General biorthogonal projected bases as applied to second-order Møller-Plesset perturbation theory

With low-order scaling correlated wave function theories in mind, we present second quantization formalism as well as biorthonormalization procedures for general--singular or nonsingular--bases. Of particular interest are the so-called projected atomic orbital bases, which are obtained from a set of atom-centered functions and feature a separation of occupied and virtual spaces. We demonstrate the formalism by deriving and implementing second-order Møller-Plesset perturbation theory in it, and discuss the convergence and preconditioning of the iterative amplitude equations in detail.