Reply to Comment on "Efficient implementation of the superposition of atomic potentials initial guess for electronic structure calculations in Gaussian basis sets"

Abstract

We reply to the Comment by Surjuse, Deng, Asadchev, and Valeev [arXiv:2603.16989] on our article "Efficient implementation of the superposition of atomic potentials initial guess for electronic structure calculations in Gaussian basis sets" [J. Chem. Phys. 152, 144105 (2020)]. We do not disagree with their work, but point out that they appear to have misinterpreted a statement in our original abstract: our suggestion to evaluate the matrix elements of the superposition of atomic potentials (SAP) using two-electron integral code was made on grounds of portability rather than as a recommendation against a dedicated one-electron implementation. Such an implementation is in fact already available in existing codes - in Dirac, for example, where a Gaussian SAP potential is formally indistinguishable from a Gaussian finite-nucleus model at the level of the nuclear attraction integral routine. We further note that both routes reduce to the same three-Gaussian overlap kernel through the Obara-Saika Laplace transform, and that SAP itself enjoys a rigorous theoretical justification through Theophilou's theorem on spherical densities and its extensions by Nagy.