Shortcomings in computational chemistry

Abstract

ABSTRACT:The purpose of the paper is to point out some weaknesses in computational chemistry. The weaknesses we list arise from issues that are not properly solved and that can either stand on the pure numerical domain or go back to difficulties already present at the modeling stage, or even stem from fundamental open questions in theoretical chemistry itself. To name just a few, the domain decomposition method used in (QM/MM) calculations, the definition of effective core potentials (ECP) or the foundations of various stationary Schrö dinger approximations, such as SCF or MCSCF theories or density functional-type methods are examined.

Theoretical methods for small-molecule ro-vibrational spectroscopy

“…The rigorous mathematical study of the Hartree-Fock method, and indeed of all quantum chemical methods, is difficult and has received comparatively little attention as most research in the field is based on numerical experimentation and not on rigorous proofs [127][128][129][142][143][144][145]. For example, the proof that the Hartree-Fock equations for a molecule admit a ground-state solution for neutral or positively charged systems was given by Lieb and Simon only in 1977 [127,128], some 30 years after such solutions were found numerically.…”

The Use of Kriging Within the SCF Procedure

“…However, as Le Bris and coworkers [14] mention, it can still take a high number of iterations before convergence is reached which subsequently consumes a lot of memory. They also stress the need for understanding, that this is a purely ad hoc type of procedure driven by the desire for faster convergence which is still not rigorously mathematically explainable.…”