Generalization of the electronic susceptibility for arbitrary molecular geometries

Abstract

We generalize the explicit representation of the electronic susceptibility χ[R](r, r') for arbitrary molecular geometries R. The electronic susceptibility is a response function that yields the response of the molecular electronic charge density at linear order to an arbitrary external perturbation. We address the dependence of this response function on the molecular geometry. The explicit representation of the molecular geometry dependence is achieved by means of a Taylor expansion in the nuclear coordinates. Our approach relies on a recently developed low-rank representation of the response function χ[R](r, r') which allows a highly condensed storage of the expansion and an efficient application within dynamical chemical environments. We illustrate the performance and accuracy of our scheme by computing the vibrationally induced variations of the response function of a water molecule and its resulting Raman spectrum.

Reduced eigensystem representation of the linear density‐density response function

“…The regular eigensystem representation as well as theorem 1 and 3 were recently published by our group. [29,30,[47][48][49][50] In particular, we generalized these theorems to arbitrary linear, self-adjoint, positive-definite, and compact operators. [50] Within this article, we derived the reduced eigensystem representation as a completion of our development effort toward an efficient representation combined with an efficient determination of the static linear density-density response function.…”

“…Scherrer already demonstrated the use of the for the efficient calculation of the response density of a water molecule disturbed by neighboring water molecules . Also the dependency of the on geometric distortions was investigated for the application of the linear density‐density response function toward molecular dynamics simulations . The principal applicability for the calculation of Raman spectra resulting from a post processed ab inito molecular dynamics trajectory was demonstrated …”

“…Also the dependency of the on geometric distortions was investigated for the application of the linear density‐density response function toward molecular dynamics simulations . The principal applicability for the calculation of Raman spectra resulting from a post processed ab inito molecular dynamics trajectory was demonstrated …”

“…[47] Also the dependency of the ξ m l j l∈N, m∈ −l, …, l f g È É on geometric distortions was investigated for the application of the linear density-density response function toward molecular dynamics simulations. [48] The principal applicability for the calculation of Raman spectra resulting from a post processed ab inito molecular dynamics trajectory was demonstrated. [48] The transformation of the eigenstates into the ξ m l j l∈N, m∈ − l,…, l f g È É is algorithmically involved and takes place by iterative Givens rotations of thousands of eigenstates.…”

“…[48] The principal applicability for the calculation of Raman spectra resulting from a post processed ab inito molecular dynamics trajectory was demonstrated. [48] The transformation of the eigenstates into the ξ m l j l∈N, m∈ − l,…, l f g È É is algorithmically involved and takes place by iterative Givens rotations of thousands of eigenstates. The calculation of eigenstates (without transformations) requires an ab initio perturbation calculation per eigenstate.…”