Density functional theory of electron transfer beyond the Born-Oppenheimer approximation: Case study of LiF

Abstract

We perform model calculations for a stretched LiF molecule, demonstrating that nonadiabatic charge transfer effects can be accurately and seamlessly described within a density functional framework. In alkali halides like LiF, there is an abrupt change in the ground state electronic distribution due to an electron transfer at a critical bond length R = R, where an avoided crossing of the lowest adiabatic potential energy surfaces calls the validity of the Born-Oppenheimer approximation into doubt. Modeling the R-dependent electronic structure of LiF within a two-site Hubbard model, we find that nonadiabatic electron-nuclear coupling produces a sizable elongation of the critical R by 0.5 bohr. This effect is very accurately captured by a simple and rigorously derived correction, with an M prefactor, to the exchange-correlation potential in density functional theory, M = reduced nuclear mass. Since this nonadiabatic term depends on gradients of the nuclear wave function and conditional electronic density, ∇χ(R) and ∇n(r, R), it couples the Kohn-Sham equations at neighboring R points. Motivated by an observed localization of nonadiabatic effects in nuclear configuration space, we propose a local conditional density approximation-an approximation that reduces the search for nonadiabatic density functionals to the search for a single function y(n).

N‐centered ensemble density‐functional theory for open systems

“…It is often used as a lab for testing new ideas in DFT, gaining more insight into those and their approximate formulations. [14,44,[46][47][48][49][50][51][52][53] In this model, the ab initio HamiltonianĤ is simplified as follows:…”

Many-body Green's function theory of electrons and nuclei beyond the Born-Oppenheimer approximation

“…From Eqs. (52), (81), and (A5), it follows that T (1) cvr + T (2) cvr = −ih dr dr γ dz 2 (rz, r z ) ×G(r z , rz).…”

“…The zeroth-order approximations for the SEs c (1, 2) can be obtained by using the relations given by Eqs. (52) and (83). After the Hedin equations are solved, we calculate the nuclear SE, see for example Sec.…”

“…, given the nuclei are at R. Likewise, the standard Hohenberg-Kohn-Sham ground-state density functional theory is based on the conditional probability density n R (r 1 ) of finding an electron at r 1 , given the nuclei are at R. Using the framework of the exact factorization [48,49], a density functional framework beyond the BO limit has been developed [50][51][52][53] on the basis of the exact (rather than BO) conditional density. A Green's function approach based on the exact factorization has not been attempted so far.…”

Different flavors of nonadiabatic molecular dynamics

“…A question arises, as to whether one can employ the representation-free nature of the Exact Factorization for excited-state molecular dynamics without the support of quantum-chemistry calculations to determine electronic-structure properties. Recent works 25,26 have set the first basis for such a development.…”