# Equations

Here is a summary of the equations used in the AutoDock force field.

### Free Energy Coefficients

The molecular mechanics-based and empirical terms are multiplied by coefficients that are determined by linear regression analysis of complexes with known 3D-structures and known binding free energies. In the equations on this page, these weights are *W _{vdW}*,

*W*,

_{H-bond}*W*,

_{elec}*W*and

_{desolv}*W*. In AutoDock 4, these free energy weights, FE_coeff_vdW, FE_coeff_hbond, FE_coeff_estat, FE_coeff_desolv and FE_coeff_tors, can be set in the parameter file.

_{tor}### Molecular Mechanics Terms

- van der Waals
*ΔG*=_{vdW}*W*∑_{vdW}(_{i, j}*A*/_{ij}*r*_{ij}^{12}-*B*/_{ij}*r*_{ij}^{6}) - Hydrogen Bonding
*ΔG*=_{H-bond}*W*∑_{H-bond}_{i, j}*E(t)** (*C*/_{ij}*r*_{ij}^{12}-*D*/_{ij}*r*_{ij}^{10}+*E*)_{hbond} - Electrostatics - see Coulomb's Law

*ΔG*=_{elec}*W*∑_{elec}(_{i, j}*q**_{i}*q*) / ( ε(_{j}*r*) *_{ij}*r*)_{ij} - Desolvation (AutoDock 3)

*ΔG*=_{desolv}*W*∑_{desolv}_{i}_{ (C)}(_{, j}*S**_{i}*V** exp ( -_{j}*r*_{ij}^{2}/ (2 * σ^{2}) ) ) - see also AutoDock 4 Desolvation Free Energy for more details about the AutoDock 4 desolvation term.

### Estimated Change in Torsional Free Energy when the Ligand goes from Unbound to Bound

- Torsional
*ΔG*=_{tor}*W*_{tor}*N*_{tor}

(where*N*is the number of all rotatable bonds, excluding guanidinium and amide bonds_{tor}*etc*.)

### Complete equation:

### Changing Atom Types and Parameters

Note that in AutoDock 4, there are more atom types allowed for the molecules, and these are specified in PDBQT-formatted files.

The default force-field parameters for these atom types can be overrided using the "parameter_file" command in the GPF and DPF. This command requires one argument, namely the filename of the ".dat" file that contains the linear free energy model's coefficients and the atom parameters; the default values can be found in "AD4_parameters.dat" which resides in the source code distribution. For more details, read the FAQs, Where do I set the AutoDock 4 force field parameters? and How do I add new atom types to AutoDock 4?.