# BasisSetCorrection

## Table of Contents

## 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

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

*The Journal of Chemical Physics*154 (June): 234103. doi:10.1063/5.0050054.