Potential energy function determination

Potential Energy Function Determination The Minimal Expansion... 

The explicit expressions used for each of the terms in (16.94) define what is called a molecular-mechanics force field, since the derivatives of the potential-energy function determine the forces on the atoms. A force field contains analytical formulas for the terms in (16.94) and values for all the parameters that occur in these formulas. The MM method is sometimes called the empirical-force-field method. Empirical force fields are used not only for single-molecule molecular-mechanics calculations of energy differences, geometries, and vibrational frequencies, but also for molecular-dynamics simulations of liquids and solutions, where Newton s second law is integrated to follow the motions of atoms with time in systems containing hundreds of molecules. 

A potential advantage of methods based on a series expansion of the free energy is that the convergence of the series is determined by the A dependence of the potential energy function meaning that the efficiency of the approach could be enhanced by a judicious choice of coupling scheme. 

A particularly important application of molecular dynamics, often in conjunction with the simulated annealing method, is in the refinement of X-ray and NMR data to determine the three-dimensional structures of large biological molecules such as proteins. The aim of such refinement is to determine the conformation (or conformations) that best explain the experimental data. A modified form of molecular dynamics called restrained moleculai dynarrdcs is usually used in which additional terms, called penalty functions, are added tc the potential energy function. These extra terms have the effect of penalising conformations... 

The hot bond fracture stress Morse potential energy function by [1]... 

The force constant that is associated with the stretching vibration of a bond is often taken as a measure of the strength of the bond, although it is more correctly a measure of the curvature of the potential energy function around the minimum (Figure 2.1) that is, the rigidity of the bond. For a diatomic molecule, the frequency of vibration v is determined by the force constant k and the reduced mass /x = + m2), where m and m2 are the masses of... 

It is also possible to build the order parameter directly into the potential energy function. This would enable one to determine the free energy difference between a given potential and a reference potential. In a sense, this is complementary to the previous discussion of reaction coordinates rather than further subdividing configuration space by various order parameters, we are considering multiple configuration... 

Table 16-4 shows the IUPAC classification of pores by size. Micropores are small enough that a molecule is attracted to both of the opposing walls forming the pore. The potential energy functions for these walls superimpose to create a deep well, and strong adsorption results. Hysteresis is generally not observed. (However, water vapor adsorbed in the micropores of activated carbon shows a large hysteresis loop, and the desorption branch is sometimes used with the Kelvin equation to determine the pore size distribution.) Capillary condensation occurs in mesopores and a hysteresis loop is typically found. Macropores form important paths for molecules to diffuse into a par-... 

One of the important electrochemical interfaces is that between water and liquid mercury. The potential energy functions for modeling liquid metals are, in general, more complex than those suitable for modeling sohds or simple molecular liquids, because the electronic structure of the metal plays an important role in the determination of its structure." However, based on the X-ray structure of liquid mercury, which shows a similarity with the solid a-mercury structure, Heinzinger and co-workers presented a water/Hg potential that is similar in form to the water/Pt potential described earlier. This potential was based on quantum mechanical calculations of the adsorption of a water molecule on a cluster of mercury atoms. ... 

The parameterized, analytical representations of fi, ., fiy, fifi determined in the fitting are in a form suitable for the calculation of the vibronic transition moments V fi V") (a—O, +1), that enter into the expression for the line strength in equation (21). These matrix elements are computed in a manner analogous to that employed for the matrix elements of the potential energy function in Ref. [1]. 

Klein-Rydberg method phys chem A method for determining the potential energy function of the distance between the nuclei of a diatomic molecule from the molecule s vibrational and rotational levels. klTn rid,berg. meth ad )... 

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