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Helgaker T., Jorgensen P., Olsen J. — Molecular Electronic-Structure Theory. Part 2 |
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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, and systems 320
R12 methods, R12 interaction energy of 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 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 (table) 149
Slater-type orbitals (STOs), minimal STO basis for 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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