Abstract
We consider three aspects of potential energy surface representations for dynamics calculations on polyatomic systems, with special emphasis on generalized transition state theory and tunneling calculations, (i) We present methods for calculating the vibrational energies of generalized transition states from either a cartesian or internal coordinate force field and including the effect of raode-mode coup!.ings on the rate constant by perturbation theory and the Pitzer-Gwinn approximation, (ii) We discuss practical aspects in the use of ab initio gradient-based electronic structure calculations for the calculation of cartesian force fields for a set of stationary points on the potential energy surface or for a sequence of generalized transition states. (iii) We discuss recent progress on the development of global analytic representations for potential energy surfaces of polyatomic reactions. Such global representations can be used to generate either cartesian or internal-coordinate force fields for generalized transition states, and they can also be used to compute the potential energy surface far from the minimum energy path as may be required for tunneling calculations in some cases.
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References
Potential Energy Surfaces and Dynamics Calculations, edited by D.G. Truhlar (Plenum, New York, 1981).
J.N. Murrell, S. Carter, S.C. Farantos, P. Huxley, and A.J.C. Varandas, Molecular Potential Energy Functions (John Wiley and Sons, Chichester, 1984).
Dynamics of Molecular Collisions, Part B, edited by W.H. Miller (Plenum, New York, 1976).
D.G. Truhlar, F.B. Brown, D.W. Schwenke, R. Steckler, and B.C. Garrett, in Comparison of Ab Initio Quantum Chemistry with Experiment, edited by R.J. Bartlett (D. Reidel, Dordrecht, Holland), in press.
R.A. Marcus, J. Phys. Chem. 83, 204 (1979).
K. Fukui, Acc. Chem. Res. 14, 363 (1981).
K. Morokuma and S. Kato, in Potential Energy Surfaces and Dynamics Calculations, edited by D.G. Truhlar (Plenum, New York, 1981), p. 243.
W.H. Miller, J. Phys. Chem. 87, 3811 (1983).
D.G. Truhlar and B.C. Garrett, Acc. Chem. Res. 13, 440 (1980).
D.G. Truhlar, A.D. Isaacson, R.T. Skodje, and B.C. Garrett, J. Phys. Chem. 86, 2252 (1982), 87, 4554E (1983).
D.G. Truhlar and B.C. Garrett, Annu. Rev. Phys. Chem. 35, 159 (1984).
D.G. Truhlar and A.D. Isaacson, J. Chem. Phys. 77. 3516 (1982).
D.C. Clary, B.C. Garrett, and D.G. Truhlar, J. Chem. Phys. 78, 777 (1983).
D.G. Truhlar, W.L. Hase, and J.T. Hynes, J. Phys. Chem. 87, 2664, 5523E (1983).
B.C. Garrett and D.G. Truhlar, J. Chem. Phys. 81, 309 (1984).
D.G. Truhlar, B.C. Garrett, P.G. Hipes, and A. Kuppermann, J. Chem. Phys. 81, 3542 (1984).
A.D. Isaacson, M.T. Sund, S.N. Rai, and D.G. Truhlar, J. Chem. Phys. 82, 1338 (1985).
B.C. Garrett and D.G. Truhlar, J. Phys. Chem. 89, 2204 (1985).
B.C. Garrett, N. Abusalbi, D.J. Kouri, and D.G. Truhlar, J. Chem. Phys. 83, in press.
B.C. Glrrett, D.G. Truhlar, A.F. Wagner, and T.H. Dunning, Jr., J. Chem. Phys. 78, 4400 (1983).
D.K. Bondi, J.N.L. Connor, B.C. Garrett, and D.G. Truhlar, J. Chem. Phys. 78, 5981 (1983).
B.C. Garrett and D.G. Truhlar, J. Chem. Phys. 79, 4931 (1983).
R. Steckler, D.G. Truhlar, B.C. Garrett, N.C. Blais, and R.B. Walker, J. Chem. Phys. 81, 5700 (1984).
F.B. Brown, R. Steckler, D.W. Schwenke, D.G. Truhlar, and B.C. Garrett, J. Chem. Phys. 82, 188 (1985).
B.C. Garrett and D.G. Truhlar, J. Phys. Chem. 86, 1136 (1982), 87, 4554E (1983).
B.C. Garrett, D.G. Truhlar, R.S. Grev, G.C. Schatz, and R.B. Walker, J. Phys. Chem. 85, 3806 (1981).
R.T. Skodje, D.W. Schwenke, D.G. Truhlar, and B.C. Garrett, J. Phys. Chem. 88, 628 (1984).
R.T. Skodje, D.W. Schwenke, D.G. Truhlar, and B.C. Garrett, J. Chem. Phys. 80, 3569 (1984).
B.C. Garrett, D.W. Schwenke, R.T. Skodje, D. Thirumalai, T.C. Thompson, and D.G. Truhlar, in Resonances, edited by D.G. Truhlar (American Chemical Society, Washington, 1984), p. 375.
F.B. Brown, S.C. Tucker, and D.G. Truhlar, J. Chem. Phys. 83, in press.
W.H. Miller and S.-H. Shi, J. Chem. Phys. 75, 2258 (1981).
C.J. Cerjan, S. Shi, and W.H. Miller, J. Phys. Chem. 86, 2244 (1982).
K. Morokuma, S. Kato, K. Kitaura, S. Obara, K. Ohta, and M. Hanamura, in New Horizons of Quantum Chemistry, edited by P.-O. Lowdin and B. Pullman (D. Reidel, Dordrecht, Holland, 1983), p. 221.
W.H. Miller, N.C. Handy, and J.E. Adams, J. Chem. Phys. 72, 99 (1980).
G. Natanson, Mol. Phys. 46, 481 (1982).
D.G. Truhlar, Int. J. Quantum Chem. Symp. 17, 77 (1983).
G.L. Hofacker, Z. Naturforsch. A 18, 607 (1963).
R.A. Marcus, J. Chen. Phys. 41, 4493, 4500 (1966).
D.G. Truhlar, J. Chem. Phys. 53, 2041 (1970).
K. Fukui, A. Tachibana, and K Yamashita, Int. J. Quantum Chem. Symp. 15, 621 (1981).
A. Tweedale and K.J. Laidler, J. Chem. Phys. 53, 2045 (1970).
B.C. Garrett and D.G. Truhlar, J. Phys. Chem. 83, 1079 (1979), 84, 682E (1980), 87, 4553E (1983).
B.C. Garrett and D.G. Truhlar, J. Amer. Chem. Soc. 101, 4534 (1979).
B.C. Garrett, D.G. Truhlar, R.S. Grev, and A.W. Magnuson, J. Phys. Chem. 84, 1730 (1980), 87, 4554E (1983).
S. Glasstone, K.J. Laidler, and H. Eyring, Theory of Rate Processes (McGraw-Hill, New York, 1941).
J.C. Keck, Adv. Chem. Phys. 13, 85 (1967).
I. Shavitt, Theoretical Chemistry Laboratory Report WIS-AEC-23, University of Wisconsin, 11 August 1959 (unpublished).
D.G. Truhlar and A. Kuppermann, J. Amer. Chem. Soc. 93, 1840 (1971).
K. Fukui, S. Kato, and H. Fujimoto, J. Amer. Chem. Soc. 97, 1 (1975).
H.F. Schaefer III, Chem. Brit. 11, 227 (1975).
B.C. Garrett and D.G. Truhlar, J. Phys. Chem. 83, 1052, 3058E (1979), 87, 4553E (1983).
R.T. Skodje, D.G. Truhlar, and B.C. Garrett, J. Phys. Chem. 85, 3019 (1981).
R.T. Skodje, D.G. Truhlar, and B.C. Garrett, J. Chem. Phys. 77, 5955 (1982).
D.G. Truhlar, A.D. Isaacson, and B.C. Garrett, in The Theory of Chemical Reaction Dynamics, edited by M. Baer (CRC Press, Boca Raton, FL, 1985), Vol. 4, p. 1.
V.K. Babamov and R.A. Marcus, J. Chem. Phys. 74,1790 (1978).
P. Pechukas and F.J. McLafferty, J. Chem. Phys. 58, 1622 (1973).
B.C. Garrett and D.G. Truhlar, J. Phys. Chem. 83, 1915 (1979).
B.C. Garrett and D.G. Truhlar, J. Amer. Chem. Soc. 101, 5207 (1979).
A.D. Isaacson and D.G. Truhlar, J. Chem. Phys. 76, 1380 (1982).
G.C. Schatz and H. Elgersma, Chem. Phys. Lett. 73, 21 (1980).
S.P. Walch and T.H. Dunning, J. Chem. Phys. 72, 13O3 (1980).
W.B. Wilson, Jr., J.C. Decius, and P.C. Cross, Molecular Vibrations (McGraw-Hill, New York, 1955), p. 19, (a) p. 172.
D.G. Truhlar, J. Mol. Spectrosc. 38, 415 (1971).
A.D. Isaacson, D.G. Truhlar, K. Scanlon, and J. Overend, J. Chem. Phys. 75, 3017 (1981).
B.C. Garrett and D.G. Truhlar, J. Chem. Phys. 72, 3460 (1980).
H.H. Nielsen, Encycl. Phys. 37/part one, 173 (1959).
M.A. Pariseau, I. Suzuki, and J. Overend, J. Chem. Phys. 42, 2335 (1965).
D.G. Truhlar, R.W. Olson, A.C. Jeannotte, and J. Overend, J. Amer. Chem. Soc. 98, 2373 (1976).
D. Papousek and M.R. Aliev, Molecular Vibrational-Rotational Spectra (Elsevier, Amsterdam, 1982), p. 38.
B.C. Garrett, D.G. Truhlar, and A.W. Magnuson, J. Chem. Phys. 76, 2321 (1982).
H.S. Johnston and C.A. Parr, J. Amer. Chem. Soc. 85, 2544 (1963).
A.R. Hoy, I.M. Mills, and G. Strey, Mol. Phys. 24, 1265 (1972).
M.A. Pariseau, I. Suzuki, and J. Overend, J. Chem. Phys. 44, 3561 (1966).
S. Califano, Vibrational States (Wiley, London, 1976).
B. Crawford, Jr. and J. Overend, J. Mol. Spectrosc. 12, 307 (1964).
W.B. Brown and E. Steiner, J. Mol. Spectrosc. 10, 348 (1963).
S. Brodersen and J. Christoffersen, J. Mol. Spectrosc. 12, 303 (1964).
K. Machida, J. Chem. Phys. 44, 4186 (1966).
I. Suzuki and J. Overend. Spectrochim. Acta 3, 1093 (1981).
N.W. Bazley and D.W. Fox, Phys. Rev. 124, 483 (1961).
K.S. Pitzer and U.D. Gwinn, J. Chem. Phys. 10, 428 (1942).
A.D. Isaacson and D.G. Truhlar, J. Chem. Phys. 75, 4090 (1981).
D.A. McQuarrie, Statistical Mechanics (Harper and Row, New York, 1976).
D.L. Bunker, J. Chem. Phys. 37, 393 (1962).
W.L. Hase and D.G. Buckowski, Chem. Phys. Lett. 74,284 (1980).
J.E. Adams and J.D. Doll, J. Chem. Phys. 74,5332 (1981).
A.E. Barton and B.J. Howard, Faraday Discuss. Chem. Soc. 73, 45 (1982).
A.F. Voter, J. Chem. Phys. 82, 1890 (1985).
D.L. Freeman and J.D. Doll, J. Chem. Phys. 80, 5709 (1984).
P. Pulay, Mol. Phys. 17, 197 (1969).
P. Pulay, in Applications of Electronic Structure Theory, edited by H.F. Schaefer (Plenum, New York, 1977), p. 153.
P. Pulay, in The Force Concept in Chemistry, edited by B.M. Deb (Van Nostrand Reinhold, New York, 1981), p. 449.
J.A. Pople, R. Krishnan, H. B. Schlegel, and J.B. Binkley, Int. J. Quantum Chem. Symp. 13, 225 (1979).
J.D. Goddard, N.C. Handy, and H.F. Schaefer, J. Chem. Phys. 71, 1525 (1979).
S. Kato and K. Morokuma, Chem. Phys. Lett. 65, 19 (1979).
B.R. Brooks, W.D. Laidig, P. Saxe, J.D. Goddard, Y. Yamaguchi, and H.F. Schaefer, J. Chem. Phys. 72, 4652 (1980).
R. Krishnan, H.B. Schlegel, and J.A. Pople, J. Chem. Phys. 72, 4654 (1980).
Y. Osamura, Y. Yamaguchi, and H.F. Schaefer, J. Chem. Phys. 77, 383 (1982).
M. Page, P. Saxe, G.F. Adams, and B.H. Lengsfield, J. Chem. Phys. 81, 434 (1984).
G. Fitzgerald, R. Harrison, W.D. Laidig, and R.J. Bartlett, J. Chem. Phys. 82, 4379 (1985).
J.W. Mclver, Jr. and A. Komornicki, Chem. Phys. Lett. 10, 303 (1971).
D. Poppinger, Chem. Phys. Lett. 34, 332 (1975).
D. Poppinger, Chem. Phys. Lett. 35, 550 (1975).
A. Komornicki, K. Ishida, K. Morokuma, R. Ditchfield, and M. Conrad, Chem. Phys. Lett. 45, 595 (1977).
B. Schlegel, J. Comput. Chem. 3, 214 (1982).
A. Banerjee, N. Adams, J. Simons, and R. Shepard, J. Phys. Chem. 89, 52 (1985).
Y. Osamura, Y. Yamaguchi, P. Saxe, M.A. Vincent, J.F. Gaw, and H.F. Schaefer, Chem. Phys. 72, 131 (1982).
Y. Yamaguchi, Y. Osamura, G. Fitzgerald, and H.F. Schaefer, J. Chem. Phys. 78, 1607 (1983).
R.N. Camp, H.F. King, J.W. Mclver, Jr., and D. Mullally, J. Chem. Phys. 79, 1088 (1983).
D.J. Fox, Y. Osamura, M.R. Hoffman, J.F. Gaw, G. Fitzgerald, Y. Yamaguchi, and H.F. Schaefer, Chem. Phys. Lett. l02, 17 (1983).
M.S. Hoffman, D.J. Fox, J.F. Gaw, Y. Osamura, Y. Yamaguchi, R.S. Grev, G. Fitzgerald, H.F. Schaefer, P.J. Knowles, and N.C. Handy, J. Chem. Phys. 80, 2660 (1984).
P. Pulay, J. Chem. Phys. 78, 5043 (1983).
P. Jørgensen and J. Simons, J. Chem. Phys. 79, 334 (1983).
J.F. Gaw, Y. Yamaguchi, and H.F. Schaefer, J. Chem. Phys. 81, 6395 (1984).
S. Kato, H. Kato, and H. Fukui, J. Amer. Chem. Soc. 99, 684 (1977).
S.K. Gray, W.H. Miller, Y. Yamaguchi, and H.F. Schaefer, J. Chem. Phys. 73,2733 (1980).
K. Yamashita and Y. Yamabe, Int. J. Quantum Chem. Symp. 17, 177 (1983).
S.M. Colwell and N.C. Handy, J. Chem. Phys. 82, 1281 (1985).
A. Tachibana, T. Okazaki, M. Koizumi, K. Hori and T. Yamabe, J. Amer. Chem. Soc. 107, 1190 (1985).
D.G. Truhlar, N.J. kilpatrick, and B.C. Garrett, J. Chem. Phys. 78, 2438 (1983).
H.S. Johnston and J. Heicklen, J. Phys. Chem. 66, 532 (1962).
B.C. Garrett and D.G. Truhlar, J. Phys. Chem. 83, 2921 (1979).
M. Quack and J. Troe, Ber. Bunsenges. Phys. Chem. 78, 240 (1974).
M. Quack and J. Troe, Ber. Bunsenges. Phys. Chem. 79, 170, 469 (1975).
D.G. Truhlar and A. Kuppermann, J. Chem. Phys. 52, 2232 (1970).
M.J. Stern, A. Persky, and F.S. Klein, J. Chem. Phys. 58, 5697 (1973).
J.T. Muckerman, Theor. Chem. Adv. Perspect. A 6, 1 (1981).
J.W. Duff and D.G. Truhlar, J. Chem. Phys. 62, 2477 (1975).
T. Carrington, Jr., L.M. Hubbard, H.F. Schaefer III, and W.H. Miller, J. Chem. Phys. 80, 4347 (1984).
M.V. Basilevsky and V.M. Ryaboy, Chem. Phys. 41, 461 (1979).
B.C. Garrett, R.T. Skodje, and D.G. Truhlar, unpublished calculations.
L.M. Raff, J. Chem. Phys. 60, 2220 (1974).
T. Valencich and D.L. Bunker, J. Chem. Phys. 61, 21 (1974).
S. Chapman and D.L. Bunker, J. Chem. Phys. 62,2890 (1975).
W.A. Lathan, W.J. Hehre, L.A. Curtiss, and J.A. Pople, J. Amer. Chem. Soc. 93, 6377 (1971).
S. Ehrenson and M.D. Newton, Chem. Phys. Lett. 13, 24 (1972).
K. Morokuma and R.E. Davis, J. Amer. Chem. Soc. 94, 1060 (1972).
K. Fukui, S. Kato, and H. Fujimoto, J. Amer. Chem. Soc. 97, 1 (1975).
K. Niblaeus, B.O. Roos, and P.E.M. Siegbahn, Chem. Phys. 26, 59 (1977).
P. Cársky and R. Zahradnik, J. Mol. Struct. 54, 247 (1979).
P. Cársky and R. Zahradnik, Int. J. Quantum Chem. 16, 243 (1979).
P. Cársky, Coll. Czech. Chem. Comm. 44, 3452 (1979).
S.P. Walch, J. Chem. Phys. 72,4932 (1980).
G.C. Schatz, S.P. Walch, and A.F. Wagner, J. Chem. Phys. 73, 4536 (1980).
G.C. Schatz, A.F. Wagner, and T.H. Dunning, Jr., J. Phys. Chem. 88, 221 (1984).
M.J.S. Gordon, D.R. Gano, and J.A. Boatz, J. Amer. Chem. Soc. 105, 5771 (1983).
S. Sana, G. Leroy, and J.L. Villaveces, Theoret. Chim. Acta 65, 109 (1984).
B. Maessen, P. Bopp, D.R. McLaughlin, and M. Wolfsberg, Z. Naturfor. 39a, 1005 (1984).
M.W. Schmi M.S. Gordon, and M. Dupuis, J. Amer. Chem. Soc. 107, 2585 (1985).
K. Ishida, K. Morokuma, and A. Komornicki, J. Chem. Phys. 66, 2153 (1977).
S.M. Colwell, Mol. Phys. 51, 1217 (1984).
D.G. Truhlar and C.J. Horowitz, J. Chem. Phys. 68, 2466 (1978), 71, 1514E (1979).
M. Dupuis, D. Spangler, and J.J. Wendoloski, Program QG01, in NRCC Software Catalog (Lawrence Berkeley Laboratory technical report LBL-10811, Berkeley, CA, 1980), p. 60.
P.J. Kuntz, E.M. Nemeth, J.C. Polanyi, S.D. Rosner, and C.E. Young, J. Phys. Chem. 44, 1168 (1966).
C.A. Parr and D.G. Truhlar, J. Phys. Chem. 71, 1844 (1971).
N.C. Blais and D.G. Truhlar, J. Chem. Phys. 58, 4186 (1974), 65, 3803E (1976).
F.B. Brown, R. Steckler, D.W. Schwenke, D.G. Truhlar, and B.C. Garrett, J. Chem. Phys. 82, 188 (1985).
W.H. Miller, J. Phys. Chem. 87, 21 (1983).
D.L. Bunker and W.L. Hase, J. Chem. Phys. 59, 4621 (1973), 69, 4711E (1978).
W.L. Hase, G. Mrowka, R.J. Brudzynski, and C.S. Sloane, J. Chem. Phys. 69, 3548 (1978).
W.L. Hase, D.M. Ludlow, R.J. Wolf, and T. Schlick, J. Phys. Chem. 85, 958 (1981).
E.R. Grant and D.L. Bunker, J. Chem. Phys. 68, 628 (1978).
C.S. Sloane and W.L. Hase, Discuss. Faraday Soc. 62, 210 (1977).
P.J. Nagy and W.L. Hase, Chem. Phys. Lett. 54, 73 (1978).
W.L. Hase and K.C. Bhalla, J. Chem. Phys. 75, 2807 (1981).
R.J. Duchovic, W.L. Hase, and H.B. Schlegel, J. Phys. Chem. 88, 1339 (1984).
C.J. Cobos and J. Troe, Chem. Phys. Lett. 113, 41 (1985).
H.S. Johnston and P. Goldfinger, J. Chem. Phys. 37, 700 (1962).
G.W. Burton, L.B. Sims, J.C. Wilson, and A. Fry, J. Amer. Chem. Soc. 99, 3371 (1977).
L.B. Sims and D.E. Lewis, Isotopes in Organic Chemistry, Vol. 6, “Isotopic Effects: Recent Developments in Theory and Experiment”, edited by E. Buncel and C.C. Lee (Elsevier, Amsterdam, 1984), p. 161.
R.A. Marcus and M.E. Coltrin, J. Chem. Phys. 67, 2609 (1977).
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Truhlar, D.G., Brown, F.B., Steckler, R., Isaacson, A.D. (1986). The Representation and use of Potential Energy Surfaces in the Wide Vicinity of a Reaction Path for Dynamics Calculations on Polyatomic Reactions. In: Clary, D.C. (eds) The Theory of Chemical Reaction Dynamics. NATO ASI Series, vol 170. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4618-7_12
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