The tensor properties of energy gradients within a non-orthogonal basis

The application of standard minimization techniques to electronic structure theory calculations often requires the formation of an electronic energy gradient. The tensor nature of the electronic gradient, while implicitly treated within an orthogonal basis set, manifests itself explicitly in a non-orthogonal basis set. We apply simple tensor theory to define the electronic gradient in an arbitrary reference frame using the energy minimization method of Li, Nunes and Vanderbilt in a non-orthogonal basis as a concrete example. The minimal basis HeH+ energy surface is used to portray the strong effect of consistently accounting for these tensor properties versus neglecting them.