Nuclear velocity perturbation theory for vibrational circular dichroism: An approach based on the exact factorization of the electron-nuclear wave function

Abstract

The nuclear velocity perturbation theory (NVPT) for vibrational circular dichroism (VCD) is derived from the exact factorization of the electron-nuclear wave function. This new formalism offers an exact starting point to include correction terms to the Born-Oppenheimer (BO) form of the molecular wave function, similarly to the complete-adiabatic approximation. The corrections depend on a small parameter that, in a classical treatment of the nuclei, is identified as the nuclear velocity. Apart from proposing a rigorous basis for the NVPT, we show that the rotational strengths, related to the intensity of the VCD signal, contain a new contribution beyond-BO that can be evaluated with the NVPT and that only arises when the exact factorization approach is employed. Numerical results are presented for chiral and non-chiral systems to test the validity of the approach.

An exact factorization perspective on quantum interferences in nonadiabatic dynamics

“…When inserted into the molecular time-dependent Schrödinger equation, the Exact Factorization (EF) leads to coupled equations driving the dynamics of the two components of the wavefunction: a timedependent Schrödinger equation [39][40][41][42] describes the evolution a) Electronic address: agostini@mpi-halle.mpg.de of the nuclear wavefunction, where the effect of the electrons is fully accounted for by a time-dependent vector potential and a time-dependent scalar potential (or time-dependent potential energy surface, TDPES); electronic dynamics is generated by an evolution equation where the coupling to the nuclei is expressed by the so-called electron-nuclear coupling operator. [43][44][45][46][47] The EF has been developed both in the time-independent [48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64] and in the time-dependent [37][38][39][40][41][42][43][65][66][67][68] versions and analyzed under different perspectives. [44][45][46][47][69][70]…”

“…[43][44][45][46][47] The EF has been developed both in the time-independent [48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63][64] and in the time-dependent [37][38][39][40][41][42][43][65][66][67][68] versions and analyzed under different perspectives. [44][45][46][47][69][70][71][72] When nuclear dynamics undergoes a single nonadiabatic event, we have pointed out the properties of the TDPES and related them to the, more standard, picture provided in the BO framework, i.e., BO nuclear wavefunctions evolving on multiple static potential energy surfaces (PESs). In this situation, the TDPES shows (i) a diabatic shape in the vicinity of an avoided crossing, smoothly connecting the BO PESs involved in the process, and (ii) dynamical steps bridging piecewise adiabatic shapes, far from the avoided crossing.…”

The adiabatic limit of the exact factorization of the electron-nuclear wave function

“…[8][9][10][11][12][13] For similar reasons, the vibrational circular dichroism computed within the BOA requires corrections [14][15][16][17] to yield agreement with experimental measurements. Various approaches 5,6,11,12,15,[17][18][19][20] have been proposed to cure these inconsistencies perturbatively. In this paper we further develop this idea by focusing on the following questions: Is there a procedure to systematically identify corrections to the BOA?…”

“…In order to express Hamiltonian (15) in the new units, we have to derive the values of fundamental constants c and in our unit system, c = c…”

“…The dependence on the electron-nuclear mass ratio is shown analytically to be µ − 1 2 . Several numerical schemes have been proposed 12,14,15,17,30,[41][42][43][44][45][46] which consider only non-adiabatic effects induced by the dependence of electronic motion on the nuclear momentum. Higher order terms 38 are usually discarded.…”