We introduce a new theoretical and computational framework for treating molecular quantum mechanics without the Born–Oppenheimer approximation. The molecular wavefunction is represented in a tensor-product space of electronic and vibrational basis functions, with electronic basis chosen to reproduce the mean-field electronic structure at all geometries. We show how to transform the Hamiltonian to a fully second-quantized form with creation/annihilation operators for electronic and vibrational quantum particles, paving the way for polynomial-scaling approximations to the tensor-product space formalism. In addition, we make a proof-of-principle application of the new Ansatz to the vibronic spectrum of C2.
Sibaev, M., Polyak, I., Manby, F. R., & Knowles, P. J. (2020). Molecular second-quantized Hamiltonian: Electron correlation and non-adiabatic coupling treated on an equal footing. Journal of Chemical Physics, 153(12), . https://doi.org/10.1063/5.0018930