Solvents potential surfaces

In the previous chapter we considered a rather simple solvent model, treating each solvent molecule as a Langevin-type dipole. Although this model represents the key solvent effects, it is important to examine more realistic models that include explicitly all the solvent atoms. In principle, we should adopt a model where both the solvent and the solute atoms are treated quantum mechanically. Such a model, however, is entirely impractical for studying large molecules in solution. Furthermore, we are interested here in the effect of the solvent on the solute potential surface and not in quantum mechanical effects of the pure solvent. Fortunately, the contributions to the Born-Oppenheimer potential surface that describe the solvent-solvent and solute-solvent interactions can be approximated by some type of analytical potential functions (rather than by the actual solution of the Schrodinger equation for the entire solute-solvent system). For example, the simplest way to describe the potential surface of a collection of water molecules is to represent it as a sum of two-body interactions (the interac-... 

How to Obtain Refined Potential Surfaces for the Solvent Molecules... 

With a realistic solvent model, we can explore the properties of solvated molecules. As before, we take a classical approach by adding the solute-solvent interaction term (USs) to the potential surface of the system and write... 

The term Uss is the solvent-solvent interaction term [the Unb and Uqq terms of eq. (3.1)] and t/ind is the induced dipoles three-body term which includes now the field both from the solute and the solvent. With a potential surface for a solvated solute we can address the important issue of evaluating solvation energies. In principle, one can try to evaluate the average poten-... 

Now knowing how to evaluate solvation-free energies, we are ready to explore the effect of the solvent on the potential surface of the reacting solute atoms. Adapting the EVB approach we can describe the reaction by including the solute-solvent interaction in the diagonal elements of the solute Hamiltonian, using... 

With the gas-phase potential surface we can obtain the solution Hamiltonians by eq. (3.23), adding the solvent-solute interaction to the classical part of the diagonal EVB matrix elements. That is, we use... 

With these AG we can estimate the energetics of the key asymptotic point on the potential surface of the reference reaction in which AH and R-O-R are kept in the same solvent cage. First, we note that (AG2) is... 

Subtilisin, 170 active site of, 171,173 autocorrelation function of, 216, 216 potential surfaces for, 218 site-specific mutations, 184, 185, 187-188 Sugars, see Oligosaccharides Surface-constrained solvent model, 125... 

In summary, all the experiments expressly selected to check the theoretical description provided fairly clear evidence in favour of both the basic electronic model proposed for the BMPC photoisomerization (involving a TICT-like state) and the essential characteristics of the intramolecular S and S, potential surfaces as derived from CS INDO Cl calculations. Now, combining the results of the present investigation with those of previous studies [24,25] we are in a position to fix the following points about the mechanism and dynamics of BMPC excited-state relaxation l)photoexcitation (So-Si)of the stable (trans) form results in the formation of the 3-4 cis planar isomer, as well as recovery of the trans one, through a perpendicular CT-like S] minimum of intramolecular origin, 2) a small intramolecular barrier (1.-1.2 kcal mol ) is interposed between the secondary trans and the absolute perp minima, 3) the thermal back 3-4 cis trans isomerization requires travelling over a substantial intramolecular barrier (=18 kcal moM) at the perp conformation, 4) solvent polarity effects come into play primarily around the perp conformation, due to localization of the... 

PPII helix-forming propensities have been measured by Kelly et al. (2001) and A. L. Rucker, M. N. Campbell, and T. P. Creamer (unpublished results). In the simulations the peptide backbone was constrained to be in the PPII conformation, defined as (0,VO = ( — 75 25°, +145 25°), using constraint potentials described previously (Yun and Hermans, 1991 Creamer and Rose, 1994). The AMBER/ OPLS potential (Jorgensen and Tirado-Rives, 1988 Jorgensen and Severance, 1990) was employed at a temperature of 298° K, with solvent treated as a dielectric continuum of s = 78. After an initial equilibration period of 1 x 104 cycles, simulations were run for 2 x 106 cycles. Each cycle consisted of a number of attempted rotations about dihedrals equal to the total number of rotatable bonds in the peptide. Conformations were saved for analysis every 100 cycles. Solvent-accessible surface areas were calculated using the method of Richmond (1984) and a probe of 1.40 A radius. 

From the chemical point of view, the solvent in which the CL experiment is carried out can have a dramatic influence on the efficiency of the CL reaction as solvation can alter the shapes, the depths, and the densities of the vibrational states of the potential surfaces representing the ground states of products and reactants and the lowest excited singlet state of the potential fluorophore. The alteration of the intersections of these potential energy surfaces can affect the enthalpies of reaction and the enthalpies of activation for dark and lumigenic reactions. In some cases, these changes will favor CL (if AH decreases relative to AHa) and in some cases, they will make it thermodynamically unfavorable for CL to occur. 

Another attempt to find solute geometries without explicitly including solvent molecules in the calculations is due to Sinanoglu 245,246). jn a recent paper he proposed a C-potential" effective for molecules in solution, which is derived from the potential surface of a naked solute molecule by inclusion of additive solvation terms obtainable from simple macroscopic properties of the pure liquid solvent. This method is an extension of an earlier formalism applicable to intermolecular potentials between solvated molecules 247,248). 

The applications of NN to solvent extraction, reported in section 16.4.6.2., suffer from an essential limitation in that they do not apply to processes of quantum nature therefore they are not able to describe metal complexes in extraction systems on the microscopic level. In fact, the networks can describe only the pure state of simplest quantum systems, without superposition of states. Neural networks that indirectly take into account quantum effects have already been applied to chemical problems. For example, the combination of quantum mechanical molecular electrostatic potential surfaces with neural networks makes it possible to predict the bonding energy for bioactive molecules with enzyme targets. Computational NN were employed to identify the quantum mechanical features of the... 

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... 

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