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Helgaker T., Jorgensen P., Olsen J. — Molecular Electronic-Structure Theory. Part 2 |
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Предметный указатель |
method 456
in minimal basis 146
in minimal basis, antibonding configuration 148 150
in minimal basis, bonding configuration 148 150
in minimal basis, configuration interaction 152
in minimal basis, density functions 151 153 156 157
in minimal basis, density matrices 148
in minimal basis, dissociation limit 159
in minimal basis, MOs 146
in minimal basis, N-electron basis 148
in minimal basis, one-electron basis 146
in minimal basis, open-shell states 156
in minimal basis, potential-energy curves (illustration) 161
3-21G basis set 297
6-311G basis set 300
6-31G basis set 297
6-31G basis set, 6-31G* basis set 300
6-31G basis set, 6-31G** basis set 300
6-31G basis set, carbon exponents and contraction coefficients 298
6-31G basis set, scaling of exponents 298
Active electrons 178
Active orbitals 178 434 526 599
Addition theorem for regular solid harmonics 407
Addition theorem for spherical harmonics 263 280
Addition theorem for spherical harmonics in Racah’s normalization 406
Alpha strings 550 (see also “Spin strings”)
Analytic continuation 782
Angular-momentum integrals 348 (see also “Molecular integral evaluation”)
Angular-momentum operators, orbital angular momentum 110 205 240
Angular-momentum operators, spin angular momentum 38 45 47 65 109 704
Annihilation operators 4 8
Annihilation operators, nonorthogonal spin orbitals 28
Annihilation operators, spin properties 43
Annihilation operators, unitary transformations 86
ANO, atomic natural orbital 304
Anticommutation relations 5 8
Anticommutation relations in nonorthogonal spin-orbital basis 28
Anticommutation relations, annihilation operators 4
Anticommutation relations, creation and annihilation operators 5
Anticommutation relations, creation operators 4
Anticommutators 25 (see also “Commutation relations”)
Anticommutators, expansion rules 26
AO, atomic orbital 144
Apparent error 819 (see also “Errors in calculations”)
Asymptotic behaviour of electronic systems 110
Atomic natural orbitals (ANOs) 301 304
Atomic natural orbitals (ANOs), ANO basis sets 305
Atomic natural orbitals (ANOs), ANO energy contributions in carbon atom 306
Atomic natural orbitals (ANOs), ANO occupation numbers of carbon atom 305
Atomic natural orbitals (ANOs), ANO radial distribution functions 306
Atomic orbitals (AOs) 144 201 287 336
Atomization energies 854 (see also “Calibration of methods”)
Atomization energies, basis-set extrapolation 858
Atomization energies, calculated and experimental atomization energies (table) 865
Atomization energies, comparison of CCSD(T) and CCSDT 863
Atomization energies, core correlation 861
Atomization energies, experimental atomization energies 854
Atomization energies, experimental reference data (table) 855
Atomization energies, statistical analysis of errors in calculated atomization energies 855
aug-cc-pCVXZ, augmented cc-pCVXZ [basis] 312
aug-cc-pVXZ basis sets 312 314
aug-cc-pVXZ basis sets, dipole moments 837
aug-cc-pVXZ basis sets, weak interactions 328 331
aug-cc-pVXZ, augmented cc-pVXZ [basis] 312 314
Back-door intruders 772
Baker — Campbell — Hausdorff (BCH) expansion 81
Baker — Campbell — Hausdorff (BCH) expansion of annihilation and creation operators 88 102
Baker — Campbell — Hausdorff (BCH) expansion of CCPT energy function 753
Baker — Campbell — Hausdorff (BCH) expansion of CCPT similarity-transformed Fock operator 750 762
Baker — Campbell — Hausdorff (BCH) expansion of coupled-cluster similarity-transformed Hamiltonian 661 701 710
Baker — Campbell — Hausdorff (BCH) expansion of Hartree — Fock energy function 437
Baker — Campbell — Hausdorff (BCH) expansion of state-averaged MCSCF energy function 639
Baker — Campbell — Hausdorff (BCH) expansion, asymmetric BCH expansion 85 469
Baker — Campbell — Hausdorff (BCH) expansion, standard BCH expansion 81
Balanced level of description 820 (see also “Errors in calculations”)
Basis functions (one-electron) see also “Basis sets”
Basis functions (one-electron), algebraic approach 201
Basis functions (one-electron), angular basis 207
Basis functions (one-electron), atoms-in-molecule approach 204
Basis functions (one-electron), comparison of radial functions (Box. 6.1) 219
Basis functions (one-electron), Gaussian-type orbitals (GTOs) 232 287 336
Basis functions (one-electron), general considerations 201
Basis functions (one-electron), harmonic-oscillator (HO) functions 230 236
Basis functions (one-electron), hydrogenic functions 221
Basis functions (one-electron), Laguerre functions 222
Basis functions (one-electron), numerical orbitals 201 223 264 291 296 307 318 319
Basis functions (one-electron), separation in angular and radial parts 205
Basis functions (one-electron), Slater-type orbitals (STOs) 225
Basis functions (one-electron), universal HO basis 203
Basis sets, basis functions (one-electron), Gaussian basis sets 287
Basis sets, STO basis sets 227
Basis-set convergence see also “Basis-set extrapolation”
Basis-set convergence, torsional barrier 877
Basis-set convergence, barrier to linearity 875
Basis-set convergence, dimer interaction energy 332
Basis-set convergence, total energy and geometry 320
Basis-set convergence, inversion barrier 876
Basis-set convergence, total energy, binding energy and geometry 320 323
Basis-set convergence, atomization energies 854
Basis-set convergence, BH total energy and binding energy 326 333
Basis-set convergence, bond angles 832
Basis-set convergence, bond distances 821
Basis-set convergence, carbon total energy 311 314 315
Basis-set convergence, conformational energies 874
Basis-set convergence, convergence with respect to the cardinal number 322 842
Basis-set convergence, convergence with respect to the number of AOs 324
Basis-set convergence, correlated models 317 844
Basis-set convergence, correlation-consistent and R12 (MP2 and CCSD) energies 320 328 331 333
Basis-set convergence, dipole moments 836
Basis-set convergence, electronic energies of sample molecules 841 844
Basis-set convergence, Hartree — Fock convergence (energy) 315 844
Basis-set convergence, Hartree — Fock convergence (geometry) 317 821 832
Basis-set convergence, helium atom (cc-pVXZ) 318
Basis-set convergence, helium atom (partial-wave expansion) 271
Basis-set convergence, helium atom (principal expansion) 274 318
Basis-set convergence, neon dimer interaction energy 329
Basis-set convergence, reaction enthalpies 865
Basis-set convergence, relation to BSSE 329 333
Basis-set error 819 (see also “Errors in calculations”)
Basis-set extrapolation 322 (see also “Basis-set convergence”)
Basis-set extrapolation, dimer interaction energy 333
Basis-set extrapolation, atomization energies 858
Basis-set extrapolation, electronic energies of sample molecules 841
Basis-set extrapolation, helium atom 272 274
Basis-set extrapolation, Ne, and correlation energies 320 322 323
Basis-set extrapolation, reaction enthalpies 870
Basis-set extrapolation, relation to principal expansion 322 324
Basis-set extrapolation, two-point extrapolation 323 842
Basis-set superposition error (BSSE) 327
Basis-set superposition error (BSSE), dimer interaction energy 331
Basis-set superposition error (BSSE), BH binding energy 333
Basis-set superposition error (BSSE), counterpoise correction 327
Basis-set superposition error (BSSE), ghost basis 327
Basis-set superposition error (BSSE), neon dimer interaction energy 328
BCC, Brueckner coupled-cluster [model] 701
BCH, Baker — Campbell — Hausdorff [expansion] 81
Beta strings 550 (see also “Spin strings”)
Binding energy see Dissociation energy
Binomial probability distribution 539
Biorthogonal configuration basis in closed-shell CCPT 762
Biorthogonal configuration basis in closed-shell CCSD theory 691
Biorthogonal configuration basis in EOM-CC theory 679
Biorthogonal operators 30 570
Bipolar multipole expansion 407
Bond angles 832 (see also “Calibration of methods”)
Bond angles, calculated and experimental bond angles (table) 836
Bond angles, experimental bond angles 832
Bond angles, experimental reference data (table) 833
Bond angles, statistical analysis of errors in calculated bond angles 833
Bond distances 821 (see also “Calibration of methods”)
| Bond distances, calculated and experimental bond distances (table) 831
Bond distances, comparison of CCSD(T) and CCSDT bond distances 827
Bond distances, core correlation 828
Bond distances, experimental bond distances 822
Bond distances, experimental reference data (table) 823
Bond distances, maximum errors of calculated distances 827
Bond distances, mean absolute errors of calculated distances 825
Bond distances, mean errors of calculated distances 822
Bond distances, normal distributions of errors in calculated distances 825
Bond distances, standard deviations of calculated distances 822
Bond distances, trends in convergence 829
Born-Oppenheimer approximation 111
Boxes, Box. 1.1: fundamentals of second quantization 8
Boxes, Box. 1.2: first and second quantizations compared 18
Boxes, Box. 13.1: excitation commutators 688
Boxes, Box. 13.2: excitation commutators applied to Hartree — Fock state 688
Boxes, Box. 6.1: one-electron radial functions 219
Boys function 363 365
Boys function as special case of the confluent hypergeometric function 372
Boys function, evaluation of Boys function 366
Boys function, properties of Boys function 365
Boys function, recurrence relations for Boys function 367
Boys function, relation to error function 369
Boys function, relation to incomplete gamma function 368
Branching diagram 54
Brillouin theorem 441
Brillouin theorem in Hartree — Fock theory 441
Brillouin theorem, GBT in MCSCF theory 608
Brillouin theorem, GBT in OCC theory 700
Brillouin theorem, GBT vector 491
Brillouin theorem, generalized Brillouin theorem (GBT) 442 491 608 700
Brillouin — Wigner perturbation theory (BWPT) 728 804
Brueckner coupled-cluster (BCC) theory 701
BSSE, basis-set superposition error 327
BWPT, Brillouin — Wigner perturbation theory 728 804
Calibration of methods 817
Calibration of methods, atomization energies 854
Calibration of methods, bond angles 832
Calibration of methods, bond distances 821
Calibration of methods, conformational energies 874
Calibration of methods, dipole moments 836
Calibration of methods, electronic energies of sample molecules 841
Calibration of methods, errors in calculations 819
Calibration of methods, experimental reference data reaction enthalpies 865
Calibration of methods, relativistic corrections 849
Calibration of methods, statistical measures of errors 821
Calibration of methods, vibrational energies 847
Canonical commutators 17 18
Canonical orbitals 169 444
Canonical orbitals in CASPT 797
Canonical orbitals in coupled-cluster theory 662 672
Canonical orbitals in MCSCF optimization (as initial orbitals) 628
Canonical orbitals in Muller — Plesset theory 192 740 760
Canonical orbitals in Roothaan — Hall SCF theory 459
Canonical orbitals, canonical conditions 446
Canonical orbitals, comparison of canonical and variational conditions 449
Canonical orbitals, Hartree — Fock electronic Hessian in canonical representation 488 512
Canonical orbitals, Koopmans’ theorem 454
Canonical orbitals, orbital energies 450
Canonical orbitalssuitability as correlating orbitals 304
cardinal number 308 (see also “Correlation-consistent basis sets”)
Cardinal number, convergence with respect to cardinal number 322
Cardinal number, dependence of computational cost on cardinal number 310
Cardinal number, number of AOs as a function of cardinal number 310 312 314
Cartesian GTOs 237 336 339
Cartesian GTOs, derivatives 340
Cartesian GTOs, factorization in Cartesian directions 339
Cartesian GTOs, illustration of Cartesian GTOs 340
Cartesian GTOs, recurrence relations 340
Cartesian GTOs, self-overlap integral 340 351
Cartesian GTOs, transformation to spherical-harmonic GTOs 337
CAS see “Complete active space (CAS)”
CAS, complete active space 178 526 599
CASPT 796 (see also “Multiconfigurational perturbation theory”)
CASPT, CAS perturbation theory 796
CASPTn, nth-order CASPT 800
CASSCF 178 599
CASSCF, CAS self-consistent field [model] 178 599
Cauchy’s interlace theorem 116
cc-pCVXZ basis sets 312 (see also “Correlation-consistent basis sets”)
cc-pCVXZ, correlation-consistent polarized core-valence X-tuple zeta [basis] 312
cc-pVXZ basis sets 308 (see also “Correlation-consistent basis sets”)
cc-pVXZ, correlation-consistent polarized valence X-tuple zeta [basis] 308
CCD, coupled-cluster doubles [model] 649
CCn, coupled-cluster [rank] n [hybrid model] 790
CCPT, coupled-cluster perturbation theory 724 750
CCS, coupled-cluster singles [model] 789
CCSD + T(CCSD) CCSD [model] with approximate triples correction 794
CCSD theory (closed-shell) 685
CCSD theory (closed-shell), AO-based (integral-direct) algorithm 697
CCSD theory (closed-shell), biorthogonal configuration basis 692
CCSD theory (closed-shell), computational considerations 697
CCSD theory (closed-shell), energy expression 686
CCSD theory (closed-shell), norm of wave function (singles and doubles part) 692
CCSD theory (closed-shell), numerical illustration of size-extensivity in CCSD theory 669
CCSD theory (closed-shell), projected equations 661
CCSD theory (closed-shell), projected equations (explicit doubles part) 695
CCSD theory (closed-shell), projected equations (explicit singles part) 693
CCSD theory (closed-shell), projection manifold 691
CCSD theory (closed-shell), singlet CCSD cluster operator 685
CCSD theory (closed-shell), T1 transformed integrals 690
CCSD theory (closed-shell), T1-transformed Hamiltonian 687
CCSD(T), CCSD [model] with approximate triples correction 191 793
CCSD, coupled-cluster singles-and-doubles [model] 188 656
CCSDT, coupled-cluster singles-doubles-and-triples [model] 188 656
CCSDTQ, coupled-cluster singles-doubles-triples-and-quadruples [model] 657
CCSD[T], CCSD [model] with approximate triples correction 794
Central-field systems (one-electron) 204
Centrifugal potential 206
CFMM, continuous fast multipole method 424
Chebyshev polynomials 358 (see also “Orthogonal polynomials”)
Chemical accuracy 267 858 870
CI, configuration-interaction [model] 181 523
CID, CI doubles [model] 529
CISD, CI singles-and-doubles [model] 182 526
CISDT, CI singles-doubles-and-triples [model] 183
CISDTQ, CI singles-doubles-triples-and-quadruples [model] 183
Clebsch — Gordan coefficients 56
Cluster operator in CCPT 750 760
Cluster operator in iterative hybrid methods 789
Cluster operator in noniterative hybrid methods 793
Cluster operator in spin-adapted coupled-cluster theory 710
Cluster operator in spin-restricted coupled-cluster theory 706
Cluster operator, contribution to coupled-cluster energy 660 686
Cluster operator, relation to MP1 wave-function correction 742
Cluster operator, singlet doubles cluster operator 686
Cluster operator, singlet singles cluster operator 685
Cluster operator, spin-orbital cluster operator 188 654
Cluster-commutation condition 661 663
Commutation relations, canonical commutators 17
Commutation relations, cluster operators 655
Commutation relations, cluster-commutation relations 663
Commutation relations, coupled-cluster excitation operators 650
Commutation relations, elementary (annihilation and creation) operators 5 28
Commutation relations, excitation operators (orbital basis) 46
Commutation relations, excitation operators (spin-orbital basis) 26
Commutation relations, Fock operator 662 741 761
Commutation relations, ON operators 7
Commutation relations, orbital angular-momentum operators 240
Commutation relations, shift operators 39 41
Commutation relations, spin tensor operators 41
Commutators 25 (see also “Commutation relations”)
Commutators, double commutators 27
Commutators, expansion rules 26
Commutators, nested commutators 27
Commutators, S commutators 85 469
Complementary error function 370 401 402 424
Complete active space (CAS) 178 526
Complete active space (CAS), CASSCF 178 599
Complete active space (CAS), minimal active space 178
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