O'Reilly logo

Electronic Structure by Richard M. Martin

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

Appendix C

Adiabatic approximation

 

Summary

The only small parameter in the electronic structure problem is the inverse nuclear mass 1/M, i.e. the nuclear kinetic energy terms. The adiabatic or Born-Oppenheimer approximation is a systematic expansion in the small parameter that is fundamental to all electronic structure theory. It comes to the fore in the theory of phonons, electron-phonon interactions, and superconductivity (Ch. 19).

C.1 General formulation

The fundamental hamiltonian for a system of nuclei and electrons, Eq. (3.1), can be written

image

(C.1)

where U contains all the potential interaction terms involving the set of all-electron ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required