量子化学

preface ix1 the schrodinger equation1.1 quantum chemistry,1.2 historical background of quantum mechanics,1.3 the uncertainty principle,1.4 the time-dependent schr6dinger equation,1.5 the time-independent schr6dinger equation,1.6 probability,1.7 complex numbers,1.8 units,1.9 calculus,1.10 summary,2 the particle in a box2.1 differential equations,2.2 particle in a one-dimensional box,2.3 the free particle in one dimension,2.4 particle in a rectangular well,2.5 tunneling,2.6 summary,3 operators3.1 operators,3.2 eigenfunctions and eigenvalues,3.3 operators and quantum mechanics,3.4 the three-dimensional, many-particle schr6dingerequation,3.5 the particle in a three-dimensional box,3.6 degeneracy,3.7 average values,3.8 requirements for an acceptable wave function,3.9 summary,4 the harmonic oscillator4.1 power-series solution of differential equations,4.2 the one-dimensional harmonic oscillator,4.3 vibration of molecules,4.4 numerical solution of the one-dimensional time-independentschrodinger equation,4.5 summary,5 angular momentum5.1 simultaneous specification of several properties,5.2 vectors,5.3 angular momentum of a one-particle system,5.4 the ladder-operator method for angular momentum,5.5 summary,6 the hydrogen atom6.1 the one-particle central-force problem,6.2 noninteracting particles and separation ofvariables,6.3 reduction of the two-particle problem to two one-particleproblems,6.4 the two-particle rigid rotor,6.5 the hydrogen atom,6.6 the bound-state hydrogen-atom wave functions,6.7 hydrogenlike orbitals,6.8 the zeeman effect,6.9 numerical solution of the radial schrodingerequation,6.10 summary,7 theorems of quantum mechanics7.1 introduction,7.2 hermitian operators,7.3 expansion in terms of eigenfunctions,7.4 eigenfunctions of commuting operators,7.5 parity,7.6 measurement and the superposition of states,7.7 position eigenfunctions,7.8 the postulates of quantum mechanics,7.9 measurement and the interpretation of quantummechanics,7.10 matrices,7.11 summary,8 the variation method8.1 the variation theorem,8.2 extension of the variation method,8.3 determinants,8.4 simultaneous linear equations,8.5 linear variation functions,8.6 matrices, eigenvalues, and eigenvectors,8.7 summary,9 perturbation theory9.1 introduction,9.2 nondegenerate perturbation theory,9.3 perturbation treatment of the helium-atom groundstate,9.4 variation treatments of the ground state of helium,9.5 perturbation theory for a degenerate energy level,9.6 simplification of the secular equation,9.7 perturbation treatment of the first excited states ofhelium,9.8 comparison of the variation and perturbationmethods,9.9 time-dependent perturbation theory,9.10 interaction of radiation and matter,9.11 summary,10 electron spin and the spin-statistics theorem10.1 electron spin,10.2 spin and the hydrogen atom,10.3 the spin-statistics theorem,10.4 the helium atom,10.5 the pauli exclusion principle,10.6 slater determinants,10.7 perturbation treatment of the lithium groundstate,10.8 variation treatments of the lithium ground state,10.9 spin magnetic moment,10.10 ladder operators for electron spin,10.11 summary,11 many-electron atoms11.1 the hartree-fock self-consistent-field method,11.2 orbitals and the periodic table,11.3 electron correlation,11.4 addition of angular momenta,11.5 angular momentum in many-electron atoms,11.6 spin-orbit interaction,11.7 the atomic hamiltonian,11.8 the condon-slater rules,11.9 summary,12 molecular symmetry12.1 symmetry elements and operations,12.2 symmetry point groups,12.3 summary,13 electronic structure of diatomic molecules13.1 the born-oppenheimer approximation,13.2 nuclear motion in diatomic molecules,13.3 atomic units,13.4 the hydrogen molecule ion,13.5 approximate treatments of the h 2 ground electronicstate,13.6 molecular orbitals for hi excited states,13.7 mo configurations of homonuclear diatomicmolecules,13.8 electronic terms of diatomic molecules,13.9 the hydrogen molecule,13.10 the valence-bond treatment of h2,13.11 comparison of the mo and vb theories,13.12 mo and vb wave functions for homonuclear diatomicmolecules,13.13 excited states of he,13.14 scf wave functions for diatomic molecules,13.15 mo treatment of heteronuclear diatomic molecules,13.16 vb treatment of heteronuclear diatomic molecules,13.17 the valence-electron approximation,13.18 summary,14 theorems of molecular quantum mechanics14.1 electron probability density,14.2 dipole moments,43814.3 the hartree-fock method for molecules,14.4 the virial theorem,14.5 the virial theorem and chemical bonding,14.6 the hellmann-feynman theorem,14.7 the electrostatic theorem,14.8 summary,15 molecular electronicstructure15.1 ab initio, density-functional, semiempirical,and molecular-mechanics methods,15.2 electronic terms of polyatomic molecules,15.3 the scf mo treatment of polyatomic molecules,15.4 basis functions,15.5 the scf mo treatment of h20,15.6 population analysis and bond orders,15.7 the molecular electrostatic potential, molecularsurfaces,and atomic charges,15.8 localized mos,15.9 the scf mo treatment of methane, ethane, andethylene,15.10 molecular geometry,15.11 conformational searching,15.12 molecular vibrational frequencies,15.13 thermodynamic properties,15.14 ab initio quantum chemistry programs,15.15 performing ab initio calculations,15.16 speeding up hartree-fock calculations,15.17 solvent effects,16 electron-correlation methods16.1 configuration interaction,16.2 m011er-plesset (mp) perturbation theory,16.3 the coupled-cluster method,16.4 density-functional theory,16.5 composite methods for energy calculations,16.6 the diffusion quantum monte carlo method,16.7 relativistic effects,16.8 valence-bond treatment of polyatomic molecules,16.9 the gvb, vbscf, and bovb methods,16.10 chemical reactions,17 semiempirical and molecular-mechanics treatments ofmolecules17.1 semiempirical mo treatments of planar conjugatedmolecules,17.2 the hiickel mo method,17.3 the pariser-parr-pople method,17.4 general semiempirical mo and dft methods,17.5 the molecular-mechanics method,17.6 empirical and semiempirical treatments of solventeffects,17.7 chemical reactions,18 comparisons of methods18.1 molecular geometry,18.2 energy changes,18.3 other properties,18.4 hydrogen bonding,18.5 conclusion,18.6 the future of quantum chemistry,appendixbibliographyanswers to selected problemsindex

　　a solutions manual for the problems in thebook is available.　　 the expanding role of quantum chemistry makes it highlydesirable for students in all areas of chemistry to understandmodern methods of electronic structure calcula-tion, and this bookhas been written with this goal in mind.　　 i have tried to make explanations clear and complete, withoutglossing over diffi-cult or subtle points. derivations are givenwith enough detail to make them easy to fol-low, and i avoidresorting to the frustrating phrase "it can be shown that" whereverpossible. the aim is to give students a solid understanding of thephysical and mathe-matical aspects of quantum mechanics andmolecular electronic structure. the book is designed to be usefulto students in all branches of chemistry, not just future quantumchemists. however, the presentation is such that those who do go onin quantum chem-istry will have a good foundation and will not behampered by misconceptions.　　 an obstacle faced by many chemistry students in learning quantummechanics is their unfamiliarity with much of the requiredmathematics. in this text i have included detailed treatments ofoperators, differential equations, simultaneous linearequations,and other needed topics. rather than putting all themathematics in an introductory chapter or a series of appendices, ihave integrated the mathematics with the physics and chemistry.immediate application of the mathematics to solving aquantum-mechanical problem will make the mathematics moremeaningful to students than would separate study of themathematics. i have also kept in mind the limited physicsbackground of many chemistry students by reviewing topics inphysics.