Second-order many-body perturbation theory: an eternal frontier.

Second-order many-body perturbation theory [MBPT(2)] is the lowest-ranked member of a systematic series of approximations convergent at the exact solutions of the Schrödinger equations. It has served and continues to serve as the testing ground for new approximations, algorithms, and even theories. This article introduces this basic theory from a variety of viewpoints including the Rayleigh-Schrödinger perturbation theory, the many-body Green's function theory based on the Dyson equation, and the related Feynman-Goldstone diagrams. It also explains the important properties of MBPT(2) such as size consistency, its ability to describe dispersion interactions, and divergence in metals. On this basis, this article surveys three major advances made recently by the authors to this theory. They are a finite-temperature extension of MBPT(2) and the resolution of the Kohn-Luttinger conundrum, a stochastic evaluation of the correlation and self-energies of MBPT(2) using the Monte Carlo integration of their Laplace-transformed expressions, and an extension to anharmonic vibrational zero-point energies and transition frequencies based on the Dyson equation.

Solvent induced shifts in the UV spectrum of amides.

Solvent effects on the electronic spectra of formamide and trans-N-methylacetamide are studied using four different levels of theory: singly excited configuration interaction (CIS), equations of motion coupled-cluster theory with singles and doubles (EOM-CCSD), completely renormalized coupled-cluster theory with singles and doubles with perturbative triple excitations (CR-EOM-CCSD(T)), and time-dependent density functional theory (TDDFT), employing small clusters of water molecules. The simulated electronic spectrum is obtained via molecular dynamics simulations with 100 waters modeled with the effective fragment potential method and exhibits a blue-shift and red-shift, respectively, for the n → π* and πnb → π* vertical excitation energies, in good agreement with the experimental electronic spectra of amides.

Solvent-induced shift of the lowest singlet π → π* charge-transfer excited state of p-nitroaniline in water: an application of the TDDFT/EFP1 method.

The combined time-dependent density functional theory effective fragment potential method (TDDFT/EFP1) is applied to a study of the solvent-induced shift of the lowest singlet π → π* charge-transfer excited state of p-nitroaniline (pNA) from the gas to the condensed phase in water. Molecular dynamics simulations of pNA with 150 EFP1 water molecules are used to model the condensed-phase and generate a simulated spectrum of the lowest singlet charge-transfer excitation. The TDDFT/EFP1 method successfully reproduces the experimental condensed-phase π → π* vertical excitation energy and solvent-induced red shift of pNA in water. The largest contribution to the red shift comes from Coulomb interactions, between pNA and water, and solute relaxation. The solvent shift contributions reflect the increase in zwitterionic character of pNA upon solvation.