## Wednesday, July 26, 2006

### Free energy calculation

Changes in enthalpy (Van de Waals and Coulomb interactions, and internal energy) and entropy (configurational: translational and rotational deegrees of freedom, conformational and vibrational) on formation of the complex: $\Delta G_{bi nd} = \Delta H - T \Delta S$

• Enthalpy can be calculated using a molecular mechanics force fields like:

$E_{MM} = \sum_{bonds} K_r (r-r_{e q})^2+\sum_{angl es} K_{\theta} (\theta-\theta_{e q})^2$
$+\sum_{dihedrals}\frac{V_{n}}{2}[1+cos(n\phi-\gamma)]$
$+\sum_{i < j}[\frac{A_{ij}}{R_{ij}^{12}}-\frac{B_{ij}}{R_{ij}^{6}}+\frac{q_i q_j}{\epsilon R_{ij}}]$
• Entropy can be obtained using Boltzmann's law:
$S = -k \sum_{j} P_{j} \ln P_{j}$
$P_{j} = \frac{e^{-\frac{E_{j}}{kT}}}{\sum_{j} e^{ -\frac{E_{j}}{kT} }}$

Entropy can be split into four terms:

$\Delta S_{t otal} = \Delta S_{trans}+\Delta S_{rot}+\Delta S_{conf} + \Delta S_{vibr}$

Both entropy and enthalpy are strongly temperature dependent. Other conditions: pH, ionic strength, and water activity.

Solvent influences:
• short-range solute-solvent interactions: nonpolar solvation free energies assumed to be proportional to the solvent accessible surface area (SASA),
• long-range electrostatic interactions: represented by a macroscopic dielectric constant (screening effect).

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