Fighting the curse of dimensionality with semiclassical approaches in reaction rate theory

Reaction rate constants can be, in principle, exactly calculated by simulating the real-time quantum dynamics for the reactive system,[1] which is a formidable task, especially for high-dimensional systems. The semiclassical approximation offers a rigorous way to fight the so-called curse of dimensionality.[2] In this talk, I will focus on Semiclassical Transition State Theory (SCTST).[3] This approach incorporates the non-separable coupling between the different degrees of freedom (DOFs) of reactive systems and includes the effects of reaction path curvature and anharmonicity, as well as quantum tunneling contributions, in the rate constant. The SCTST rate expression, which directly connects to the Semiclassical Instanton (SCI),[4] is derived by relying on a perturbative expansion for the vibrational energy. This way, it is possible to express the semiclassical cumulative reaction probability conveniently, without any assumption about the DOF separability. I will introduce a complete and parallel implementation of SCTST that is released open source into the MultiWell suite of codes.[5] I will also show how to employ the method to obtain accurate and quantum-corrected rate constants for high dimensional tunneling reactions, even at a high level of electronic structure theory, without needing a fitted potential energy surface.[6-8] In the last part of the talk, I will address the issue of including real-time dynamics information in accurate rate constant calculations by presenting a quantum mechanical technique related to Miller's Quantum Instanton (QI)[9] that is more flexible than the original QI in choosing the dividing surface position.[10] References [1]W. Miller, S. Schwartz, J. Tromp, The Journal of Chemical Physics, 79, 4889-4898 (1983) [2]W. Miller, Science, 233, 171-177 (1986) [3]W. Miller, R. Hernandez, N. Handy, D. Jayatilaka, A. Willetts, Chemical Physics Letters, 172, 62-68 (1990) [4]W. Miller, The Journal of Chemical Physics, 62, 1899-1906 (1975) [5]J.R. Barker, T.L. Nguyen, J.F. Stanton, C. Aieta, M. Ceotto, F. Gabas, T.J.D. Kumar, C.G.L. Li, L.L. Lohr, A. Maranzana, N.F. Ortiz, J.M. Preses, J.M. Simmie, J.A. Sonk, and P.J. Stimac; MultiWell-2022 Software Suite; J.R. Barker, University of Michigan, Ann Arbor, Michigan, USA, 2022; https://multiwell.engin.umich.edu. [6]G. Mandelli, C. Aieta, M. Ceotto, J. Chem. Theory Comput., 18, 623-637 (2022) [7]C. Aieta, F. Gabas, M. Ceotto, J. Chem. Theory Comput., 15, 2142-2153 (2019) [8]C. Aieta, F. Gabas, M. Ceotto, J. Phys. Chem. A, 120, 4853-4862 (2016) [9]W. Miller, Y. Zhao, M. Ceotto, S. Yang, The Journal of Chemical Physics, 119, 1329-1342 (2003) [10]C. Aieta, M. Ceotto, J. Chem. Phys., 146, 214115 (2017)