The time-dependent Born-Oppenheimer approximation

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...

On the Time-dependent Born-oppenheimer Approximation with Smooth Potential

We give a general reduction scheme for the study of the quantum propagator of molecular Schrr odinger operators with smooth potentials. This reduction is made up to innnitely (resp. exponentially) small error terms with respect to the inverse square root of the mass of the nuclei, depending on the C 1 (resp. analytic) smoothness of the interactions. Then we apply this result to the case when an...

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...

How good is the born-oppenheimer approximation?

Born-oppenheimer approximation near level crossing

We consider the Born-Oppenheimer problem near conical intersection in two dimensions. For energies close to the crossing energy we describe the wave function near an isotropic crossing and show that it is related to generalized hypergeometric functions 0F3. This function is to a conical intersection what the Airy function is to a classical turning point. As an application we calculate the anoma...