XEDs

The accurate calculation of molecular fields is crucial if these fields are to be used successfully to predict a molecule's biological properties. In particular, the charge distribution within a molecule must be adequately described. Most widely-used molecular models approximate the charge distribution within a molecule by placing a small partial charge at the centre of each atom. This Atom-Centred Charge (ACC) approximation is too crude to allow the generation of precise molecular fields.

Cresset's eXtended Electron Distribution (XED) model (Vinter 1994) explicitly models the asymmetric distribution of electrons around atoms. This gives not only improved molecular conformations and interaction energies, but allows the rapid calculation of molecular fields with a quality comparable to that obtained from high-level quantum mechanical calculations.

XED successfully reproduces experimental observations such as aromatic ring stacking qualitatively and quantitatively where all other known systems fail. Many other observed structural phenomena are handled naturally by XED where other systems can only succeed by adding special terms (Chessari et al 1999).

Benzene on benzene sandwich (wrong)

Left: Benzene docked onto benzene using conventional molecular mechanics. This direct face-to-face arrangement is not observed experimentally.


Right: Benzene docked onto benzene using XED molecular mechanics. This T-shaped arrangement is experimentally observed, along with a face-to-face offset stacking.

 Benzene on benzene t-stack (correct)

Validation

Aromatic-aromatic interactions experimentally measured
Graph of experimental vs calculated aromatic-aromatic interaction energies

Significant validation of XEDs has been accumulated with the help of third parties over the last few years.

The interaction of a series of small molecules (Chessari et al 2002), docked in pairs, has been measured in Prof. Chris Hunter's labs at Sheffield University. A typical aromatic-aromatic interaction of interest is shown on the left. Below it, the graph of experimental versus calculated interaction energies using the XED modelling force field correlated to a statistical r2 value of 0.96

Other well-known force fields correlated less well: MM2 0.68, MM3 0.68, OPLS 0.42, AMBER 0.17

Commercially available modelling packages provide access to all the commonly used molecular mechanics force fields that can be regarded as in competition with XED. In the table below, the deviations from experimental measurements (relative conformation energies in kcal/mol) of nine of the most used force fields have been compared against each other by a number of different workers. In each case, the XED force field has been applied to the same molecules in a set and compared by the same criteria. The XED results are recorded in the last column.

MM2 MM3 CVFF CFF Tripos MMFF Amber CHARMM OPLS XED
Gundertofte(1996) - 38 Compounds Absolute mean errors 0.55 0.51 1.94 1.13 1.11 0.51 0.86 0.64 n/a 0.24
Halgren (1999) - 35 Compounds Standard Deviations 1.75 0.72 2.36 1.06 n/a 0.37 1.29 0.78 1.68 0.30
Halgren(1999) - 19 Compounds Standard Deviations 0.68 0.78 2.86 2.21 n/a 0.74 1.03 0.70 1.28 0.41

Our own internal validation set for XEDs contains 92 experimental conformational energies. XED gives an absolute mean deviation of 0.26 and a standard deviation of 0.35 kcal/mol on this set. In summary, the XED force field out-performs all other available force fields in its reproduction of experimentally-measured conformational energies. In fact, the XED errors are of the same order as the experimental errors.