Comprehensive Analysis of the Neglect of Diatomic Differential Overlap Approximation

TL;DR

This paper provides a detailed analysis of the NDDO approximation used in semiempirical molecular orbital models, evaluating its errors and proposing correction strategies to improve accuracy in electron-electron interaction calculations.

Contribution

It offers a comprehensive comparison of ERIs in different bases and introduces a new correction method for errors caused by the NDDO approximation.

Findings

Errors in energy calculations grow linearly with basis set size

Different correction approaches can mitigate NDDO approximation errors

Proposed correction strategy improves the accuracy of two-electron matrices

Abstract

Many modern semiempirical molecular orbital models are built on the neglect of diatomic differential overlap (NDDO) approximation. An in-depth understanding of this approximation is therefore indispensable to rationalize the success of these semiempirical molecular orbital models and to develop further improvements on them. The NDDO approximation provides a recipe to approximate electron-electron repulsion integrals (ERIs) in a symmetrically orthogonalized basis based on a far smaller number of ERIs in a locally orthogonalized basis. We first analyze the NDDO approximation by comparing ERIs in both bases for a selection of molecules and for a selection of basis sets. We find that the errors in Hartree-Fock and second-order Moller-Plesset perturbation theory energies grow roughly linearly with the number of basis functions. We then examine different approaches to correct for the errors caused by the NDDO approximation and propose a strategy to directly correct for them in the two-electron matrices that enter the Fock operator.