# BasisSetCorrection

## 1.Brief description

This algorithm evaluates a correction to the basis-set-incompeteness error (BSIE) of CCSD correlation energies.

## 2.Algorithm call

A typical input file snippet to call the `BasisSetCorrection` algorithm is given below.

```- name: BasisSetCorrection
in:
slicedEigenEnergies: EigenEnergies
amplitudes: Amplitudes
coulombIntegrals: CoulombIntegrals
mp2PairEnergies: Mp2PairEnergies
deltaIntegralsHH: DeltaIntegralsHH
deltaIntegralsPPHH: DeltaIntegralsPPHH
out:
{}
```

## 3.Algorithm input

Table 1: Input keywords
Keyword Value
`amplitudes` Singles and doubles amplitudes
`deltaIntegralsPPHH` DeltaIntegrals
`deltaIntegralsHH` DeltaIntegrals
`mp2PairEnergiese` MP2 pair energies matrix
`coulombIntegrals` Coulomb Integrals
`slicedEigenEnergies` Sliced one-electron energies

## 4.Algorithm output

The output of the algorithm is the CCSD BSIE correction. This energy contains the 2nd-order energy correction and a pair-specific contribution that accounts for the BSIE of the particle-particle ladder term (see theory).

### 4.1.Sample `stdout`

Below an example standard output stream is shown for a successful run.

```step: 11, BasisSetCorrection
Ccsd-Bsie energy correction:      -5.2998024502
realtime 0.080797438 s
--
```

## 5.Sample `yaml` output

Below an example `yaml` output stream is shown for a successful run.

```name: BasisSetCorrection
out:
energy:
correction: -5.2998024502064709
pplCorrection: 1.2013851788124801
secondOrderCorrection: -6.5011876290189505
uncorrectedCorrelation: -25.445624886202786
unit: 0.036749322175638782
realtime: 0.080797438
```

## 6.Computational complexity

This algorithm is a post-processing algorithm. However, the 2nd-order energy is re-evaluated and other operations of the same computational complexity are performed. The memory footprint is also in the order of a 2nd-order energy calculation.

## 7.Theory

This algorithm evaluates a correction to the basis-set-incompleteness error (BSIE) of CCSD correlation energies as descibed in Ref. (Irmler, Gallo, and Grüneis 2021). The algorithm requires the converged CCSD amplitudes together with δ-integrals. Futhermore, a complete-basis-set-limit estimate of the MP2 pair-correlation-energies is needed.

As discussed in Ref. (Irmler, Gallo, and Grüneis 2021), the CCSD-BSIE in a finite basis-set calculation is primarily due to the 2nd-order term, and the so-called particle-particle ladder (ppl) term. There exists a variety of algorithms which allow a reliable CBS estimate for the 2nd-order term at modest computational costs (compared to a the corresponding CCSD calculation for the same system). The missing ppl BSIE contribution is approximated using a pair-specific expression which requires the MP2 pair-correlation-energies, CCSD amplitudes, as-well-as the δ-integrals. The implemented ppl-correction is defined by Eq.(31) in Ref. (Irmler, Gallo, and Grüneis 2021) . The provided CCSD-BSIE energy correction is the sum of the 2nd-order energy correction and the ppl-correction-term.

## 8.Literature

Irmler, Andreas, Alejandro Gallo, and Andreas Grüneis. 2021. “Focal-Point Approach with Pair-Specific Cusp Correction for Coupled-Cluster Theory.” The Journal of Chemical Physics 154 (June): 234103. doi:10.1063/5.0050054.

Created: 2023-03-16 Thu 10:59