SecondOrderPerturbationTheory

1. Example Cc4s input
2. Input Description
3. Output
4. Computational Complexity and memory footprint
5. Theory
6. Literature

1. Example `Cc4s` input

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

- name: SecondOrderPerturbationTheory
  in:
    coulombIntegrals: CoulombIntegrals
    slicedEigenEnergies: EigenEnergies
  out:
    energy:

2. Input Description

Table 1: Input keywords for PerturbativeTriples
Input Keyword	Description	Default
`coulombIntegrals`	Coulomb Integrals
`slicedEigenEnergies`	Sliced one-electron energies

3. Output

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

step: 9, SecondOrderPerturbationTheory
Contracting second order energy...
correlation energy: -24.3605
  singles:  0
  direct:   -35.3032
  exchange: 10.9427
realtime 0.170357500 s
--

4. Computational Complexity and memory footprint

Two objects of size \(\mathcal{O}{(N_\mathrm{o}^2 N_\mathrm{v}^2)}\) are stored in main memory. The computational complexity should be negligible as is of order \(\mathcal{O}{(N_o^2 N_v^2)}\).

5. Theory

The implemented expression assumes Hartree–Fock one-electron energies and can be found in Ref.(Moller and Plesset 1934).

6. Literature

Moller, C, and MS Plesset. 1934. “Note on an Approximation Treatment for Many-Electron Systems.” Phys. Rev. 46 (7): 0618–22.