Abstract
We propose a methodology to unify electronic and nuclear quantum wavepacket dynamics in molecular processes including nonadiabatic chemical reactions. The canonical and traditional approach in the full quantum treatment both for electrons and nuclei rests on the Born–Oppenheimer fixed nuclei strategy, the total wavefunction of which is described in terms of the Born–Huang expansion. This approach is already realized numerically but only for small molecules with several number of coupled electronic states for extremely hard technical reasons. Besides, the stationary-state view of the relevant electronic states based on the Born–Oppenheimer approximation is not always realistic in tracking real-time electron dynamics in attosecond scale. We therefore incorporate nuclear wavepacket dynamics into the scheme of nonadiabatic electron wavepacket theory, which we have been studying for a long time. In this scheme thus far, electron wavepackets are quantum mechanically propagated in time along nuclear paths that can naturally bifurcate due to nonadiabatic interactions. The nuclear paths are in turn generated simultaneously by the so-called matrix force given by the electronic states involved, the off-diagonal elements of which represent the force arising from nonadiabatic interactions. Here we advance so that the nuclear wavepackets are directly taken into account in place of path (trajectory) approximation. The nuclear wavefunctions are represented in terms of the Cartesian Gaussians multiplied by plane waves, which allows for feasible calculations of atomic and molecular integrals together with the electronic counterparts in a unified manner. The Schrödinger dynamics of the simultaneous electronic and nuclear wavepackets are to be integrated by means of the dual least action principle of quantum mechanics [K. Takatsuka, J. Phys. Commun. 4, 035007 (2020)], which is a time-dependent variational principle. Great contributions of Vincent McKoy in the electron dynamics in the fixed nuclei approximation and development in time-resolved photoelectron spectroscopy are briefly outlined as a guide to the present work.
Highlights
We propose a methodology to unify electronic and nuclear quantum wavepacket dynamics in molecular processes including nonadiabatic chemical reactions
Vincent McKoy was a pioneer and had been the central figure in these fields. Another interesting feature of the BO approximation is that it is valid even for fast nuclear wavepacket dynamics, in the time scale of as fast as femtoseconds. It had been predicted by Domcke [19], Engel[20], and their coworkers that such nuclear wavepacket dynamics can be observed with time-resolved photoelectron spectroscopy (TRPES)
The present paper aims at a full quantum mechanical construction of electronic and nuclear wavepackets beyond the Born–Huang representation, yet with a deep appreciation of the great heritage and methodologies that have been developed in the long history of quantum chemistry
Summary
Theoretical foundation of molecular science was established far long ago in 1927 by Born and Oppenheimer [9], shortly after the birth of quantum mechanics, and is later followed by the so-called Born– Huang expansion [10] to describe a total electronicnuclear molecular wavefunction This view naturally brought about the Born–Oppenheimer (BO) approximation, or fixed nuclei approximation, in which nuclei are supposed to undergo their dynamics on stationary electronic state energy hypersurfaces (potential energy hypersurfaces abbreviated as PES) [11,12,13,14,15,16]. We have been developing a theory of such nonadiabatic electron dynamics, in which electron wavepackets propagate in time along simultaneously generated nuclear “paths” [1,2,3,4,5,6,7] These paths can naturally and smoothly branch into pieces at each significant nonadiabatic transition region as many as the number of adiabatic potential energy surfaces that commit the nonadiabatic avoided crossings and conical intersections.
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