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Авторизация |
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Helgaker T., Jorgensen P., Olsen J. — Molecular Electronic-Structure Theory. Part 2 |
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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, 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 166
Molecular-orbital energy-level diagram for 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 194
Muller — Plesset perturbation theory (MPPT), dissociation of 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 178
Multiconfigurational SCF (MCSCF) theory, ground state of 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 168
Natural-orbital occupation numbers of 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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