Accurate and efficient pre-exponential factor approximations for the semiclassical initial value representation propagator

The semiclassical (SC) theory[1,2] is a very powerful tool to describe molecular reactivity, electronic transitions and molecular vibrations.[3-9] In semiclassical methods quantum informations are obtained by evolving classical trajectories. This is computationally less intense than grid methods. Unfortunately, when the system is complex, the calculation of the SC Herman-Kluk (HK) prefactor[10] is prohibitive, due to the trajectories' instability.[11] For this reason, it is not possible to employ the basic SC-HK approach for large systems. In the past years, several approximations to the HK prefactor have been proposed[12,13] to solve this issue, but they have never been thoroughly assessed. In this work, first we test some of the most common prefactor approximations on small systems. Then, we put forward a new one starting from the Log-Derivative[13] formulation, and that is potentially suitable for bigger systems. This approximation depends only on the Hessian matrix and does not require the calculation of the monodromy matrix elements, which are often unstable. As a consequence, even chaotic trajectories can be employed for vibrational spectra simulations. The results show that our approximation is very reliable for molecules like H2, H2O, CO2, CH2O, CH4 and CH2D2. Future applications of our new prefactor will concern the evaluation of power spectra of large systems, for which quantum calculations are currently out of reach. References [1] W.H. Miller J. Phys. Chem. A 105, 2942 (2001). [2] W.H. Miller Proc. Natl. Acad. Sci. USA 102, 6660 (2005). [3] M. Ceotto, S. Atahan, S. Shim, G.F. Tantardini, and A. Aspuru-Guzik, Phys. Chem. Chem. Phys. 11, 3861 (2009). [4] M. Ceotto, S. Atahan, G.F Tantardini, A. Aspuru-Guzik., J. Chem. Phys. 130, 234113 (2009). [5] M. Ceotto, D. Dell'Angelo, G.F Tantardini, J. Chem. Phys. 133 (5), 054701 (2010). [6] M. Ceotto, G.F. Tantardini, and A. Aspuru-Guzik, J. Chem. Phys. 135, 214108 (2011). [7] R. Conte, A. Aspuru-Guzik, M. Ceotto J. Phys. Chem. Lett., 4, 3407 (2013). [8] D. Tamascelli, F.S. Dambrosio, R. Conte, M. Ceotto J. Chem Phys., 140, 174109 (2014). [9] M.L. Brewer, J.S. Hulme, and D.E. Manolopoulos J. Chem. Phys. 106, 4832 (1997). [10] M.F. Herman, E. Kluk Chem. Phys. 91, 27 (1984). [11] K.G. Kay J. Chem. Phys. 101, 2250 (1994). [12] V. Guallar, V.S. Batista, and W.H. Miller J. Chem. Phys. 110, 9922 (1999). [13] R. Gelabert, X. Gimenez, M. Thoss, H. Wang, and W.H. Miller J. Phys. Chem. A, 104, 10321 (2000)