Holdings: Elementary molecular quantum mechanics

Elementary molecular quantum mechanics: mathematical methods and applications

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Main Author:	Magnasco, Valerio (Author)
Format:	Book
Language:	English
Published:	Amsterdam [u.a.] Elsevier 2013
Edition:	2. ed.
Subjects:	Quantenchemie Quantenmechanik
Online Access:	Inhaltsverzeichnis Klappentext
Item Description:	1. Aufl. u.d.T.: Magnasco, Valerio: Elementary methods of molecular quantum mechanics
Physical Description:	XX, 932 S. graph. Darst.
ISBN:	9780444626479

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adam_text	Contents Preface ................................................................................................................................................xix PART 1 MATHEMATICAL METHODS CHAPTER 1 Mathematical foundations and approximation methods .................. з 1.1. Mathematical Foundations ........................................................................................4 .1.1. Regular functions ............................................................................................4 . 1.2. Schmidt orthogonalization ..............................................................................5 .1.3. Löwdin orthogonalization ...............................................................................8 .1.4. Set of orthonormal functions and basis set ....................................................8 .1.5. Linear operators ..............................................................................................9 .1.6. Hermitian operators ......................................................................................10 1.1.7. Expansion theorem .......................................................................................14 1.1.8. Basic principles of quantum mechanics .......................................................17 1.2. The variational method ............................................................................................19 1.2.1. Non-linear parameters ..................................................................................21 1.2.2. Linear parameters: the Ritz method .............................................................21 1.3. Perturbative Methods for Stationary States .............................................................25 1.3.1. RS perturbation theory .................................................................................25 1.3.2. Second-order approximation methods in RS perturbation theory ...............32 1.3.3. BW perturbation theory ................................................................................37 1.3.4. Perturbation methods without partitioning of the Hamiltonian ..................40 1.3.5. Perturbation theories including exchange (SAPTs) .....................................45 1.3.6. The moment method .....................................................................................53 1.4. The Wentzel-Kramers-Brillouin Method ...............................................................55 1.5. Problems 1...............................................................................................................59 1.6. Solved Problems ......................................................................................................62 CHAPTER 2 Coordinate systems ...................................................................69 2.1. Introduction ..............................................................................................................69 2.2. Systems of Orthogonal Coordinates ........................................................................71 2.3. Generalized Coordinates ..........................................................................................73 2.4. Cartesian Coordinates (x,y,z) ...................................................................................74 2.5. Spherical Coordinates (r,6,<p) ..................................................................................74 2.6. Spheroidal Coordinates (μ,ν,φ) ...............................................................................75 2.7. Parabolic Coordinates (ξ,η,φ) ..................................................................................76 2.8. Problems 2...............................................................................................................78 2.9. Solved Problems ......................................................................................................80 CHAPTER 3 Differential equations in quantum mechanics ..............................87 3.1. Introduction ..............................................................................................................88 3.2. Partial Differential Equations ..................................................................................88 « ■ VII viii Contents 3.3. Separation of Variables ............................................................................................89 3.3.1. The particle in a three-dimensional box ......................................................89 3.3.2. The three-dimensional harmonic oscillator .................................................91 3.3.3. The atomic one-electron system ..................................................................91 3.3.4. The molecular one-electron system .............................................................93 3.3.5. The hydrogen atom in a uniform electric field ............................................96 3.4. Solution by Series Expansion ..................................................................................98 3.5. Solution Near Singular Points ...............................................................................100 3.6. The One-Dimensional Harmonic Oscillator .........................................................101 3.7. The Atomic One-Electron System ........................................................................104 3.7.1. Solution of the radial equation ...................................................................105 3.7.2. Solution of the Ф -equatíon ......................................................................... 109 3.7.3. Solution of the Θ -equation ........................................................................ 109 3.7.4. The hydrogen-like atomic orbitais .............................................................115 3.8. The Hydrogen Atom in an Electric Field .............................................................117 3.9. The Hydrogen Molecular Ion H~ľ .........................................................................120 3.10. The Stark Effect in Atomic Hydrogen ..................................................................124 3.10.1. Solution of the ^-equation in the zero-field case .....................................124 3.10.2. The first-order Stark effect .......................................................................128 3.11. Appendix: Checking the Solutions ........................................................................131 3.11.1- The radial equation of the H-atom in spherical coordinates ...................131 3.11.2. The Θ -equation of the H-atom in spherical coordinates .........................132 3.11.3. The ^-equation of the H-atom in parabolic coordinates ..........................135 3.12. Problems 3.............................................................................................................135 3.13. Solved Problems ....................................................................................................137 CHAPTER 4 Special functions ....................................................................151 4.1. Introduction ............................................................................................................152 4.2. Legendre Functions ...............................................................................................152 4.2.1. Legendre polynomials and associated Legendre polynomials ..................152 4.2.2. Recurrence relations for Legendre polynomials ........................................154 4.2.3. Series of Legendre polynomials .................................................................154 4.2.4. Legendre functions of first and second kind .............................................155 4.2.5. Neumann s formula for the Legendre functions ........................................157 4.3. Laguerre Functions ................................................................................................158 4.3.1. Laguerre polynomials and Laguerre functions ..........................................158 4.3.2. Associated Laguerre polynomials ..............................................................159 4.3.3. Basic integrals over associated Laguerre functions ...................................161 4.4. Hermite Functions .................................................................................................163 4.4.1. Hermite polynomials ..................................................................................163 4.4.2. Hermite functions .......................................................................................164 4.4.3. Integrals over Hermite functions ................................................................165 4.5. Hypergeometric Functions ....................................................................................166 4.5.1. Hypergeometric series and differential equation .......................................166 4.5.2. Confluent hypergeometric functions ..........................................................168 Contents ix 4.6. Bessel Functions................................................................................................... 170 4.6.1. Bessel functions of integral order .............................................................170 4.6.2. Bessel functions of half-integral order ......................................................171 4.6.3. Spherical Bessel functions ........................................................................172 4.6.4. Modified Bessel functions .........................................................................176 4.7. Functions Defined by Integrals .............................................................................178 4.7.1. The gamma function ..................................................................................178 4.7.2. The incomplete gamma function ...............................................................178 4.7.3. From the gamma function to the exponential integral function ................179 4.7.4. The exponential integral function ..............................................................180 4.7.5. The generalized exponential integral function ..........................................181 4.7.6. Further functions ........................................................................................181 4.8. The Dirac ¿-Function ............................................................................................184 4.9. The Fourier Transform ..........................................................................................185 4.10. The Laplace Transform .........................................................................................188 4.11. Spherical Tensors ...................................................................................................190 4.11.1. Spherical tensors in complex form ..........................................................190 4.11.2. Spherical tensors in real form ..................................................................191 4.11.3. Generalized spherical tensors ...................................................................195 4.12. Orthogonal Polynomials ........................................................................................195 4.13. Padé Approximants ................................................................................................197 4.14. Green s Functions ..................................................................................................199 4.15. Problems 4.............................................................................................................202 4.16. Solved Problems ....................................................................................................203 CHAPTER 5 Functions of a complex variable ...............................................215 5.1. Functions of a Complex Variable ..........................................................................215 5.1.1. Complex numbers .......................................................................................215 5.1.2. Functions of a complex variable ................................................................217 5.1.3. Regular functions ........................................................................................218 5.1.4. Elementary operations ................................................................................219 5.1.5. Power series of elementary functions ........................................................219 5.1.6. Many-valued functions ...............................................................................223 5.2. Complex Integral Calculus ....................................................................................223 5.2.1. Line integrals ..............................................................................................223 5.2.2. Integrals in the complex plane and the Cauchy theorem ..........................224 5.2.3. Integration over a not simply connected domain ......................................225 5.2.4. Cauchy s integral representation ................................................................227 5.2.5. Taylor s expansion around a singularity ....................................................228 5.2.6. Laurent s expansion ....................................................................................228 5.2.7. Zeros of a regular function .........................................................................230 5.2.8. Analytic continuation .................................................................................230 5.3. Calculus of Residues .............................................................................................232 5.3.1. The residue theorem ...................................................................................232 5.3.2. The Jordan lemma ......................................................................................234 Contents 5.3.3. Sum of non-convergent series ....................................................................235 5.3.4. Evaluation of integrals of functions of real variable .................................238 5.4. Problems 5.............................................................................................................241 5.5. Solved Problems ....................................................................................................242 CHAPTERS Matrices .................................................................................247 6.1. Definitions and Elementary Properties .................................................................247 6.2. The Partitioning of Matrices .................................................................................248 6.3. Properties of Determinants ....................................................................................250 6.4. Special Matrices ....................................................................................................255 6.5. The Matrix Eigenvalue Problem ...........................................................................256 6.6. Functions of Hermitian Matrices ..........................................................................261 6.6.1. Analytic functions ......................................................................................261 6.6.2. Projectors and canonical form ...................................................................262 6.6.3. Examples ....................................................................................................262 6.7. The Matrix Pseudoeigenvalue Problem ................................................................266 6.8. The Lagrange Interpolation Formula ....................................................................268 6.9. The Cayley-Hamilton Theorem ............................................................................270 6.10. The Eigenvalue Problem in Hiickeľs Theory of the π Electrons of Benzene .... 270 6.10.1. General considerations .............................................................................270 6.10.2. Unitary transformation diagonalizing the Hiickeľs matrix .....................272 6.11. Problems 6.............................................................................................................273 6.12. Solved Problems ....................................................................................................278 CHAPTER 7 Molecular symmetry ................................................................297 7.1. Introduction ............................................................................................................297 7.2. Symmetry and Quantum Mechanics .....................................................................298 7.3. Molecular Symmetry .............................................................................................299 7.4. Symmetry Operations as Transformation of the Coordinate Axes ......................302 7.4.1. Passive and active representations of symmetry operations ......................302 7.4.2. Symmetry transformations in coordinate space .........................................303 7.4.3. Symmetry operators and transformations in function space .....................305 7.4.4. Matrix representatives of symmetry operators ..........................................308 7.4.5. Similarity transformations ..........................................................................310 7.5. Applications ...........................................................................................................310 7.5.1. The fundamental theorem of symmetry .....................................................310 7.5.2. Selection rules ............................................................................................311 7.5.3. Ground state electron configuration of polyatomic molecules ..................312 7.6. Problems 7.............................................................................................................313 7.7. Solved Problems ....................................................................................................315 CHAPTER 8 Abstract group theory ..............................................................323 8.1. Introduction ............................................................................................................323 8.2. Axioms of Group Theory ......................................................................................324 Contents XI 8.3. Examples of Groups ............................................................................................325 8.4. Multiplication Table ............................................................................................326 8.5. Subgroups ............................................................................................................327 8.6. Isomorphism ........................................................................................................328 8.7. Conjugation and Classes .....................................................................................331 8.8. Direct-Product Groups ........................................................................................332 8.9. Representations and Characters ..........................................................................333 8.10. Irreducible Representations .................................................................................338 8.11. Projectors and Symmetry-Adapted Functions ....................................................340 8.12. The Symmetric Group .........................................................................................345 8.13. Molecular Point Groups ......................................................................................351 8.14. Continuous Groups ..............................................................................................353 8.15. Rotation Groups ..................................................................................................356 8.15.1. Axial groups ...........................................................................................356 8.15.2. The spherical group ...............................................................................358 8.15.3. Transformation properties of spherical harmonics ................................362 8.16. Problems 8...........................................................................................................364 8.17. Solved Problems ..................................................................................................368 CHAPTER 9 The electron spin ..................................................................381 9.1. Introduction .........................................................................................................381 9.2. Electron Spin according to Pauli and the Zeeman Effect ..................................382 9.3. Theory of One-Electron Spin ..............................................................................386 9.4. Matrix Representation of Spin Operators ...........................................................389 9.5. Theory of Two-Electron Spin .............................................................................392 9.6. Theory of Many-Electron Spin ...........................................................................394 9.7. The Kotani Synthetic Method ...........................................................................397 9.8. Löwdin Spin Projection Operators ....................................................................398 9.9. Problems 9...........................................................................................................400 9.10. Solved Problems ..................................................................................................402 CHAPTER 10 Angular momentum methods for atoms ....................................417 10.1. Introduction .........................................................................................................417 10.2. The Vector Model ...............................................................................................418 10.2.1. Coupling of angular momenta ...............................................................418 10.2.2. LS coupling and multiplet structure ......................................................421 10.3. Construction of States of Definite Angular Momentum ....................................425 10.3.1. The matrix method .................................................................................425 10.3.2. The projection operator method ............................................................431 10.4. An Outline of Advanced Methods for Coupling Angular Momenta .................431 10.4.1. Clebsch-Gordan coefficients and Wigner 3-j and 9-у symbols ............431 10.4.2. Gaunt coefficients and coupling rules ...................................................433 10.5. Problems 10.........................................................................................................434 10.6. Solved Problems ..................................................................................................437 XII Contents PART 2 APPLICATIONS _____________________________________________ CHAPTER 11 The physical principles of quantum mechanics .......................449 11.1. The Orbital Model ..............................................................................................449 11.2. The Fundamental Postulates of Quantum Mechanics ........................................450 11.2.1. Correspondence between observables and operators ............................450 11.2.2. State function and average values of observables .................................454 11.2.3. Time evolution of state function ............................................................455 11.3. The Physical Principles of Quantum Mechanics ...............................................456 11.3.1. Wave-particle dualism ...........................................................................456 11.3.2. Atomicity of matter ................................................................................458 1 1 .3.3. Schroedinger s wave equation ...............................................................459 11.3.4. Born interpretation .................................................................................460 11.3.5. Measure of observables .........................................................................461 11.4. Problems 11.........................................................................................................463 11.5. Solved Problems ..................................................................................................464 CHAPTER 12 Atomic orbitais ......................................................................467 12.1. Introduction .........................................................................................................467 12.2. Hydrogen-Like Atomic Orbitals.........................................................................468 12.3. Slater-Type Orbitals............................................................................................473 12.4. Gaussian-Type Orbitals.......................................................................................475 12.5. Problems 12.........................................................................................................477 12.6. Solved Problems ..................................................................................................478 CHAPTER 13 Variational calculations .........................................................483 13.1. Introduction .........................................................................................................483 13.2. The Variational Method ......................................................................................484 13.2.1. Variational principles in first order ........................................................484 13.2.2. Variational approximations ....................................................................485 13.2.3. Basis functions and variational parameters ...........................................486 13.3. Non-Linear Parameters .......................................................................................487 13.3.1. The Is ground state of the atomic one-electron system .......................487 13.3.2. The first 2s, 2p excited states of the atomic one-electron system ........490 13.3.3. The Is2 ground state of the atomic two-electron system ......................493 13.4. Linear Parameters and the Ritz Method .............................................................496 13.5. Atomic Applications of the Ritz Method ...........................................................497 13.5.1. The first h2s excited state of the atomic two-electron system ............497 13.5.2. The first s2p excited state of the atomic two-electron system ............499 13.5.3. Results for hydrogen-like AOs ..............................................................502 13.6. Molecular Applications of the Ritz Method .......................................................503 13.6.1. The ground and first excited state of the Н^ molecular ion .................503 13.6.2. The interaction energy and its components ...........................................505 13.7. Variational Principles in Second Order ..............................................................510 13.7.1. The dipole polarizability of the H atom ................................................510 13.7.2. The London attraction between two ground-state H atoms ..................512 Contents xiii 13.8. Problems 13.........................................................................................................514 13.9. Solved Problems..................................................................................................517 CHAPTER 14 Many-electron wavefunctions and model Hamiltonians ............533 14.1. Introduction......................................................................................................... 534 14.2. Antisymmetry of the Electronic Wavefunction and the Pauli s Principle .........534 14.2.1. Two-electron wavefunctions ..................................................................534 14.2.2. Many-electron wavefunctions and the Slater method ...........................535 14.3. Electron Distribution Functions ..........................................................................539 14.3.1. One-electron distribution functions: general definitions .......................539 14.3.2. Electron density and spin density ..........................................................540 14.3.3. Two-electron distribution functions: general definitions ......................543 14.4. Average Values of One- and Two-Electron Operators .......................................544 14.4.1. Symmetrical sums of one-electron operators ........................................544 14.4.2. Symmetrical sums of two-electron operators ........................................545 14.4.3. Average value of the electronic energy .................................................546 14.5. The Slater s Rules ...............................................................................................546 14.6. Pople s Two-Dimensional Chart of Quantum Chemistry ..................................548 14.7. Hartree-Fock Theory for Closed Shells .............................................................550 14.7.1. Basic theory and properties of the fundamental invariant ρ .................550 14.7.2. Electronic energy for the HF wavefunction ..........................................552 14.7.3. Roothaan s variational derivation of the HF equations .........................553 14.7.4. Hall-Roothaan s formulation of the LCAO-MO-SCF equations .........555 14.7.5. Mulliken population analysis .................................................................558 14.7.6. Atomic bases in quantum chemical calculations ..................................561 14.7.7. Localization of molecular orbitais .........................................................565 14.8. Hückel s Theory ..................................................................................................567 14.8.1. Recurrence relation for the linear chain ................................................568 14.8.2. General solution for the linear chain .....................................................569 14.8.3. General solution for the closed chain ....................................................570 14.8.4. Alternant hydrocarbons ..........................................................................572 14.8.5. An introduction to band theory of solids ..............................................577 14.9. Semiempirical MO Methods ...............................................................................579 14.9.1. Extended Hückel s theory ......................................................................580 14.9.2. The CNDO method ................................................................................580 14.9.3. The INDO method .................................................................................584 14.9.4. The ZINDO method ...............................................................................584 14.10. Problems 14.........................................................................................................585 14.11. Solved Problems ..................................................................................................588 CHAPTER 15 Valence bond theory and the chemical bond ...........................599 15.1. Introduction .........................................................................................................600 15.2. The Chemical Bond in H2 ..................................................................................601 15.2.1. Failure of the MO theory for ground-state H2 ......................................602 15.2.2. The Heitler-London theory for H2 ........................................................608 xiv Contents 15.2.3. Equivalence between МО -CI and full VB for ground-state H2 and improvements in the wavefunction ........................................................611 15.2.4. The orthogonality catastrophe in the covalent VB theory for ground-state H2 ......................................................................................618 15.3. Elementary VB Methods ....................................................................................623 15.3.1. General formulation of VB theory ........................................................623 15.3.2. Construction of VB structures for multiple bonds ................................626 15.3.3. The allyl radical (N=3)........................................................................627 15.3.4. Cyclobutadiene (N = 4)..........................................................................630 15.3.5. VB description of simple molecules .....................................................631 15.4. Pauling s VB Theory for Conjugated and Aromatic Hydrocarbons ..................641 15.4.1. Pauling s formula for the matrix elements of singlet covalent VB structures ................................................................................................642 15.4.2. Cyclobutadiene .......................................................................................644 15.4.3. Butadiene ................................................................................................645 15.4.4. Allyl radical ...........................................................................................646 15.4.5. Benzene ..................................................................................................647 15.4.6. Naphthalene ............................................................................................655 15.4.7. Derivation of The Pauling s formula for H2 and cyclobutadiene .........657 15.5. Hybridization and Directed Valency in Polyatomic Molecules .........................661 15.5.1. sp2 Hybridization in H20 .......................................................................661 15.5.2. VB description of H2O ..........................................................................662 15.5.3. Properties of hybridization ....................................................................664 15.5.4. The principle of maximum overlap in VB theory ................................667 15.6. Problems 15.........................................................................................................669 15.7. Solved Problems ..................................................................................................671 CHAPTER 16 Post-Hartree-Fock methods ...................................................681 16.1. Introduction .........................................................................................................682 16.2. Matrix Elements between Slater Determinants ..................................................682 16.2.1. Slater s rules for orthonormal determinants ..........................................682 16.2.2. Löwdin s density matrices for non-orthogonal determinants ...............683 16.3. Spinless Pair Functions and the Correlation Problem ........................................685 16.4. Configurational Interaction Methods ..................................................................686 16.4.1. Configuration interaction .......................................................................687 16.4.2. Large-scale CI methods .........................................................................687 16.4.3. Generalized valence bond methods .......................................................688 16.4.4. Cusp-corrected configurational interaction ...........................................691 16.4.5. Kołos-Wolniewicz wavefunctions .........................................................692 16.5. Mul ticonfigurational-SCF Method ......................................................................695 16.6. Môller-Plesset Perturbation Theory ....................................................................696 16.7. Second Quantization ...........................................................................................702 16.7.1. Creation and annihilation operators ......................................................702 16.7.2. One-electron operators ...........................................................................703 Contents xv 16.7.3. Two-electron operators ..........................................................................704 16.7.4. Energy expressions ................................................................................705 16.7.5. The Fock space ......................................................................................706 16.8. Diagrammatic Theory .........................................................................................706 16.8.1. Second- and third-order diagrammatic theory ......................................707 16.8.2. Fourth-order diagrammatic theory .........................................................708 16.8.3. Padé approximants and perturbation expansions ..................................710 16.8.4. Coupled-cluster many-body perturbation theory ...................................711 16.8.5. CC-RH-MBPT ......................................................................................712 16.9. The Density Functional Theory ..........................................................................713 16.10. Problems 16.........................................................................................................716 16.11. Solved Problems ..................................................................................................717 CHAPTER 17 Atomic and molecular interactions .........................................723 17.1. Introduction .........................................................................................................723 17.2. Electric Properties of Molecules .........................................................................724 17.2.1. Molecular moments and polarizabilities ...............................................724 17.2.2. Molecular moments ...............................................................................726 17.2.3. Polarizabilities ........................................................................................727 17.3. Interatomic Potentials .........................................................................................731 17.3.1. The H-H^ non-expanded interaction up to second order .....................731 17.3.2. The H -Н non-expanded interaction up to second order .......................735 17.3.3. The multipole analysis of the H -Н non-expanded second-order induction energy .....................................................................................737 17.3.4. The multipole analysis of the H -Н non-expanded second-order dispersion energy ...................................................................................740 17.3.5. The H -Н expanded interaction up to second order ..............................742 17.3.6. Higher-order terms in the H -Н long-range dispersion interaction .......746 17.3.7. The expanded dispersion interaction for many-electron atoms ............748 17.4. Molecular Interactions ........................................................................................752 17.4.1. Non-expanded molecular energy corrections up to second order ........753 17.4.2. Expanded molecular energy corrections up to second order ................756 17.4.3. Multipole expansion of the first-order electrostatic energy in(HF)2 ..................................................................................................761 17.5. The Pauli Repulsion between Closed Shells ......................................................765 17.6. The Van der Waals Bond ....................................................................................767 17.7. Accurate Theoretical Results for Simple Diatomic Systems .............................772 17.8. A Generalized Multipole Expansion for Molecular Interactions .......................773 17.8.3. Generalized expansion of the intermolecular potential ........................773 17.8.2. Generalized molecular moments and polarizabilities ...........................776 17.8.3. Molecular interaction energies ..............................................................777 17.8.4. The damping of dispersion in the (HF>2 homodimer ............................778 17.9. Problems 17.........................................................................................................779 17.10. Solved Problems ..................................................................................................780 xvi Contents CHAPTER 18 Evaluation of molecular integrals ...........................................789 18.1. Introduction .........................................................................................................790 18.2. The Basic Integrals .............................................................................................790 18.2.1- The indefinite integral ............................................................................790 18.2.2. Definite integrals and auxiliary functions .............................................791 18.3. One-Centre Integrals ...........................................................................................793 18.3.1. One-electron integrals ............................................................................793 18.3.2. Two-electron integrals ...........................................................................795 18.4. Evaluation of the Electrostatic Potential J s .......................................................795 18.4.1. Spherical coordinates .............................................................................795 18.4.2. Spheroidal coordinates ...........................................................................797 18.5. The (Is2!Is2) Electron Repulsion Integral ..........................................................798 18.5.1. Same orbital exponent ...........................................................................798 18.5.2. Different orbital exponents ....................................................................799 18.6. General Formula for One-centre Two-electron Integrals ...................................799 18.7. Two-centre Integrals Over is STOs ....................................................................800 18.7.1. One-electron integrals ............................................................................801 18.7.2. Two-electron integrals ...........................................................................803 18.7.3. Limiting values of two-centre integrals ................................................809 18.8. On the General Formulae for Two-centre Integrals ...........................................812 18.8.1. Spheroidal coordinates ...........................................................................812 18.8.2. Spherical coordinates .............................................................................813 18.9. A Short Note on Multicentre Integrals ...............................................................814 18.9.1. Three-centre one-electron integral over Is STOs .................................814 18.9.2. Four-centre two-electron integral over Is STOs ...................................815 18.10. Molecular Integrals Over GTOs .........................................................................817 18.10.1. Some properties of Gaussian functions ...............................................817 18.10.2. Integrals of Gaussian functions ...........................................................819 18.10.3. Integral transforms ...............................................................................820 18.10.4. Molecular integrals ..............................................................................822 18.11. Problems 18.........................................................................................................824 18.12. Solved Problems ..................................................................................................825 CHAPTER 19 Relativistic molecular quantum mechanics .............................831 19.1. Introduction .........................................................................................................831 19.2. The Schroedinger s Relativistic Equation ..........................................................832 19.3- The Klein-Gordon Relativistic Equation ...........................................................833 19.4. Dirac s Relativistic Equation for the Electron ...................................................834 19.5. Spinors: Small and Large Components ..............................................................835 19.6. Dirac s Equation for a Central Field ..................................................................838 19.6.1. Separation of the radial equation ...........................................................841 19.6.2. The hydrogen-like atom .........................................................................843 19.7. One-Electron Molecular Systems: H? and HHe+2 ...........................................846 Contents xvii 19.8. Two-Electron Atomic System: The He Atom ....................................................847 19.9. Two-Electron Molecular Systems: Њ and HHe ..............................................850 19.10. Many-Electron Atoms and Molecules ................................................................854 19.11. Problems 19.........................................................................................................857 19.12. Solved Problems ..................................................................................................858 CHAPTER 20 Molecular vibrations ..............................................................863 20.1. Introduction .........................................................................................................863 20.2. Separation of Translational and Rotational Motions .........................................863 20.3. Normal Coordinates in Classical and Quantum Mechanics ..............................864 20.4. The Born-Oppenheimer Approximation ............................................................867 20.5. Electronically Degenerate States and the Renner s Effect in NH2 ....................872 20.6. The Jahn-Teller Effect in СЩ ..........................................................................874 20.7. The Von Neu mann- Wigner Non-crossing Rule in Diatomics ...........................878 20.8. Conical Intersections in Polyatomic Molecules .................................................878 20.9. Problems 20.........................................................................................................883 20.10. Solved Problems ..................................................................................................884 References ..........................................................................................................................................895 Author Index ......................................................................................................................................911 Subject Index .....................................................................................................................................919 Second Edition Elementary Molecular Quantum Mechanics Mathematical Methods and Applications Valerio Magnasco The second edition of Elementary Molecular Quantum Mechanics explains the mathematical background and applications of quantum mechanics to physics and chemical problems. This readable book has a dual purpose: to teach the mathematics required to understand molecular quantum mechanics and to examine the applications of the mathematics to understand and predict molecules. This book greatly expands on the previous edition, presenting both mathematical methods and also their application. Many examples and mathematical points are given as problems at the end of each chapter, with a hint for their solution. Solutions are then worked out in detail in the last section of each chapter. Key Features • Clearly explains the mathematical background required to understand quantum mechanics • Illustrates the applications of quantum mechanics to physics and chemical problems • Uses clear and simplified examples to demonstrate the methods of molecular quantum mechanics Dr. Valerio Magnasco, MRSC, is past Professor of Theoretical Chemistry at the Department of Chemistry and Industrial Chemistry (DCCI), University of Genoa (Italy). He is the author of 180 international scientific papers and three books on Molecular Quantum Mechanics. ISBN 978-0-444-62647-9 siore-etsevier-com 9 l780 444ll6 2 6
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spelling	Magnasco, Valerio Verfasser aut Elementary molecular quantum mechanics mathematical methods and applications Valerio Magnasco 2. ed. Amsterdam [u.a.] Elsevier 2013 XX, 932 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier 1. Aufl. u.d.T.: Magnasco, Valerio: Elementary methods of molecular quantum mechanics Quantenchemie (DE-588)4047979-1 gnd rswk-swf Quantenmechanik (DE-588)4047989-4 gnd rswk-swf Quantenchemie (DE-588)4047979-1 s DE-604 Quantenmechanik (DE-588)4047989-4 s Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026255309&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026255309&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext
spellingShingle	Magnasco, Valerio Elementary molecular quantum mechanics mathematical methods and applications Quantenchemie (DE-588)4047979-1 gnd Quantenmechanik (DE-588)4047989-4 gnd
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title	Elementary molecular quantum mechanics mathematical methods and applications
title_auth	Elementary molecular quantum mechanics mathematical methods and applications
title_exact_search	Elementary molecular quantum mechanics mathematical methods and applications
title_full	Elementary molecular quantum mechanics mathematical methods and applications Valerio Magnasco
title_fullStr	Elementary molecular quantum mechanics mathematical methods and applications Valerio Magnasco
title_full_unstemmed	Elementary molecular quantum mechanics mathematical methods and applications Valerio Magnasco
title_short	Elementary molecular quantum mechanics
title_sort	elementary molecular quantum mechanics mathematical methods and applications
title_sub	mathematical methods and applications
topic	Quantenchemie (DE-588)4047979-1 gnd Quantenmechanik (DE-588)4047989-4 gnd
topic_facet	Quantenchemie Quantenmechanik
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026255309&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026255309&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA
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