, two-electron Coulomb integrals      383
OCC, orbital-optimized coupled-cluster [model]      699
OCCD, OCC doubles [model]      701
Occupation numbers as diagonal elements of density matrix      20 63
Occupation numbers as elements of ON vector natural-orbital occupation numbers      21 63 304
Occupation-number (ON) operator for orbitals      51
Occupation-number (ON) operator for spin orbitals      6 8
Occupation-number (ON) vector      1 8
Occupation-number (ON) vector as string of creation operators      3
Occupation-number (ON) vector, relation to Slater determinants      2
ON, occupation-number [vector, operator]      1 6
One- and A’-electron expansions      143 819
One-electron integrals      see also “Molecular integrals”
One-electron integrals in orbital basis for mixed operators      40
One-electron integrals in orbital basis for spin operators      38
One-electron integrals in orbital basis for spin-free operators      36
One-electron integrals in spin-orbital basis      10 14
One-electron integrals, molecular integral evaluation      336
One-electron operators (in second quantization)      9
One-electron operators (in second quantization) for nonorthogonal spin orbitals      29
One-electron operators (in second quantization) for orthonormal orbitals      35
One-electron operators (in second quantization) for orthonormal spin orbitals      9
One-index transformations in AO basis      490 510 511
One-index transformations in MO basis      67 488 624
Operation count      484
Orbital configuration      51
Orbital energies      169 444 450 455
Orbital rotations      80
Orbital rotations in CI theory      569
Orbital rotations in Hartree — Fock theory      435 497
Orbital rotations in MCSCF theory      600 601 605
Orbital rotations in OCC theory      698
Orbital rotations, exponential unitary operator      86
Orbital rotations, redundant parameters      435 440 507 605 643
Orbital-optimized coupled-cluster (OCC) theory      698
Orbital-optimized coupled-cluster (OCC) theory, generalized Brillouin theorem (GBT)      700
Orbital-optimized coupled-cluster (OCC) theory, numerical comparison of OCCD and CCSD      702
Orbital-optimized coupled-cluster (OCC) theory, OCC ansatz      699
Orbital-optimized coupled-cluster (OCC) theory, OCC doubles (OCCD) model      701
Orbital-optimized coupled-cluster (OCC) theory, OCC Lagrangian      700
Orthogonal polynomials      358
Orthogonal polynomials, Chebyshev polynomials      358
Orthogonal polynomials, Hermite polynomials      236 358
Orthogonal polynomials, Laguerre polynomials      219 358
Orthogonal polynomials, Legendre polynomials      208 358
Orthogonal polynomials, orthogonality relations      358
Orthogonal polynomials, Rodrigues expression      207 219 236 352
Orthogonal polynomials, Rys polynomials      390
Orthogonal polynomials, two-term recurrence relations      358
OSn, Obara — Saika [type] n [two-electron integral scheme]      386
Overlap integrals      see also “Molecular integral evaluation”
Overlap integrals of spherical Gaussian charge distributions      344
Overlap integrals, Gauss — Hermite quadrature      361
Overlap integrals, linear scaling for large systems      398
Overlap integrals, McMurchie — Davidson method      357
Overlap integrals, Obara — Saika method      345
Overlap integrals, STO overlap      146 196
Pair clusters      649 (see also “Coupled-cluster theory”)
Pair occupations      22 63
Partial-wave expansion      267 (see also “Helium atom”)
Partial-wave expansion of helium wave function      268
Partial-wave expansion of interelectronic distance      267
Partial-wave expansion, comparison with principal expansion      275
Partial-wave expansion, energy convergence for helium atom      270
Partial-wave expansion, extrapolation of helium energy      272
Partial-wave expansion, truncation error in helium atom      272
Partially spin-adapted open-shell coupled-cluster theory      711
Particle rank      25 663
Particle-number operator      7 8 108
Pauli antisymmetry principle      22 44 108 158 169 278 528
Pauli repulsion      330
Perturbation analysis of coupled-cluster hierarchy      784
Perturbation analysis of coupled-cluster hierarchy, CCSD model      786 787
Perturbation analysis of coupled-cluster hierarchy, CCSDT model      786 787
Perturbation analysis of coupled-cluster hierarchy, CCSDTQ model      787
Perturbation analysis of coupled-cluster hierarchy, numerical illustration      788 789
Perturbation analysis of coupled-cluster hierarchy, [3N/2] rule for truncation levels      787
Perturbation theory      724
Perturbation theory, 2n+2 rule      733 734
Perturbation theory, Brillouin — Wigner perturbation theory (BWPT)      728 804
Perturbation theory, convergence in perturbation theory      193 769
Perturbation theory, Epstein — Nesbet zero-order Hamiltonian      739
Perturbation theory, hybrid methods      191 789 793 795
Perturbation theory, Hylleraas functional      734
Perturbation theory, Hylleraas variation method      734 736
Perturbation theory, introduction      192
Perturbation theory, Muller — Plesset perturbation theory (MPPT)      192 739
Perturbation theory, multiconfigurational perturbation theory      196 796
Perturbation theory, perturbation analysis of coupled-cluster hierarchy      784
Perturbation theory, Pochhammer symbol      371
Perturbation theory, Rayleigh — Schrodinger perturbation theory (RSPT)      725
Perturbation theory, Wigner’s 2n+1 rule      728 733 734
Points of degeneracy      771
Polarization functions      165 299
Polarization functions, choice of exponents      299 300
Polarization functions, effect on geometries      300 316
Polarization functions, relation to correlating orbitals      307
Pre-exponential factor      341
Primitive GTOs      291 294
Principal expansion      see also “Helium atom”
Principal expansion of helium wave function      263 273
Principal expansion, basis-set extrapolation      322
Principal expansion, comparison with partial-wave expansion      275
Principal expansion, energy convergence in helium atom      274
Principal expansion, relationship to correlation-consistent basis sets      307 318
Principal expansion, truncation error in helium atom      274
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