O'Reilly logo

Propagators in Quantum Chemistry, 2nd Edition by Yngve Öhrn, Jan Linderberg

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

Chapter 4

Double-Time Green’s Functions

The proper electron interaction hamiltonian is

Image

with

Image

This hamiltonian is correct because it gives the correct expectation values. The average value with respect to a two-electron state is Imagekl\Hint\klImage = (kk\ll) – (kl\lk) exactly as the result (coulomb minus exchange) of calculating the average of 1/|Image1Image2| with respect to a two-electron Slater determinant with the spin orbitals uk and ul in “first-quantization”. The full electronic hamiltonian can be expressed as

Image

It is common to use an alternative notation for the electron-electron interaction integrals Imagerr|ss = (rs|r s), i.e., with the complex conjugate spin orbitals, belonging to the a operators, ...

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