Quantum nuclear densities from semiclassical on-the-fly molecular dynamics

Semiclassical molecular dynamics is a rigorous approximation to quantum dynamics obtained from the exact quantum propagator expressed as Feynman’s path integral.[1] Recently, our group has introduced the Multiple Coherent Semiclassical Initial Value Representation (MC SCIVR) technique to reduce the number of classical trajectories required to converge vibrational spectra calculations from thousands to just a handful.[2-4] MC SCIVR has been applied successfully to several medium- and large-size molecular systems,[4-10] including fluxional and condensed phase ones.[11-13] In addition to the accurate anharmonic vibrational eigenvalue calculations, MC SCIVR yields vibrational eigenfunctions for both the ground and excited vibrational states.[14] In this talk, I will survey how we obtain the quantum anharmonic vibrational eigenfunctions from ab-initio on-the-fly trajectory simulations and how we extract the quantum nuclear densities and the geometry parameters probability distributions.[15,16] This information allows us to assign each peak in vibrational spectra, going beyond the usual harmonic normal-mode analysis. Our technique quantitatively determines how normal modes involving different functional groups cooperate to originate the spectroscopic signal. Furthermore, it allows for the visualization of the nuclear vibrations in a purely quantum picture, letting us both directly observe and quantify the effects of the full potential energy surface anharmonicity on the molecular structure. In particular, I will illustrate applications to the protonated glycine to reveal quantum mechanical and anharmonic vibrational features. The method will allow for a better rationalization of experimental spectroscopy. [1] W.H. Miller, J. Phys. Chem. A 2001, 105, 2942. [2] M. Ceotto, S. Atahan, S. Shim, G.F. Tantardini, A. Aspuru-Guzik, Phys. Chem. Chem. Phys. 2009, 11, 3861. [3] M. Ceotto, S. Atahan, G.F. Tantardini, A. Aspuru-Guzik J. Chem. Phys. 2009, 130, 234113. [4] R. Conte, M. Ceotto, In Quantum Chemistry and Dynamics of Excited States: Methods and Applications (eds L. González and R. Lindh) 2020. [5] M. Ceotto, G. Di Liberto, R. Conte, Phys. Rev. Lett. 2017, 119, 010401. [6] F. Gabas, R. Conte, M. Ceotto, J. Chem. Theory Comput. 2017, 13, 2378. [7] G. Di Liberto, R. Conte, M. Ceotto, J. Chem. Phys. 2018, 148, 014307. [8] F. Gabas, G. Di Liberto, R. Conte, M. Ceotto, Chem. Sci. 2018, 9, 7894. [9] F. Gabas, G. Di Liberto, M. Ceotto, J. Chem. Phys. 2019, 150, 224107. [10] F. Gabas, R. Conte, M. Ceotto, J. Chem. Theory Comput. 2020, 16, 3476. [11] G. Bertaina, G. Di Liberto, M. Ceotto, J. Chem. Phys. 2019, 151, 114307. [12] A. Rognoni, R. Conte, M. Ceotto, Chem. Sci., 2021, 12, 2060. [13] M. Cazzaniga, M. Micciarelli, F. Moriggi, A. Mahmoud, F. Gabas, and M. Ceotto, J. Chem. Phys. 2020, 152, 104104. [14] M. Micciarelli, R. Conte, J. Suarez, M. Ceotto, J. Chem. Phys. 2018 149, 064115. [15] C. Aieta, M. Micciarelli, G. Bertaina, M. Ceotto, Nat. Commun 2020, 11, 1. [16] C. Aieta, M. Micciarelli, G. Bertaina, M. Ceotto, J. Chem. Phys., 2020, 153, 214117