A quantum approximate method for the calculation of thermal reaction rate constants

The calculation of thermal reaction rate constants is a central problem in theoretical chemistry, and exact classical and quantum expressions have been formulated [1]. However, approximate approaches are necessary when dealing with complex reactions, and several techniques have been developed in recent years. They include the inclusion of quantum corrections to the classical transition state theory (TST) [2], semiclassical theories [3], and ring polymer molecular dynamics (RPMD) TST [4].
In this work, we have developed a new quantum mechanical method to compute reaction rate constants, which is related to Miller's quantum instanton [5]. Starting from the exact definition of the thermal rate constant as the time integral of the quantum flux-flux correlation function, upon introduction of a stationary phase approximation, we have derived an expression which has the same structure of the original quantum instanton but includes a contribution from real-time dynamics. This new method has been tested on the one-dimensional Eckart barrier problem, and on the two-dimensional H+H2 collinear reaction. Results over a wide range of temperatures have been found to be in agreement within 10% with exact quantum mechanical estimates.

[1] W.H. Miller, S.D. Schwartz, J.W. Tromp, J. Chem. Phys. 79, 4889 (1983); W.H. Miller, J. Phys. Chem. A 102 (5), 793, (1998)
[2] H. Eyring J. Chem. Phys. 3 (1935), p. 107; E. Wigner J. Chem. Phys, 5 (1937), p. 720
[3] W.H. Miller, J. Chem. Phys, 62, 1899 (1975); R. Hernandez, W.H. Miller Chem. Phys. Lett., 214 (1993), p. 129; T. L. Nguyen, J. F. Stanton, and J. R. Barker, Chem. Phys. Lett. 499, 9 (2010).
[4] J. O. Richardson and S. C. Althorpe, J. Chem. Phys. 131, 214106 (2009); T. J. H. Hele and S. C. Althorpe J. Chem. Phys. 138, 084108 (2013)
[5] W.H. Miller, Y. Zhao, M. Ceotto, S. Yang J. Chem. Phys. 119, 1329 (2003); M. Ceotto, S. Yang, and W.H. Miller J. Chem. Phys. 122, 044109 (2005)