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Abstract

Molecular structure is a reflection of the Born–Oppenheimer separation of electronic and nuclear motion, which is in turn a consequence of the large difference between the electron and nuclear masses. One consequence of this separation is the concept of a potential energy surface for nuclear motion created by the faster moving electrons. Corollaries include equilibrium structures, transition states, and reaction paths which are the foundation of the description of molecular structure and reactivity. However the Born–Oppenheimer approximation is not uniformly applicable and its breakdown results in perturbations in molecular spectra, radiationless decay, and nonadiabatic chemical reactions.

There are many issues that can be addressed in a discussion of molecular structure, including the structure and bonding of individual classes of molecules, computational and/or experimental techniques used to determine or infer molecular structure, the accuracy of those methods, etc. In an effort to provide a broad view of the essential aspects of molecular structure, this Chapter considers issues in molecular structure from a theoretical/computational perspective using the Born–Oppenheimer approximation as the point of origin. Rather than providing a compendium of results, this chapter will explain how issues in molecular structure are investigated and how the questions that can be addressed reflect the available methodology. Even with these restrictions the scope of this topic remains enormous and precludes a detailed presentation of any one issue. Thus the abbreviated discussions in this work are supplemented by ample references to the literature.

Several aspects of potential energy surfaces and their relation to molecular structure will be considered: (i) the electronic structure techniques used to determine a single point on a potential energy surface, and the interactions that couple the electronic states in question, (ii) the local properties of potential energy surfaces, in particular equilibrium structures and rovibrational levels that provide the link to experimental inferences concerning molecular structure, (iii) global chemistry deduced from potential energy surfaces including reaction mechanisms and reaction paths and (iv) phenomena resulting from the nonadiabatic interactions that couple potential energy surfaces.

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References

  • Bethe, H.A., Salpeter, E.E.: Quantum Mechanics of One and Two Electron Atoms. Plenum/Rosetta, New York (1977)

    MATH  Google Scholar 

  • Born, M., Huang, K.: Dynamical Theory of Crystal Lattices. Oxford University Press, Oxford (1954)

    MATH  Google Scholar 

  • Herzberg, G., Longuet-Higgins, H.C.: Disc. Faraday Soc. 35, 77 (1963)

    Google Scholar 

  • Berry, M.V.: Proc. R. Soc. Lond. 45(1984), A392

    ADS  Google Scholar 

  • Longuet-Higgins, H.C.: Adv. Spectrosc. 2, 429 (1961)

    ADS  Google Scholar 

  • Gerber, W.H., Schumacher, E.: J. Chem. Phys. 69, 1692 (1978)

    ADS  Google Scholar 

  • Kahn, L.R., Baybutt, P., Truhlar, D.G.: J. Chem. Phys. 65, 3826 (1976)

    ADS  Google Scholar 

  • Tully, J.C.: In: Miller, W.H. (ed.) Modern Theoretical Chemistry, vol. 2, p. 217. Plenum, New York (1976)

    Google Scholar 

  • Garrett, B.C., Truhlar, D.G.: Theoretical Chemistry Advances and Perspectives. Academic Press, New York (1981)

    Google Scholar 

  • Bishop, D.M., Cheung, L.M.: J. Chem. Phys. 78, 1396 (1983)

    ADS  Google Scholar 

  • Bishop, D.M., Cheung, L.M.: J. Chem. Phys. 80, 4341 (1984)

    ADS  Google Scholar 

  • Jensen, J.O., Yarkony, D.R.: J. Chem. Phys. 89, 3853 (1988)

    Google Scholar 

  • Vidal, C.R., Stwalley, W.C.: J. Chem. Phys. 77, 883 (1982)

    ADS  Google Scholar 

  • Chen, Y.C., Harding, D.R., Stwalley, W.C., Vidal, C.R.: J. Chem. Phys. 85, 2436 (1986)

    ADS  Google Scholar 

  • Murrell, J.N., Carter, S., Farantos, S.C., Huxley, P., Varandas, A.J.C.: Molecular Potential Energy Surfaces. Wiley, New York (1984)

    Google Scholar 

  • Truhlar, D.G., Steckler, R., Gordon, M.S.: Chem. Rev. 87, 217 (1987)

    Google Scholar 

  • Fukui, K.: Acc. Chem. Res. 14, 363 (1981)

    Google Scholar 

  • Cerjan, C.J., Miller, W.H.: J. Chem. Phys. 75, 2800 (1981)

    ADS  Google Scholar 

  • Schlegel, H.B.: Adv. Chem. Phys. 67, 249 (1987)

    Google Scholar 

  • Schlegel, H.B.: In: Yarkony, D.R. (ed.) Modern Electronic Structure Theory, Part 1. World Scientific, Singapore (1995)

    Google Scholar 

  • Schaefer, H.F. (ed.): Modern Theoretical Chemistry. Plenum, New York (1976)

    Google Scholar 

  • Yarkony, D.R. (ed.): Modern Electronic Structure Theory. World Scientific, Singapore (1995)

    Google Scholar 

  • McLachlan, A.D.: Mol. Phys. 4, 417 (1961)

    ADS  Google Scholar 

  • Smith, F.T.: Phys. Rev. 179, 111 (1969)

    ADS  Google Scholar 

  • Lichten, W.: Phys. Rev. 131, 339 (1963)

    Google Scholar 

  • Lichten, W.: Phys. Rev. 164, 131 (1967)

    ADS  Google Scholar 

  • Mead, C.A., Truhlar, D.G.: J. Chem. Phys. 77, 6090 (1982)

    ADS  Google Scholar 

  • Baer, M.: Chem Phys Lett 35, 112 (1975)

    ADS  Google Scholar 

  • Baer, M.: Chem Phys 15, 49 (1976)

    Google Scholar 

  • Pacher, T., Mead, C.A., Cederbaum, L.S., Koppel, H.: J. Chem.phys. 91, 7057 (1989)

    ADS  Google Scholar 

  • Sidis, V.: In: Baer, M., Ng, C.Y. (eds.) State-Selected and State-to-State Ion-Molecule Reaction Dynamics Part 2, Theory,  82 edn., p. 73. Wiley, New York (1992)

    Google Scholar 

  • Renner, R.: Z. Phys 92, 172 (1934)

    ADS  Google Scholar 

  • von Neumann, J., Wigner, E.: Z. Phys. 30, 467 (1929)

    Google Scholar 

  • Mead, C.A.: J. Chem. Phys. 70, 2276 (1979)

    ADS  Google Scholar 

  • Szabo, A., Ostlund, N.S.: Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory. McMillan, New York (1982)

    Google Scholar 

  • rgensen, P.J., Simons, J.: Second Quantization Based Methods in Quantum Chemistry. Academic Press, New York (1981)

    Google Scholar 

  • Alml f, J.: In: Yarkony, D.R. (ed.) Modern Electronic Structure Theory, Part 1, p. 1. World Scientific, Singapore (1995)

    Google Scholar 

  • Dunning, T.H., Hay, P.J.: In: Schaefer, H.F. (ed.) Modern Theoretical Chemistry, vol. 3, Plenum, New York (1976)

    Google Scholar 

  • Roos, B.O., Linse, P., Siegbahn, P.E.M., Blomberg, M.R.A.: Chem Phys 66, 197 (1982)

    Google Scholar 

  • Moshinsky, M.: Group Theory and the Many Body Problem. Gordon and Breach, New York (1968)

    Google Scholar 

  • Hinze, J.: The Unitary Group, Lecture Notes in Chem. Springer, Berlin, Heidelberg, p 22 (1979)

    Google Scholar 

  • Shavitt, I.: In: Schaefer, H.F. (ed.) Modern Theoretical Chemistry, vol. 3, p. 189. Plenum, New York (1976)

    Google Scholar 

  • Yamaguchi, Y., Osamura, Y., Goddard, J.D., Schaefer, H.F.: A New Dimension to Quantum Chemistry: Analytic Derivative Methods in ab initio Molecular Electronic Structure Theory. Oxford University Press, Oxford (1994)

    Google Scholar 

  • Lengsfield, B.H., Yarkony, D.R.: In: Baer, M., Ng, C. (eds.) State-Selected and State to State Ion-Molecule Reaction Dynamics: Part 2, Theory, vol. 82, Wiley, New York (1992)

    Google Scholar 

  • Pulay, P.: Mol. Phys. 17, 197 (1969)

    ADS  Google Scholar 

  • Roothaan, C.C.J.: Rev. Mod. Phys. 23, 69 (1951)

    ADS  Google Scholar 

  • Gaw, J.F., Yamaguchi, Y., Schaefer, H.F.: J. Chem. Phys. 81, 6395 (1984)

    ADS  Google Scholar 

  • Gaw, J.F., Yamaguchi, Y., Schaefer, H.F., Handy, N.C.: J. Chem.phys. 85, 5132 (1986)

    ADS  Google Scholar 

  • Alml f, J.: J. Comput. Chem. 3, 385 (1982)

    Google Scholar 

  • Docken, K., Hinze, J.: J. Chem. Phys. 57, 4928 (1972)

    ADS  Google Scholar 

  • Hinze, J.: J. Chem. Phys. 59, 6424 (1973)

    ADS  MathSciNet  Google Scholar 

  • Werner, H., Meyer, W.: J. Chem. Phys. 74, 5794 (1981)

    ADS  Google Scholar 

  • Lengsfield, B.H.: J. Chem. Phys. 77, 4073 (1982)

    ADS  Google Scholar 

  • ller, C.M., Plesset, M.S.: Phys. Rev. 46, 618 (1934)

    ADS  Google Scholar 

  • Alml f, J.: Chem Phys Lett 181, 319 (1991)

    ADS  Google Scholar 

  • Cizek, J.: J. Chem. Phys. 45, 4256 (1966)

    ADS  Google Scholar 

  • Cizek, J.: Adv. Chem. Phys. 14, 35 (1969)

    Google Scholar 

  • Paldus, J., Cizek, J.: In: Smith, D., McRae, W.B. (eds.) Energy Structure and Reactivity, p. 35. Wiley, New York (1973)

    Google Scholar 

  • Bartlett, R.J., Purvis III, G.D.: Int. J. Quantum Chem. Symp. 14, 561 (1978)

    Google Scholar 

  • Pople, J.A., Krishnan, R., Schlegel, H.B., Binkley, J.S.: Int. J. Quantum Chem. 14, 545 (1978)

    Google Scholar 

  • Löwdin, P.O.: Phys. Rev. 97, 1474 (1955)

    ADS  MathSciNet  Google Scholar 

  • Bartlett, R.J., Watts, J.D., Kucharski, S.A., Noga, J.: Chem Phys Lett 165, 513 (1990)

    ADS  Google Scholar 

  • Kucharski, S.A., Bartlett, R.J.: Chem Phys Lett 158, 550 (1989)

    ADS  Google Scholar 

  • Raghavachari, K., Trucks, G.W., Pople, J.A., Head-Gordon, M.: Chem. Phys. Lett. 157, 479 (1989)

    ADS  Google Scholar 

  • Watts, J.D., Gauss, J., Bartlett, R.J.: J. Chem. Phys. 98, 8718 (1993)

    ADS  Google Scholar 

  • Bartlett, R.J.: In: Yarkony, D.R. (ed.) Modern Electronic Structure Theory, p. 2. World Scientific, Singapore (1995)

    Google Scholar 

  • Diffenderfer, R.N., Yarkony, D.R.: J. Chem. Phys. 86, 5098 (1982)

    Google Scholar 

  • Roos, B.O., Taylor, P.R., Siegbahn, P.E.M.: Chem Phys 48, 157 (1980)

    MathSciNet  Google Scholar 

  • Roos, B.O.: Int. J. Quantum Chem. Symp. 14, 175 (1980)

    Google Scholar 

  • Siegbahn, P., Heiberg, A., Roos, B., Levy, B.: Phys. Scr. 21, 323 (1980)

    ADS  Google Scholar 

  • Bauschlicher, C.W., Langhoff, S.R., Taylor, P.R.: Adv. Chem. Phys. 77, 103 (1990)

    Google Scholar 

  • Silverstone, H.J., Sinanoglu, O.: J. Chem. Phys. 44, 1899 (1966)

    ADS  Google Scholar 

  • Dalgaard, E., rgensen, P.J.: J. Chem. Phys. 69, 3833 (1978)

    ADS  Google Scholar 

  • Davidson, E.R.: J Comput Phys 17, 87 (1975)

    ADS  MathSciNet  Google Scholar 

  • Roos, B.O.: Chem Phys Lett 15, 153 (1972)

    ADS  Google Scholar 

  • Siegbahn, P.E.M.: J. Chem. Phys. 72, 1647 (1980)

    ADS  MathSciNet  Google Scholar 

  • Harrison, R.J.: J. Chem. Phys. 94, 5021 (1991)

    ADS  Google Scholar 

  • Caballol, R., Malrieu, J.P.: Chem Phys Lett 188, 543 (1992)

    ADS  Google Scholar 

  • Povill, A., Rubio, J., Illas, F.: Theo. Chim. Acta 82, 229 (1992)

    Google Scholar 

  • Knowles, P.J., Werner, H.: Chem Phys Lett 115, 259 (1985)

    ADS  Google Scholar 

  • Knowles, P.J., Werner, H.: Chem Phys Lett 145, 514 (1988)

    ADS  Google Scholar 

  • Werner, H., Knowles, P.J.: J. Chem. Phys. 82, 5053 (1985)

    ADS  Google Scholar 

  • Werner, H., Knowles, P.J.: J. Chem. Phys. 89, 5803 (1988)

    ADS  Google Scholar 

  • Andersson, K., Malmqvist, P.Å., Roos, B.O., Sadlej, A.J., Wolinski, K.: J. Phys. Chem. 94, 5483 (1990)

    Google Scholar 

  • Andersson, K., Malmqvist, P.Å., Roos, B.O.: J. Chem. Phys. 96, 1218 (1992)

    ADS  Google Scholar 

  • Parr, R.G., Yang, W.: Density-Functional Theory of Atoms and Molecules. Oxford, New York (1989)

    Google Scholar 

  • Hohenberg, P., Kohn, W.: Phys. Rev. B 136, 864 (1964)

    ADS  Google Scholar 

  • Kohn, W., Sham, L.J.: Phys. Rev. A 140, 1133 (1965)

    ADS  Google Scholar 

  • Becke, A.D.: In: Yarkony, D.R. (ed.) Modern Electronic Structure Theory, Part 2. World Scientific, Singapore (1995)

    Google Scholar 

  • Pula, P.: In: Yarkony, D.R. (ed.) Modern Electronic Structure Theory, Part 2. World Scientific, Singapore (1995)

    Google Scholar 

  • Liu, B., McLean, A.D.: J. Chem. Phys. 59, 4557 (1973)

    ADS  Google Scholar 

  • Liu, B., McLean, A.D.: J. Chem. Phys. 91, 2348 (1989)

    ADS  Google Scholar 

  • Boys, S.F., Bernardi, F.: Mol. Phys. 19, 553 (1970)

    ADS  Google Scholar 

  • Gutowski, M., van Lenthe, J., van Duijneveldt, J.C.G.M., van Duijneveldt, F.B.: J. Chem. Phys. 98, 4728 (1993)

    ADS  Google Scholar 

  • Lefebvre-Brion, H., Field, R.W.: Perturbations in the Spectra of Diatomic Molecules. Academic Press, New York (1986)

    Google Scholar 

  • Han, S., Hettema, H., Yarkony, D.R.: J. Chem. Phys. 102, 1955 (1995)

    ADS  Google Scholar 

  • Lengsfield, B.H., Saxe, P., Yarkony, D.R.: J. Chem. Phys. 81, 4549 (1984)

    ADS  Google Scholar 

  • Saxe, P., Lengsfield, B.H., Yarkony, D.R.: Chem Phys Lett 113, 159 (1985)

    ADS  Google Scholar 

  • Buenker, R.J., Hirsch, G., Peyerimhoff, S.D., Bruna, P.J., Romelt, J., Bettendorff, M., Petrongolo, C.: In: Carbo, R. (ed.) Current Aspects of Quantum Chemistry 1981, vol. 21, p. 81. Elsevier, New York (1982)

    Google Scholar 

  • Mead, C.A.: J. Chem. Phys. 78, 807 (1993)

    ADS  Google Scholar 

  • Hellmann, J.: Einf hrung in die Quantenchemie. Deuticke, Leipzig (1937)

    Google Scholar 

  • Feynman, R.P.: Phys. Rev. 56, 340 (1939)

    ADS  Google Scholar 

  • Langhoff, S.R., Kern, C.W.: In: Schaefer, H.F. (ed.) Modern Theoretical Chemistry, vol. 4, p. 381. Plenum, New York (1977)

    Google Scholar 

  • Blume, M., Watson, R.E.: Proc. R. Soc. Lond. A 270, 127 (1962)

    ADS  Google Scholar 

  • Blume, M., Watson, R.E.: Proc. R. Soc. Lond. A 271, 565 (1963)

    ADS  Google Scholar 

  • Fraga, S., Saxena, K.M.S., Lo, B.W.N.: At. Data 3, 323 (1971)

    ADS  Google Scholar 

  • Ermler, W.C., Ross, R.B., Christiansen, P.A.: Advances in Quantum Chemistry vol. 19. Academic Press, New York, p 139 (1988)

    Google Scholar 

  • Ermler, W.C., Lee, Y.S., Christiansen, P.A., Pitzer, K.S.: Chem Phys Lett 81, 70 (1981)

    ADS  Google Scholar 

  • Lee, Y.S., Erlmer, W.C., Pitzer, K.S.: J. Chem. Phys. 67, 5861 (1977)

    ADS  Google Scholar 

  • Pitzer, R.M., Winter, N.W.: J. Chem. Phys. 92, 3061 (1988)

    Google Scholar 

  • Stevens, W.J., Krauss, M.: J. Chem. Phys. 76, 3834 (1982)

    ADS  Google Scholar 

  • Desclaux, J.P.: Comp. Phys. Comm. 9, 31 (1975)

    ADS  Google Scholar 

  • Balasubramanian, K.: J. Phys. Chem. 93, 6585 (1989)

    Google Scholar 

  • Hess, B.A.: Phys. Rev. A 33, 3742 (1986)

    ADS  Google Scholar 

  • Hess, B.A., Chandra, P.: Phys. Scr. 36, 412 (1987)

    ADS  Google Scholar 

  • Sucher, J.: Phys. Rev. A 22, 348 (1980)

    ADS  MathSciNet  Google Scholar 

  • Marian, C.M.: J. Chem. Phys. 93, 1176 (1990)

    ADS  Google Scholar 

  • Marian, C.M.: J. Chem. Phys. 94, 5574 (1991)

    ADS  Google Scholar 

  • Furlani, T.R., King, H.F.: J. Chem. Phys. 82, 5577 (1985)

    ADS  Google Scholar 

  • Hess, B.A., Buenker, R.J., Marian, C.M., Peyerimhoff, S.D.: Chem Phys 71, 79 (1982)

    Google Scholar 

  • Yarkony, D.R.: J. Chem. Phys. 84, 2075 (1986)

    ADS  Google Scholar 

  • Jensen, J.O., Yarkony, D.R.: Chem Phys Lett 141, 391 (1987)

    ADS  Google Scholar 

  • Liu, B., Yoshimine, M.: J. Chem. Phys. 74, 612 (1981)

    ADS  Google Scholar 

  • Yarkony, D.R.: Int. Rev. Phys. Chem. 11, 195 (1992)

    Google Scholar 

  • Manaa, M.R., Yarkony, D.R.: J. Chem. Phys. 99, 5251 (1993)

    ADS  Google Scholar 

  • Yarkony, D.R.: J. Chem. Phys. 97, 4407 (1993)

    Google Scholar 

  • Yarkony, D.R.: J. Chem. Phys. 100, 3639 (1994)

    ADS  Google Scholar 

  • Fletcher, R.: Practical Methods of Optimization vol. 2. Wiley, New York Vol (1981)

    MATH  Google Scholar 

  • Radazos, I.N., Robb, M.A., Bernardi, M.A., Olivucci, M.: Chem Phys Lett 197, 217 (1992)

    ADS  Google Scholar 

  • Herzberg, G., Longuet-Higgins, H.C.: Disc. Faraday Soc. 35, 77 (1963)

    Google Scholar 

  • Berry, M.V.: Proc. R. Soc. Lond. A 392, 45 (1984)

    ADS  Google Scholar 

  • Xantheas, S., Elbert, S.T., Ruedenberg, K.: J. Chem. Phys. 93, 7519 (1990)

    ADS  Google Scholar 

  • Tennyson, J., Miller, S., Sutcliffe, B.T.: J. Chem. Soc. Faraday Trans. 84, 1295 (1988)

    Google Scholar 

  • Van Vleck, J.H.: Rev. Mod. Phys. 23, 213 (1951)

    ADS  Google Scholar 

  • Mizushima, M.: The Theory of Rotating Diatomic Molecules. Wiley, New York (1975)

    Google Scholar 

  • Lee, T.J., Fox, D.J., Schaefer, H.F., Pitzer, R.M.: J. Chem.phys. 81, 356 (1984)

    ADS  Google Scholar 

  • Dixon, R.N.: Mol. Phys. 54, 333 (1985)

    ADS  Google Scholar 

  • Whitehead, R.J., Handy, N.C.: J. Mol. Spec. 55, 356 (1975)

    ADS  Google Scholar 

  • Rose, M.E.: Elementary Theory of Angular Momentum. Wiley, New York (1957)

    MATH  Google Scholar 

  • Mills, I.M.: In: Rao, K.N., Mathews, C.W. (eds.) Molecular Spectroscopy: Modern Research, p. 115. Academic Press, New York (1970)

    Google Scholar 

  • Eckart, C.: Phys. Rev. 47, 552 (1935)

    ADS  Google Scholar 

  • Wilson Jr., E.B., Howard, J.B.: J. Chem. Phys. 4, 260 (1936)

    ADS  Google Scholar 

  • Darling, B.T., Dennison, D.M.: Phys. Rev. 57, 128 (1940)

    ADS  Google Scholar 

  • Wilson, E.B., Decius, J.C., Cross, P.C.: Molecular Vibrations. McGraw-Hill, New York (1955)

    Google Scholar 

  • Watson, J.K.G.: Mol. Phys. 15, 479 (1968)

    ADS  Google Scholar 

  • Zare, R.N.: Angular Momentum. Wiley, New York (1988)

    Google Scholar 

  • Sutcliffe, B.T., Tennyson, J.: Mol. Phys. 58, 1053 (1986)

    ADS  Google Scholar 

  • Segall, J., Zare, R.N., Dubal, H.R., Lewerenz, M., Quack, M.: J. Chem. Phys. 86, 634 (1987)

    ADS  Google Scholar 

  • Green, W.H., Lawrence, W.D., Moore, C.B.: J. Chem. Phys. 86, 6000 (1987)

    ADS  Google Scholar 

  • Amos, R.D., Gaw, J.G., Handy, N.C., Carter, S.: J. Chem. Soc. Faraday Trans. 84, 1247 (1988)

    Google Scholar 

  • Botschwina, P.: Chem Phys 68, 41 (1982)

    Google Scholar 

  • Botschwina, P.: J. Chem. Soc. Faraday Trans. 84, 1263 (1988)

    Google Scholar 

  • Hutson, J.M.: In: Bowman, J.M., Ratner, M.A. (eds.) Advances in Molecular Vibrations and Collision Dynamics, vol. 1A, JAI Press, Greenwich (1991)

    Google Scholar 

  • Dubernet, M.L., Flower, D., Hutson, J.M.: J. Chem. Phys. 94, 7602 (1991)

    ADS  Google Scholar 

  • Alexander, M.H., Gregurick, S., Dagdigian, P.J.: J. Chem. Phys. 101, 2887 (1994)

    ADS  Google Scholar 

  • Brink, D.M., Satchler, G.R.: Angular Momentum. Clarendon, Oxford (1968)

    MATH  Google Scholar 

  • Arthurs, A., Dalgarno, A.: Proc. Roy. Soc. Lond. A 256, 540 (1960)

    ADS  Google Scholar 

  • Alexander, M.: Chem Phys 92, 337 (1985)

    Google Scholar 

  • Werner, H., Follmeg, B., Alexander, M.H.: J. Chem. Phys. 89, 3139 (1988)

    ADS  Google Scholar 

  • Werner, H., Follmeg, B., Alexander, M.H., Lemoine, D.: J. Chem. Phys. 91, 5425 (1989)

    ADS  Google Scholar 

  • Chakravarty, C., Clary, D.: J. Chem. Phys. 94, 4149 (1991)

    ADS  Google Scholar 

  • Alexander, M.H., Gregurick, S., Dagdigian, P.J., Lemire, G.W., McQuaid, M.J., Sausa, R.C.: J. Chem. Phys. 101, 4547 (1994)

    ADS  Google Scholar 

  • Miller, W.H.: In: Clary, D.C. (ed.) The Theory of Chemical Reaction Dynamics. Reidel, Dordrecht (1986)

    Google Scholar 

  • Miller, W.H., Handy, N., Adams, J.: J. Chem. Phys. 72, 99 (1980)

    ADS  Google Scholar 

  • Page, M., McIver, J.W.: J. Chem. Phys. 88, 922 (1988)

    ADS  Google Scholar 

  • Kato, S., Jaffe, R.L., Komornicki, A., Morokuma, K.: J. Chem. Phys. 78, 4567 (1983)

    ADS  Google Scholar 

  • Strobel, D.F.: Planet. Space. Sci. 30, 839 (1982)

    ADS  Google Scholar 

  • Berman, M.R., Lin, M.C.: J. Phys. Chem. 87, 3933 (1983)

    Google Scholar 

  • Fenimore, C.P.: 13th International Symposium on Combustion. The Combustion Institute, Pittsburgh, p 373 (1971)

    Google Scholar 

  • Blauwens, J., Smets, B., Peeters, J.: 16th International Symposium on Combustion. The Combustion Institute, Pittsburgh, p 1055 (1977)

    Google Scholar 

  • Dean, A.J., Hanson, R.K., Bowman, C.T.: 23rd International Symposium on Combustion. The Combustion Institute, Pittsburgh, p 259 (1990)

    Google Scholar 

  • Tully, J.C.: J. Chem. Phys. 61, 61 (1974)

    ADS  Google Scholar 

  • Zahr, G.E., Preston, R.K., Miller, W.H.: J. Chem. Phys 62, 1127 (1975)

    ADS  Google Scholar 

  • Manaa, M.R., Yarkony, D.R.: J. Chem. Phys. 95, 1808 (1991)

    ADS  Google Scholar 

  • Manaa, M.R., Yarkony, D.R.: Chem Phys Lett 188, 352 (1992)

    ADS  Google Scholar 

  • Martin, J.M.L., Taylor, P.R.: Chem Phys Lett 209, 143 (1993)

    ADS  Google Scholar 

  • Walch, S.P.: Chem Phys Lett 208, 214 (1993)

    ADS  Google Scholar 

  • Seideman, T., Walch, S.P.: J. Chem. Phys. 101, 3656 (1994)

    ADS  Google Scholar 

  • Tinkham, M.: Group Theory and Quantum Mechanics. McGraw-Hill, New York (1964)

    MATH  Google Scholar 

  • Seideman, T.: J. Chem. Phys. 101, 3662 (1994)

    ADS  Google Scholar 

  • Becker, K.H., Engelhardt, B., Geiger, H., Kurtenbach, R., Schrey, G., Wissen, P.: Chem Phys Lett 154, 342 (1992)

    ADS  Google Scholar 

  • Lindackers, D., Burmeister, M., Roth, P.: 23rd International Symposium on Combustion. Combustion Institute, Pittsburgh, p 251 (1990)

    Google Scholar 

  • Lindackers, D., Burmeister, M., Roth, P.: Combust Flame 81, 251 (1990)

    Google Scholar 

  • Hu, X., Schulten, K.: Phys. Tod. 50, 28 (1997)

    ADS  Google Scholar 

  • Weber, W., Helms, V., Mc Mammon, A., Langhoff, P.W.: Proc. Natl. Acad. Sci. U.S.A. 96, 6177 (1999)

    ADS  Google Scholar 

  • Yarkony, D.R.: J. Phys. Chem. A. 105, 6277 (2001)

    Google Scholar 

  • Yarkony, D.R.: J Chem Phys 121, 628 (2004)

    ADS  Google Scholar 

  • Yarkony, D.R.: J. Phys. Chem. A. 108, 3200 (2004)

    Google Scholar 

  • Matsika, S., Yarkony, D.R.: J Chem Phys 117, 6907 (2002)

    ADS  Google Scholar 

  • Matsika, S., Yarkony, D.R.: J. Phys. Chem. B. 106, 8108 (2002)

    Google Scholar 

  • Matsika, S., Yarkony, D.R.: J Chem Phys 115, 5066 (2001)

    ADS  Google Scholar 

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Correspondence to David R. Yarkony .

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Yarkony, D.R. (2023). Molecular Structure. In: Drake, G.W.F. (eds) Springer Handbook of Atomic, Molecular, and Optical Physics. Springer Handbooks. Springer, Cham. https://doi.org/10.1007/978-3-030-73893-8_33

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