Higher order alchemical derivatives from coupled perturbed self-consistent field theory

Abstract

We present an analytical approach to treat higher order derivatives of Hartree-Fock (HF) and Kohn-Sham (KS) density functional theory energy in the Born-Oppenheimer approximation with respect to the nuclear charge distribution (so-called alchemical derivatives). Modified coupled perturbed self-consistent field theory is used to calculate molecular systems response to the applied perturbation. Working equations for the second and the third derivatives of HF/KS energy are derived. Similarly, analytical forms of the first and second derivatives of orbital energies are reported. The second derivative of Kohn-Sham energy and up to the third derivative of Hartree-Fock energy with respect to the nuclear charge distribution were calculated. Some issues of practical calculations, in particular the dependence of the basis set and Becke weighting functions on the perturbation, are considered. For selected series of isoelectronic molecules values of available alchemical derivatives were computed and Taylor series expansion was used to predict energies of the "surrounding" molecules. Predicted values of energies are in unexpectedly good agreement with the ones computed using HF/KS methods. Presented method allows one to predict orbital energies with the error less than 1% or even smaller for valence orbitals.

Exploring chemical space with alchemical derivatives: alchemical transformations of H through Ar and their ions as a proof of concept

“…20. In this method, energy derivatives with respect to nuclear charges are playing a fundamental role. These "Alchemical Derivatives" 21,22 were shown by some of the present authors to find a natural place in the context of Conceptual Density Functional Theory (CDFT) 23,24 where the   , Ev N functional plays a central role. The energy of an atom, molecule is thereby written as a functional of the number of electrons N and the external potential   v r .…”

First principles view on chemical compound space: Gaining rigorous atomistic control of molecular properties

“…Nevertheless, based on coupled perturbed selfconsistent field theory, the improved accuracy of higher order predictions has been demonstrated very recently. [49] Other applications Instead of varying the proton distribution n p ðrÞ ¼ P I Z I dðjr À R I jÞ in a compound, we can interpolate the external potential vðrÞ ¼ P I Z I =jr À R I j just as well. Albeit mixing up spatial and compositional degrees of freedom, this is more in line with conventional thought in quantum chemistry and conceptual DFT [15] where the nuclear charge distribution is hardly ever mentioned explicitly.…”

New Insights and Horizons from the Linear Response Function in Conceptual DFT

“…Some years ago, one of the present authors (R.B.) presented a strategy to calculate these derivatives for any atom or atom-atom combination analytically and to use them, starting from a single SCF calculation on the parent or reference molecule, to explore the CCS of first neighbours, implying changes of nuclear charges of +1 or À1 [65]. In this way, simple arithmetic can be used, starting from a Taylor expansion…”