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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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Название: Molecular Electronic-Structure Theory. Part 2

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

Аннотация:

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.


Язык: en

Рубрика: Химия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 386

Добавлена в каталог: 21.02.2007

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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, $\mathrm{H_2}$ 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 $\mathrm{H_2O}$      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 $\mathrm{H_2O}$      875
Conformational energies, inversion barrier of $\mathrm{NH_3}$      876
Conformational energies, torsional barrier of $\mathrm{C_2H_6}$      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 $\mathrm{H_2O}$      802
Convergence in perturbation theory, numerical example of MPPT convergence for $\mathrm{H_2}$      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 $\mathrm{H_2O}$      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, $\mathrm{H_2}$ 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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