The kernel energy method (KEM) delivers fast and accurate QTAIM electrostatic charge for atoms in large molecules

Abstract

The kernel energy method (KEM) is a soft scaling fragment quantum chemical calculation method that proved very useful for the estimation of ab initio energies of very large biological molecules. In this approach, a large molecule is broken into computationally tractable pieces (kernels), which reduces the otherwise rapidly rising computational difficulty with the number of atoms. The formula which delivers the KEM approximation to the total molecular energy includes sums over the energies of double kernels corrected for over-counting by subtracting a sum over single kernels. KEM has been shown to deliver numerically accurate energies of unperturbed large molecules and the energies and dipole moments of large molecules under strong external perturbing electric fields. A recent study has also shown that the full molecular localization–delocalization matrix and the electron density at bond and ring critical point can also be reconstructed from formulae of the same form of the KEM master equation. It is shown that the KEM formula can also be used to reconstruct accurate approximations to the two-particle and one-particle reduced density matrices. This paper shows three numerical examples, of increasing complexity and size, that the atomic charge of an atom in a molecule, calculated from Bader’s quantum theory of atoms in molecules, is accurately predicted from the KEM formula. The error introduced by the KEM approximation is found to be smaller than 0.01 % of the total number of electrons as our calculations demonstrate on three interesting compounds that represent a variety of bonding situations: a highly explosive compound N,N′-dinitrourea (C3H6N4O5, 92 electrons), a strong chelating agent (pyridine-2-azo-p-phenyl)tetramethylguanidine (PAPT) (C16H20N6, 158 electrons), and the conformationally restricted synthetic peptide acetyl-Cα,α-dipropylglycine heptapeptide (Ac-Dpg-7) (C39H71N7O9, 426 electrons).