PM6-DH+ - Accuracy

PM6-DH+ gives much improved interaction energies compared to PM6.  Whereas in PM6, the average unsigned error for interaction energies for the complexes in the S22 set, using the S22 geometries, is 3.27 Kcal/mol, for PM6-DH+, the equivalent average unsigned error is 0.57 Kcal/mol. For details of PM6-DH+, see: M. Korth, "Third-Generation Hydrogen-Bonding Corrections for Semiempirical QM Methods and Force Fields," J. Chem. Theory Comput., 2010, 6 (12), pp 3808-3816. 

Unlike PM6-DH2, there are no errors in the gradient of the energy with respect to geometry, so PM6-DH+ can be used to optimize geometries.

However, the errors in the PM6-DH2 gradients are small, and the average unsigned error in hydrogen bonding energy from PM6-DH+ for the optimized structures is 0.87 kcal/mol compared to PM6-DH2 average of 0.60 kcal/mol.

The following table is provided to assist users in deciding which method to use. Intermolecular interactions that are different between PM6-DH2 and PM6-DH+ are shown in black, where hydrogen bonds are absent the results are in green, and should be the same for both methods. (There are small differences in the optimized geometry results because PM6-DH+ uses derivatives calculated by diatomic finite difference, and PM6-DH2 uses derivatives calculated by differences of full SCF calculations.)

      PM6 - type calculations at the S22 geometry   PM6 - type calculations at the PM6-type geometry
Chemical Sample Ref. : CCSD(T)/CBS   PM6 error    PM6-DH2 error mod   PM6-DH+ error mod   PM6 error    PM6-DH2 error mod   PM6-DH+ error mod
01 Ammonia dimer -3.170   0.865   -0.034 0.034 -0.042 0.008 0.008   0.809   -0.905 0.905   -2.149 2.149
02 Water dimer -5.020   1.084   0.121 0.121 1.573 -1.452 1.452   1.132   -0.103 0.103   -1.620 1.620
03 Formic acid dimer -18.610   7.474   -0.044 0.044 -0.916 0.872 0.872   8.573   0.275 0.275   2.290 2.290
04 Formamide dimer -15.960   3.412   0.095 0.095 1.987 -1.892 1.892   5.130   1.754 1.754   -0.427 0.427
05 Uracil HB -20.470   7.146   -0.727 0.727 -1.841 1.114 1.114   7.973   -0.068 0.068   2.055 2.055
06 Pyridoxine aminopyridine -16.710   6.729   0.355 0.355 0.427 -0.072 0.072   7.111   0.339 0.339   0.605 0.605
07 Adenine thymine WC -16.370   7.311   -0.083 0.083 -0.579 0.496 0.496   7.482   -0.411 0.411   0.964 0.964
08 Methane dimer -0.530   0.466   0.082 0.082 0.000 0.082 0.082   0.461   0.082 0.082   0.082 0.082
09 Ethylene dimer -1.510   1.109   0.449 0.449 0.000 0.449 0.449   1.103   0.426 0.426   0.426 0.426
10 Benzene methane -1.500   1.026   0.107 0.107 0.000 0.107 0.107   1.007   -0.008 0.008   -0.002 0.002
11 Benzene dimer stack -2.730   2.856   -0.840 0.840 0.000 -0.840 0.840   2.156   -0.884 0.884   -0.884 0.884
12 Pyrazine dimer -4.420   2.614   -0.921 0.921 0.000 -0.921 0.921   2.275   -1.371 1.371   -1.371 1.371
13 Uracil dimer stack -9.880   5.422   0.439 0.439 -0.027 0.466 0.466   5.440   0.937 0.937   0.696 0.696
14 Indole benzene stack -5.220   5.291   0.168 0.168 0.000 0.168 0.168   2.664   0.111 0.111   0.213 0.213
15 Adenine thymine stack -12.230   7.288   0.541 0.541 -0.026 0.567 0.567   6.921   0.571 0.571   0.511 0.511
16 Ethene ethyne -1.530   0.982   0.580 0.580 0.000 0.580 0.580   0.984   0.552 0.552   0.552 0.552
17 Benzene water -3.280   0.999   0.101 0.101 0.000 0.101 0.101   0.644   -0.277 0.277   -0.277 0.277
18 Benzene ammonia -2.350   0.822   -0.193 0.193 0.000 -0.193 0.193   0.327   -1.041 1.041   -1.039 1.039
19 Benzene hydrogen cyanide -4.460   2.475   1.472 1.472 0.000 1.472 1.472   2.444   1.455 1.455   1.452 1.452
20 Benzene dimer T -2.740   1.965   0.152 0.152 0.000 0.152 0.152   1.937   0.125 0.125   0.125 0.125
21 Indole benzene T -5.730   3.326   0.801 0.801 0.000 0.801 0.801   3.219   0.614 0.614   0.615 0.615
22 Phenol dimer -7.050   3.673   -0.007 0.007 0.001 -0.008 0.008   2.758   -1.115 1.115   -1.113 1.113
23 Methanol dimer -5.700   2.201   -0.552 0.552 0.105 -0.657 0.657   0.933   -0.583 0.583   0.235 0.235
24 Methanol formaldehyde -5.310   1.899   0.099 0.099 0.321 -0.222 0.222   1.418   -0.363 0.363   -1.052 1.052
                                   
    Average: 3.268   0.090 0.373   0.049 0.571   3.121   0.005 0.599   0.037 0.865

Note: Heats of formation predicted by PM6-DH+ should not be compared to reference heats of formation.  This is because PM6-DH+ is designed for predicting energies of interaction.  If heats of formation are wanted then use PM6, for which the predicted  ΔHf  can be compared to experimental values.

The above values are for the S22 set.  M. Korth has also supplied data for two other sets.  First, results for the 105 small, H-bonded complexes of the PM6-DH1 Fit Set; giving Mean Signed (MSE), Mean Unsigned (MUEs), and Root Mean Square Errors (RMSE) as well as the Maximum Error Span, r, with respect to the Benchmark CCSD(T)/CBS Interaction Energies.  All values are in kcal/mol.

  PM6-D PM6-DH2 PM6-DH+
MSE -1.66   -0.43   0.46  
MUE 1.77   1.15   1.21  
RMSE 2.35   1.54   1.44  
r 9.61   7.37   6.18  

Second, results for the JSCH2005 H-bonded DNA base pairs with respect to the Benchmark CCSD(T)/CBS Interaction Energies are presented. Again all values are in kcal/mol.

  PM6-D PM6-DH2 PM6-DH+
MSE -6.10   -0.54   -0.87  
MUE 6.10   1.76   1.35  
RMSE 6.30   2.23   1.59  
r 7.67   7.94   5.94  

 

PM6-DH+ has some theoretical and practical advantages over the other hydrogen bonding correction methods in PM6; for a detailed discussion of these issues see: M. Korth, "Third-Generation Hydrogen-Bonding Corrections for Semiempirical QM Methods and Force Fields," J. Chem. Theory Comput., 2010, 6 (12), pp 3808-3816.