Molecular geometric phase from the exact electron-nuclear factorization

Abstract

The Born-Oppenheimer electronic wavefunction Φ BO R (r) picks up a topological phase factor ±1, a special case of Berry phase, when it is transported around a conical intersection of two adiabatic potential energy surfaces in R-space. We show that this topological quantity reverts to a geometric quantity e iγ if the geometric phase γ = Im ΦR|∇µΦR · dRµ is evaluated with the conditional electronic wavefunction ΦR(r) from the exact electron-nuclear factorization ΦR(r)χ(R) instead of the adiabatic function Φ BO R (r). A model of a pseudorotating molecule, also applicable to dynamical Jahn-Teller ions in bulk crystals, provides the first examples of induced vector potentials and molecular geometric phase from the exact factorization. The induced vector potential gives a contribution to the circulating nuclear current which cannot be removed by a gauge transformation. The exact potential energy surface is calculated and found to contain a term depending on the Fubini-Study metric for the conditional electronic wavefunction.

An exact factorization perspective on quantum interferences in nonadiabatic dynamics

“…41,59,64 When a nuclear wavefunction evolves solely in a given electronic state, the corresponding TDPES resembles its adiabatic BO surface (continuous curve, right panel of Fig. 1).…”

“…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]…”

Asymptotic analysis of the Berry curvature in theE⊗eJahn-Teller model

“…(1) by the conditional electronic wave function Φ R (r) = Ψ(r, R)/χ(R) derived within the exact factorization scheme, where χ(R) = e iS(R) |Ψ(r, R)| 2 dr 1/2 is the nuclear wave function with arbitrary phase S(R) [25,27,29,30]. Calculations for a model pseudorotating triatomic molecule found that the exact geometric phase deviates from the LonguetHiggins phase of π due to nonadiabatic effects near the conical intersection of the adiabatic potential energy surfaces [27]. To understand these deviations, we write the molecular geometric phase as a surface integral over the exact Berry curvature…”

“…Evidence for the dynamical Jahn-Teller effect in the excited states of the nitrogen-vacancy center in diamond has been reported [14][15][16][17][18], making the Longuet-Higgins phase rele- * Electronic address: rrequist@mpi-halle.mpg.de vant to its optical properties. Recent theoretical work has explored the sign change in the bound states of small molecules by ab initio and model calculations [19][20][21][22][23][24][25][26][27].…”

Spooky correlations and unusual van der Waals forces between gapless and near-gapless molecules

“…If the molecules pass near the high-symmetry, electronically degenerate states sufficienly often during these combined motions, an appreciable weight of D −3 vdW interaction should be observable. The analysis in [24] and in the recent work of Requist, Tandetzky and Gross [33] may be useful in analyzing this situation.…”