Towards an accurate Kohn-Sham Density Functional Theory Molecular Energy Decomposition scheme

Abstract

The most important result of a quantum chemical calculation is the total energy of the molecular system. However, being a single number, it provides little immediate chemical information. Energy decomposition schemes provide additional chemical information by decomposing the total energy of a molecular system into the sum of atomic and diatomic contributions. In this work we have implemented in the program APOST3D the Kohn-Sham Density Functional Theory (KS-DFT) energy partitioning for open-shell system for a number of pure and hybrid DFT functionals. This has permitted to study in some detail some polyradical systems, but most importantly it will allow us in the future to apply the methodology to transition metal complexes. The KS-DFT energy decomposition differs from the well-established Hartree-Fock (HF) one on the exchange-correlation term. Within DFT these contributions are obtained solely from one-electron integrations, whereas in HF they originate from two-electron ones. The extremely good correlations we have obtained for a set of molecules between both schemes provides the opportunity to calculate hybrid KS-DFT exchange energies or even the exact HF ones from pure KS-DFT exchange expressions, thus dramatically reducing the computational cost. Finally, one of the technical problems of these energy decomposition schemes is the evaluation of the necessary 6D numerical integrations, basically because of their large integration error associated. In this work, an improvement of the numerical integration method for the two-electron one-center numerical integration has been developed, based on the double rotation of a second set of integration grid points. The new scheme has been implemented first using a simple model, and then into the APOST3D program. The results obtained are promising, but further studies using a more diverse set of molecules including transition metal complexes are required