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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 |
Complete active space (CAS), valence active space 179
Completeness in the norm 202
Completeness of angular and radial parts 206
Completeness of GTOs 233 237
Completeness of HO functions 231
Completeness of hydrogenic functions 221
Completeness of Laguerre functions 222
Completeness of N-electron functions 144 145
Completeness of one-electron functions 144 201 202
Completeness of one-electron radial functions 219
Completeness of spherical harmonics 206
Completeness of STOs 226
Completeness with respect to Sobolev norms 202
Condon — Shortley phase convention, solid harmonics 210
Condon — Shortley phase convention, spherical harmonics 207
Configuration state functions (CSFs), construction of CSFs 53
Configuration state functions (CSFs), definition 51
Configuration state functions (CSFs), numbers of CSFs and Slater determinants compared 52
Configuration state functions (CSFs), singlet and triplet CSFs 148 434
Configuration state functions (CSFs), transformation to determinant basis 59
Configuration state functions (CSFs), use in CI theory 524
Configuration-interaction (CI) theory 523
Configuration-interaction (CI) theory, in minimal basis 152
Configuration-interaction (CI) theory, alpha and beta strings 550
Configuration-interaction (CI) theory, choice of orbitals 527
Configuration-interaction (CI) theory, CID 529 535
Configuration-interaction (CI) theory, CISD 182 526
Configuration-interaction (CI) theory, CISDT 183
Configuration-interaction (CI) theory, CISDTQ 183
Configuration-interaction (CI) theory, complete active space (CAS) 526
Configuration-interaction (CI) theory, construction of density matrices 568
Configuration-interaction (CI) theory, Davidson correction 530 531 537
Configuration-interaction (CI) theory, Davidson method 548 550 582
Configuration-interaction (CI) theory, Davidson step 548
Configuration-interaction (CI) theory, derivatives of CI energy function 542 578
Configuration-interaction (CI) theory, direct CI methods 554
Configuration-interaction (CI) theory, dissociation of 184
Configuration-interaction (CI) theory, distribution of excitation levels 534 538 575 656
Configuration-interaction (CI) theory, electronic gradient 113 542
Configuration-interaction (CI) theory, electronic Hessian 113 542
Configuration-interaction (CI) theory, full CI (FCI) 162 524
Configuration-interaction (CI) theory, helium atom 262
Configuration-interaction (CI) theory, introduction 181
Configuration-interaction (CI) theory, inverse-iteration method 545
Configuration-interaction (CI) theory, MRSDC1 183 526
Configuration-interaction (CI) theory, multireference CI wave functions 183 526 599
Configuration-interaction (CI) theory, Newton’s method 544
Configuration-interaction (CI) theory, numerical examples of optimization 546 549 581
Configuration-interaction (CI) theory, optimization methods 543
Configuration-interaction (CI) theory, orbital rotations 569
Configuration-interaction (CI) theory, parametrization of CI energy 542
Configuration-interaction (CI) theory, parametrization of CI expansion 540
Configuration-interaction (CI) theory, quasi-Newton method 547 580
Configuration-interaction (CI) theory, Rayleigh method 545
Configuration-interaction (CI) theory, redundancy of CI parametrization 540 541
Configuration-interaction (CI) theory, reference configuration 182 526
Configuration-interaction (CI) theory, relation to coupled-cluster theory 186 577 650 652 655 662 716
Configuration-interaction (CI) theory, relation to EOM-CC 678
Configuration-interaction (CI) theory, relation to QCI 702
Configuration-interaction (CI) theory, restricted active space (RAS) 526 551 564 572
Configuration-interaction (CI) theory, simplification for zero projected spin 567 580
Configuration-interaction (CI) theory, size-extensivity 129 131 186 527
Configuration-interaction (CI) theory, sparsity of determinantal Hamiltonian representation 552
Configuration-interaction (CI) theory, spin strings 550
Configuration-interaction (CI) theory, spin-combined basis 567
Configuration-interaction (CI) theory, truncated expansions 181 182 526
Configuration-interaction (CI) theory, variational conditions 114 181 524
Confluent hypergeometric function (Kummer function) 371
Conformational energies 874 (see also “Calibration of methods”)
Conformational energies, barrier to linearity of 875
Conformational energies, inversion barrier of 876
Conformational energies, torsional barrier of 877
Connected and disconnected cluster amplitudes 651 759
Continuous FMM (CFMM) 423
Continuous FMM (CFMM), fast multipole method (FMM) 421
Continuous FMM (CFMM), multipole method for large systems 417
Contracted GTOs 294 338
Contracted GTOs, 3-21G basis set 297
Contracted GTOs, 6-31G basis set 297
Contracted GTOs, contraction coefficients 294 338
Contracted GTOs, Dunning — Huzinaga basis sets 295
Contracted GTOs, Gaussian-type orbitals (GTOs) 232
Contracted GTOs, general contraction 294 338
Contracted GTOs, primitive GTOs 291 294
Contracted GTOs, segmented contraction 294 295 338
Convergence in perturbation theory 193 769
Convergence in perturbation theory, analytic continuation 782
Convergence in perturbation theory, back-door intruders 772
Convergence in perturbation theory, conditions for convergence 771
Convergence in perturbation theory, conditions for convergence of two-state model with gap shift 773
Convergence in perturbation theory, conditions for convergence of two-state model without gap shift 771
Convergence in perturbation theory, convergence in CASPT 802
Convergence in perturbation theory, energy corrections for HF 780
Convergence in perturbation theory, energy corrections of two-state model with gap shift 775
Convergence in perturbation theory, energy corrections of two-state model without gap shift 770
Convergence in perturbation theory, front-door intruders 772
Convergence in perturbation theory, gap-shift parameter 772
Convergence in perturbation theory, high-excitation back-door intruders 776 779
Convergence in perturbation theory, intruder states 772
Convergence in perturbation theory, low-excitation front-door intruders 777 781
Convergence in perturbation theory, numerical example of CASPT convergence for 802
Convergence in perturbation theory, numerical example of MPPT convergence for 195
Convergence in perturbation theory, numerical example of MPPT convergence for HF 778
Convergence in perturbation theory, numerical examples of intruders in MPPT for HF 778
Convergence in perturbation theory, points of degeneracy 771
Convergence in perturbation theory, prototypical intruders 776
Convergence in perturbation theory, radius of convergence 771
Convergence in perturbation theory, scans on the real axis for HF 779
Convergence in perturbation theory, scans on the real axis for the identification of intruders 776
Convergence in perturbation theory, strength parameter 771
Convergence in perturbation theory, two-state model with gap shift 772
Convergence in perturbation theory, two-state model without gap shift 770
Convergence of multipole expansion 409
Core correlation see also “Electron correlation”
Core correlation, atomization energies 861
Core correlation, BH potential-energy curve 302
Core correlation, bond distances 828
Core correlation, conformational energies 874
Core correlation, contribution to total energy 844
Core correlation, core correlation energy 301
Core correlation, core orbitals 301
Core correlation, core-core correlation energy 303
Core correlation, core-valence basis sets cc-pCVA’Z 312
Core correlation, core-valence correlation energy 303
Core correlation, frozen-core approximation 301 303
Core correlation, reaction enthalpies 871
Core orbitals 301 (see also “Core correlation”)
Correlating functions 265 280
Correlating operators 650
Correlating orbitals 180 304
Correlation see “Electron correlation”
Correlation energy see also “Electron correlation”
Correlation energy, all-electron correlation energy 301
Correlation energy, contribution to total energy 842
Correlation energy, core correlation 301
Correlation energy, core-core correlation energy 303
Correlation energy, core-valence correlation energy 303
Correlation energy, definition 170
Correlation energy, valence correlation energy 301
Correlation energy, valence-valence correlation energy 303
Correlation-consistent basis sets 301 307
Correlation-consistent basis sets, augmented basis sets aug-cc-p(C)VAZ 312 314
Correlation-consistent basis sets, cardinal number 308
Correlation-consistent basis sets, comparison with ANOs 308 310
Correlation-consistent basis sets, comparison with numerical orbitals 318
Correlation-consistent basis sets, core-valence basis sets cc-pCVXZ 312
Correlation-consistent basis sets, distribution of exponents 313
Correlation-consistent basis sets, energy convergence for carbon atom 311 314 315
Correlation-consistent basis sets, illustrations of radial distribution functions 308 309 310
Correlation-consistent basis sets, number of contracted functions 310 312 314
| Correlation-consistent basis sets, relation to principal expansion 307
Correlation-consistent basis sets, structure of basis sets 310 313
Correlation-consistent basis sets, valence basis sets cc-pVXZ 308
Coulomb cusp 259 (see also “Helium atom”)
Coulomb cusp, electronic cusp condition 110 261 262
Coulomb cusp, illustration 262 277 319
Coulomb cusp, nuclear cusp condition 110 260 262
Coulomb cusp, relation to singularities 260
Coulomb hole 256 (see also “Helium atom”)
Coulomb hole, convergence of principal expansion 276 319
Coulomb hole, illustration 258 262 277 319
Coulomb integrals 361 (see also “Molecular integral evaluation”)
Coulomb integrals for spherical Gaussian distributions 361 364
Coulomb integrals, classical and nonclassical contributions 401
Coulomb integrals, contribution in direct Hartree — Fock theory 464
Coulomb integrals, electron-transfer recurrence relation 386
Coulomb integrals, Gaussian extent 402 424
Coulomb integrals, linear scaling of nonclassical integrals 402
Coulomb integrals, McMurchie — Davidson method 372
Coulomb integrals, multipole method for Coulomb integrals 405
Coulomb integrals, Obara — Saika method 381
Coulomb integrals, positive definiteness of two-electron integrals 404
Coulomb integrals, quadratic scaling for large systems 399 400
Coulomb integrals, Rys quadrature 387
Coulomb integrals, Schwarz inequality and upper bounds 404
Coulomb integrals, screening of integrals 404
Coulomb integrals, upper bound to nonclassical contribution 402
Coulomb potential in Hartree — Fock theory 169 451
Counterpoise correction 327
Coupled-cluster amplitude equations 188 657 660
Coupled-cluster amplitudes 188 649 651
Coupled-cluster energy expression 189 652 660 686
Coupled-cluster perturbation theory (CCPT) 749
Coupled-cluster perturbation theory (CCPT), amplitude equations 751
Coupled-cluster perturbation theory (CCPT), closed-shell energies to fourth order using Wigner’s rule 766
Coupled-cluster perturbation theory (CCPT), closed-shell wave-function corrections to second order 763
Coupled-cluster perturbation theory (CCPT), energy corrections 753
Coupled-cluster perturbation theory (CCPT), energy corrections to fifth order using Wigner’s rule 758
Coupled-cluster perturbation theory (CCPT), exponential ansatz 749
Coupled-cluster perturbation theory (CCPT), Muller — Plesset partitioning of Hamiltonian 750
Coupled-cluster perturbation theory (CCPT), similarity-transformed Harniltonian SI 750
Coupled-cluster perturbation theory (CCPT), size-extensivity 754 759
Coupled-cluster perturbation theory (CCPT), variational equations 756
Coupled-cluster perturbation theory (CCPT), variational Lagrangian 755 761
Coupled-cluster perturbation theory (CCPT), wave-function corrections 752
Coupled-cluster theory 648
Coupled-cluster theory, approximate triples treatment 191 789 793 795
Coupled-cluster theory, Brueckner coupled-cluster (BCC) theory 701
Coupled-cluster theory, canonical representation of coupled-cluster theory 662
Coupled-cluster theory, CC2 790 791
Coupled-cluster theory, CC3 790 791
Coupled-cluster theory, CCD 649
Coupled-cluster theory, CCS 789
Coupled-cluster theory, CCSD 188 656
Coupled-cluster theory, CCSD + T(CCSD) 794
Coupled-cluster theory, CCSD energies (table) 841
Coupled-cluster theory, CCSD theory (closed-shell) 685
Coupled-cluster theory, CCSD(T) 191 793
Coupled-cluster theory, CCSD(T) energies (table) 841
Coupled-cluster theory, CCSDT 188 656
Coupled-cluster theory, CCSDTQ 189 657
Coupled-cluster theory, CCSD[T] 794
Coupled-cluster theory, closed under de-excitation 659
Coupled-cluster theory, cluster operator 188 654
Coupled-cluster theory, cluster-commutation condition 661 663
Coupled-cluster theory, commutation of cluster (excitation) operators 650 655
Coupled-cluster theory, connected cluster amplitudes 651 759
Coupled-cluster theory, coupled-cluster amplitude equations 188 657 660
Coupled-cluster theory, coupled-cluster amplitudes 188 649 651 685
Coupled-cluster theory, coupled-cluster energy 189 652 660 686
Coupled-cluster theory, coupled-cluster Schrodinger equation 188 651 704
Coupled-cluster theory, coupled-cluster wave function in product form 186 650
Coupled-cluster theory, diagrammatic coupled-cluster theory 658
Coupled-cluster theory, DIIS convergence acceleration 672
Coupled-cluster theory, disconnected cluster amplitudes 651
Coupled-cluster theory, disconnected clusters 655
Coupled-cluster theory, dissociation of 190
Coupled-cluster theory, down rank 660 663
Coupled-cluster theory, equation-of-motion coupled-cluster (EOM-CC) theory 677
Coupled-cluster theory, equivalence of linked and unlinked forms 659
Coupled-cluster theory, excitation rank 660 663
Coupled-cluster theory, expectation value of coupled-cluster energy 652 653
Coupled-cluster theory, exponential ansatz 132 187 654 749
Coupled-cluster theory, high-spin theory 704
Coupled-cluster theory, hybrid methods 191 789 793 795
Coupled-cluster theory, introduction 186
Coupled-cluster theory, Jacobian matrix 671 681 683
Coupled-cluster theory, Lagrangian density matrix 676 714
Coupled-cluster theory, linked coupled-cluster equations 658 665
Coupled-cluster theory, manifest separability 134 186
Coupled-cluster theory, Newton’s method 671
Coupled-cluster theory, numerical example of distribution of excitation levels 656
Coupled-cluster theory, numerical examples of optimization 673
Coupled-cluster theory, numerical illustration of size-extensivity in CCSD theory 669
Coupled-cluster theory, optimization techniques 670
Coupled-cluster theory, orbital-optimized coupled-cluster (OCC) theory 698
Coupled-cluster theory, pair clusters 649
Coupled-cluster theory, partially spin-adapted open-shell coupled-cluster theory 711
Coupled-cluster theory, particle rank 663
Coupled-cluster theory, perturbation analysis of coupled-cluster hierarchy 784
Coupled-cluster theory, perturbation-based optimization 672
Coupled-cluster theory, projected coupled-cluster equations 188 657 661 705
Coupled-cluster theory, projected Schrodinger equation 652
Coupled-cluster theory, quadratic CI (QCI) theory 702
Coupled-cluster theory, quasi-Newton method 672 673
Coupled-cluster theory, relation to CI theory 186 577 650 652 655 662 716
Coupled-cluster theory, relaxed density matrix 677 714
Coupled-cluster theory, similarity-transformed Hamiltonian 657 680 750
Coupled-cluster theory, size-extensivity 186 665
Coupled-cluster theory, size-extensivity in linked coupled-cluster theory 665
Coupled-cluster theory, size-extensivity in unlinked coupled-cluster theory 668
Coupled-cluster theory, size-extensivity of first-order properties 712
Coupled-cluster theory, spin-adapted open-shell coupled-cluster theory 709
Coupled-cluster theory, spin-restricted open-shell coupled-cluster theory 704
Coupled-cluster theory, T1-transformed Hamiltonian 687
Coupled-cluster theory, T1-transformed integrals 690
Coupled-cluster theory, termination of BCH Hamiltonian expansion 661
Coupled-cluster theory, termwise size-extensivity 667
Coupled-cluster theory, truncation of cluster operator 188 654
Coupled-cluster theory, unlinked coupled-cluster equations 658 668
Coupled-cluster theory, unrestricted coupled-cluster model 191
Coupled-cluster theory, up rank 660 663
Coupled-cluster theory, variational and nonvariational coupled-cluster energies compared 653
Coupled-cluster theory, variational conditions on coupled-cluster energy 652
Coupled-cluster theory, variational density matrix 677 714
Coupled-cluster theory, variational Lagrangian 674
Coupled-cluster theory, vector function 671
Covalent state 154
Creation operators 3 8
Creation operators, nonorthogonal spin orbitals 28
Creation operators, spin properties 43
Creation operators, unitary transformations 86
CSF, configuration state function 51
Cubic convergence 546
Cusp see “Coulomb cusp”
Darwin operator see also “Relativistic corrections”
Darwin operator, one-electron operator 852
Darwin operator, two-electron operator 66 853
Davidson correction 530 531 537
Davidson method 548 550 582
Density functions and matrices, density-function plots 151 153 156 157
Density functions and matrices, CI density matrix (construction) 568
Density functions and matrices, coupled-cluster density matrix 676
Density functions and matrices, coupled-cluster Lagrangian density matrix 676
Density functions and matrices, coupled-cluster variational density matrix 677
Density functions and matrices, differential-operator integrals 347 (see also “Molecular integral evaluation”)
Density functions and matrices, electron-density function 65
Density functions and matrices, Hartree — Fock density matrix (properties) 467 468
Density functions and matrices, N-representability 108
Density functions and matrices, one-electron density matrix in orbital basis 62
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