A wave function perspective and efficient truncation of renormalised second-order perturbation theory

Abstract: We present an approach to renormalized second-order Green's function perturbation theory (GF2) which avoids all dependency on continuous variables, grids or explicit Green's functions, and is instead formulated entirely in terms of static quantities and wave functions. Correlation effects from MP2 diagrams are iteratively incorporated to modify the underlying spectrum of excitations by coupling the physical system to fictitious auxiliary degrees of freedom, allowing for the single-particle orbitals to delocalize into this additional space. The overall approach is shown to be rigorously $\mathcal{O}[N^5]$, after an appropriate compression of this auxiliary space. This is achieved via a novel scheme which ensures that a desired number of moments of the underlying occupied and virtual spectra are conserved in the compression, allowing a rapid and systematically improvable convergence to the limit of the effective dynamical resolution. The approach is found to then allow for the qualitative description of stronger correlation effects, avoiding the divergences of MP2, as well as its orbital-optimized version. On application to the G1 test set, we find that modifications to only up to the third spectral moment of the underlying spectrum from which the double excitations are built is required for accurate energetics, even in strongly correlated regimes. This is beyond simple self-consistent changes to the density matrix of the system, but far from requiring a description of the full dynamics of the frequency-dependent self-energy.