# PerturbativeTriples

## 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

Table 1: Input keywords for PerturbativeTriples
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.

## 9.Literature

Bartlett, R.J., and Monika Musiał. 2007. “Coupled-cluster theory in quantum chemistry.” Rev. Mod. Phys. 79 (1): 291–352. doi:10.1103/RevModPhys.79.291.
Raghavachari, Krishnan, Gary W. Trucks, John A. Pople, and Martin Head-Gordon. 1989. “A Fifth-Order Perturbation Comparison of Electron Correlation Theories.” Chemical Physics Letters 157 (6): 479–83. doi:https://doi.org/10.1016/S0009-2614(89)87395-6.

Created: 2023-03-16 Thu 10:59