# Møller–Plesset perturbation theory (MP2)

## Description

Second-order Møller–Plesset perturbation theory (MP2) calculations are performed with density fitting using the keyword `"title" : "mp2"`.

## Keywords

`frozen`

Description: to have frozen orbitals or not
Datatype: bool
Default: true

`ncore`

Description: manually specify number of frozen orbitals, used when ‘frozen’ is turned on
Datatype: int

`aux_basis`

Description: specify an auxiliary basis set for MP2
Datatype: string
Default: use the same density fitting basis as in Required keywords
Recommendation: use MP2-fit auxiliary basis (auxiliary basis ends with ‘ri’)

## Example

    { "bagel" : [

    {
      "title" : "molecule",
      "basis" : "cc-pvdz",
      "df_basis" : "cc-pvdz-jkfit",
      "angstrom" : "true",
      "geometry" : [
        { "atom" : "C", "xyz" : [ -1.20433891360,  0.54285096106, -0.04748199659] },
        { "atom" : "C", "xyz" : [ -1.20543291352, -0.83826393986,  0.12432899108] },
        { "atom" : "C", "xyz" : [ -0.00000600000, -1.52953889027,  0.20833398505] },
        { "atom" : "C", "xyz" : [  1.20544091352, -0.83825393987,  0.12432799108] },
        { "atom" : "C", "xyz" : [  1.20433091360,  0.54284396106, -0.04748099659] },
        { "atom" : "C", "xyz" : [  0.00000400000,  1.23314191154, -0.13372399041] },
        { "atom" : "H", "xyz" : [ -2.13410484690,  1.07591192282, -0.12500499103] },
        { "atom" : "H", "xyz" : [ -2.13651384673, -1.37179190159,  0.18742198655] },
        { "atom" : "H", "xyz" : [  0.00000000000, -2.59646181374,  0.33932597566] },
        { "atom" : "H", "xyz" : [  2.13651384673, -1.37179290159,  0.18742198655] },
        { "atom" : "H", "xyz" : [  2.13410684690,  1.07591292282, -0.12500599103] },
        { "atom" : "H", "xyz" : [ -0.00000000000,  2.29608983528, -0.28688797942] }
      ]
    },

    {
      "title" : "hf"
    },

    {
      "title" : "mp2",
      "aux_basis" : "cc-pvdz-ri",
      "frozen" : true
    }

    ]}

The SCF calculation should converge after 11 iterations with energy -230.72159477. The DF-MP2 output is as follows:

    === DF-MP2 calculation ===

      * freezing 6 orbitals
    Number of auxiliary basis functions:      420

    Since a DF basis is specified, we compute 2- and 3-index integrals:
      o Being stored without compression. Storage requirement is 0.044 GB
         - 3-index ints prep                         0.00
         - 3-index ints                              0.06
         - 2-index ints                              0.00
         - computing inverse                         0.02
          elapsed time:        0.09 sec.

    Number of basis functions:      114
    Number of electrons      :       42

      * 3-index integral transformation done
      * ncache = 20
      * assembly done

        MP2 correlation energy:   -0.7813195576      0.19

        MP2 total energy:       -231.5029143295

      * METHOD: MP2                                  0.34

## References

Description of Reference | Reference
--- | ---
Original reference for MP2 | C. Møller and M. S. Plesset, Phys. Rev. 46, 618 (1934).