Limited Resurrection of the Born Approximation

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...

Time Domain Born Approximation

The time domain Born approximation for ultrasonic scattering from volume flaws in an elastic medium is described. Results are given both for the direct and the inverse problem. The time domain picture leads to simple intuitive formulas which we illustrate by means of several simple examples. Particular emphasis is given to the front surface echo and its use in reconstructing the properties of t...

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?

Effective Born radii in the generalized Born approximation: The importance of being perfect

Generalized Born (GB) models provide, for many applications, an accurate and computationally facile estimate of the electrostatic contribution to aqueous solvation. The GB models involve two main types of approximations relative to the Poisson equation (PE) theory on which they are based. First, the self-energy contributions of individual atoms are estimated and expressed as "effective Born rad...