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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
Principal quantum number of ANOs      305
Principal quantum number of GTOs      234
Principal quantum number of HO functions      230 231 236
Principal quantum number of hydrogenic functions      221
Principal quantum number of Laguerre functions      222
Principal quantum number of principal expansion      263 273
Principal quantum number of STOs      226 227
Principal quantum number, dependence of helium energy contribution on      275
Principal quantum number, dependence of helium energy error on      266 274 276 322
Principal quantum number, relation to cardinal number      322
Products of second-quantization operators      14
Projected coupled-cluster equations      188 657
Projected coupled-cluster equations in orbital basis (CCSD)      693 695
Projected coupled-cluster equations in spin-orbital basis      188 657 661
Projected coupled-cluster equations in spin-restricted coupled-cluster theory      705
Projected coupled-cluster equations, perturbation analysis of      784
Purification of Hartree — Fock AO density matrix      470
Purification of Hartree — Fock AO density matrix, convergence of purification      471
QCI, quadratic CI [model]      702
QCISD, QCI singles-and-doubles [model]      702
Quadratic CI (QCI) theory      702
Quadratic CI (QCI) theory, QCISD model      702
Quadratic CI (QCI) theory, relation to CCSD      702
Quadratic CI (QCI) theory, relation to CISD      703
Quadratic CI (QCI) theory, size-extensivity      703
Quadratic convergence      479 545
Quadratic convergence, numerical examples in CI theory      546
Quadratic convergence, numerical examples in Hartree — Fock theory      463 496
Quadratic convergence, numerical examples in MCSCF theory      628
Quasi-Newton method, CI optimization      547 548
Quasi-Newton method, coupled-cluster optimization      672 673
R12 methods      265 267
R12 methods, CI-R12      265
R12 methods, comparison with extrapolation      323 324 842
R12 methods, ground-state helium energy      264 266
R12 methods, R12 energies of Ne, $\mathrm{H_2O}$ and $\mathrm{N_2}$ systems      320
R12 methods, R12 interaction energy of $\mathrm{H_2O}$ dimer      333
Raising operator      38
Random-phase approximation (RPA)      501
Rank of operators      25 663
Rank reduction      25
Rank reduction, examples of rank reduction      26 46 445 447
Rank reduction, rank-reduction rule      25 127
RAS      see “Restricted active space (RAS)”
RAS, restricted active space      526 599
RASSCF      599 (see also “Multiconfigurational SCF (MCSCF) theory”)
RASSCF, RAS self-consistent field [model]      599
Rayleigh method      545
Rayleigh — Schrodinger perturbation theory (RSPT)      725
Rayleigh — Schrodinger perturbation theory (RSPT), 2n+2 rule      733 734
Rayleigh — Schrodinger perturbation theory (RSPT), energy corrections to fifth order using Wigner’s rule      733
Rayleigh — Schrodinger perturbation theory (RSPT), explicit corrections to third order      728
Rayleigh — Schrodinger perturbation theory (RSPT), Hylleraas functional      734
Rayleigh — Schrodinger perturbation theory (RSPT), Hylleraas variation method      734 736
Rayleigh — Schrodinger perturbation theory (RSPT), nth-order energy      727 730
Rayleigh — Schrodinger perturbation theory (RSPT), nth-order energy using Wigner’s rule      733
Rayleigh — Schrodinger perturbation theory (RSPT), nth-order Lagrangian      731
Rayleigh — Schrodinger perturbation theory (RSPT), nth-order wave-function corrections      727 730
Rayleigh — Schrodinger perturbation theory (RSPT), RSPT Lagrangian      730
Rayleigh — Schrodinger perturbation theory (RSPT), size-extensivity      736
Rayleigh — Schrodinger perturbation theory (RSPT), Wigner’s 2n+1 rule      728 733 734
Reaction enthalpies      865 (see also “Calibration of methods”)
Reaction enthalpies, basis-set extrapolation      870
Reaction enthalpies, calculated and experimental reaction enthalpies (table)      874
Reaction enthalpies, core correlation      871
Reaction enthalpies, experimental reaction enthalpies      865
Reaction enthalpies, experimental reference data (table)      866
Reaction enthalpies, statistical analysis of errors in calculated reaction enthalpies      867
Reduced density matrices      24 65 66
Reduced exponent      341 364
Redundant parameters for closed-shell CSFs in Hartree — Fock theory      436 507
Redundant parameters for two-electron open-shell CSFs in Hartree — Fock theory      436 608
Redundant parameters in CASPT      797
Redundant parameters in Hartree — Fock MO theory      435 437 440
Redundant parameters in OCC theory      701
Redundant parameters of Hartree — Fock AO density matrix      469
Redundant parameters of linear CI expansions      540 541 544 601
Redundant parameters of MCSCF CI parametrization      601 604 605 610 627 630
Redundant parameters of MCSCF orbital parametrization      601 605 608 627 628 643
Redundant parameters of triples excitation manifold      761
Redundant parameters, phase factors      83
Relativistic corrections      849
Relativistic corrections, corrections for neon atom      853
Relativistic corrections, corrections to atomization energies      854
Relativistic corrections, corrections to atomization energies (table)      855
Relativistic corrections, corrections to electronic energies (table)      852
Relativistic corrections, corrections to reaction enthalpies      865
Relativistic corrections, corrections to reaction enthalpies (table)      866
Relativistic corrections, first-order spin-orbit correction from experiment      851
Relativistic corrections, mass-velocity operator      852
Relativistic corrections, one-electron Darwin operator      852
Relativistic corrections, spin-orbit coupling      851
Relativistic corrections, spin-orbit operator (effective)      40 45
Relativistic corrections, spin-spin contact operator      66 853
Relativistic corrections, two-electron Darwin operator      66 853
Restricted active space (RAS)      526 551 564 572
Restricted active space (RAS), RAS1, RAS2, RAS3      526
Restricted active space (RAS), RASSCF      599 607
Restricted Hartree — Fock (RHF) theory      170 434 497 498 499
Restricted-step method      see “Trust-region method”
RFF, remote FF [box]      421
RHF, restricted Hartree — Fock [model]      170 434
Rn, Rys [type] n [two-electron integral scheme]      397
Rodrigues expression, Hermite polynomials      236 352
Rodrigues expression, Laguerre polynomials      218
Rodrigues expression, Legendre polynomials      207
Root flipping in MCSCF theory      610
Roothaan — Hall SCF equations      458 465 475 476 490 509
RPA, random-phase approximation      501
RSPT, Rayleigh — Schrodinger perturbation theory      724 728
Rys polynomials, plot of Rys polynomials      391
Rys polynomials, plot of Rys roots and weights      392
Rys polynomials, relation to Hermite polynomials      391 392
Rys polynomials, relation to Legendre polynomials      391 392
Rys polynomials, Rys polynomials (J- and R-type)      390
Rys quadrature      387 (see also “Molecular integral evaluation”)
Rys quadrature, Cartesian Coulomb integrals (one-electron)      394
Rys quadrature, Cartesian Coulomb integrals (two-electron)      395
Rys quadrature, computational considerations      397
Rys quadrature, Obara — Saika recursion for Cartesian intermediates      395
Rys quadrature, R1 scheme      398
Rys quadrature, R2 scheme      397
Rys quadrature, R4 scheme      397
Rys quadrature, Rys scheme for Hermite integrals      392
S commutators      85 469
Scaling properties for large systems      398
Scaling properties for large systems, classical and nonclassical Coulomb contributions      401
Scaling properties for large systems, extent of Gaussian      402 424
Scaling properties for large systems, linear scaling of CFMM      425
Scaling properties for large systems, linear scaling of density-based Hartree — Fock method      477
Scaling properties for large systems, linear scaling of FMM      423
Scaling properties for large systems, linear scaling of kinetic-energy integrals      398
Scaling properties for large systems, linear scaling of nonclassical Coulomb interaction      401
Scaling properties for large systems, linear scaling of overlap integrals      398
Scaling properties for large systems, quadratic scaling of Coulomb integrals      400
Scaling properties for large systems, upper bound to nonclassical Coulomb contribution      402
SCF, self-consistent field [model]      169 448
Schrodinger equation, time-independent for central-field systems      205
Schrodinger equation, time-independent for helium atom      259
Schrodinger equation, time-independent for N-electron systems      107 143
Schrodinger equation, time-independent for one-electron radial functions      206
Schwarz inequality for density-matrix elements      21 23
Schwarz inequality for two-electron integrals      404
Second quantization compared with first quantization      18
Second-order optimization      478 543 610 671
Second-order optimization in density-based Hartree — Fock theory      480
Second-order optimization, augmented-Hessian method in MCSCF theory      620
Second-order optimization, comparison with other methods (in Hartree — Fock theory)      463 480 494 496
Second-order optimization, GBT-vector optimization in Hartree — Fock theory      491
Second-order optimization, Newton eigenvector method in MCSCF theory      616
Second-order optimization, Newton’s method      478 543 610 671
Second-order optimization, Newton’s method in CI theory      543
Second-order optimization, Newton’s method in coupled-cluster theory      671
Second-order optimization, Newton’s method in Hartree — Fock theory      478 511
Second-order optimization, Newton’s method in MCSCF theory      610
Second-order optimization, norm-extended optimization (NEO) in MCSCF theory      619 628
Second-order optimization, quadratic convergence      479 545
Second-order optimization, trust-region method      479 610
Secondary orbitals      178 434 526 599
Self-consistent field (SCF) method      169 448 475 495 496 509
Separability      see also “Size-extensivity”
Separability, additive      127
Separability, manifest      134 186
Separability, multiplicative      127
Sherman — Morrison formula      545
shift operators      38 40 48 240
Similarity-transformed Hamiltonian in CCPT      750
Similarity-transformed Hamiltonian in coupled-cluster theory      657
Similarity-transformed Hamiltonian in EOM-CC      680
Singlet instabilities      see also “Triplet instabilities”
Singlet instabilities in allyl radical (CISD)      573
Singlet instabilities in allyl radical (RHF)      502
Singlet instabilities, general discussion      496 498
Singlet instabilities, removal of allyl instability by MCSCF theory      641
Singlet operators      42 (see also “Spin tensor operators”)
Size-extensivity for exact states      109 126
Size-extensivity for exponential wave functions      132 187 665 754
Size-extensivity for FCI wave functions      131 528
Size-extensivity for linear variational wave functions      129 186 527
Size-extensivity for truncated CI wave functions      131 529
Size-extensivity in CASPT      798
Size-extensivity in CCPT      754 759
Size-extensivity in EOM-CC theory      683
Size-extensivity in Hartree — Fock theory      442
Size-extensivity in linked coupled-cluster theory      665
Size-extensivity in MPPT      747
Size-extensivity in RSPT      736
Size-extensivity in unlinked coupled-cluster theory      668
Size-extensivity, additive separability      127 132 443 528 667 748 798
Size-extensivity, CID model calculations for noninteracting $\mathrm{H_2}$ molecules      535
Size-extensivity, manifest separability      134 186
Size-extensivity, multiplicative separability      127 132 443 533 667 669 737 798
Size-extensivity, numerical study for CCSD      669
Size-extensivity, numerical study for CISD      531
Size-extensivity, termwise size-extensivity      667 749
Slater determinants      1
Slater determinants as products of spin strings      550
Slater determinants for closed-shell states      51
Slater determinants for high-spin states      51
Slater determinants, orbital rotations of      86 89
Slater determinants, relation to ON vectors      2
Slater determinants, spin projection of      47
Slater determinants, total spin of      49
Slater determinants, transformation to CSFs      59
Slater — Condon rules      9 554
Slater-type orbitals (STOs)      see also “Basis functions (one-electron)”
Slater-type orbitals (STOs), definition      225 288
Slater-type orbitals (STOs), expectation value of r      226
Slater-type orbitals (STOs), integrals of minimal STO basis for $\mathrm{H_2}$ (table)      149
Slater-type orbitals (STOs), minimal STO basis for $\mathrm{H_2}$      146
Slater-type orbitals (STOs), overlap integral      146 196
Slater-type orbitals (STOs), relation to Laguerre functions      225
Slater-type orbitals (STOs), relation to STO-fcG basis sets      288
Slater-type orbitals (STOs), STO basis sets      227
Slater-type orbitals (STOs), use in helium wave function      262
Sobolev norms      202 (see also “Completeness”)
Solid harmonics, addition theorem      407
Solid harmonics, Cartesian expansion of complex solid harmonics      209
Solid harmonics, Cartesian expansion of real solid harmonics      215
Solid harmonics, complex solid harmonics      209
Solid harmonics, Condon — Shortley phase convention      210 248
Solid harmonics, irregular solid harmonics      407
Solid harmonics, normalization of      241
Solid harmonics, pictorial representation of      212
Solid harmonics, Racah’s normalization      210
Solid harmonics, real solid harmonics      210
Solid harmonics, recurrence relations for real solid harmonics      215 218
Solid harmonics, recurrence relations for scaled irregular solid harmonics      416
Solid harmonics, recurrence relations for scaled regular solid harmonics      416
Solid harmonics, regular solid harmonics      407
Solid harmonics, relation to spherical harmonics      209
Solid harmonics, symmetries of      210
Solid harmonics, table of      211
Spatial symmetries of the exact state      109
Spherical harmonics      see also “Basis functions (one-electron)”
Spherical harmonics, addition theorem      263 406
Spherical harmonics, central-field system      205
Spherical harmonics, Condon — Shortley phase convention      207
Spherical harmonics, definition in terms of Legendre polynomials      207
Spherical harmonics, Racah’s normalization      209
Spherical harmonics, relation to solid harmonics      209
Spherical harmonics, table of      208
Spherical-harmonic GTOs      232 234 287 337
Spin functions (one-electron)      34
Spin operators      38
Spin orbitals      1 35
Spin properties of the exact state      109
Spin strings      550 (see also “Direct CI methods”)
Spin strings, allowed vertices      556
Spin strings, alpha and beta strings      550
Spin strings, arc and vertex weights      557
Spin strings, factorization of determinants in spin strings      550
Spin strings, graphical representation      556
Spin strings, head and tail of graph      556
Spin strings, number of strings      551
Spin strings, paths      556
Spin strings, reverse lexical ordering scheme      557
Spin strings, separation into substrings      566
Spin strings, string classes      552
Spin strings, vertical and diagonal arcs      556
Spin strings, vertices      556
Spin tensor operators, definition      41
Spin tensor operators, doublet creation and annihilation operators      43
Spin tensor operators, genealogical coupling of operators      60
Spin tensor operators, singlet cluster operators      685
Spin tensor operators, singlet excitation operators      44
Spin tensor operators, singlet Hamiltonian      45
Spin tensor operators, singlet two-body creation operators      43
Spin tensor operators, triplet excitation operators      44
Spin tensor operators, triplet spin-orbit operator      45
Spin tensor operators, triplet two-body creation operators      43
Spin tensor state      42
Spin-adapted open-shell coupled-cluster theory      709
Spin-combined basis      567
Spin-flip operators      97
Spin-flip operators, use in CI theory      567
Spin-free operators      36
Spin-orbit corrections      see “Relativistic corrections”
Spin-orbit operator (effective)      40 45
Spin-restricted open-shell coupled-cluster theory      704
Spin-restricted open-shell coupled-cluster theory, projected energy and spin equations      705
Spin-restricted open-shell coupled-cluster theory, relation to partially spin-adapted theory      711
Spin-restricted open-shell coupled-cluster theory, spin-restricted coupled-cluster ansatz      707
Spin-restricted open-shell coupled-cluster theory, structure and solution of spin equations      706
Spin-restricted open-shell coupled-cluster theory, structure of projection manifold      708
Spin-restricted open-shell coupled-cluster theory, total spin in spin-restricted theory      707
Spin-restricted open-shell coupled-cluster theory, variational Lagrangian      708
Spin-spin contact operator      66 853
Split-valence basis sets      297
Square-integrable functions, N-electron      108
Square-integrable functions, one-electron      201 202
Standard deviation      539 821
Standard models      142
State-averaged MCSCF theory      638
State-transfer operators      639
Static correlation      162 165 278 526
Statistical analysis, atomization energies      855
Statistical analysis, bond angles      833
Statistical analysis, bond distances      822
Statistical analysis, dipole moments      839
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