Empirical Hydrogen‐Bond Potential Functions—An Old Hat Reconditioned

Abstract

The accurate description of hydrogen-bond interactions is of vital importance for the computational modeling of biological systems. Standard force field (FF) as well as semiempirical quantum mechanical (SQM) methods are now known to have considerable problems with the accurate description of hydrogen bonds. It was found that the performance of SQM methods can be greatly improved with empirical hydrogen-bond correction terms. In the first part of this work we review the improvements developed during the recent revival of dedicated hydrogen-bond terms, also in the light of earlier FF-related work. The second part presents new findings connected to open questions in this field, namely, a study on the importance of angular and torsional information, a scheme how to avoid atom-type-defined target angles and a reduced version of our DH(+) model for the application to force-field methods and physically motivated protein-ligand scoring functions. Our results highlight the importance of using a complete geometric description (including angular and torsional coordinates) for the accurate treatment of hydrogen bonding. The reduced DH(+) model-applied to a modified version of the UFF force field-shows a much improved accuracy for non-covalent interactions also with FF methods, with gains in accuracy by more than one order of magnitude.

Benchmark of electronic structure methods for protein–ligand interactions based on high-level reference data

“…At least for our PLI10 set, this path seems to be an equally valid approach, with similar MADs of about 1.7 kcal/mol for M06 and MO6-2X, though it has to be mentioned that due to convergence problems one system (2hdr) could not be treated at all with these methods and was thus excluded from the statistics and that the values are signi¯cantly worse than those of the D2/D3-based methods. At the bottom of Table 2 we give PM6-DH+ values, a SQM approach with empirical corrections for dispersion and hydrogen-bond interactions, [68][69][70]72 and for comparison of the estimated e®ects from D2 to D3 and D3 to D3+D abc . We¯nd a substantial improvement from D3, but not D abc and an overall MAD of only 3.3 kcal/mol (5.0 kcal/mol without estimated e®ects), lower than for instance the one of BP86-D3+D abc /def2-TZVPP.…”

“…DH+ is an empirical correction for non-covalent interactions, which are usually not treated accurately enough at SQM level. 72 SQM methods augmented with the DH+ correction reach the accuracy of dispersion-corrected density functional theory (DFT-D) approaches for a large number of cases investigated, while still being about three orders of magnitude faster. 69,70 Interaction energies are computed in the following way (where the geometries of the protein pockets as well as the ligands are the same as in the complexes): Table 1 shows data for the comparison of WFT methods: Our best reference values, deviations with respect to these reference values for each WFT method, as well as error statistics for these deviations.…”

Semiempirical quantum–chemical methods

“…Many of them are based on the MNDO model in one of its standard implementations. For example, there are several early MNDO, AM1, and PM3 variants with a special treatment of hydrogen bonds, which have recently been refined with elaborate PM6‐based hydrogen‐bond potential functions . These special approaches exploit the flexibility offered in MNDO‐type methods by the presence of the effective core–core repulsion term, which can be modified for fine tuning.…”

New methods for computational drug design

“…Target angles are the optimal (text-book) angles for a given H-bond arrangement. H-bond energies are computed based on the deviation of all angular coordinates from their respective target (optimal) angles, see reference [28] for a detailed explanation. The target angle would switch during optimization steps as the definition of the torsion angle would switch, and never find a minimum, as the torsion angle is defined as seen in Figure 3.1a.…”