Variational Lang-Firsov approach plus Møller-Plesset perturbation theory with applications to ab initio polariton chemistry

Abstract

We apply the Lang-Firsov (LF) transformation to electron-boson coupled Hamiltonians and variationally optimize the transformation parameters and molecular orbital coefficients to determine the ground state. Møller-Plesset (MP-$n$, with $n=2$ and $4$) perturbation theory is then performed on top of the optimized LF mean-field state to improve the description of electron-electron and electron-boson correlations. The method (LF-MP) is applied to several electron-boson coupled systems, including the Hubbard-Holstein model, diatomic molecule dissociation (${\text{H}}_2$, $\text{HF}$), and the modification of proton transfer reactions (malonaldehyde and aminopropenal) via the formation of polaritons in an optical cavity. We show that with a correction for the electron-electron correlation, the method gives quantitatively accurate energies comparable to exact diagonalization or coupled-cluster theory. The effect of multiple photon modes, spin polarization, and the comparison to the coherent state MP theory are also discussed.

16 pages, 8 figures