Variational Lang–Firsov Approach Plus Møller–Plesset Perturbation Theory with Applications to Ab Initio Polariton Chemistry

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 applied 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 (H2, 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 that by exact diagonalization or coupled-cluster theory. The effects of multiple photon modes, spin polarization, and the comparison to the coherent state MP theory are also discussed.