介紹一套叢書 Theoretical chemistry: a series of monographs

02-04

David Parker Craig是一位傑出的理論化學家，曾任澳大利亞科學院的主席，是國際量子分子科學院 (IAQMS) 的院士，他的學術生涯基本上是在悉尼大學度過的。作為主編，D. P. Craig 曾經與Roy McWeeny 一同主持出版過一套叢書 Theoretical Chemistry: A series of monographs (Academic Press, 1965~)，R. McWeeny 應當在國際上更有名氣，他是著名的理論化學家 Charles Coulson 的學生，名著 Valence 就是這師徒二人合寫的。Craig和McWeeny共同主編的這套叢書中，大部分都是佳作，蘭州化物所的汪漢卿老師在80年代曾翻譯過其中一本：C.D.H.奇澤姆所著的《量子化學中的群論方法》。目前來看，這套叢書中大概包含七本專著：

Electronic Properties of Aromatic and Heterocyclic Molecules (T. E. Peacock)
Methods of Molecular Quantum Mechanics (R. McWeeny)
Propagators in Quantum Chemistry (J. Linderberg and Y. ?hrn)
Molecular Collision Theory (Mark Sheard Child)
Group Theoretical Techniques in Quantum Chemistry (C. D. H. Chisholm)
Reduced Density Matrices in Quantum Chemistry (E. R. Davidson)
Electron Correlation in Small Molecules (A. C. Hurley)

這些書都可以在上海圖書館查到。

2-6 經過幾十年的大浪淘沙，已經成為本領域中的經典著作，其中一些在21世紀又被其他出版社翻印（AP出版社本世紀初被Elsevier收購），如 Molecular Collision Theory (M. S. Child) 被 Dover Publications 翻印，Propagators in Quantum Chemistry (J. Linderberg and Y. ?hrn)被 Wiley 翻印，所以還容易找得到實體書，但是R. McWeeny 的 Methods of Molecular Quantum Mechanics 和 E. R. Davidson 的 Reduced Density Matrices in Quantum Chemistry 已經不大容易在市面上看得到了，所以我們重點介紹一下這兩本書。

Methods of Molecular Quantum Mechanics 在這七本書中名氣最大，它的內容要比經典的 QC 入門書 Modern Quantum Chemistry (Szabo) 更高級一些，比如Szabo中沒有的CI的酉群方法、動力學效應等等，但是沒有單獨地介紹CC理論和Green函數。我們把它的目錄和封面貼出來，以便讀者自行判斷是否對味（我很喜歡封面）：

1 Introductory Surveynt1.1 Schrodingers equationnt1.2 Example: the helium atomnt1.3 Example: the hydrogen molecule ntProblems 1n2 Mathematical Methodsnt2.1 Complete set expansions nt2.2 Vector spaces and matrices nt2.3 The eigenvalue equation nt2.4 Variation theorynt2.5 Partitioning and perturbation methodsntProblems 2n3 Many-Electron Wavefunctionsnt3.1 Antisymmetry and the Slater Methodnt3.2 Calculation of the energy: helium atomnt3.3 Matrix elements between antisymmetrized productsnt3.4 Configuration interactionnt3.5 An example: the hydrogen moleculent3.6 An alternative approach: Fock spacentProblems 3n4 Spin and Permutation Symmetrynt4.1 Spin eigenfunctionsnt4.2 Methods for constructing spin eigenfunctionsnt4.3 Permutation symmetry and its implicationsnt4.4 Young tableaux nt4.5 The standard irreps of SN nt4.6 Connections between different basesntProblems 4n5 Digression: The Electron Distributionnt5.1 Electron density functionsnt5.2 Density matrices nt5.3 Density functions for 1-determinant wavefunctionsnt5.4 Transition densities. Generalizations nt5.5 Localized orbitals. Population analysisnt5.6 Natural expansionsnt5.7 Molecular properties: An introductionnt5.8 The pair function. Electron correlationnt5.9 Spin densitynt5.10 Other density functionsntProblems 5n6 Self-Consistent Field Theorynt6.1 Hartree-Fock theory. The independent-particle modelnt6.2 Finite-basis approximations. Closed-shell systemsnt6.3 Unrestricted Hartree-Fock theorynt6.4 Some further properties of density matricesnt6.5 Restricted HF theory. An open-shell systemnt6.6 Other open-shell situations. Ensemble averaging 187nt6.7 States of given spin 194nt6.8 Physical significance of MOs. Localization 200ntProblems 6n7 Valence Bond Theorynt7.1 The Heitler-London calculationn7.2 Generalizationsnt7.3 Perfect pairing and resonancent7.4 One-configuration VB theory. Non-orthogonal orbitalsnt7.5 Multiconfiguration VB theory. Orthogonal orbitalsnt7.6 Multiconfiguration VB theory. Non-orthogonal orbitalsnt7.7 A non-variational methodntProblems 7n8 Multiconfiguration SCF Theorynt8.1 The optimization problemnt8.2 Orbital variation. Stationary-value conditionsnt8.3 Solution of the stationary-value equationsnt8.4 Gradient methodsnt8.5 Use of the Brillouin-Levy-Berthier theoremnt8.6 Variation of all parametersntProblems 8n9 Perturbation Theory and Diagram Techniquesnt9.1 Perturbation methodsnt9.2 The Hartree-Fock reference functionnt9.3 The cluster developmentnt9.4 Diagrammatic perturbation theorynt9.5 The linked-cluster (Goldstones) theoremnt9.6 Extensions of the diagrammatic approachnt9.7 GeneralizationsntProblems 9n10 Large-Scale Cl and the Unitary-Group Approachnt10.1 The general approachnt10.2 Transformations and tensorsnt10.3 Irreducible bases in CI spacent10.4 Generators of the unitary group. The Hamiltoniannt10.5 The matrix-eigenvalue problem. Direct CI ntProblems 10 n11 Small Terms in the Hamiltonian. Static Properties nt11.1 Electric and magnetic interactions. The classical approachnt11.2 Relativistic effects: one particle nt11.3 Relativistic treatment of many-particle systems nt11.4 A variation-perturbation approach nt11.5 Effect of a uniform electric field nt11.6 Effect of a uniform magnetic field nt11.7 Some spin-coupling effects (first-order) nt11.8 Some spin-coupling effects (second-order) nt11.9 Variational methods. Coupled Hartree-Fock theory nt11.10 Generalizations of CHF theory ntProblems 11n12 Dynamic Properties and Response Theorynt12.1 Preliminaries. Linear responsent12.2 Time-dependent variation theorynt12.3 Free and forced oscillationsnt12.4 Significance of the response matrixnt12.5 Time-dependent Hartree-Fock theorynt12.6 Density-matrix form of TDHF theorynt12.7 Multiconfiguration (MC) TDHF theoryntProblems 12tn13 Propagator and Equation-of-Motion Methodsnt13.1 Preliminary notionsnt13.2 Propagators. The polarization propagatornt13.3 Propagators, Greens functions and density matricesnt13.4 Some properties of the electron propagatornt13.5 The calculation of propagatorsnt13.6 Equation-of-motion (EOM) methodsntProblems 13n14 Intermolecular Forcesnt14.1 Weak interactions. Generalized product functionsnt14.2 Variation theory for subsystemsnt14.3 Configuration interaction. Interpretation of the termsnt14.4 Long-range effects. The dispersion energynt14.5 Non-orthogonality and short-range effectsnt14.6 Excited states and resonance interactionsntProblems 14nAppendix 1: Atomic Orbitals 521nAppendix 2: Angular Momentum 527nAppendix 3: Symmetry and Group Concepts 531nAppendix 4: Relativistic terms in the Hamiltonian 545n

第二本是 Reduced Density Matrices in Quantum Chemistry，作者E. R. Davidson 是IAQMS的院士，其實上面的 RcWeeny 和叢書第二冊的作者 Linderberg 也是該院院士。當然，Molecular Collision Theory的作者 Child 也是很有名的。

此書前身是作者在 Ohio State University 訪問時上課所用的講義，課程容量是半學期。

由於對密度矩陣不熟悉，我不作評論，只貼一下目錄，感興趣的閱讀者可以在libgen下載到該書的電子版。此書頁數不多，僅有120多頁，能夠讀完的概率還是很大的，當然，書薄一點，總是更容易讀完的。

1 Ensemble Density-matrixntA. Pure State FormalismntB. Mixed StatesntC. Thermodynamics nt General Referencesnn2 Reduced Density-matrixntA. Energy ExpressionsntB. Elementary Examplesnt General Referencesnn3 Properties of Reduced Density-matrixntA. Least Squares Approximation to the Density-matrixntB. Least Squares Approximation to the WavefuntionntC. Comments on the Natural Expansionnt General Referencesnn4 Analytic Properties of the First-Order Reduced Density-matrixntA. Spin Structures of rho_1ntB. Symmetry Properties of rho_1ntC. Cusp Conditions on rho_1ntD. Hellman-Feynman ConditionsntE. Other PropertiesntF. N-RepresentabilityntG. Asymptotic Behaviournt General Referencesnn5 Physical Properties of the First-Order Reduced Density-matrixntA. Population AnalysisntB. Perturbation TheoryntC. Natural Orbitals for Two-Electron SystemsntD. Natural Orbitals for Several-Electron SystemsntE. Density Functionalsnt General Referencesnn6 Analytic Properties of the Second-Order Reduced Density-matrixntA. Spin Structures of rho_1ntB. Symmetry Properties of rho_1ntC. Cusp Conditions on rho_1ntD. N-Representabilitynt General Referencesnn7 Physical Interpretation of the Two-Body Density-matrixntA. Bopp ApproximationntB. Direct Calculation of the Density nt General ReferencesnnReferencesn