Exact Results in Quantum Theory

Obtaining highly accurate energies of molecular systems requires a well-optimized set of basis functions. The commonly used explicitly correlated Gaussian (ECG) functions, despite the simplicity of integration algorithms, exhibit slow convergence and expectation values for some singular operators can converge to incorrect limit. In this talk I will present the techniques allowing the use of a much better class of functions for hydrogen molecule calculations: an explicitly correlated exponential basis. So far these functions were rarely used due to cumbersome integrals that arise during calculations. The algorithm for evaluation of these integrals via Taylor series, which is stable for all possible values of variational parameters, will be presented, together with a benchmark of nonrelativistic Born-Oppenheimer H2 energies.