Polarizable continuum model dispersion energies

C. Amovilli and B. Mennucci, Self-consistent-field calculation of Pauli repulsion and dispersion contributions to the solvation free energy in the polarizable continuum model, J. Phys. Chem. B, 101 (1997) 1051. 

The electrostatic solvation energy is only a part of the total solvation energy. Cavitation, dispersion and repulsion terms must be added. We show below that the MPE method leads to similar electrostatic energies than the polarizable continuum model (PCM) of Tomasi and co-workers [10], provided the same cavities are used. Therefore, non-electrostatic terms in these methods may be computed using the same computational strategies [15]. We emphasize the fact that accurate non-electrostatic contributions are often difficult to compute since they are based on parameterized formulae that cannot be directly compared to experiment. The obtained data must therefore be used with prudence, especially if they are expected to play a major role in the process under study. Fortunately, in many circumstances, non-electrostatic terms are small and/or vary little, so that they can be neglected. Tunon et al. [80] developed a parameterized expression for the MPE method using an expression of the type... 

In section II we focused on an accurate description of electrostatic interactions between solute and solvent. Although these interactions accormt for the largest parts of the free energy of solvent, other interactions may contribute as well. These interactions, due to dispersion and repulsion, were studied by Curutchet et al Amoville and Mennucci had earlier developed a formalism for including these interactions in the polarizable continuum model and Curutchet et al. tested it on a larger set of solvent-solute systems for which they also calculated these interactions with force-field methods. 

In order to model the surrounding enzyme and solvent, a continuum-solvation method is typically used, such as the polarizable continuum model (PCM) or the conductor-like solvent model (COSMO),employing a dielectric constant (e) close to 4, a common value to model the hydrophobic environment of an enzyme active site. For small QM models, the results may be very sensitive to this value, but the results typically become independent of the dielectric constant after the addition of -200 atoms. Often only the polar part of the solvation energy is included in QM-cluster calculations, although the non-polar parts (the cavitation, dispersion and repulsion energies) are needed to obtain valid solvation energies, as will be discussed below. 

In Eq. (6) Ecav represents the energy necessary to create a cavity in the solvent continuum. Eel and Eydw depict the electrostatic and van-der-Waals interactions between solute and the solvent after the solute is brought into the cavity, respectively. The van-der-Waals interactions divide themselves into dispersion and repulsion interactions (Ed sp, Erep). Specific interactions between solute and solvent such as H-bridges and association can only be considered by additional assumptions because the solvent is characterized as a structureless and polarizable medium by macroscopic constants such as dielectric constant, surface tension and volume extension coefficient. The use of macroscopic physical constants in microscopic processes in progress is an approximation. Additional approximations are inherent to the continuum models since the choice of shape and size of the cavity is arbitrary. Entropic effects are considered neither in the continuum models nor in the supermolecule approximation. Despite these numerous approximations, continuum models were developed which produce suitabel estimations of solvation energies and effects (see Refs. 10-30 in 68)). 

Here, we note only that the properties computed from these models are extremely sensitive to how the molecular cavity (solute/continuum interface) is constructed, and that nonelectrostatic solvation effects are typically (though not always ) neglected in the PCMs such as COSMO, GCOSMO, lEF-PCM, and SS(V)PE that are derived from Poisson s equation for continuum electrostatics. In contrast, such effects are built into the empirical SMx models and are crucial to accurate prediction of solvation free energies. " It is unclear how the neglect of nonelectrostatic effects might impact the calculation of anion VDEs cavitation effect should cancel, but dispersion effects may not, as the anion is intrinsically more polarizable. One may hope that these effects will disappear if a sufficiently large number of explicit solvent molecules is included as part of the QM solute. 

---