Molecular ElectronicStructure TheoryISBN: 9781118531471
944 pages
February 2013

Ab initio quantum chemistry has emerged as an important tool in chemical research and is applied 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 quantummechanical methods.
This is the first comprehensive uptodate and technical work to cover all the important aspects of modern molecular electronicstructure theory. Topics covered in the book include:
 Second quantization with spin adaptation
 Gaussian basis sets and molecularintegral evaluation
 HartreeFock theory
 Configurationinteraction and multiconfigurational selfconsistent theory
 Coupledcluster theory for ground and excited states
 Perturbation theory for single and multiconfiguration states
 Linearscaling techniques and the fast multiple method
 Explicitly correlated wave functions
 Basisset convergence and extrapolation
 Calibration and benchmarking of computational methods, with applications to molecular equilibrium structures, atomization energies and reaction enthalpies.
Molecular ElectronicStructure 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 electronicstructure theory and its applications to problems in chemistry and physics. It is also highly recommended for the teaching of graduates and advanced undergraduates.
Preface xxi
Overview xxv
Programs used in the preparation of this book xxix
1. Second Quantization 1
1.1 The Fock space 1
1.2 Creation and annihilation operators 2
1.3 Numberconserving operators 6
1.4 The representation of one and twoelectron operators 9
1.5 Products of operators in second quantization 14
1.6 First and secondquantization operators compared 18
1.7 Density matrices 19
1.8 Commutators and anticommutators 25
1.9 Nonorthogonal spin orbitals 27
2. Spin in Second Quantization 34
2.1 Spin functions 34
2.2 Operators in the orbital basis 35
2.3 Spin tensor operators 41
2.4 Spin properties of determinants 46
2.5 Configuration state functions 51
2.6 The genealogical coupling scheme 53
2.7 Density matrices 61
3. Orbital Rotations 80
3.1 Unitary transformations and matrix exponentials 80
3.2 Unitary spinorbital transformations 86
3.3 Symmetryrestricted unitary transformations 89
3.4 The logarithmic matrix function 93
4. Exact and Approximate Wave Functions 107
4.1 Characteristics of the exact wave function 107
4.2 The variation principle 111
4.3 Sizeextensivity 126
4.4 Symmetry constraints 135
5. The Standard Models 142
5.1 One and Nelectron expansions 143
5.2 A model system: the hydrogen molecule in a minimal basis 146
5.3 Exact wave functions in Fock space 162
5.4 The HartreeFock approximation 167
5.5 Multiconfigurational selfconsistent field theory 176
5.6 Configurationinteraction theory 181
5.7 Coupledcluster theory 186
5.8 Perturbation theory 192
6. Atomic Basis Functions 201
6.1 Requirements on oneelectron basis functions 201
6.2 One and manycentre expansions 203
6.3 The oneelectron centralfield system 204
6.4 The angular basis 207
6.5 Exponential radial functions 218
6.6 Gaussian radial functions 229
7. ShortRange Interactions and Orbital Expansions 256
7.1 The Coulomb hole 256
7.2 The Coulomb cusp 259
7.3 Approximate treatments of the groundstate helium atom 262
7.4 The partialwave expansion of the groundstate helium atom 267
7.5 The principal expansion of the groundstate helium atom 273
7.6 Electroncorrelation effects summarized 278
8. Gaussian Basis Sets 287
8.1 Gaussian basis functions 287
8.2 Gaussian basis sets for HartreeFock calculations 288
8.3 Gaussian basis sets for correlated calculations 300
8.4 Basisset convergence 315
8.5 Basisset superposition error 327
9. Molecular Integral Evaluation 336
9.1 Contracted sphericalharmonic Gaussians 336
9.2 Cartesian Gaussians 338
9.3 The ObaraSaika scheme for simple integrals 344
9.4 Hermite Gaussians 349
9.5 The McMurchieDavidson scheme for simple integrals 352
9.6 Gaussian quadrature for simple integrals 357
9.7 Coulomb integra;s over spherical Gaussians 361
9.8 The Boys function 365
9.9 The McMurchieDavidson scheme for Coulomb integrals 372
9.10 The ObaraSaika scheme for Coulomb integrals 381
9.11 Rys quadrature for Coulomb integrals 387
9.12 Scaling properties of the molecular integrals 398
9.13 The multipole method for Coulomb integrals 405
9.14 The multipole method for large systems 417
10. HartreeFock Theory 433
10.1 Parametrization of the wave function and the energy 433
10.2 The HartreeFock wave function 438
10.3 Canonical HartreeFock theory 443
10.4 The RHF total energy and orbital energies 450
10.5 Koopmans’ theorem 454
10.6 The RoothaanHall selfconsistent field equations 458
10.7 Densitybased HartreeFock theory 465
10.8 Secondorder optimization 478
10.9 The SCF method as an approximate secondorder method 490
10.10 Singlet and triplet instabilities in RHF theory 496
10.11 Multiple solutions in HartreeFock theory 504
11. ConfigurationInteraction Theory 523
11.1 The CI model 523
11.2 Sizeextensivity and the CI model 527
11.3 A CI model system for noninteracting hydrogen molecules 535
11.4 Parametrization of the CI model 540
11.5 Optimization of the CI wave function 543
11.6 Slater determinants as products of alpha and beta strings 550
11.7 The determinantal representation of the Hamiltonian operator 552
11.8 Direct CI methods 554
11.9 CI orbital transformations 569
11.10 Symmetrybroken CI solutions 573
12. Multiconfigurational SelfConsistent Field Theory 498
12.1 The MCSCF model 498
12.2 The MCSCF energy and wave function 600
12.3 The MCSCF Newton trustregion method 610
12.4 The Newton cigenvector method 616
12.5 Computational considerations 621
12.6 Exponential parametrization of the configuration space 630
12.7 MCSCF theory for several electronic states 637
12.8 Removal of RHF instabilities in MCSCF theory 640
13. CoupledCluster Theory 648
13.1 The coupledcluster model 648
13.2 The coupledcluster exponential ansatz 654
13.3 Sizeextensivity in coupledcluster theory 665
13.4 Coupledcluster optimization techniques 670
13.5 The coupledcluster variational Lagrangian 674
13.6 The equationofmotion coupledcluster method 677
13.7 The closedshell CCSD model 685
13.8 Special treatments of coupledcluster theory 698
13.9 Highspin openshell coupledcluster theory 704
14. Perturbation Theory 724
14.1 RayleighSchrödinger perturbation theory 725
14.2 MøllerPlesset perturbation theory 739
14.3 Coupledcluster perturbation theory 749
14.4 MøllerPlesset theory for closedshell systems 759
14.5 Convergence in perturbation theory 769
14.6 Perturbative treatments of coupledcluster wave functions 783
14.7 Multiconfigurational perturbation theory 796
15. Calibration of the ElectronicStructure Models 817
15.1 The sample molecules 817
15.2 Errors in quantumchemical calculations 819
15.3 Molecular equilibrium structures: bond distances 821
15.4 Molecular equilibrium structures; bond angles 832
15.5 Molecular dipole moments 836
15.6 Molecular and atomic energies 840
15.7 Atomization energies 854
15.8 Reaction enthalpies 865
15.9 Conformational barriers 874
15.10 Conclusions 879
List of Acronyms 885
Index 887