The Electrostatic Term

In more eomplex moleeules, the ES(R) funetion has a complex shape that often determines the salient features of the whole AEab(R) function. This is the reason why in the studies of moleeular reeognition and moleeular doeking, great attention is paid to a proper representation of ES(R). 

In the various methods for the deeomposition of AEab(R) there are no differences in the definition of ES. This quantity ean be easily computed with ab initio methods, and the following recipe is the speediest and more used way of doing it. 

The electronic wave functions of A and B are separately computed, each with its own Hamiltonian and Hg. Ab initio methods give at every level of the formulation of the the- 

The two antisymmelrie wave funetions Pa and Pb are then used, without modifiea-tions, in eonneetion wifli the Hamiltonian of the whole system Hab to get the expeetation value of flie energy aeeording to the standard notation of quantum chemistry we can write  

Hab differs from flie sum of Ha and Hb aeeording to the following expression 

Hab differs from the siun of Ha and Hb according to the following expression 

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Fhe van der Waals and electrostatic interactions between atoms separated by three bonds (i.c. the 1,4 atoms) are often treated differently from other non-bonded interactions. The interaction between such atoms contributes to the rotational barrier about the central bond, in conjunction with the torsional potential. These 1,4 non-bonded interactions are often scaled down by an empirical factor for example, a factor of 2.0 is suggested for both the electrostatic and van der Waals terms in the 1984 AMBER force field (a scale factor of 1/1.2 is used for the electrostatic terms in the 1995 AMBER force field). There are several reasons why one would wish to scale the 1,4 interactions. The error associated wilh the use of an repulsion term (which is too steep compared with the more correct exponential term) would be most significant for 1,4 atoms. In addition, when two 1,4... 

Consider the electrostatic terms. These are hard to evaluate because the output charge density is a complicated non spherical function in space. In traditional LMTO calculations the charge density is first spheridised before Ees is calculated. In this method p(r) is reduced to a sum of spherically symmetric balls of charge inside each ASA sphere [2]. 

The modification by method 2 is more acceptable. Although several types of modifications have been reported, Abraham and Liszi [15] proposed one of the simplest and well-known modifications. Figure 2(b) shows the proposed one-layer model. In this model, an ion of radius r and charge ze is surrounded by a local solvent layer of thickness b — r) and dielectric constant ej, immersed in the bulk solvent of dielectric constant ),. The thickness (b — r) of the solvent layer is taken as the solvent radius, and its dielectric constant ej is supposed to become considerably lower than that of the bulk solvent owing to dielectric saturation. The electrostatic term of the ion solvation energy is then given by... 

For the electrostatic term, there is a lack of reliable data and predictions dealing with the variation of the ions -polyion interactions with temperature. If one considers the relation (8), the product D T is a decreasing function of temperature but the term 7 decreases for the high values of and increases for the low values of . Nervertheless, these variations are negligeable and we have considered, in a first approximation, that the electrostatic term remains constant for 20 < T < 80°C. 

Table 1. Dependence of free energies (kcal/mol) on the residue-based cutoff radii Rc (A) for generation of cation-solvent (c-s) and solvent-solvent (s-s) interaction lists. Free energy changes are given for the forward AGf (i.e. 8-methyl-N5-deazapterin — 8-methyl-pterin) and reverse AGr mutations of the electrostatic terms. ...

The electrostatic terms can be reasonably well handled in solvents of high dielectric constant, but problems are raised by some solvents of widespread use in spin trapping, for example dichloromethane ( ) = 8.9), chloroform (D = 4.8) and benzene (D = 2.3), in which the electrostatic terms calculated as above for acetonitrile become -24.8, -46 and —96 kcal mol-1, respectively. Already in dichloromethane the effective standard potential of Fe(CN)6 /Fe(CN)6- is increased by 1.08 V and in benzene by an absurdly high 4.2 V ... 

The first term on the right in the sum of potentials in equation 9.12 is the electrostatic term (represented here as a simple dipole moment). Factor / is the angular function of dipole orientation ... 

Values in parentheses do not include the electrostatic term (otherwise, e=3)... 

In this formula, m and n are the number of ligand and receptor atoms, respectively r is the interatomic distance between atoms i and j the q s are the point charges on the atom, and A and B are adjustable van der Waals repulsion and attraction parameters, and D is the dielectric function. They assumed that this scoring function could account for hydrogen bond energies in the electrostatic term. 

In this expression, the dipole dipole interactions are included in the electrostatic term rather than in the van der Waals interactions as in Eq. (9.43). Of the four contributions, the electrostatic energy can be derived directly from the charge distribution. As discussed in section 9.2, information on the nonelectrostatic terms can be deduced indirectly from the charge density. The polarizability a, which occurs in the expressions for the Debye and dispersion terms of Eqs. (9.41) and (9.42), can be expressed as a functional of the density (Matsuzawa and Dixon 1994), and also obtained from the quadrupole moments of the experimental charge density distribution (see section 12.3.2). However, most frequently, empirical atom-atom pair potential functions like Eqs. (9.45) and (9.46) are used in the calculation of the nonelectrostatic contributions to the intermolecular interactions. 

For the symmetrical case it is easier to obtain the value of this pressure using the fact that at the mid-plane, where Y = Y, the electrostatic term disappears (i.e. dY/dX = 0, l l = 0) and the total pressure is equal to the osmotic pressure at this plane, which can then be easily calculated once the value of Ym is known. 

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... 

Avogadro s number is included in the electrostatic term to convert to units of per mole rather than per molecule.)... 

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