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

Variational Lang-Firsov approach plus M\o{}ller-Plesset perturbation theory with applications to ab initio polariton chemistry