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Helgaker T., Jorgensen P., Olsen J. — Molecular Electronic-Structure Theory. Part 2
Helgaker T., Jorgensen P., Olsen J. — Molecular Electronic-Structure Theory. Part 2



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Íàçâàíèå: Molecular Electronic-Structure Theory. Part 2

Àâòîðû: Helgaker T., Jorgensen P., Olsen J.

Àííîòàöèÿ:

Ab initio quantum chemistry has emerged as an important tool in chemical research and is appliced to a wide variety of problems in chemistry and molecular physics. Recent developments of computational methods have enabled previously intractable chemical problems to be solved using rigorous quantum-mechanical methods.
This is the first comprehensive, up-to-date and technical work to cover all the important aspects of modern molecular electronic-structure theory. Topics covered in the book include:
* Second quantization with spin adaptation
* Gaussian basis sets and molecular-integral evaluation
* Hartree-Fock theory
* Configuration-interaction and multi-configurational self-consistent theory
* Coupled-cluster theory for ground and excited states
* Perturbation theory for single- and multi-configurational states
* Linear-scaling techniques and the fast multipole method
* Explicity correlated wave functions
* Basis-set convergence and extrapolation
* Calibration and benchmarking of computational methods, with applications to moelcular equilibrium structure, atomization energies and reaction enthalpies.
Molecular Electronic-Structure Theory makes extensive use of numerical examples, designed to illustrate the strengths and weaknesses of each method treated. In addition, statements about the usefulness and deficiencies of the various methods are supported by actual examples, not just model calculations. Problems and exercises are provided at the end of each chapter, complete with hints and solutions.
This book is a must for researchers in the field of quantum chemistry as well as for nonspecialists who wish to acquire a thorough understanding of ab initio molecular electronic-structure theory and its applications to problems in chemistry and physics. It is also highly recommended for the teaching of graduates and advanced undergraduates.


ßçûê: en

Ðóáðèêà: Õèìèÿ/

Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

ed2k: ed2k stats

Ãîä èçäàíèÿ: 2000

Êîëè÷åñòâî ñòðàíèö: 386

Äîáàâëåíà â êàòàëîã: 21.02.2007

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
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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, $\mathbb{Q}$ 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 $\mathrm{H_2O}$      175
Hartree — Fock theory, dissociation of $\mathrm{H_2}$      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 $\matrm{H_2O}$      174
Hartree — Fock theory, ground state of $\matrm{H_2}$      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 $\mathrm{H_2}$      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 $\mathrm{H_2O}$ and $\mathrm{N_2}$      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
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