Electrostatic energies parameterization

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... 

The EFP method attempts to overcome this parameterization problem by including electrostatics and polarization from first principles. This represents a considerable departure from the traditional MM potentials used in biomolecular simulations. The electrostatic energy remains an approximation, however, as the multipole expansions in Ueie are left uncorrected for the effects of charge penetration (C/pen). This penetration energy, Upen, is then implicit in Urep. Thus a limitation that is characteristic of all force-field methods, from the crudest MM to the most sophisticated QM/MM, is a certain lack of generality, i.e., there are arbitrary parameters that have to be refined and fitted for a particular application. 

Because the electrostatic energy terms for an uncharged pure system (such as a bulk structure) is zero, the energy contribution of COMB for such a system is from the short-range interactions [eqn (7.18)] and the formalism is reduced to the Tersoff type of potential. This case is straightforward for the parameterization of the COMB potential, which only fits parameters in the pairwise term and bond-order terms, as shown in Table 7.2. The van der Waals interaction will be considered for hydrocarbon systems. 

Assisted model building with energy refinement (AMBER) is the name of both a force field and a molecular mechanics program. It was parameterized specifically for proteins and nucleic acids. AMBER uses only five bonding and nonbonding terms along with a sophisticated electrostatic treatment. No cross terms are included. Results are very good for proteins and nucleic acids, but can be somewhat erratic for other systems. 

The consistent force field (CFF) was developed to yield consistent accuracy of results for conformations, vibrational spectra, strain energy, and vibrational enthalpy of proteins. There are several variations on this, such as the Ure-Bradley version (UBCFF), a valence version (CVFF), and Lynghy CFF. The quantum mechanically parameterized force field (QMFF) was parameterized from ah initio results. CFF93 is a rescaling of QMFF to reproduce experimental results. These force fields use five to six valence terms, one of which is an electrostatic term, and four to six cross terms. 

G. D. Hawkins, C. J. Cramer, and D. G. Truhlar, Parameterized model for aqueous free energies of solvation using geometry-dependent atomic surface tensions with implicit electrostatics, J. Phys. Chem. B 101 7147 (1997) erratum to be published. 

Here Vij denotes the distance between atoms i and j and g(i) the type of the amino acid i. The Leonard-Jones parameters Vij,Rij for potential depths and equilibrium distance) depend on the type of the atom pair and were adjusted to satisfy constraints derived from as a set of 138 proteins of the PDB database [18, 17, 19]. The non-trivial electrostatic interactions in proteins are represented via group-specific dielectric constants ig(i),g(j) depending on the amino-acid to which atom i belongs). The partial charges qi and the dielectric constants were derived in a potential-of-mean-force approach [20]. Interactions with the solvent were first fit in a minimal solvent accessible surface model [21] parameterized by free energies per unit area (7j to reproduce the enthalpies of solvation of the Gly-X-Gly family of peptides [22]. Ai corresponds to the area of atom i that is in contact with a ficticious solvent. Hydrogen bonds are described via dipole-dipole interactions included in the electrostatic terms... 

Collection of numbers that parameterize the potential energy functions. These include the force constants, the ideal distances and angles, and parameters for van der Waals, electrostatic and other terms. Since the force field parameters are dependent on the potential energy functions, the entire set of functions and parameters are sometimes referred to as the force field . 

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