Normalization of the effective exchange hole in Becke's nondynamical correlation model: Closed-form analytic representation

An analytical approximation to the implicit 'x-function' appearing in a recent real-space model for non-dynamical correlation (A. D. Becke, J. Chem. Phys. 119 (2003) 2972) has been constructed as a continuous function sewed of three pieces. The ansatz avoids iterative techniques. The x-Function enters the expression of the so-called normalization of the effective exchange hole, which provides a measure of the importance of nondynamical correlation (NDC) effects at a given point in space. Our approximation has been evaluated in quantum-chemical calculations of several reaction energies. Differences between the results obtained with and without analytical approximation are very small and far below the 'chemical accuracy' threshold. The present analytical approximation to the x-function should aid future self-consistent implementations of the NDC model.