Verfügbarkeit: Molecular electronic-structure theory

Molecular electronic-structure theory:

Ab initio quantum chemistry is increasingly paired with computational methods to solve intractable problems in chemistry and molecular physics. Now in a paperback edition, this comprehensive and technical work covers all the important aspects of modern molecular electronic-structure theory, clearly...

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Hauptverfasser:	Helgaker, Trygve (VerfasserIn), Jørgensen, Poul 1944- (VerfasserIn), Olsen, Jeppe (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Chichester Wiley-Blackwell 2012
Ausgabe:	Reprinted as paperback
Schlagworte:	Kemiske bindinger Molekülstruktur Elektronenstruktur Ab-initio-Rechnung Quantenchemie
Online-Zugang:	Inhaltsverzeichnis
Zusammenfassung:	Ab initio quantum chemistry is increasingly paired with computational methods to solve intractable problems in chemistry and molecular physics. Now in a paperback edition, this comprehensive and technical work covers all the important aspects of modern molecular electronic-structure theory, clearly explaining quantum-mechanical methods and applications to molecular equilibrium structure, atomization energies, and reaction enthalpies. Extensive numerical examples illustrate each method described. An excellent resource..
Beschreibung:	XXVII, 908 S. graph. Darst.
ISBN:	9781118531471

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520			\|a Ab initio quantum chemistry is increasingly paired with computational methods to solve intractable problems in chemistry and molecular physics. Now in a paperback edition, this comprehensive and technical work covers all the important aspects of modern molecular electronic-structure theory, clearly explaining quantum-mechanical methods and applications to molecular equilibrium structure, atomization energies, and reaction enthalpies. Extensive numerical examples illustrate each method described. An excellent resource..
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Datensatz im Suchindex

_version_	1804150565665505280
adam_text	CONTENTS Preface Overview Programs used in the preparation of this book 1 Second Quantization The Fock space Creation and annihilation operators 121 Creation operators 122 Annihilation operators 123 Anticommutation relations Number-conserving operators 131 Occupation-number operators 132 The number operator 133 Excitation operators The representation of one- and two-electron operators 141 One-electron operators 142 Two-electron operators 143 The molecular electronic Hamiltonian Products of operators in second quantization 151 Operator products 152 The canonical commutators First- and second-quantization operators compared Density matrices 171 The one-electron density matrix 172 The two-electron density matrix 173 Density matrices in spin-orbital and coordinate representations Commutators and anticommutators Nonorthogonal spin orbitals 191 Creation and annihilation operators 192 One- and two-electron operators 193 Biorthogonal operators References Further reading WOwoOATANAAA HR WN m vi CONTENTS Exercises Solutions 2 Spin in Second Quantization 2 1 Spin functions 2 2 Operators in the orbital basis 221 Spin-free operators 222 Spin operators 223 Mixed operators 2 3 Spin tensor operators 231 Spin tensor operators 232 Creation and annihilation operators 233 Two-body creation operators 234 Excitation operators 235 Singlet excitation operators 2 4 Spin properties of determinants 241 General considerations 242 Spin projection of determinants 243 Total spin of determinants 2 5 Configuration state functions 2 6 The genealogical coupling scheme 261 Representations of determinants and CSFs 262 Genealogical coupling 263 Coupling coefficients 264 An example: three electrons in three orbitals 265 Completeness and orthonormality 266 Transformations between determinant and CSF bases 267 Genealogical coupling of operators 2 7 Density matrices 271 Orbital-density matrices 272 Spin-density matrices 273 Density functions References Further reading Exercises Solutions 3 Orbital Rotations 3 1 Unitary transformations and matrix exponentials 311 Matrix exponentials 312 Exponential representations of unitary matrices 313 Special unitary matrices 314 Orthogonal matrices 315 Evaluation of matrix exponentials 316 Nonunitary transformations 4] al CONTENTS Vii 3 2 Unitary spin-orbital transformations 321 Unitary matrix expansions of creation and annihilation operators 322 Exponential unitary transformations of the elementary operators 323 Exponential unitary transformations of states in Fock space 3 3 Symmetry-restricted unitary transformations 331 The need for symmetry restrictions 332 Symmetry restrictions in the spin-orbital basis 333 Symmetry restrictions in the orbital basis 3 4 The logarithmic matrix function 341 Definition of the logarithmic matrix function 342 Expansion of the logarithmic matrix function 343 Properties of the logarithmic matrix function References Further reading - Exercises Solutions 4 Exact and Approximate Wave Functions 4 1 Characteristics of the exact wave function 4 2 The variation principle 421 The variation principle 422 The variation method 423 Linear expansions and eigenvalue equations 424 Upper bounds and the Hylleraas—Undheim theorem 425 Nonlinear expansions 426 The Hellmann-Feynman theorem 427 The molecular electronic virial theorem 428 Variational reformulation of nonvariational energies 429 The variation principle summarized 4 3 Size-extensivity 431 Size-extensivity of exact wave functions 432 Size-extensivity of linear variational wave functions 433 Matrix representation of the noninteracting eigenvalue problem 434 Size-extensivity of exponential wave functions 4 4 Symmetry constraints References Further reading Exercises Solutions 5 The Standard Models 5 1 One- and N-electron expansions 52A model system: the hydrogen molecule in a minimal basis 521 One-electron basis 522 N-electron basis viii 523 Density matrices and molecular integrals 524 Bonding and antibonding configurations 525 Superposition of configurations 526 Covalent and ionic states 527 Open-shell states 528 Electron correlation 529 The dissociation limit 5 2 10 Static and dynamical correlation Exact wave functions in Fock space 531 Full configuration-interaction wave functions 532 The electronic ground state of the hydrogen molecule 533 The electronic ground state of the water molecule The Hartree-Fock approximation 541 The Hartree-Fock model 542 The Fock operator and the canonical representation 543 Restricted and unrestricted Hartree-Fock theory 544 The correlation energy 545 The ground state of the hydrogen molecule 546 The bonded hydrogen molecule 547 The RHF dissociation of the hydrogen molecule 548 The UHF dissociation of the hydrogen molecule 549 The ground state of the water molecule 5 4 10 The dissociation of the water molecule 5 4 11 Final comments Multiconfigurational self-consistent field theory 551 The multiconfigurational self-consistent field model 552 The ground state of the hydrogen molecule 553 The selection of MCSCF configuration spaces 554 The ground state of the water molecule 555 Final comments Configuration-interaction theory 561 The configuration-interaction model 562 Single-reference CI wave functions 563 Multireference CI wave functions 564 Final comments Coupled-cluster theory 571 The coupled-cluster model 572 The exponential ansatz of coupled-cluster theory 573 The ground state of the water molecule 574 The unrestricted coupled-cluster model 575 Approximate treatments of triple excitations 576 Final comments Perturbation theory 581 Meller—Plesset perturbation theory 582 The ground state of the water molecule 583 Convergence of the Mgller—Plesset perturbation series CONTENTS ‘ 154 ° 170 \| 177 \| 181° CONTENTS ix 584 The ground state of the hydrogen molecule 194 585 Final comments 196 References 196 Further reading 196 Exercises 196 Solutions 198 6 Atomic Basis Functions 201 6 1 Requirements on one-electron basis functions 201 6 2 One- and many-centre expansions 203 6 3 The one-electron central-field system 204 6 4 The angular basis 207 641 The spherical harmonics 207 642 The solid harmonics 209 643 Explicit Cartesian expressions for the complex solid harmonics 210 644 Explicit Cartesian expressions for the real solid harmonics 214 645 Recurrence relations for the real solid harmonics 215 6 5 Exponential radial functions 218 651 The Laguerre polynomials 219 652 The hydrogenic functions 221 653 The Laguerre functions 222 654 The carbon orbitals expanded in Laguerre functions 223 655 The nodeless Slater-type orbitals 225 656 STOs with variable exponents 226 657 STO basis sets 227 6 6 Gaussian radial functions 229 661 The harmonic-oscillator functions in polar coordinates 230 662 The carbon orbitals expanded in HO functions 231 663 The nodeless Gaussian-type orbitals 232 664 The GTOs with variable exponents 233 665 The carbon orbitals expanded in GTOs 235 666 The HO functions in Cartesian coordinates 236 667 The Cartesian GTOs 237 References 238 Further reading 239 Exercises 239 Solutions 245 7 Short-Range Interactions and Orbital Expansions 256 7 1 The Coulomb hole 256 7 2 The Coulomb cusp 259 7 3 Approximate treatments of the ground-state helium atom 262 731 Configuration-interaction expansions 262 732 Correlating functions and explicitly correlated methods 264 CONTENTS j 733 The Hylleraas function 734 Conclusions The partial-wave expansion of the ground-state helium atom 741 Partial-wave expansion of the interelectronic distance 742 Partial-wave expansion of the wave function 743 The asymptotic convergence of the partial-wave expansion 744 The truncation error of the partial-wave expansion The principal expansion of the ground-state helium atom 751 The principal expansion and its asymptotic convergence 752 Comparison of the partial-wave and principal expansions 753 The Coulomb hole in the principal expansion 754 Conclusions Electron-correlation effects summarized References Further reading Exercises Solutions 8 Gaussian Basis Sets Gaussian basis functions 8 2 Gaussian basis sets for Hartree—Fock calculations 821 STO-kG basis sets 822 Primitive expansions of Hartree—Fock orbitals 823 Even-tempered basis sets 824 Contracted Gaussians 825 Segmented contractions 826 Simultaneous optimization of exponents and coefficients 827 Polarization functions Gaussian basis sets for correlated calculations 831 Core and valence correlation energies 832 Atomic natural orbitals 833 Correlation-consistent basis sets 834 Extended correlation-consistent basis sets Basis-set convergence 841 Basis-set convergence of the Hartree~Fock model 842 Basis-set convergence of correlated models 843 The asymptotic convergence of the correlation energy 844 Basis-set convergence of the binding energy Basis-set superposition error 851 Basis-set superposition error and 852 BSSE in the neon dimer 853 BSSE in the water dimer 854 BSSE in the BH molecule 855 Summary the counterpoise correction 270 \| 297 \| 322 ° 327 - 334° CONTENTS xi References 335 Further reading 335 9 Molecular Integral Evaluation 336 9 1 Contracted spherical-harmonic Gaussians 336 911 Primitive Cartesian GTOs 336 912 Spherical-harmonic GTOs 337 913 Contracted GTOs 338 914 Computational considerations 338 9 2 Cartesian Gaussians 339 921 Cartesian Gaussians 339 922 Recurrence relations for Cartesian Gaussians 340 923 The Gaussian product rule 341 924 Gaussian overlap distributions 341 925 Properties of Gaussian overlap distributions 343 926 Integrals over spherical overlap distributions 344 9 3 The Obara-Saika scheme for simple integrals 344 931 Overlap integrals 345 932 Multipole-moment integrals 346 933 Integrals over differential operators 347 934 Momentum and kinetic-energy integrals 348 9 4 Hermite Gaussians 349 941 Hermite Gaussians 349 942 Derivative and recurrence relations for Hermite Gaussians 350 943 Integrals over Hermite Gaussians 351 944 Hermite Gaussians and HO functions compared 352 9 5 The McMurchie-Davidson scheme for simple integrals 352 951 Overlap distributions expanded in Hermite Gaussians 353 952 Overlap distributions from Hermite Gaussians by recursion 355 953 The McMurchie-Davidson scheme for multipole-moment integrals 356 9 6 Gaussian quadrature for simple integrals 357 961 Orthogonal polynomials 358 962 Gaussian quadrature 359 963 Proof of the Gaussian-quadrature formula 360 964 Gauss-Hermite quadrature for simple integrals 361 9 7 Coulomb integrals over spherical Gaussians 361 971 Spherical Gaussian charge distributions 361 972 The potential from a spherical Gaussian charge distribution 362 973 The repulsion between spherical Gaussian charge distributions 363 974 The electrostatics of spherical Gaussian distributions 364 9 8 The Boys function 365 981 The Boys function 365 982 Evaluation of the Boys function 366 983 The incomplete gamma function 368 xii 984 The error function 985 The complementary error function 986 The confluent hypergeometric function The McMurchie-Davidson scheme for Coulomb integrals 991 Hermite Coulomb integrals 992 The evaluation of Hermite Coulomb integrals 993 Cartesian Coulomb integrals by Hermite expansion 994 Cartesian Coulomb integrals by Hermite recursion 995 Computational considerations for the one-electron integrals 996 Computational considerations for the two-electron integrals The Obara—Saika scheme for Coulomb integrals 9 10 1 The Obara—Saika scheme for one-electron Coulomb integrals 9 10 2 The Obara—Saika scheme for two-electron Coulomb integrals 9 10 3 The electron-transfer and horizontal recurrence relations 9 10 4 Computational considerations for the two-electron integrals Rys quadrature for Coulomb integrals 9 11 1 Motivation for the Gaussian-quadrature scheme 9 11 2 Gaussian quadrature for even polynomials and weight functions 9 11 3 Rys polynomials and Gauss—Rys quadrature 9 11 4 The Rys scheme for Hermite Coulomb integrals 9 11 5 The Rys scheme for Cartesian Coulomb integrals 9 11 6 Obara—Saika recursion for the two-dimensional Rys integrals 9 11 7 Computational considerations for the two-electron integrals Scaling properties of the molecular integrals 9 12 1 Linear scaling of the overlap and kinetic-energy integrals 9 12 2 Quadratic scaling of the Coulomb integrals 9 12 3 Linear scaling of the nonclassical Coulomb integrals 9 12 4 The Schwarz inequality The multipole method for Coulomb integrals 9 13 1 The multipole method for primitive two-electron integrals 9 13 2 Convergence of the multipole expansion 9 13 3 The multipole method for contracted two-electron integrals 9 13 4 Translation of multipole moments 9 13 5 Real multipole moments 9 13 6 The real translation matrix 9 13 7 The real interaction matrix 9 13 8 Evaluation of the scaled solid harmonics The multipole method for large systems 9 14 1 The naive multipole method 9 14 2 The two-level multipole method 9 14 3 The fast multipole method 9 14 4 The continuous fast multipole method References Further reading Exercises Solutions CONTENTS xiii 10 Hartree-Fock Theory Parametrization of the wave function and the energy 10 1 1 Singlet and triplet CSFs 10 1 2 Orbital rotations 10 1 3 Expansion of the energy The Hartree-Fock wave function 10 2 1 The Hartree-Fock wave function 10 2 2 Redundant parameters 10 2 3 The Brillouin theorem 10 2 4 Size-extensivity Canonical Hartree—Fock theory 10 3 1 The Fock operator 10 3 2 Identification of the elements of the Fock operator 10 3 3 The Fock matrix 10 3 4 The self-consistent field method 10 3 5 The variational and canonical conditions compared The RHF total energy and orbital energies 10 4 1 The Hamiltonian and the Fock operator 10 4 2 The canonical representation and orbital energies 10 4 3 The Hartree-Fock energy 10 4 4 Hund’s rule for singlet and triplet states 10 4 5 The fluctuation potential Koopmans’ theorem 10 5 1 Koopmans’ theorem for ionization potentials 10 5 2 Koopmans’ theorem for electron affinities 10 5 3 Ionization potentials of H2O and N2 The Roothaan—Hall self-consistent field equations 10 6 1 The Roothaan—Hall equations 10 6 2 DIIS convergence acceleration 10 6 3 Integral-direct Hartree—Fock theory Density-based Hartree—Fock theory 10 7 1 Density-matrix formulation of Hartree—Fock theory 10 7 2 Properties of the MO density matrix 10 7 3 Properties of the AO density matrix 10 7 4 Exponential parametrization of the AO density matrix 10 7 5 The redundancy of the exponential parametrization 10 7 6 Purification of the density matrix 10 7 7 Convergence of the purification scheme 10 7 3 The Hartree—Fock energy and the variational conditions 10 7 9 The density-based SCF method 10 7 10 Optimization of the SCF orbital-energy function 10 7 11 Linear scaling of the density-based SCF scheme 10 8 Second-order optimization 10 8 1 Newton’s method 10 8 2 Density-based formulation of Newton’s method 10 8 3 The electronic gradient in orbital-based Hartree—Fock theory 44] 11 10 8 4 The inactive and active Fock matrices 10 8 5 Computational cost for the calculation of the Fock matrix 10 8 6 The electronic Hessian in orbital-based Hartree—Fock theory 10 8 7 Linear transformations in the MO basis 10 8 8 Linear transformations in the AO basis The SCF method as an approximate second-order method 10 9 1 The GBT vector 10 9 2 The Fock operator 10 9 3 Identification from the gradient 10 9 4 Identification from the Hessian 10 9 5 Convergence rates 10 9 6 The SCF and Newton methods compared 10 10 Singlet and triplet instabilities in RHF theory 10 10 1 Orbital-rotation operators in RHF and UHF theories 10 10 2 RHF instabilities for nondegenerate electronic states 10 10 3 RHF energies of degenerate electronic states 10 10 4 Triplet instabilities in Hz 10 10 5 Triplet instabilities in H O 10 10 6 Singlet instabilities in the allyl radical 10 11 Multiple solutions in Hartree-Fock theory References Further reading Exercises Solutions Configuration-Interaction Theory IL The CI model 11 1 1 The CI model 11 1 2 Full CI wave functions 11 1 3 Truncated CI wave functions: CAS and RAS expansions Size-extensivity and the CI model 11 2 1 FCI wave functions 11 2 2 Truncated CI wave functions 11 2 3 The Davidson correction 11 24 A numerical study of size-extensivity A CI model system for noninteracting hydrogen molecules 11 3 1 The CID wave function and energy 11 3 2 The Davidson correction 11 3 3 The CID one-electron density matrix 11,34 The FCI distribution of excitation levels Parametrization of the CI model 11 4 1 The CI expansion 11 4 2 The CI energy Optimization of the CI wave function 11 5 1 The Newton step 11 5 2 Convergence rate of Newton’s method for the CI energy CONTENTS 482 \| 484 \| 496 \| 496 \| 500 \| 530 ° 535 538 540 - 545° CONTENTS XV 11 5 3 Approximate Newton schemes 547 11 5 4 Convergence rate of quasi-Newton schemes for the CI energy 548 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 354 11 8 1 General considerations 554 11 8 2 Ordering and addressing of spin strings 555 11 8 3 The N-resolution method 558 11 8 4 The minimal operation-count method 560 11 8 5 Direct CI algorithms for RAS calculations 564 11 8 6 Simplifications for wave functions of zero projected spin 567 11 8 7 Density matrices 568 11 9 CI orbital transformations 569 11 10 Symmetry-broken CI solutions 573 References 574 Further reading 575 Exercises 575 Solutions 583 12 Multiconfigurational Self-Consistent Field Theory 598 12 1 The MCSCF model 598 12 2 The MCSCF energy and wave function 600 12 2 1 The parametrization of the MCSCF state 600 12 2 2 The Taylor expansion of the MCSCF energy 601 12 2 3 The MCSCF electronic gradient and Hessian 603 12 2 4 Invariance of the second-order MCSCF energy 604 12 2 5 Rank-I contributions to the MCSCF electronic Hessian 604 12 2 6 Redundant orbital rotations 605 12 2 7 The MCSCF electronic gradient at stationary points 608 12 2 8 The MCSCF electronic Hessian at stationary points 609 12 3 The MCSCF Newton trust-region method 610 12 3 1 The Newton step 610 12 3 2 The level-shifted Newton step 6ll 12 3 3 The level-shift parameter 612 12 3 4 Step control for ground states 614 12 3 5 Step control for excited states 614 12 3 6 Trust-radius update schemes 615 12 4 The Newton eigenvector method 616 12 4 1 The MCSCF eigenvalue problem 616 12 4 2 The Newton eigenvector method 617 12 4 3 Norm-extended optimization 619 12 4 4 The augmented-Hessian method 620 12 5 Computational considerations 621 12 5 1 The MCSCF electronic gradient 622 12 5 2 MCSCF Hessian transformations 623 12 5 3 Inner and outer iterations CONTENTS Xvi 12 5 4 The structure of the MCSCF electronic Hessian 626; 12 5 5 Examples of MCSCF optimizations 628; 12 6 Exponential parametrization of the configuration space 630; 12 6 1 General exponential parametrization of the configuration space 630 12 6 2 Exponential parametrization for a single reference state 631 12 63A basis for the orthogonal complement to the reference state 633 12 6 4 Exponential parametrization for several reference states 634 12 7 MCSCF theory for several electronic states 637 12 7 1 Separate optimization of the individual states 637 12 7 2 State-averaged MCSCF theory 638 ! 12 8 Removal of RHF instabilities in MCSCF theory 12 8 1 Bond breaking in H,O 12 8 2 The ground state of the allyl radical References Further reading Exercises 643 i Solutions 645 \| 13 Coupled-Cluster Theory 648 13 1 The coupled-cluster model 648 i 13 1 1 Pair clusters 649 5 13 1 2 The coupled-cluster wave function 650 \| 13 1 3 Connected and disconnected clusters 650 \| 13 1 4 The coupled-cluster Schrödinger equation 651 13 2 The coupled-cluster exponential ansatz 654 \|; 13 2 1 The exponential ansatz 654 13 2 2 The coupled-cluster hierarchy of excitation levels 654 13 2 3 The projected coupled-cluster equations 657 13 2 4 The coupled-cluster energy 660 : 13 2 5 The coupled-cluster amplitude equations 660 - 13 2 6 Coupled-cluster theory in the canonical representation 662° 13 2 7 Comparison of the CI and coupled-cluster hierarchies 662 13 2 8 Cluster-commutation conditions and operator ranks 663 : 13 3 Size-extensivity in coupled-cluster theory 665 13 3 1 Size-extensivity in linked coupled-cluster theory 665 13 3 2 Termwise size-extensivity 667- 13 3 3 Size-extensivity in unlinked coupled-cluster theory 668, 13 34A numerical study of size-extensivity 669: 13 4 Coupled-cluster optimization techniques 13 4 1 Newton’s method 671: 13 4 2 The perturbation-based quasi-Newton method 672 13 4 3 DIIS acceleration of the quasi-Newton method 672 13 4 4 Examples of coupled-cluster optimizations 673 - CONTENTS XVii 13 5 The coupled-cluster variational Lagrangian 674 13 5 1 The coupled-cluster Lagrangian 674 13 5 2 The Hellmann—Feynman theorem 675 13 5 3 Lagrangian density matrices 676 13 6 The equation-of-motion coupled-cluster method 677 13 6 1 The equation-of-motion coupled-cluster model 677 13 6 2 The EOM-CC eigenvalue problem 679 13 6 3 The similarity-transformed Hamiltonian and the Jacobian 680 13 6 4 Solution of the EOM-CC eigenvalue problem 681 13 6 5 Size-extensivity of the EOM-CC energies 683 13 6 6 Final comments 684 13 7 The closed-shell CCSD model 685 13 7 1 Parametrization of the CCSD cluster operator 685 13 7 2 The CCSD energy expression 686 13 7 3 The Tl-transformed Hamiltonian 687 13 7 4 The Ti-transformed integrals 690 13 7 5 Representation of the CCSD projection manifold 691 13 7 6 The norm of the CCSD wave function 692 13 7 7 The CCSD singles projection 693 13 7 8 The CCSD doubles projection 695 13 7 9 Computational considerations 697 13 8 Special treatments of coupled-cluster theory 698 13 8 1 Orbital-optimized and Brueckner coupled-cluster theories 698 13 8 2 Quadratic configuration-interaction theory 702 13 9 High-spin open-shell coupled-cluster theory 704 13 9 1 Spin-restricted coupled-cluster theory 704 13 9 2 Total spin of the spin-restricted coupled-cluster wave function 707 13 9 3 The projection manifold in spin-restricted theory 708 13 9 4 Spin-adapted CCSD theory 709 References 711 Further reading 712 Exercises 712 Solutions 717 14 Perturbation Theory 724 14 1 Rayleigh-Schrödinger perturbation theory 725 14 1 1 RSPT energies and wave functions 726 14 1 2 Wigner’s 2n + 1 rule 728 14 1 3 The Hylleraas functional 734 14 1 4 Size-extensivity in RSPT 736 14 2 M@gller—Plesset perturbation theory 739 14 2 1 The zero-order MPPT system 740 14 2 2 The MPI wave function 741 xvili CONTENTS 14 2 3 The MP2 wave function 14 2 4 The Maller—Plesset energies 14 2 5 Explicit expressions for MPPT wave functions and energies 14 2 6 Size-extensivity in MgHer—Plesset theory Coupled-cluster perturbation theory 14 3 1 The similarity-transformed exponential ansatz of CCPT 14 3 2 The CCPT amplitude equations 14 3 3 The CCPT wave functions 14 3 4 The CCPT energies 14 3 5 Size-extensivity in CCPT 14 3 6 The CCPT Lagrangian 14 3 7 The CCPT variational equations 14 3 3 CCPT energies that obey the 2n + 1 rule 14 3 9 Size-extensivity of the CCPT Lagrangian Mgller—Plesset theory for closed-shell systems 14 4 1 The closed-shell zero-order system 14 4 2 The closed-shell variational Lagrangian 14 4 3 The closed-shell wave-function corrections 14 4 4 The closed-shell energy corrections Convergence in perturbation theory 14 51A two-state model 14 5 2 Conditions for convergence 14 5 3 Intruders in the general two-state model 14 5 4 Prototypical intruders 14 5 5 Convergence of the Mdller—Plesset series 14 5 6 Analytic continuation Perturbative treatments of coupled-cluster wave functions 14 6 1 Perturbation analysis of the coupled-cluster hierarchy 14 6 2 Iterative hybrid methods 14 6 3 Noniterative hybrid methods: the CCSD(T) model 14 6 4 Hybrid and nonhybrid methods compared Multiconfigurational perturbation theory 14 7 1 The zero-order CASPT Hamiltonian 14 7 2 Size-extensivity in CASPT 14 7 3 The CASPT wave function and energy 14 74 Sample CASPT calculations References Further reading Exercises Solutions 15 Calibration of the Electronic-Structure Models 15 1 The sample molecules 15 2 Errors in quantum-chemical calculations 15 2 1 Apparent and intrinsic errors 15 2 2 Statistical measures of errors 746 \| 752 \| 754 \| 756° 758 761 \| TIL: 804 - u rare 809 \| CONTENTS xix 15 3 Molecular equilibrium structures: bond distances 821 15 3 1 Experimental bond distances 822 15 3 2 Mean errors and standard deviations 822 15 3 3 Normal distributions 825 15 3 4 Mean absolute deviations 825 15 3 5 Maximum errors 827 15 3 6 The CCSDT and CCSD(T) models 827 15 3 7 The effect of core correlation on bond distances 828 15 3 8 Trends in the convergence towards experiment 829 15 3 9 Summary 831 15 4 Molecular equilibrium structures: bond angles 832 15 4 1 Experimental bond angles 832 15 4 2 Calculated bond angles 833 15 4 3 Summary 834 15 5 Molecular dipole moments 836 15 5 1 Experimental dipole moments 836 15 5 2 Calculated dipole moments 837 15 5 3 Predicted dipole moments 838 15 5 4 Analysis of the calculated dipole moments 839 15 5 5 Summary 840 15 6 Molecular and atomic energies 840 15 6 1 The total electronic energy 841 15 6 2 Contributions to the total electronic energy 842 15 6 3 Basis-set convergence 844 15 6 4 CCSDT corrections 846 15 6 5 Molecular vibrational corrections 847 15 6 6 Relativistic corrections 849 15 6 7 Summary 853 15 7 Atomization energies 854 15 7 1 Experimental atomization energies 854 15 7 2 Statistical analysis of atomization energies 855 15 7 3 Extrapolation of atomization energies 858 15 7 4 Core contributions to atomization energies 861 15 7 5 CCSDT corrections 863 15 7 6 Summary 864 15 8 Reaction enthalpies 865 15 8 1 Experimental reaction enthalpies 865 15 8 2 Statistical analysis of reaction enthalpies 867 15 8 3 Extrapolation and convergence to the basis-set limit 870 15 8 4 Core contributions to reaction enthalpies 871 15 8 5 Summary 873 15 9 Conformational barriers 874 15 9 1 The barrier to linearity of water 875 15 9 2 The inversion barrier of ammonia 876 15 9 3 The torsional barrier of ethane 877 15 9 4 Summary 879 15 10 Conclusions 879 XX CONTENTS \| References Further reading Exercises Solutions List of Acronyms Index 882 \| 882 \| 882 ° 883 \| 885 \| 887 \|
any_adam_object	1
author	Helgaker, Trygve Jørgensen, Poul 1944- Olsen, Jeppe
author_GND	(DE-588)131710974
author_facet	Helgaker, Trygve Jørgensen, Poul 1944- Olsen, Jeppe
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dewey-hundreds	500 - Natural sciences and mathematics
dewey-ones	541 - Physical chemistry
dewey-raw	541.22
dewey-search	541.22
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dewey-tens	540 - Chemistry and allied sciences
discipline	Chemie / Pharmazie
edition	Reprinted as paperback
format	Book
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id	DE-604.BV041159668
illustrated	Illustrated
indexdate	2024-07-10T00:40:57Z
institution	BVB
isbn	9781118531471
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-026134951
oclc_num	842199345
open_access_boolean
owner	DE-188 DE-384 DE-29T DE-11
owner_facet	DE-188 DE-384 DE-29T DE-11
physical	XXVII, 908 S. graph. Darst.
publishDate	2012
publishDateSearch	2012
publishDateSort	2012
publisher	Wiley-Blackwell
record_format	marc
spelling	Helgaker, Trygve Verfasser aut Molecular electronic-structure theory Trygve Helgaker ; Poul Jørgensen ; Jeppe Olsen Reprinted as paperback Chichester Wiley-Blackwell 2012 XXVII, 908 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Ab initio quantum chemistry is increasingly paired with computational methods to solve intractable problems in chemistry and molecular physics. Now in a paperback edition, this comprehensive and technical work covers all the important aspects of modern molecular electronic-structure theory, clearly explaining quantum-mechanical methods and applications to molecular equilibrium structure, atomization energies, and reaction enthalpies. Extensive numerical examples illustrate each method described. An excellent resource.. Kemiske bindinger Molekülstruktur (DE-588)4170383-2 gnd rswk-swf Elektronenstruktur (DE-588)4129531-6 gnd rswk-swf Ab-initio-Rechnung (DE-588)4141062-2 gnd rswk-swf Quantenchemie (DE-588)4047979-1 gnd rswk-swf Molekülstruktur (DE-588)4170383-2 s Elektronenstruktur (DE-588)4129531-6 s Ab-initio-Rechnung (DE-588)4141062-2 s Quantenchemie (DE-588)4047979-1 s DE-604 Jørgensen, Poul 1944- Verfasser (DE-588)131710974 aut Olsen, Jeppe Verfasser aut HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026134951&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Helgaker, Trygve Jørgensen, Poul 1944- Olsen, Jeppe Molecular electronic-structure theory Kemiske bindinger Molekülstruktur (DE-588)4170383-2 gnd Elektronenstruktur (DE-588)4129531-6 gnd Ab-initio-Rechnung (DE-588)4141062-2 gnd Quantenchemie (DE-588)4047979-1 gnd
subject_GND	(DE-588)4170383-2 (DE-588)4129531-6 (DE-588)4141062-2 (DE-588)4047979-1
title	Molecular electronic-structure theory
title_auth	Molecular electronic-structure theory
title_exact_search	Molecular electronic-structure theory
title_full	Molecular electronic-structure theory Trygve Helgaker ; Poul Jørgensen ; Jeppe Olsen
title_fullStr	Molecular electronic-structure theory Trygve Helgaker ; Poul Jørgensen ; Jeppe Olsen
title_full_unstemmed	Molecular electronic-structure theory Trygve Helgaker ; Poul Jørgensen ; Jeppe Olsen
title_short	Molecular electronic-structure theory
title_sort	molecular electronic structure theory
topic	Kemiske bindinger Molekülstruktur (DE-588)4170383-2 gnd Elektronenstruktur (DE-588)4129531-6 gnd Ab-initio-Rechnung (DE-588)4141062-2 gnd Quantenchemie (DE-588)4047979-1 gnd
topic_facet	Kemiske bindinger Molekülstruktur Elektronenstruktur Ab-initio-Rechnung Quantenchemie
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026134951&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT helgakertrygve molecularelectronicstructuretheory AT jørgensenpoul molecularelectronicstructuretheory AT olsenjeppe molecularelectronicstructuretheory

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