|
|
Àâòîðèçàöèÿ |
|
|
Ïîèñê ïî óêàçàòåëÿì |
|
|
|
|
|
|
|
|
|
|
Helgaker T., Jorgensen P., Olsen J. — Molecular Electronic-Structure Theory. Part 2 |
|
|
Ïðåäìåòíûé óêàçàòåëü |
Gaussian product rule, reduced exponent 341
Gaussian quadrature 357
Gaussian quadrature, abscissae 359
Gaussian quadrature, Gauss — Hermite quadrature for multipole-moment integrals 361
Gaussian quadrature, Gaussian quadrature for even functions 388
Gaussian quadrature, Gaussian quadrature formula 359
Gaussian quadrature, Lagrange interpolating polynomial 360
Gaussian quadrature, Rys quadrature 387
Gaussian quadrature, weight function 358
Gaussian quadrature, weights 359
Gaussian radial functions 229 (see also “Basis functions (one-electron)”)
Gaussian-type orbitals (GTOs) 232 (see also “Basis functions (one-electron)”)
Gaussian-type orbitals (GTOs), angular-momentum quantum number 337
Gaussian-type orbitals (GTOs), Cartesian GTOs 237 336 339
Gaussian-type orbitals (GTOs), Cartesian quantum numbers 337
Gaussian-type orbitals (GTOs), completeness of GTOs 234
Gaussian-type orbitals (GTOs), contracted GTOs 294 338
Gaussian-type orbitals (GTOs), expansion of carbon orbitals 235
Gaussian-type orbitals (GTOs), expectation value of r 234
Gaussian-type orbitals (GTOs), primitive GTOs 291 294 336
Gaussian-type orbitals (GTOs), relation to HO functions 232
Gaussian-type orbitals (GTOs), shell of GTOs 337
Gaussian-type orbitals (GTOs), spherical GTOs 337
Gaussian-type orbitals (GTOs), spherical-harmonic GTOs 232 234 287 337
GBT, generalized Brillouin theorem 442 608 700
Genealogical coupling scheme 53
Genealogical coupling scheme for operators 60
Genealogical coupling scheme for states (CSFs) 55
Genealogical coupling scheme, Clebsch — Gordan coefficients 56
Genealogical coupling scheme, genealogical coupling coefficients 56
Genealogical coupling scheme, vector-coupling coefficients 56
Generalized Brillouin theorem (GBT) see “Brillouin theorem”
Generalized Fock matrix see “Fock matrix”
Ghost basis 327
Graphical representation of spin strings, see “Spin strings”
GTO basis sets see “Gaussian basis sets”
GTO, Gaussian-type orbital 232
Hamiltonian operator for central-field systems 205
Hamiltonian operator for helium atom (Cartesian coordinates) 259
Hamiltonian operator for helium atom (radial coordinates for S states) 260
Hamiltonian operator for HO system (Cartesian coordinates) 236
Hamiltonian operator for HO system (polar coordinates) 230
Hamiltonian operator for hydrogen atom 221
Hamiltonian operator in determinantal representation 552
Hamiltonian operator in first quantization 120
Hamiltonian operator in second quantization (orbital basis) 38
Hamiltonian operator in second quantization (spin-orbital basis) 13
Hamiltonian operator, Laplacian in polar coordinates 205
Hamiltonian operator, one-electron radial Hamiltonian 206
Hamiltonian operator, similarity-transformed Hamiltonian 657
Hamiltonian operator, singularities of 259
Harmonic polynomials 209
Harmonic potential 203
Harmonic-oscillator (HO) functions see also “Basis functions (one-electron)”
Harmonic-oscillator (HO) functions in Cartesian coordinates 236
Harmonic-oscillator (HO) functions in polar coordinates 230
Harmonic-oscillator (HO) functions, expansion of carbon orbitals 231
Harmonic-oscillator (HO) functions, relation to GTOs 232
Harmonic-oscillator (HO) functions, relation to Hermite Gaussians 352
Harmonic-oscillator (HO) functions, table of 231
Harmonic-oscillator (HO) system 203
Harmonic-oscillator (HO) system, eigenstates in Cartesian coordinates 236
Harmonic-oscillator (HO) system, eigenstates in polar coordinates 230
Harmonic-oscillator (HO) system, force constant 203
Hartree — Fock equations 169 444 447 460
Hartree — Fock theory 433
Hartree — Fock theory, matrix 483
Hartree — Fock theory, active Fock matrix 482
Hartree — Fock theory, ASCF method 456
Hartree — Fock theory, Brillouin theorem 441
Hartree — Fock theory, canonical conditions 446 449 459
Hartree — Fock theory, canonical orbitals 169 444
Hartree — Fock theory, convergence comparison of optimization methods 462 494
Hartree — Fock theory, Coulomb potential 169 451
Hartree — Fock theory, density matrix in AO basis 460 467
Hartree — Fock theory, density matrix in MO basis 448 452 466
Hartree — Fock theory, density-based Hartree — Fock theory 465
Hartree — Fock theory, DIIS convergence acceleration 460
Hartree — Fock theory, direct Hartree — Fock theory 463
Hartree — Fock theory, dissociation of 175
Hartree — Fock theory, dissociation of 172
Hartree — Fock theory, electronic gradient 437 474 481 506
Hartree — Fock theory, electronic Hessian 437 474 485 512
Hartree — Fock theory, exchange potential 169 451
Hartree — Fock theory, fluctuation potential 192 453
Hartree — Fock theory, Fock matrix 169 447 460
Hartree — Fock theory, Fock operator 169 192 444 450 491 494
Hartree — Fock theory, Fock potential 169 450
Hartree — Fock theory, GBT vector 491
Hartree — Fock theory, generalized Brillouin theorem (GBT) 442 491
Hartree — Fock theory, generalized Fock matrix 481
Hartree — Fock theory, ground state of 174
Hartree — Fock theory, ground state of 171
Hartree — Fock theory, Hartree — Fock energies (table) 841
Hartree — Fock theory, Hartree — Fock energy 168 452 453
Hartree — Fock theory, Hartree — Fock equations 169 444 447 460
Hartree — Fock theory, Hartree — Fock instabilities 496 512
Hartree — Fock theory, Hund’s rule 452 508
Hartree — Fock theory, inactive Fock matrix 482
Hartree — Fock theory, instabilities for degenerate and nondegenerate states 498 499
Hartree — Fock theory, integral-direct Hartree — Fock theory 463
Hartree — Fock theory, introduction 167
Hartree — Fock theory, Jacobian matrix 491
Hartree — Fock theory, Koopmans’ theorem 454
Hartree — Fock theory, multiple solutions 174 502 504
Hartree — Fock theory, orbital energies 169 444 450 455
Hartree — Fock theory, redundant parameters 435 440
Hartree — Fock theory, restricted Hartree — Fock (RHF) theory 170 434 497 498 499
Hartree — Fock theory, Roothaan — Hall SCF equations 458 465 475 476 490 509
Hartree — Fock theory, second-order optimization 478 494 496 511
Hartree — Fock theory, self-consistent field (SCF) method 169 448 475 495 496 509
Hartree — Fock theory, singlet instabilities 499
Hartree — Fock theory, size-extensivity 442
Hartree — Fock theory, triplet instabilities 499 500
Hartree — Fock theory, unrestricted Hartree — Fock (UHF) theory 170 435 497
Hartree — Fock theory, variational conditions 438 449 474 497
Helium atom in minimal Gaussian basis 427
Helium atom, CI wave function 263
Helium atom, CI-R12 wave function 265
Helium atom, contribution of orbitals to CI energy 275
Helium atom, Coulomb cusp 259
Helium atom, Coulomb cusp (illustration) 262 277 319
Helium atom, Coulomb hole 256
Helium atom, Coulomb hole (illustration) 258
Helium atom, energy-convergence comparison (illustration) 264
Helium atom, Hamiltonian operator 259 260
Helium atom, Hylleraas function 266
Helium atom, local kinetic energy (illustration) 260
Helium atom, partial-wave expansion 267
Helium atom, principal expansion 273
Helium atom, test of correlation-consistent basis sets 318
Helium atom, total energy of ground-state helium atom 272
Hellmann — Feynman theorem 119
Hellmann — Feynman theorem for approximate states 120
Hellmann — Feynman theorem for coupled-cluster energies 675
Hellmann — Feynman theorem for exact states 119
Hellmann — Feynman theorem for nonvariational wave functions 123 675
Hellmann — Feynman theorem for spin in spin-restricted coupled-cluster theory 707
Hellmann — Feynman theorem for variable basis sets 120
Hermite Coulomb integrals 373
Hermite Coulomb integrals, evaluation by McMurchie — Davidson scheme 374
Hermite Coulomb integrals, evaluation by Rys scheme 392
Hermite Gaussians 349 (see also “McMurchie — Davidson method”)
Hermite Gaussians, definition 349
Hermite Gaussians, illustration 350
Hermite Gaussians, integrals over Hermite Gaussians 351
Hermite Gaussians, recurrence relations 351
Hermite Gaussians, relation to HO functions 352
Hermite polynomials see also “Orthogonal polynomials”
Hermite polynomials, definition 236 358
| Hermite polynomials, table of 237
Hierarchies of approximations 142 145
High-spin coupled-cluster theory 704
Hilbert space 202
HO, harmonic oscillator 203 230
Horizontal recurrence relations 345 347 386
Hund’s rule 452 508
Huzinaga basis sets 291 (see also “Gaussian basis sets”)
Huzinaga basis sets, Dunning’s contraction 295
Huzinaga basis sets, plot of exponents for carbon atom 293
Huzinaga basis sets, table of exponents for carbon atom 291
Hybrid methods 191 789 793 795
Hybrid methods, CC2 790 791
Hybrid methods, CC3 790 791
Hybrid methods, CCSD + T(CCSD) 794
Hybrid methods, CCSD(T) 191 793
Hybrid methods, CCSD[T] 794
Hybrid methods, evaluation of closed-shell CCSD(T) triples correction 794
Hybrid methods, iterative hybrid methods 789
Hybrid methods, noniterative hybrid methods 793
Hybrid methods, numerical comparison of hybrid and nonhybrid methods 795
Hybrid methods, order analysis of hybrid and nonhybrid methods 792
Hydrogen atom and hydrogenic systems in minimal Gaussian basis 427
Hydrogen atom and hydrogenic systems, exact solution 221
Hydrogenic functions 219 221
Hydrogenic functions, eigenfunctions of hydrogenic atoms 221
Hydrogenic functions, expectation value of r 222
Hylleraas function 266 (see also “Explicitly correlated methods”)
Hylleraas function, Hylleraas coordinates 266
Hylleraas function, Hylleraas expansion 266
Hylleraas variation method 734 736
Hylleraas variation method, Hylleraas functional 734
Hylleraas variation method, Hylleraas functional for even-order energies 735
Hylleraas variation method, stability of Hylleraas functional 736
Hylleraas — Undheim theorem 115 619
Inactive energy 623
Inactive orbitals 178 434 526 599
Incomplete gamma function 368
Inner and outer iterations 547 625
Instabilities see “Singlet instabilities and triplet instabilities”
Integral-direct Hartree — Fock theory 463 (see also “Direct Hartree — Fock theory”)
Interaction matrix, complex interaction matrix 408
Interaction matrix, real interaction matrix 414
Intermediate normalization 616 703 726 729 731
Intrinsic (N-electron) error 820 (see also “Errors in calculations”)
Intruder states 772 (see also “Convergence in perturbation theory”)
Inverse-iteration method 545
Ionic states, anionic and cationic states 454
Ionic states, covalent and ionic states of 154
Ionization potentials 454 (see also “Koopmans’ theorem”)
IP, ionization potential 454
Isogyric reactions 865
Jacobi identity 27
Jacobian matrix in coupled-cluster theory 671 681 683
Jacobian matrix in Hartree — Fock theory 491
Kinetic-energy integrals see also “Molecular integral evaluation”
Kinetic-energy integrals, linear scaling for large systems 398
Kinetic-energy integrals, Obara — Saika method 348
Koopmans’ theorem 454
Koopmans’ theorem for electron affinities 455
Koopmans’ theorem for ionization potentials 454
Koopmans’ theorem, ionization potentials of and 456
Kummer function 371
Lagrange interpolating polynomial 360
Lagrange multipliers 125
Lagrange’s method of undetermined multipliers 125
Laguerre functions 222 (see also “Basis functions (one-electron)”)
Laguerre functions, definition 222
Laguerre functions, expansion of carbon orbitals 223
Laguerre functions, expectation value of r 222
Laguerre functions, relation to STOs 225
Laguerre polynomials 219 (see also “Orthogonal polynomials”)
Laguerre polynomials, associated Laguerre polynomials 218
Laguerre polynomials, generalized Laguerre polynomials 218
Laguerre polynomials, Laguerre polynomials 219 358
Laguerre polynomials, table of 220
Laplace’s equation 211
Laplacian in polar coordinates 205
Least-squares method 223 243
Legendre polynomials 207 (see also “Orthogonal polynomials”)
Legendre polynomials, associated Legendre functions 208
Legendre polynomials, associated Legendre polynomials 207
Legendre polynomials, Legendre polynomials 208 358
Legendre polynomials, table of 209
Levenberg — Marquardt trajectories 612
LFF, local FF [box] 421
Linear response theory 501 640 684
Linear-scaling methods see also “Scaling properties for large systems”
Linear-scaling methods, continuous FMM (CFMM) 423
Linear-scaling methods, fast multipole method (FMM) 421
Linear-scaling methods, linear scaling in density-based Hartree — Fock theory 477
Linear-scaling methods, multipole method for large systems 417
Linked coupled-cluster equations 658
Local energy 259
Logarithmic matrix function, definition 93
Logarithmic matrix function, expansion 94
Logarithmic matrix function, relation to exponential matrix function 93
Lowering operator 38
LU decomposition 572
Mass-polarization operator 11
Matrix units 46 473
Maximum absolute error 821 (see also “Statistical measures of errors”)
McMurchie — Davidson method 352 372
McMurchie — Davidson method, Cartesian Coulomb integrals by Hermite expansion 375
McMurchie — Davidson method, Cartesian Coulomb integrals by Hermite recursion 377
McMurchie — Davidson method, computational considerations for one-electron integrals 377
McMurchie — Davidson method, computational considerations for two-electron integrals 379
McMurchie — Davidson method, Coulomb integrals 372
McMurchie — Davidson method, Hermite Coulomb integrals 373
McMurchie — Davidson method, Hermite Gaussians 349
McMurchie — Davidson method, MD1 scheme 387 398
McMurchie — Davidson method, MD2 scheme 381 387 398
McMurchie — Davidson method, MD4 scheme 380 387 398
McMurchie — Davidson method, multipole-moment integrals 356
McMurchie — Davidson method, nuclear-attraction integrals 377
McMurchie — Davidson method, Obara — Saika recurrence for expansions coefficients 355
McMurchie — Davidson method, overlap-distribution recursion 355
McMurchie — Davidson method, three-term recurrence for expansion coefficients 353
McMurchie — Davidson method, two-term recurrence for expansion coefficients 354
McMurchie — Davidson method, vertical-horizontal algorithm for Coulomb integrals 379
MCSCF, multiconfigurational SCF [model] 176 598
MDn, McMurchie — Davidson [type] n [two-electron integral scheme] 380
Mean absolute error 821 (see also “Statistical measures of errors”)
Mean error 821 (see also “Statistical measures of errors”)
Metric matrix 84
Micro and macro iterations 547 625
Minimal basis 147 227 235
Minimal operation-count (MOC) method 560 564
MO, molecular orbital 144
MOC, minimal operation-count [method] 560
Molecular forces 120 123
Molecular integral evaluation 336
Molecular integral evaluation, angular-momentum integrals 348
Molecular integral evaluation, Boys function 365
Molecular integral evaluation, Cartesian GTOs 336 339
Molecular integral evaluation, Coulomb integrals 361 405
Molecular integral evaluation, differential-operator integrals 347
Molecular integral evaluation, Gaussian charge distributions 361
Molecular integral evaluation, Gaussian overlap distributions 341
Molecular integral evaluation, Gaussian product rule H 238 341
Molecular integral evaluation, Gaussian quadrature 357
Molecular integral evaluation, Hermite Gaussians 349
Molecular integral evaluation, horizontal recurrence relations 345 347 386
Molecular integral evaluation, kinetic-energy integrals 348
Molecular integral evaluation, McMurchie — Davidson method 352 372
Molecular integral evaluation, momentum integrals 348
Molecular integral evaluation, multipole method for Coulomb integrals 405
Molecular integral evaluation, multipole-moment integrals 346 356
Molecular integral evaluation, Obara — Saika method 344 381
Molecular integral evaluation, overlap integrals 344 345 357 361
|
|
|
Ðåêëàìà |
|
|
|