Errors in Intermolecular Interaction Energies for S22 set (kcal/mol)

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Errors in various methods, relative to CCSD(T)/CBS (all numbers in Kcal∙mol-1)
System CCSD(T)/CBS value PM7    PM6    PM6-DH+   PM6-DH2   PM6-D3H4    B3LYP 
01 NH3 dimer -3.17 -1.18 0.87 0.01 -0.03   -0.61 -1.40
02 water dimer -5.02 0.11 1.08 -1.45 0.12 0.16 -2.30
03 formic a dimer -18.61 0.65 7.47 0.87 -0.04 0.43 -2.81
04 formamide dimer -15.96 -0.67 3.41 -1.89 0.10 -0.88 -2.60
05 uracil HB -20.47 1.45 7.15 1.11 -0.73 1.99 -1.10
06 pyridoxine aminopyridine -16.71 -0.46 6.73 -0.07 0.36 0.43 -1.22
07 adenine thymine WC -16.37 0.66 7.31 0.50 -0.08 0.88 -0.96
08 CH4 dimer -0.53 0.17 0.47 0.08 0.08 -0.13 0.74
09 Ethylene dimer -1.51 0.44 1.11 0.45 0.45 0.51 1.05
10 benzene methane -1.50 -0.29 1.03 0.11 0.11 -0.01 1.70
11 benzene dimer stack -2.73 -1.46 2.86 -0.84 -0.84 -0.21 5.07
12 pyrazine dimer -4.42 -1.25 2.61 -0.92 -0.92 -0.42 5.25
13 uracil dimer stack -9.88 1.30 5.42 0.47 0.44 0.74 5.94
14 indole benzene stack -5.22 -0.73 5.29 0.17 0.17 1.14 8.14
15 adenine thymine stack -12.23 0.92 7.29 0.57 0.54 1.49 10.03
16 ethene ethyne -1.53 0.54 0.98 0.58 0.58 0.51 -0.12
17 benzene H2O -3.28 0.51 1.00 0.10 0.10 -0.05 0.62
18 benzene NH3 -2.35 -0.54 0.82 -0.19 -0.19 -0.25 1.27
19 benzene HCN -4.46 1.41 2.48 1.47 1.47 1.63 1.38
20 benzene dimer T -2.74 -0.56 1.99 0.15 0.15 0.35 2.74
21 indole benzene T -5.73 -0.25 3.33 0.80 0.80 1.03 3.25
22 phenol dimer -7.05 0.79 3.67 -0.01 -0.01 -0.40 0.92
                     
RMSD: 0.85 4.18 0.78 0.53 0.83 3.74
MAD or AUE: 0.74 3.38 0.58 0.38 0.65 2.75
MAX: 1.46   7.47   1.89   1.47   1.99   10.03

PM6-DH+: Korth M., Pitonák M., Řezáč, J., Hobza P., "A Transferable H-bonding Correction For Semiempirical Quantum-Chemical Methods", J. Chem. Theory and Computation 6, 344-352 (2010).

PM6-DH2: Řezáč, J., Fanfrlik J., Salahub D., Hobza P., "Semiempirical Quantum Chemical PM6 Method Augmented by Dispersion and H-Bonding Correction Terms Reliably Describes Various Types of Noncovalent Complexes", J. Chem. Theory and Comp. 5, 1749-1760 (2009).

PM6-D3H4: Řezáč, J. and Hobza, P., "Advanced Corrections of Hydrogen Bonding and Dispersion for Semiempirical Quantum Mechanical Methods",   Journal of Chemical Theory and Computation, 2012 8 (1), 141-151 DOI: 10.1021/ct200751e.

 

Worked example of the calculation of the error in intermolecular interaction energies

The error in the PM7 prediction of the intermolecular interaction energy of a benzene molecule and a water molecule, entry "17 benzene H2O" in the table, can be calculated as follows:

A MOPAC dataset was constructed using the geometry from the S22 CCSD(T)/CBS results1.  This dataset was run, and from the archive file archive file the heat of formation was -37.4594 kcal mol-1.

A second dataset was constructed in which the water molecule was moved far from the benzene molecule.  This was done in two steps:
(1) The system was converted into internal coordinates using a simple calculation, see step_1.mop.
(2) The oxygen atom in the resulting geometry was moved far away from the benzene molecule.  Because the hydrogen atoms on the water were in internal coordinates, the entire water molecule moved as well.

The second dataset was then run, and from the archive file , the heat of formation was -34.6866 kcal mol-1.

From these two results, the interaction energy for the water - benzene complex, predicted by PM7, was -2.7728 kcal mol-1., so the error in PM7, when compared to the reference value of -3.28 kcal mol-1, is 0.51 kcal mol-1, in agreement with the value given in the table.

1:  http://www.begdb.com/index.php?action=oneMolecule&state=show&id=97