MP2 & MP3

ORCA includes different MP2 variants and different approximations to speed up MP2 calculations. MP3 is also available. This page demonstrates the use of all these methods.

See this recent paper for a study on the most efficient way to reach the canonical MP2 basis set limit using the different MP2 approximations in ORCA. While MP2 is not a recommended method for modern thermochemistry, it is still a very relevant method for accurate molecular geometries of organic and maingroup elements and efficient geometry optimizations can be performed in ORCA.

See RI and auxiliary basis sets for a discussion on the RI approximations and auxiliary basis sets that are being used here.

Note: The cc-pVTZ basis set is used as an example in the input below. See basis set page for general basis set recommendations. Single-point calculations are mostly shown. Analytic MP2 gradients are available for MP2, RI-MP2 and RIJCOSX-RI-MP2 geometry optimizations.

The Frozen Core (FC) approximation is used by default in MP2/MP3 calculations, where core electrons are excluded in the perturbation step. To turn the approximation off (rarely recommended) one can use the NoFrozenCore keyword. See Frozen core page for more information.

Normal MP2

This is the expensive way of doing MP2 calculations where no approximation to the basic MP2 equations is made.

This is NOT recommended.

The RI-MP2 approach (see later) is recommended.

! MP2 cc-pVTZ TIGHTSCF

ROHF-MP2

MP2 based on a restricted open-shell HF determinant for open-shell systems. This will eliminate spin contamination. Note that MP2 on an open-shell system will default to using unrestricted HF (UHF).

! MP2 cc-pVTZ TIGHTSCF

%scf

HFTyp ROHF

end

RI-MP2

MP2 using the Resolution of Identity approximation (RI) for MP2 integrals. Requires an RI-C auxiliary basis set (here cc-pVTZ/C). Speeds up MP2 calculations considerably with minimal loss in accuracy (depends on the quality of the accompanying auxiliary basis set which is usually excellent). The RI-MP2 approximation is often so fast that the Hartree-Fock calculation becomes the time-limiting part of the calculation. The HF part can be sped up by RIJK and RIJCOSX approximations (see below).

! RI-MP2 cc-pVTZ cc-pVTZ/C TIGHTSCF

RI-MP2 using RIJK approximation (single-points only)

RI-MP2 using also the RI-JK approximation for Coulomb and Exchange integrals in the HF calculation. Speeds up the HF step. Requires a RI-JK auxiliary basis set (here def2/JK). Note that cc-pVNZ/JK basis set are also available (may be more accurate but available for fewer elements).

! RI-MP2 RIJK cc-pVTZ cc-pVTZ/C def2/JK TIGHTSCF

RI-MP2 using RIJCOSX approximation (single-points and geometry optimizations)

RI-MP2 using also the RIJCOSX approximation for Coulomb (RI-J) and Exchange integrals (COSX numerical integration) in the HF calculation. Speeds up the HF step. Slower than RIJK for small systems but scales better with system size. Requires a RI-J auxiliary basis set (here def2/J).

! RI-MP2 RIJCOSX cc-pVTZ cc-pVTZ/C def2/J TIGHTSCF

RIJCOSX-RI-MP2 is also a quite efficient way of performing geometry optimizations at the MP2 level:

! RI-MP2 RIJCOSX cc-pVTZ cc-pVTZ/C def2/J TIGHTSCF Opt

MP2-F12

MP2-F12 computation using specialized F12 basis sets.

!RHF MP2-F12 cc-pVTZ-F12 cc-pVTZ-F12-CABS TIGHTSCF

RI-MP2-F12

RI-MP2-F12 computation using specialized F12 basis sets. It is recommended to go up one step in /C auxiliary basis set level for higher accuracy.

!RHF RI-MP2-F12 cc-pVTZ-F12 cc-pVTZ-F12-CABS cc-pVQZ/C TIGHTSCF

RI-MP2-F12 using the RIJK approximation

RI-MP2-F12 computation using specialized F12 basis sets and the RIJK approximation. This combination was highlighted in a recent paper as a very robust and efficient MP2 approximation. For larger molecules RI-MP2-F12 with RIJCOSX (below) will be more efficient.

!RHF RIJK RI-MP2-F12 cc-pVTZ-F12 cc-pVTZ-F12-CABS def2/JK cc-pVTZ/C TIGHTSCF

RI-MP2-F12 using the RIJCOSX approximation

RI-MP2-F12 computation using specialized F12 basis sets and the RIJCOSX approximation.

!RHF RIJCOSX RI-MP2-F12 cc-pVTZ-F12 cc-pVTZ-F12-CABS def2/J cc-pVTZ/C TIGHTSCF

RI-SCS-MP2

Spin-component-scaled MP2 using the RI-MP2 approximation. SCS-MP2 has been demonstrated to be more accurate than standard MP2 for many cases.

! RI-SCS-MP2 cc-pVTZ cc-pVTZ/C TIGHTSCF

Orbital optimized MP2

Orbital optimized MP2 and SCS-MP2 is available using the RI-MP2 approximation (only). Orbital optimized MP2 is as good as standard MP2 for normal closed-shell calculations (and considerably more expensive) but is a considerable improvement for difficult situtations such as transition states and radicals. Reduces spin contamination in open-shell MP2 calculations. Is considerably more expensive than MP2.

! OO-RI-MP2 cc-pVTZ cc-pVTZ/C TIGHTSCF

! OO-RI-SCS-MP2 cc-pVTZ cc-pVTZ/C TIGHTSCF

SCS-MP3

Grimme’s SCS-MP3 method. Very expensive.

! SCS-MP3 cc-pVTZ TightSCF

COSX implementation of Grimme’s SCS-MP3 method. Computationally more tractable.

! SCS-MP3 RIJCOSX cc-pVTZ def2/J TightSCF