MP2-F12(3C)

The explicitly correlated approach is one of the most important breakthroughs in ab initio electronic structure theory and broadly used to speed up convergence of electron correlation energy with respect to the basis set size.

The MP2-F12 method is implemented as the sum of the MP2 correlation energy in the orbital basis set (OBS) and the F12 correction:

Included Reference Implementations

• mp2f12FixedAnsatz.py: Explicitly correlated second-order Moller-Plesset Perturbation Theory (MP2-F12(3C)) with Ten-no's diagonal fixed-amplitude Ansatz
• mp2f12SpinOrbital :Explicitly correlated second-order Moller-Plesset Perturbation Theory (MP2-F12(3C)) with fully optimized amplitudes

The first code calculates the F12 correction expressed as:

with the intermediate matrix elements defined as:

and amplitudes:

In the second code the F12 correction is impemented as a sum of each electron pairs (i,j) correlation energy which are expressed as:

,

where

,

.

Indices used:

• i, j, ... - occupied orbitals
• a, b, ... - virtual orbitals
• p, q, ... - all molecular orbitals (OBS)
• x, y, ... - CABS orbitals

REFERENCES

1. H.-J. Werner, T. B. Adler, and F. R. Manby, J. Chem. Phys. 126, 164102 (2007)
2. S. Yoo Willow, J. Zhang, E. F. Valeev, and S. Hirata, J. Chem. Phys. 140, 031101 (2014)