Efficient representation of the linear density‐density response function

• Published in: Journal of computational chemistry Vol. 40; no. 31; pp. 2712 - 2721
• Main Authors: Dreßler, Christian, Scherrer, Arne, Ahlert, Paul, Sebastiani, Daniel
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 05.12.2019; Wiley Subscription Services, Inc
• Subjects: Computational chemistry; Density; density functional perturbation theory; density‐density response function; Eigenvectors; linear compact operator; Linear operators; molecular interaction; Organic chemistry; Perturbation; Representations; Response functions; Water chemistry; molecular interaction; linear compact operator; density functional perturbation theory; density-density response function
• ISSN: 0192-8651; 1096-987X; 1096-987X
• DOI: 10.1002/jcc.26046

We present a thorough derivation of the mathematical foundations of the representation of the molecular linear electronic density‐density response function in terms of a computationally highly efficient moment expansion. Our new representation avoids the necessities of computing and storing numerous eigenfunctions of the response kernel by means of a considerable dimensionality reduction about from 103 to 101. As the scheme is applicable to any compact, self‐adjoint, and positive definite linear operator, we present a general formulation, which can be transferred to other applications with little effort. We also present an explicit application, which illustrates the actual procedure for applying the moment expansion of the linear density‐density response function to a water molecule that is subject to a varying external perturbation potential. © 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc. The moment expansion of the linear density‐density response function allows a highly efficient calculation of molecular response densities due to arbitrary perturbing potentials. In this article, the authors put the moment expansion on a more solid mathematical fundament and generalize it to an entire class of linear operators. Furthermore, a protocol for the efficient calculation of the representation itself is stated.