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.