Decoupling electrons and nuclei without the Born-Oppenheimer approximation: The electron-nucleus mean-field configuration-interaction method

The Born-Oppenheimer Approximation

where R is the set of nuclear coordinates and r is the set of electronic coordinates. If spin-orbit effects are important, they can be added through a spin-orbit operator Ĥso. Unfortunately, the V̂eN(r,R) term prevents us from separating Ĥ into nuclear and electronic parts, which would allow us to write the molecular wavefunction as a product of nuclear and electronic terms, Ψ(r,R) = Ψ(r)χ(R). W...

Cavity Born–Oppenheimer Approximation for Correlated Electron–Nuclear-Photon Systems

In this work, we illustrate the recently introduced concept of the cavity Born-Oppenheimer approximation [ Flick et al. PNAS 2017 , 10.1073/pnas.1615509114 ] for correlated electron-nuclear-photon problems in detail. We demonstrate how an expansion in terms of conditional electronic and photon-nuclear wave functions accurately describes eigenstates of strongly correlated light-matter systems. F...

The Time-dependent Born-oppenheimer Approximation

We explain why the conventional argument for deriving the time-dependent Born-Oppenheimer approximation is incomplete and review recent mathematical results, which clarify the situation and at the same time provide a systematic scheme for higher order corrections. We also present a new elementary derivation of the correct second-order time-dependent Born-Oppenheimer approximation and discuss as...

How good is the born-oppenheimer approximation?

Molecular scattering and Born-Oppenheimer approximation

In this paper, we study the scattering wave operators for a diatomic molecules by using the Born-Oppenheimer approximation. Assuming that the ratio h between the electronic and nuclear masses is small, we construct adiabatic wave operators that, under some non trapping conditions, approximate the two-cluster wave operators up to any powers of the parameter h.