Derivations

Symmetry-Adapted Perturbation Theory: SAPT0

I completely derived all current equations for SAPT0, including:

• first-order exchange energy in the S2 approximation in both the density matrix and second quantization formalisms
• exact first-order exchange energy
• second-order induction with uncoupled and coupled amplitudes
• exchange-induction in both the density matrix and second quantization formalisms
• dispersion with uncoupled amplitudes (coupled amplitude formula is only briefly presented)
• exchange-dispersion in the second-quantized formalism

In all cases I present the most efficient formulae in a form directly usable for implementation. Most of the time this includes the MO and the AO formulae. Refactorization of the dispersion term using density fitting is also presented.

All equations are those implemented in the software Psi4 and were verified for correctness. If you find a mistake, please e-mail me on j [dot] gonthier01 at [Google's e-mail service].

Here is the document. It's still a draft so the formatting is not pretty. Chapter 1 contains all formulae, chapter 2 detailed (very detailed) derivations.