Modified Born model

A modified Born model (uniform continuum solvent), in that it included the effect of waters of hydration about OH , was used to extrapolate the Kbha data[12]. The electrostatic contribution to the ion-solvation may be represented by the Born equation ... 

The Born equation thus derived is based on very simple assumptions that the ion is a sphere and that the solvents are homogeneous dielectrics. In practice, however, ions have certain chemical characters, and solvents consist of molecules of given sizes, which show various chemical properties. In the simple Born model, such chemical properties of ions as well as solvents are not taken into account. Such defects of the simple Born model have been well known for at least 60 years and some attempts have been made to modify this model. On the other hand, there has been another approach that focuses on short-range interactions of an ion with solvent molecules. 

Onufriev A, Bashford D, Case DA (2004) Exploring protein native states and large-scale conformational changes with a modified generalized born model. Proteins 55(2) 383-394... 

Jayaram B, Sprous D, Beveridge DL (1998) Solvation free energy of biomacromolecules parameters for a modified generalized born model consistent with the AMBER force field, J Phys Chem B, 102 9571-9576... 

The energy of interaction of an ion with a solvent may be represented by three parts its electrostatic interaction, a solvophobic component, and a specific interaction due to the donor-acceptor interactions. In recent considerations of the electrostatic interaction energy, the basic ideas of the Born model [21] are accepted, though its shortcomings and limitations are evident and the original equation has been modified. The ion, M", in this model is represented by a nonpolarizable metallic sphere with a radius r. 

Comparison of the inequalities (9.147) and (9.169) clearly demonstrates that the accuracy of the Born approximation depends only on the order N, while the accuracy of QL approximation of the same order can be increased by a proper selection of A. This circumstance makes the QL approximation a more efficient tool for EM modeling than a conventional or modified Born series. 

If the species is charged then an appropriate Born term must also be added. The react field model can be incorporated into quantum mechanics, where it is commonly refer to as the self-consistent reaction field (SCRF) method, by considering the reaction field to a perturbation of the Hamiltonian for an isolated molecule. The modified Hamiltoniar the system is then given by ... 

An alternative strategy is to synthesize a molecular wave function, on chemical intuition, and progressively modify this function until it solves the molecular wave equation. However, chemical intuition fails to generate molecular wave functions of the required spherical symmetry, as molecules are assumed to have non-spherical three-dimensional structures. The impasse is broken by invoking the Born-Oppenheimer assumption that separates the motion of electrons and nuclei. At this point the strategy ceases to be ab initio and reduces to semi-empirical quantum-mechanical simulation. The assumed three-dimensional nuclear framework is no longer quantum-mechanically defined. The advantage of this model over molecular mechanics is that the electron distribution is defined quantum-mechanically. It has been used to simulate the H2 molecule. 

If we had assumed the simple ionic model here, the Born-Mayer equation would have given a lattice energy of 178.4 kcal. per mole. The ionization energy of silver is 176.2 and the electron affinity of bromine (2) is — 79.1, from which the atomization energy of AgBr is 81.3 kcal. per mole, in error by nearly 40 kcal. Efforts to modify the Born-Mayer equation to take other factors into account (5) have not produced satisfactory results for such compounds. 

The IPAH model incorporated a number of factors that can modify the toxicity of the sediment-borne PAHs. Equilibrium partitioning was used to estimate the concentration of each PAH in the pore water of the sediment. The assumption was that the pore water material is the fraction that is bioavail-able. QSAR was also used to estimate the interstitial water concentration based on the octanol-water partition coefficient of several PAHs. Amphipods were used as the test organism to represent environmental toxicity. A toxic unit (TU) approach was used and the toxicity is assumed to be additive. The assumption of additivity is justified since each of the PAHs has a similar mode of action. Finally, a concentration-response model was formulated using existing toxicity data to estimate the probability of toxicity. 

An important aspect of empirical potential parameterization is the question of transferability. Are, for example, models derived in the study of binary oxides, transferable to ternary oxides Considerable attention has been paid to this problem by Cormack etal who have examined the use of potentials in spinel oxides, for example, MgAl204, NiCr204, and so on in addition Parker and Price have made a very careful study of silicates especially Mg2Si04. These studies conclude that transferability works well in many cases. However, systematic modifications are needed when potentials are transferred to compounds with different coordination numbers. For example, the correct modeling of MgAl204 requires that the potential developed for MgO, in which the magnesium has octahedral coordination, be modified in view of the tetrahedral coordination of Mg in the ternary oxide. The correction factor is based on the difference Ar between the effective ionic radii for the different coordination numbers. If an exponential, Born-Mayer, repulsive term is used, the preexponential factor is modified as follows ... 

---