MOL ECULAR PR OPERTIES O PTIMIZATION PROJECT 
Thermodynamic
3D Description of
Hbonding.
Most modern procedures for threedimensional (3D) computerassisted drug design use forcefield calculations to take Hbonding into account. These calculations are used in many research areas including conformational analysis, pharmacophore identification, ligand docking, de novo ligand design, comparative molecular field analysis (CoMFA), and the identification of favorable binding sites from molecular interaction fields .
On the basis of a sophisticated and parameterized method called GRID, Goodford et al. [13] made efforts to improve the calculation of the Hbond contribution to the interaction energy of ligandmacromolecular complexes. The GRID method is parameterized by fitting experimental Xray data from protein and smallmolecule crystals, and is designed to calculate the interactions of a probe (a small molecule such as water or ammonia) and a macromolecular system. An 86 function was adopted, and was found to give satisfactory result [2]:
E_{r} = C/r^{8}  D/r^{6} (1),
where C = 3E_{m}r^{8}A^{8}/mol;
D = 4E_{m}r_{m}^{6}A^{6}/mol
; r is the distance between the acceptor atom
and the donor heavy atom; E_{m}
is optimum Hbond enthalpy in kcal/mole; r_{m}
is the optimum Hbond length.
However there are only three fixed optimum Hbond lengths in the GRID framework: 2.8 A for “O…O”, 3.0 A for “N…O” and 3.2 A for “N…N” . And the wide intervals of enthalpy values for each those type of Hbond complexes (see previous Chapter) permit to suppose any dependence between energies and distances even in the case of optimum arrangement of atoms participating in Hbonding. Hence, to create a realistic platform for the quantitative 3D description of Hbonding, one must recognize that optimum Hbond energies (E_{m}) depend on optimum Hbond distances (r_{m}) for the different types of Hbonds in complex formation. This our study is presented in [4].
First of all we selected from Cambridge Structural Database 58 "ideal" Hbond complexes where the angles of the donor heavy atom, hydrogen and acceptor atoms were in the range of 173° to 187° and angles of the acceptor nucleus, the lone pair of electrons and the hydrogen atom were in the range of 170° to 190°. There were 13 such “OH…O” complexes, 19 ”OH…N” or “N‑H…O” complexes, and 26 “NH…N” complexes among the 58 "ideal" representatives.
Because there are significant differences between the covalent and van der Waals radii of oxygen and nitrogen atoms, we decided to look for relationships between optimum energy (E_{m}) and optimum distances (r_{m}) in those three subsets. Such relationships are not expected to be linear because energy values approach zero as distances increase. In this study we used a sigmoid function:
E_{m} = k_{4}/(1 + 10^{k}_{5}^{+k}_{6}^{r}m) (2)
Values of k_{4} in eq. (2) may be fixed, and are limited by the maximum values for the enthalpies. Rearranging eq. (2) and simplifying the constants gives eq. (3):
r_{m} = k_{7}log[(k_{4}E_{m})/(E_{m})] + k_{8} (3)
Using eq. (3), we can now calculate r_{m} from E_{m }values. Thus, for each specific pair of atoms participating in an Hbond, its Hbonding potential can be calculated. The potentials fot 58 “ideal” complexes are presented on the fig.:
Hence, a scheme to calculate the Hbonding energies of atoms in a threedimension arrangement can be carried out by following steps:
Use HYBOT’s acceptor and donor enthalpy factors to estimate the optimum Hbonding energy.
Estimate the optimum Hbonding distance corresponding to the calculated energy optimum by means of eq. (3) .
Use eq. (1) or other functions to take into account the distance and angle deviations of the atoms involved.
An example of such calculation for a model system is presented in [4]. This represents the interactions of bases in double helix of RNA in A form.
These calculations were carried out by means of 3D HYBOT in UNIX, a new program, by considering only Hbonding interactions and Sybyl . We believe it is possible that this approach to Hbond calculations will not be too difficult to integrate with existing and future forcefield schemes to produce a superior method to estimate intermolecular interactions in any three dimensional framework.
3D hydrogen bond descriptors.
NN 
Descriptor 
Symbol 
1 
Van der
Waals’acceptor surface area in A^{2
}which is proportional to Hbond enthalpy factors
of acceptor atoms. n
is number of acceptors in the molecule of interest.
. S_{o} is a surface
sphere with a radius of 1.36 A (O_{sp3}) 

2 
Van der
Waals’acceptor surface area in A^{2 }which is proportional to
Hbond overall free energy factors Ca(o)
of acceptor atoms. 

3 
Van
der Waals donor surface area in A^{2 }which is proportional to
Hbond enthalpy factors of donor atoms.n
is number of donors in a molecule,
, S_{H}
is a surface sphere with a radius of 1.08 A
(H atom). 

4 
Van
der Waals donor surface area in A^{2 }which is proportional to
Hbond free energy factors of donor atoms. 

5 
Surface
area around a molecule in A^{2} where interactions of acceptor
atoms of a molecule with a Hbond donor probe have been optimumly placed
and which is proportional to product of Hbond enthalpy factor absolute
values of those atoms. Ed(probe) is the enthalpy factor of the probe Hbond donor,
, S_{rm} is the surface
area of sphere with a radius of r_{m} = 2.45 A
for the strongest Hbonding 

6 
Surface
area around a molecule in A^{2} where interactions of acceptor
atoms of a molecule with Hbond donor probe have been optimumly placed and
which is proportional to product of Hbond (overall) free energy factor
absolute values of those atoms. 

7 
Surface
area in A^{2} around a molecule where interactions of donor atoms
of a molecule with Hbond acceptor probe have been optimumly placed and
which is proportional to product of its Hbond enthalpy factor absolute
values. 

8 
Surface
area in A^{2} around a molecule where interactions of donor atoms
of a molecule with Hbond acceptor probe have been optimumly placed and
which is proportional to product of its Hbond free energy factor absolute
values. 

9 
Surface
integral for enthalpy values (kcal/M*A^{2}) of interactions
between acceptor atoms of a molecule and a donor probe on the surface OEASA
. 

10 
Surface
integral for enthalpy values (kcal/M*A^{2}) for interactions
between donor atoms of a molecule and an acceptor probe on the surface OEDSA 

References:
1. Goodford, P.J., J.Med.Chem., 28 (1985) 849.
2. Wade, R.C., Clark, K. and Goodford, P.J., J.Med.Chem., 36 (1993) 140,148.
3. Goodford, P.J., J.Chemometrics, 10 (1996) 107.
4. Raevsky O.A. and Skvortsov, V.S., 3D Hydrogen Bond Thermodynamics (HYBOT) Potentials in Molecular Modelling, Comp.Aided Mol.Des., 16, 1 (2002).