PerturbativeTriples
Table of Contents
1. Brief description
Evaluates the (T) contribution.
2. Algorithm call
A typical input file snippet to call the PerturbativeTriples algorithm is given below.
- name: PerturbativeTriples in: coulombIntegrals: CoulombIntegrals amplitudes: Amplitudes slicedEigenEnergies: EigenEnergies mp2PairEnergies: Mp2PairEnergies out: {}
3. Algorithm input
| Keyword | Value |
|---|---|
amplitudes |
Singles and doubles amplitudes |
coulombIntegrals |
Coulomb Integrals |
slicedEigenEnergies |
Sliced one-electron energies |
mp2PairEnergies |
MP2 pair energies matrix |
4. Algorithm output
4.1. Sample stdout
Below an example standard output stream is shown for a successful PerturbativeTriples algorithm run.
step: 7, PerturbativeTriples Progress(%) time(s) GFLOP/s 1 0 4.187 10 0 5.657 20 0 5.789 30 0 5.919 40 0 5.916 50 0 5.938 60 0 5.913 70 0 5.877 80 0 5.850 90 0 5.857 100 0 5.845 (T) correlation energy: -0.822530510989498 realtime 2.592587863 s --
5. Sample yaml output
Below an example yaml output stream is shown for a successful PerturbativeTriples algorithm run.
floatingPointOperations: 11703705600 flops: 729564426.2969619 in: amplitudes: 0x24cd038 coulombIntegrals: 0x247f2b8 slicedEigenEnergies: 0x2487f38 name: PerturbativeTriples out: energy: correlation: -0.82253051098949848 unit: 0.036749322175638782 realtime: 2.592587863
6. Computational complexity
The computational cost is \(\mathcal{O}{(N_o^3 N_v^3(N_o+N_v))}\) with \(N_o\) and \(N_v\) being the number of occupied and virtual orbitals, respectively. The memory footprint is mainly determined by the storage of the PPPH-integral, which is of size \(\mathcal{O}{N_o N_v^3}\).
7. Theory
The implemented expressions of (T) correspond to those from Ref. (Raghavachari et al. 1989). For more details see Ref. (Bartlett and Musiał 2007) and references therin.
8. Reference implementation
In addition to the PerturbativeTriples algorithm, there is also a slower
reference implementation called PerturbativeTriplesReference which
is used in the same way as PerturbativeTriples.
To use it, you should just change the name PerturbativeTriples by PerturbativeTriplesReference.