Exact Wigner Function Evaluation for Different Basis Sets

Abstract

In this work we present closed-form expressions for different types of Gaussian integrals that occur when evaluating the Winger function in a given basis. Wigner function represents a phase space distribution function from which positions and momentum can be, for example, sampled as initial conditions in molecular dynamics simulations. We focus on the harmonic oscillator basis and demonstrate the evaluation of the Wigner function. We also present results for the distributed Gaussian basis. Our results allows us to circumvents numerical evaluation and any imprecision associated to the procedure. Furthermore, our contribution is relevant beyond the scope of applications in quantum chemistry.

Jovan Odavić

Postdoctoral researcher