# SecondOrderPerturbationTheory

## Table of Contents

## 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

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).