Hybrid Methods of Molecular Modeling pp 1-93 | Cite as
Molecular Modeling: Problem Formulation and Wrapping Contexts
Abstract
In this chapter we start with a brief recap of the general setting of the molecular modeling problem and the quantum mechanical and quantum chemical techniques. It may be of interest for students to follow the description of nonstandard tools of quantum mechanics and quantum chemistry presented after that. These tools are then used to develop a general scheme for separating electronic variables in complex molecular systems, which yields the explicit form of its potential energy surface in terms of the electronic structure variables of the subsystem treated at a quantum mechanical level, of the force fields for the subsystem treated classically, and explicitly expressing the central object of any hybrid scheme – the inter-subsystem junction – in terms of the generalized observables of the classically treated subsystem: its one-electron Green’s function and polarization propagator.
Keywords
Wave Function Young Tableau Slater Determinant Trial Wave Function Exact Ground StatePreview
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References
- 1.P.W. Atkins. Physical Chemistry, Oxford University Press, Oxford, 1979.Google Scholar
- 2.P.W. Atkins and J. de Paula. Physical Chemistry, Oxford University Press, Oxford, 2005.Google Scholar
- 3.L.D. Landau and E.M. Lifshits. Statistical Physics. Course of Theoretical Physics, vol. 5, Pergamon, Oxford, 1978.Google Scholar
- 4.J.M. Mayer and M. Goeppert Mayer. Statistical Mechanics, Wiley, New York, 1940.Google Scholar
- 5.M. Tribus. Thermostatics and Thermodynamics. An Introduction to Energy, Information and States of Matter, with Engineering Applications, D. Van Nostrand, Princeton, NJ, 1961.Google Scholar
- 6.L.D. Landau and E.M. Lifshits. Mechanics. Course of Theoretical Physics, vol. 1, Pergamon, Oxford, 1976.Google Scholar
- 7.H. Goldstein. Classical Mechanics, Addison-Wesley. Cambridge, MA, 1950.Google Scholar
- 8.E.B. Wilson, J.C. Decius and P.C. Cross. Molecular Vibrations. The Theory of Infrared and Raman Vibrational Spectra. McGraw-Hill, New York, 1955.Google Scholar
- 9.J.W. Leech. Classical Mechanics, Methuen, Wiley, London New York, 1964.Google Scholar
- 10.H. Eyring, S.-H. Lin and S.-M. Lin. Basic Chemical Kinetics, Wiley, New York, 1980.Google Scholar
- 11.P. Hanggi, P. Talkner and M. Borkovec. Rev. Mod. Phys., 62, 251, 1990.CrossRefGoogle Scholar
- 12.B.J. Berne and M. Borkovec. J. Chem. Soc., Faraday Trans, 94, 2717, 1998.CrossRefGoogle Scholar
- 13.H. Eyring, J. Walter and G.E. Kimball. Quantum Chemistry, Wiley, New York, 1946.Google Scholar
- 14.M.P. Allen and D.J. Tildesley. Computer Simulation of Liquids. Clarendon, Oxford, 1987.Google Scholar
- 15.A.R. Leach. Molecular Modeling. Principles and Applications (2 ed.). Pearson Education, 2001.Google Scholar
- 16.F. Jensen. Introduction to Computational Chemistry. Wiley, Chichester, 1999.Google Scholar
- 17.A. Szabo and N.S. Ostlund. Modern Quantum Chemistry, McGraw Hill, New York, 1989.Google Scholar
- 18.I. Mayer. Simple Theorems, Proofs, and Derivations in Quantum Chemistry, Kluwer/Plenum, Dor- drecht/Newyork, 2003.Google Scholar
- 19.V.A. Fock. Nachala kvantovoi mekhaniki [in Russian], 1976.Google Scholar
- 20.L.D. Landau and E.M. Lifshits. Quantum Mechanics. Course of Theoretical Physics, vol. 3, Perg- amon, London, 1977.Google Scholar
- 21.D.I. Blokhintsev. Quantum Mechanics, Springer, Berlin Heidelberg New York, 1964.Google Scholar
- 22.P.A.M. Dirac. Principles of Quantum Mechanics, Oxford University Press, London 1930.Google Scholar
- 23.J. von Neumann. The Mathematical Foundations of Quantum Mechanics, Princeton Univer- sity Press, Princeton, 1932.Google Scholar
- 24.D. Bohm. Quantum Theory, Prentice Hall, New York, 1961, 1989.Google Scholar
- 25.L.C. Young. Lectures on Calculus of Variations and Optimal Control Theory, W.B. Saun- ders. Philadelphia, 1969.Google Scholar
- 26.S.T. Epstein. The Variation Method in Quantum Chemistry, Academic, New York, 1974.Google Scholar
- 27.L. Z ülicke. Quantenchemie. Band 1. Deutscher Verlag der Wissenschaften, Berlin, 1973.Google Scholar
- 28.T. Kato. Perturbation Theory for Linear Operators. Springer, Berlin Heidelberg New York, 1966.Google Scholar
- 29.R. McWeeny and B.T. Sutcliffe. Methods of Molecular Quantum Mechanics, Academic, London, 1969.Google Scholar
- 30.R. McWeeny. Methods of Molecular Quantum Mechanics, (2 ed.) Academic, London, 1992.Google Scholar
- 31.N.F. Stepanov and V.I. Pupyshev. Molecular Quantum Mechanics and Quantum Chemistry, Moscow University Publishers, Moscow, 1991.Google Scholar
- 32.P.-O. L öwdin. Studies in perturbation theory. IV. Solution of eigenvalue problem by projection oper- ator formalism, J. Math. Phys., 3, 969, 1962.Google Scholar
- 33.E.R. Davidson. Matrix Eigenvector Methods in Methods in Computational Molecular Physics (ed. G.H.F. Dierksen and S. Wilson) Reidel, Dordrecht, 1983.Google Scholar
- 34.I.G. Kaplan. Int. J. Quant. Chem., 89, 268, 2002.CrossRefGoogle Scholar
- 35.D.J. Singh. Planewaves, Pseudopotentials and the LAPW Method, Kluwer, Norwell, MA, 1994.Google Scholar
- 36.V.A. Fock. Z. Phys., 61, 126, 1930.CrossRefGoogle Scholar
- 37.E. H ückel. Z. Phys., 70, 204, 1931.CrossRefGoogle Scholar
- 38.C.C.J. Roothaan. Rev. Mod. Phys., 23, 69, 1951.CrossRefGoogle Scholar
- 39.J. Linderberg and Y. O¨hrn. Propagators in Quantum Chemistry, Academic, New York, 1973.Google Scholar
- 40.P. Jørgensen and J. Simons. Second Quantization-Based Methods in Quantum Chemistry, Academic, New York, 1981.Google Scholar
- 41.P.R. Surj án. Second Quantized Approach to Quantum Chemistry, Springer, Berlin Heidelberg New York, 1989.Google Scholar
- 42.I.G. Kaplan. Symmetry of Many-Electron Systems, Academic, New York, 1975.Google Scholar
- 43.H. Primas. Separability in many electron systems, in Modern Quantum Chemistry. Istanbul Lectures ed. by O. Sinano Ǧlu, Academic, New York, 1965.Google Scholar
- 44.I.G. Kaplan. Molecular Interactions, Physical Picture, Computational Methods, and Model Poten- tials, Wiley, Chichester, 2006.Google Scholar
- 45.R. McWeeny. Rev. Mod. Phys., 35, 335, 1960.CrossRefGoogle Scholar
- 46.K. Ruedenberg. Rev. Mod. Phys., 34, 326, 1962.CrossRefGoogle Scholar
- 47.J.P. Elliot and P.G. Dawber. Symmetry in Physics, vols. 1, 2, Macmillan, London, 1979.Google Scholar
- 48.T. Arai. J. Chem. Phys., 33, 95, 1960.CrossRefGoogle Scholar
- 49.P.-O. L öwdin. J. Chem. Phys., 35, 78, 1961.CrossRefGoogle Scholar
- 50.P.-O. L öwdin. Adv. Chem. Phys., 2, 207, 1959.CrossRefGoogle Scholar
- 51.W. Kutzelnigg. Int. J. Quant. Chem., 95, 404, 2003.CrossRefGoogle Scholar
- 52.P. Ziesche. Int. J. Quant. Chem., 90, 342, 2002.CrossRefGoogle Scholar
- 53.A.L. Tchougr éeff and I.A. Misurkin. Dokl. AN SSSR [in Russian], 291, 1177, 1986.Google Scholar
- 54.R. Constanciel. In Localization and Delocalization in Quantum Chemistry, O. Chalvet, R. Daudel, S. Diner and J.P. Malrieu. eds., Reidel, Dordrecht, 1975.Google Scholar
- 55.P.E. Schipper. J. Phys. Chem., 90(18), 4259, 1986.CrossRefGoogle Scholar
- 56.P.E. Schipper. Aust. J. Chem., 40, 635, 1987.Google Scholar
- 57.J.M. Jauch. Foundations of Quantum Mechanics, Addison-Wesley, Reading, MA, 1968.Google Scholar
- 58.S. Wilson. Electron Correlation in Molecules, Clarendon, Oxford, 1984.Google Scholar
- 59.G. N áray-Szab ó . Comput. & Chem., 24, 287, 2000.CrossRefGoogle Scholar
- 60.G.G. Ferenczy and J.G. A´ngy án. J. Comp. Chem., 22, 1679, 2001.CrossRefGoogle Scholar
- 61.A.B. Migdal. Theory of Finite Fermi Systems and Properties of Atomic Nuclei [in Rus- sian]. Nauka, Moskva, 1965.Google Scholar
- 62.A.A. Abrikosov, L.P. Gor’kov and I.E. Dzyaloshinskii. Methods of Quantum Field Theory in Statisti- cal Physics [in Russian] (2 ed.) Dobrosvet, Moscow, 1998.Google Scholar
- 63.D.J. Thouless. The Quantum Mechanics of Many-Body System. Academic, New York, 1972.Google Scholar
- 64.J.-P. Blaizot and G. Ripka. Quantum Theory of Finite Systems, The MIT Press, Cambridge, MA, 1986.Google Scholar
- 65.A.M. Tokmachev and A.L. Tchougr éeff. Int. J. Quant. Chem., 8. 84, 39, 2001.CrossRefGoogle Scholar
- 66.A.L. Tchougréeff and A.M. Tokmachev. Physical principles of constructing hybrid QM/MM procedures, In J. Maruani, R. Lefebvre, and E. Brändas, (ed), Advanced Topics in Theoretical Chemical Physics, vol. 12 of Progress in Theoretical Chemistry and Physics, Kluwer, Dordrecht, p. 207, 2003.Google Scholar
- 67.V. Magnasco and R. McWeeny. In Z.B. Maksić (ed.): Theoretical Models of Chemical Bonding, Part 2, Springer, Berlin Heidelberg New York, 1991.Google Scholar
- 68.J.E. Lennard-Jones. Trans. Faraday Soc., 25, 668, 1929.CrossRefGoogle Scholar
- 69.A.L. Tchougréeff. Phys. Chem. Chem. Phys. 1, 1051, 1999.CrossRefGoogle Scholar
- 70.E. Borel. Introduction géométrique à quelques théories physiques, Paris: Gauthier-Villars, p. 97, 1914.Google Scholar
- 71.V.I. Pupyshev. Additional chapters of molecular quantum mechanics, Parts 1-3. Moscow University Publishers [in Russian], 2008.Google Scholar