Analytic Gradients for Density Fitting MP2 Using Natural Auxiliary Functions

The natural auxiliary function (NAF) approach is an approximation
to decrease the size of the auxiliary basis set required for quantum
chemical calculations utilizing the density fitting technique. It
has been proven efficient to speed up various correlation models,
such as second-order Møller–Plesset (MP2) theory and coupled-cluster
methods. Here, for the first time, we discuss the theory of analytic
derivatives for correlation methods employing the NAF approximation
on the example of MP2. A detailed algorithm for the gradient calculation
with the NAF approximation is proposed in the framework of the method
of Lagrange multipliers. To assess the effect of the NAF approximation
on gradients and optimized geometric parameters, a series of benchmark
calculations on small and medium-sized systems was performed. Our
results demonstrate that, for MP2, sufficiently accurate gradients
and geometries can be achieved with a moderate time reduction of 15–20%
for both small and medium-sized molecules.