Mechanics, potentials

The result is that, to a very good approxunation, as treated elsewhere in this Encyclopedia, the nuclei move in a mechanical potential created by the much more rapid motion of the electrons. The electron cloud itself is described by the quantum mechanical theory of electronic structure. Since the electronic and nuclear motion are approximately separable, the electron cloud can be described mathematically by the quantum mechanical theory of electronic structure, in a framework where the nuclei are fixed. The resulting Bom-Oppenlieimer potential energy surface (PES) created by the electrons is the mechanical potential in which the nuclei move. Wlien we speak of the internal motion of molecules, we therefore mean essentially the motion of the nuclei, which contain most of the mass, on the molecular potential energy surface, with the electron cloud rapidly adjusting to the relatively slow nuclear motion. 

Here p is the chemical potential just as the pressure is a mechanical potential and the temperature Jis a thennal potential. A difference in chemical potential Ap is a driving force that results in the transfer of molecules tlnough a penneable wall, just as a pressure difference Ap results in a change in position of a movable wall and a temperaPire difference AT produces a transfer of energy in the fonn of heat across a diathennic wall. Similarly equilibrium between two systems separated by a penneable wall must require equality of tire chemical potential on the two sides. For a multicomponent system, the obvious extension of equation (A2.1.22) can be written... 

Field, M.J., Bash, P.A., Karplus, M. A combined quantum mechanical and molecular mechanical potential for molecular dynamics simulations. J. Comput. Chem. 11 (1990) 700-733. 

To see the contributions to the molecular mechanics potential energy function and their mathematical representation... 

Many molecular mechanics potentials were developed at a time when it was computationally impractical to add large numbers of discrete water m olecules to ih e calcu la Lion to sim ulate th e effect of ac ueous media. As such, tech n iq ties cam e into place that were intended to Lake into account the effect of solvent in some fashion. These tech niqiieswcre difficult to justify physically but they were used n cvcrth eless. 

Amara P and M J Field 1998. Combined Quantum Mechanical and Molecular Mechanical Potentials. In Schleyer, P v R, N L Allinger, T Clark, J Gasteiger, P A Kolhnan H F Schaefer HI and P R Schreiner (Editors). The Encyclopedia of Computational Chemistry. Chichester, John Wiley Sons. 

Gao J 1995. Methods and Applications of Combined Quantum Mechanical and Molecular Mechanical Potentials. In Lipkowitz K B and D B Boyd (Editors) Reviews in Computational Chemistry Volume 7. New York, VCH Publishers, pp. 119-185. 

Field M J, P A Bash and M Karplus 1990. A Combined Quantum Mechanical and Molecular Mechanical Potential for Molecular Dynamics Simulations. Journal of Computational Chemistry 11 700-733. 

As motivation for the rest of the chapter, a few further observations can be made. Eirst, the calculation of full electrostatics is expensive. A typical molecular mechanics potential function is of the form... 

Computations can be carried out on systems in the gas phase or in solution, and in their ground state or in an excited state. Gaussian can serve as a powerful tool for exploring areas of chemical interest like substituent effects, reaction mechanisms, potential energy surfaces, and excitation energies. 

Carotenoid oxidation products are also supposed to have detrimental effects in vivo. As mentioned earlier, they are suspected to be involved in the adverse effects of high doses of 3-carotene supplementation in smokers and asbestos workers (CARET and ATBC studies) and in smoke-exposed ferrets. The mechanisms potentially involved have been investigated in vitro. P-Apo-8 -carotenal, an eccennic cleavage oxidation product of P-carotene, was shown to be a strong inducer of CYPlAl in rats, whereas P-carotene was not active. Cytochrome P450 (CYP 450) enzymes thus induced could enhance the activation of carcinogens and the destruction of retinoic acid. ... 

Here we present and discuss an example calculation to make some of the concepts discussed above more definite. We treat a model for methane (CH4) solute at infinite dilution in liquid under conventional conditions. This model would be of interest to conceptual issues of hydrophobic effects, and general hydration effects in molecular biosciences [1,9], but the specific calculation here serves only as an illustration of these methods. An important element of this method is that nothing depends restric-tively on the representation of the mechanical potential energy function. In contrast, the problem of methane dissolved in liquid water would typically be treated from the perspective of the van der Waals model of liquids, adopting a reference system characterized by the pairwise-additive repulsive forces between the methane and water molecules, and then correcting for methane-water molecule attractive interactions. In the present circumstance this should be satisfactory in fact. Nevertheless, the question frequently arises whether the attractive interactions substantially affect the statistical problems [60-62], and the present methods avoid such a limitation. 

Beyond the clusters, to microscopically model a reaction in solution, we need to include a very big number of solvent molecules in the system to represent the bulk. The problem stems from the fact that it is computationally impossible, with our current capabilities, to locate the transition state structure of the reaction on the complete quantum mechanical potential energy hypersurface, if all the degrees of freedom are explicitly included. Moreover, the effect of thermal statistical averaging should be incorporated. Then, classical mechanical computer simulation techniques (Monte Carlo or Molecular Dynamics) appear to be the most suitable procedures to attack the above problems. In short, and applied to the computer simulation of chemical reactions in solution, the Monte Carlo [18-21] technique is a numerical method in the frame of the classical Statistical Mechanics, which allows to generate a set of system configurations... 

Bash, P. A., Field, M. J. and Karplus, M. Free energy perturbation method for chemical reactions in the condensed phase a dynamical approach based on a combined quantum and molecular mechanics potential,... 

Jiali Gao, Methods and Applications of Combined Quantum Mechanical and Molecular Mechanical Potentials. 

Type 1 are potential/potential phase diagrams. The potentials considered in chemical thermodynamics are temperature (thermal potential), pressure (mechanical potential) and the chemical potentials of the N components pj, i2, ig,. ..,... 

---