Analyte interaction energies, evaluation

Assumption of the presence of single partitioning mechanism of analyte chromatographic retention has been the basis for the development of various methods for the evaluation of specific analyte interaction energies from retention data [44-46]. All these methods are only applicable in ideal chromatographic systems with proven absence of secondary equilibria effects, and all require specific assumptions regarding the volume of the stationary phase. Equation (2-43) is the main basis for these theories. 

The study of composite cations encounters further problems for classical and conventional QM/MM simulations, as their lower symmetry makes the evaluation of interaction energy surfaces and analytical potential functions describing them difficult. In these cases the QMCF MD method provides an elegant solution as well, renouncing solute-solvent potential functions. This advantage could be well demonstrated in studies on the dimer of Hg(I) (39), the titanyl ion (64), and the uranyl ions of U(V) (65) and U(VI) (66). Whereas the Hg + ion still has a fairly regular hydration structure although with a quite peculiar shape, the... 

Koen de Vries, Coussens and Meier likewise found that a combined molecular mechanics and molecular dynamics approach is a valuable tool for rationalizing qualitative gas chromatographic trends [69]. Experimentally they evaluated the thermodynamic parameters (AG, AAG, AH, AAH, etc.) for guest-host complexation of six analytes on a variety of derivatized CD columns. Their interpretation of the computational results is that one enantiomer fits the CD cavity better than the other resulting in a larger Interaction energy and greater loss of mobility. 

The superscript FT denotes the Fourier rransform of the corresponding quantity. The coefficients are obtained by solution of the diffusion equation for Qi as functions of rg, Yb and the periodicity of the microdomains. The sums in Eq. (188) can be analytically evaluated if is assumed to be independent of the chain length of the individual species. This assumption may be compared to that made in Sect. 3.3, i.e. the interaction energies per segment do not depend on rg, and allows the effective potentials ([Pg.106]

One can evaluate f, k, and analytically for the simple shape of the specific interaction energy profile. For example, in the case when energy distributions around the primary minimum and the barrier region can be approximated by a parabolic distribution, these constants are given by [115]... 

One of the major strengths of perturbation theory is that each of the interaction energy components possesses a multipole expansion that allows us to evaluate the interaction energy analytically in terms of molecular properties alone, at least when the molecular charge densities do not overlap appreciably. 

In a statistical Monte Carlo simulation the pair potentials are introduced by means of analytical functions. In the election of that analytical form for the pair potential, it must be considered that when a Monte Carlo calculation is performed, the more time consuming step is the evaluation of the energy for the different configurations. Given that this calculation must be done millions of times, the chosen analytic functions must be of enough accuracy and flexibility but also they must be fastly computed. In this way it is wise to avoid exponential terms and to minimize the number of interatomic distances to be calculated at each configuration which depends on the quantity of interaction centers chosen for each molecule. A very commonly used function consists of a sum of rn terms, r being the distance between the different interaction centers, usually, situated at the nuclei. In particular, non-bonded interactions are usually represented by an atom-atom centered monopole expression (Coulomb term) plus a Lennard-Jones 6-12 term, as indicated in equation (51). 

It is possible to evaluate cohesive energies, packing characteristics and other properties of molecular crystals quantitatively on the basis of nonbonded interactions between atoms (Kitaigorodsky, 1973). The analytical expressions are of the form... 

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