Expanding potential, molecular systems

EWW Hamiltonian, Renner-Teller effect, triatomic molecules, 610—615 Expanding potential, molecular systems,... 

When a chemical reaction proceeds, we have established (by reference to experiment) that energy will be conserved. But we have not found a way of predicting in which direction the reaction will go. In other words we have not found a suitable definition of the position of equilibrium. We have discovered that for molecular systems (which may approach equilibrium by endothermic processes) the energy, unlike the potential energy in mechanical systems, does not provide a sufficient criterion for equilibrium. A new factor must be introduced which will enable us to understand why heat always flows from hot to cold bodies and why a perfect gas will expand to fill its container, even though no loss of energy (by the system) accompanies these processes. 

There exists another possibility for describing a molecular system in the framework of classical mechanics. This approach assumes that the potential energy of a molecular system can be expanded in a Taylor series around its equilibrium geometry. By modifying this approach to make it transferable between different systems, molecular mechanics force fields are obtained. We describe later how this is done, how these force fields are used (see the section entitled Molecular Mechanics Force Fields), and compare the advantages and disadvantages of force fields of both types. 

The classical picture of molecular interactions and their effect on macroscopic properties is well developed in statistical thermodynamics of phase equilibria. Briefly, molecular interactions determine the potential of mean force which is directly related to the pair correlation function from which all macroscopic (thermodynamic) properties such as virial coefficients, osmotic pressure, and so on can be derived as a function of temperature and pressure. The question arises if this well-developed framework of equilibrium thermodynamics can be expanded to particulate systems in equilibrium. Equihbrium systems can be best studied for coUoids in solution on which we wiU focus our discussion in the following. 

The semiclassical approach heavily relies on the empirical interactions. As in many molecular systems, diamondoids have both intramolecular and intermolecular interactions. Intramolecular interactions reflect the bonding nature of the system. For instance, C-H bonds have very different potential surfaces from those of C-C bonds, to which they are also related whether the bonds are single, double, or triple. The Lennard-Jones potential is probably the simplest one to use. In general, a two-body potential can be expanded as... 

When sufficiently high levels of expression and protein accumulation are achieved, efficient downstream processing protocols must be developed to insure product quality and the economic feasibility of production. As the demand for safe, recombinant pharmaceutical proteins continues to expand, the market potential of plant-produced recombinant proteins is considerable. Molecular farming can produce recombinant proteins at a lower cost than traditional expression systems based on microbial or animal cell culture, and without the risk of contamination with human pathogens. 

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