One has to keep in mind that dispersion interaction has only vague physical definition and from the quantum mechanical perspective it is not observable. Thus, its description largely depends on quantum-chemical scheme you pick. The direct comparison between the schemes may be complicated (e.g. http://dx.doi.org/10.1002/cphc.201000109 ).

If you want to calculate total interaction energy between low polar molecules (assuming the non-dispersion contributions are small), you have to account for the correlation energy (which is then the "objective function" of the method of choice).

As already mentioned, MPx methods (which include some portion of correlation energy) are not reliable. MP2 is well known to overestimate total interaction energies of vdW complexes of non-polar molecules (check e.g. http://dx.doi.org/10.1021/jp071486+ ). MP3 underestimates it and overall with the increasing number of excitations the accuracy doesn't converge.

As a golden standard, the coupled cluster methods starting at CCSD(T) level provide accurate results, though are quite expensive (eg. http://dx.doi.org/10.1021/ct2002946, http://dx.doi.org/10.1021/ct400057w ).

I also agree that for larger complexes, the DFT-D3 would be the method of choice.

Hi Alexey

MP2 with a large basis function with BSSE correction gives a reasonable results. However you can use MP4 if you have access to a powerful computer. 

As for most QC methods, it really depends on the size of your system and the level of chemical accuracy you need. If your system is too big to be treated at a coupled cluster level, dispersion forces can be described by empirical corrections to DFT functionals. The 2011 review by Grimme in WIREs Comput. Mol. Sci. (http://wires.wiley.com/WileyCDA/WiresArticle/wisId-WCMS30.html) is highly recommended for this topic.

I agree to Daniele. In my opinion, DFT-D2 and DFT-D3 by Grimme is good enough for most systems. MP2 is also reliable, but more expensive, and cant apply for periodic systems. vdw-DF by Dion and Cooper is another option.

"preferable" based on what criteria? SAPT is probably the method of choice. Grimme's dispersion-corrected methods are quite reliable considering their low computational cost. I would question the use the MP2... MP4 methods as the series does not converge regularly and it is difficult to know where to stop to get the most reliable answer. If I needed an accurate answer, I would definitely go with SAPT.

One has to keep in mind that dispersion interaction has only vague physical definition and from the quantum mechanical perspective it is not observable. Thus, its description largely depends on quantum-chemical scheme you pick. The direct comparison between the schemes may be complicated (e.g. http://dx.doi.org/10.1002/cphc.201000109 ).

If you want to calculate total interaction energy between low polar molecules (assuming the non-dispersion contributions are small), you have to account for the correlation energy (which is then the "objective function" of the method of choice).

As already mentioned, MPx methods (which include some portion of correlation energy) are not reliable. MP2 is well known to overestimate total interaction energies of vdW complexes of non-polar molecules (check e.g. http://dx.doi.org/10.1021/jp071486+ ). MP3 underestimates it and overall with the increasing number of excitations the accuracy doesn't converge.

As a golden standard, the coupled cluster methods starting at CCSD(T) level provide accurate results, though are quite expensive (eg. http://dx.doi.org/10.1021/ct2002946, http://dx.doi.org/10.1021/ct400057w ).

I also agree that for larger complexes, the DFT-D3 would be the method of choice.

MPx approaches are accurate and reliable for small and medium size systems (http://dx.doi.org/10.1021/jp071486+)

to Sayyed: In the past, MPx (especially MP2) were used as benchmarks, because it was the first method which included (part of) the correlation energy. In these days, there are, to my opinion, better accuracy/demands ratio methods...

In the paper you mentioned, we show by comparing the experimental and theoretical geometries of two vdW complexes that MP2 gives reasonable results only with a small or medium basis set thanks to compensation of errors.

Whether CEPA is good for?

May I ask what the size of your system is?  Among the recommended methods in the answers already posted, CCSD(T) would be good if you are dealing with only a few atoms. One might even consider CASSCF followed by MRCISD+Q. Molpro is probably the best performing code for both CCSD(T) and MRCISD+Q -- that is only an opinion, of course. For larger molecules, I don't think you have any choice but DFT+D3, with an exchange-correlation functional that has been shown to work well for your class of molecules. I agree with the critics of the Moller-Plesset methods.

DFT-D3 is not a quantum-chemical calculation. These are empirical numbers. If me enough empirical data, then I will turn to molecular mechanics.

I am wondering if there is something realistic between MP2 and CCSD(T)? SCS-CCSD  is not considered because this is not practically cheaper than the CCSD(T).

Instead of DFT-D3 you could use DFT-NL with the non local dispersion correction of the VV10 vdW functional of Vydrov and Van Hooris. This is available in the Orca software package both as a post-SCF correction to the functional being used or in a self-consistent version where the SCF is performed using the NL-modified functional. In general it seems to perform similarly to the empirical DFT-D3 method but is likely to be better for complicated cases like metallic systems.

For low-polar molecules you can use DFT-D2, Grimme's dispersion-corrected methods are quite reliable considering their semi-empirical nature and  their low computational cost.

The benchmark energy and geometry database (www.begdb.com) has a number of very reliable geometries and interaction energies for noncovalent complexes determined at the CCSD(T)/CBS and MP2 level.  Try using a couple different methods to reproduce these, perhaps focussing on dispersion, and pick the one that you like.  Often quantum packages will include many different methods that you could try including the ones previously recommended here by others.

"One has to keep in mind that dispersion interaction has only vague physical definition..."

One of the advantages of the SATP approach is that the interaction energy is expressed as a sum of physically well defined contributions so there is no such ambiguity. Details can be found here:

http://www.physics.udel.edu/~szalewic/SAPT/SAPTtheo.pdf

just to add to the answer from Karl Sohlberg: to calculate the dispersion energy ab initio is the most difficult (and time consuming) part (need higher level of electron correlation and extended basis sets). there are other programms available to get dispersion with SAPT:

MOLPRO:

http://www.molpro.net/info/2010.1/doc/manual/node419.html

PSI4:

http://sirius.chem.vt.edu/psi4manual/4.0b5/sapt.html

see also:

Jansen, G.

Symmetry-adapted perturbation theory based on density functional theory for noncovalent interactions

WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE  Volume: 4   Issue: 2   Pages: 127-144   Published: MAR 2014

I suggest M062X http://download.springer.com/static/pdf/628/art%253A10.1007%252Fs00214-007-0310-x.pdf?auth66=1412445802_c8cd2f6645cab04797835628405218fc&ext=.pdf