Coherent states, quantum gravity, and the Born-Oppenheimer approximation. I. General considerations

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...

Beyond the Born-Oppenheimer approximation with quantum Monte Carlo

In this work we develop tools that enable the study of non-adiabatic effects with variational and diffusion Monte Carlo methods. We introduce a highly accurate wave function ansatz for electronion systems that can involve a combination of both fixed and quantum ions. We explicitly calculate the ground state energies of H2, LiH, H2O and FHF − using fixed-node quantum Monte Carlo with wave functi...

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.

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?