# Møller-Plesset calculations for closed-shell systems

Closed-shell Møller-Plesset perturbation theory calculations up to fourth order can be performed by including the appropriate directive MP2, MP3, MP4SDQ or MP4 in the dataset. The geometry and basis set input is as described in chapter 1.

For example, the following dataset,

```TITLE
Formaldehyde 631g* basis MP2 energy
SYMMETRY
CNV 2
END
VARIABLES
RCO 1.21597 A
RCH 1.101978 A
HCO -121.827934 D
END
BASIS 631G*
ATOMS
XAXIS -1 1.0 0.0 0.0
CARBON 6.0 0.0 0.0 0.0
OXYGEN 8.0 0.0 0.0 RCO
H1 1.0 PTC CARBON OXYGEN XAXIS RCH HCO
END
MP2
ENERGY
START
FINISH```
sets up the geometry of H2CO using internal coordinates (see section 1.4), with a 631G* basis set.

MP2 calculates the 2nd order Møller-Plesset energy.

MP3 would calculate the 2nd and 3rd order energies.

MP4 would calculate the 2nd, 3rd and 4th order energies.

MP4SDQ results in a simplified MP4 calculation omitting the effects of the triple excitations.

If an MP4 calculation on H2CO is carried out with the above basis set and geometry then the output will contain the results of the SCF calculation, and then the following

``` MP2 CORRELATION ENERGY     -0.3106004871
TOTAL MP2 ENERGY         -114.1749063611
MP3 CORRELATION ENERGY     -0.0050632476
TOTAL MP3 ENERGY         -114.1799696087
MP4(SDQ) CORRELATION ENERGY     -0.0085727121
TOTAL MP4(SDQ) ENERGY         -114.1885423208
MP4 CORRELATION ENERGY     -0.0189456598
TOTAL MP4 ENERGY         -114.1989152685
Feenburg MP4 Energy      -114.1998700402```
For each level the correlation energy is given, as well as the total energy i.e. the sum of all terms up to that point including the SCF energy. For MP2 or MP3 calculations the results given are a subset of those above. The Feenburg MP4 energy is a particular extrapolation of the Møller-Plesset series, see Chem. Phys. Lett. 211, 272 (1993).