Correlation nonbonded interactions

Functions and partly also constants for nonbonded interactions within single molecules (intramolecular interactions) have been taken over in many cases from investigations of interactions between different molecules (intermolecular interactions) (7,3). The derivation of parameters for nonbonded interactions presents further difficulties, e.g. the problem of the anisotropy of such interactions (8, 23) and parameter correlations (Section 2.4.). There is no agreement on the question whether pairs of atoms separated by a chain of only three bonds should be counted as nonbonded interactions. Some authors include these pairs,... 

The lion s share of the computer-time for the least-squares process has to be provided for forming the Z-matrix. The elements of this matrix are evaluated partly numerically and partly analytically in the calculations of Lifson and Warshel (17). In certain cases, strong parameter correlations may occur. Therefore caution is demanded when inverting the matrix C. Also from investigations other than consistent force-field calculations it is known that such correlations frequently occur among the parameters for the nonbonded interactions (34,35). Another example of force field parameter correlations was encountered by Ermer and Lifson (19) in the course of the calculation of olefin properties. When... 

Calculations of nuclear spin-spin couplings by Karplus and co-workers (60) using valence bond functions have been gratifyingly successful. It was to be expected that valence bond functions would be more accurate than LCAO MO functions for this purpose since the former include explicitly effects of spin correlation. For interactions between nonbonded nuclei such as occur, for example, between the hydrogen atoms of CH4 or NH4+, structures of the forms (61)... 

There is a strong correlation between the parameters of different potential energy functions so that they should not be developed or refined in isolation. For example, the barrier to rotation about a bond can be modified by changing the explicit torsion angle term or by changing the nonbonded interactions. Thus, the effect of any change on a force field parameter needs to be tested extensively, i.e.,... 

The relative configuration of the aziridines may be predicted on the basis of correlation between the diastereomer ratios and nonbonded interactions in molecular models, however, this must be confirmed by, for example. X-ray structure determination. 

Electronic charge densities have fundamental influence on a wide variety of molecular properties. Electron densities are related to the formal sizes of atoms and the formal bond lengths of molecules, for example, in various crystals [278], and there are important relations between experimental electron densities and temperature [279]. Electronic charge densities p(r) can be calculated by various quantum chemical methods, both ab initio and semiempirical (see, e.g., refs. [90,91]). Density difference calculations are used for direct comparisons of electronic structures (see, e.g., ref. [280]), whereas the effects of electron correlation on charge densities are of special importance in the study of nonbonded interactions [281]. 

The fact that the second derivative, d U/db in Eq. [24], contains a slight contamination from nonbonded interactions and third-order terms is an example of how parameter correlation can arise because it is not a pure bond stretch. If this derivative were simply used as the bond-stretching force constant, as in spectroscopic force fields, it would not be transferable to other molecules where the coupling or nonbonded interaction may differ. This problem is a general one and can be quite serious. As already discussed in previous sections, one possible resolution of this problem lies in the use of many molecular environments to determine all contributing terms. If we simultaneously fit many different alkanes, i.e., ethane, propane, butane, etc., with the full force field and assume... 

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