Repulsion, excess

AMI. While MNDO was widely accepted and extensively used, there were still some deficiencies in the model. In particular, excessive repulsions were observed in MNDO potential energy surfaces just outside chemical bonding distances. This deficiency manifested itself (5,7) in the inability of MNDO to model hydrogen bonding, as well as in large positive errors in the AHf of sterically crowded molecules and in heats of activation. Again Dewar set off to correct this deficiency. 

A modified theory of the double layer is proposed in which the Boltzmann distribution is replaced with a distribution which accounts for the volume exclusion of the hydrated ionB. The double-layer repulsion force between two parallel plates thus calculated can be much greater than that predicted by the traditional theory, when the distance between the plates is sufficiently 6mall. This may at least partly explain the excess repulsive force that has been measured experimentally between two mica plate9, when the distance between the plates is sufficiently small. 

Another mechanism for the hydration repulsion between lipid bilayers was more recently proposed by Marcelja.22 It is based on the fact that in water the ions are hydrated and hence occupy a larger volume. The volume exclusion effects ofthe ions are important corrections to the Poisson— Boltzmann equation and modify substantially the doublelayer interaction at low separation distances. The same conclusion was reached earlier by Ruckenstein and Schiby,28 and there is little doubt that the hydration of individual ions modifies the double-layer interaction, providing an excess repulsion force.28 However, while the hydration of ions affects the double-layer interactions, the hydration repulsion is strong even in the absence of an electrolyte, or double-layer repulsion. 

Structures of liquids in general are dominated by influences of intermolecular repulsions. Intermolecular attractions have a comparatively minor effect on the radial distribution function and, in the case of asymmetric molecules, on intermolecular correlations as well. At the high density and close packing prevailing in the liquid state, the spatial arrangement of the molecules of a liquid can be satisfactorily described, therefore, by representing the molecules as hard bodies of appropriate size and shape whose only interactions are the excessive repulsions that would be incurred if one of them should overlap another. Once the liquid structure has been characterized satisfactorily on this basis, one may take account of the intermolecular attractions by averaging them over the molecular distribution thus determined. Mean-field theories are useful in this connection. 

It is quite clear from the data that there is substantial "excess attractive interaction in compound 4 i.e. the slight experimental preference for the axial conformation contrasts with a substantial calculated preference for the equatorial one the difference has been ascribed to the "gauche attractive effect" between oxygens (14,17). In contrast, for compounds 1 and 2 there is a substantial "excess" repulsion, i.e. the equatorial conformation is preferred more than calculated. The effect, which has been called "gauche repulsive effect" (14) is especially marked for gauche interactions between sulfur atoms, as in 2. Only in the case of compound 3 is the difference between calculated and observed preference for the equatorial position sufficiently small to make any conclusion uncertain, especially in view of the fact that, in the absence of energy minimization, the calculated energy difference (1.50 kcal/mol) may be somewhat overestimated. 

Shortcomings in the MNDO model as described in the previous section led to a reexamination of the model, leading to Austin Model 1, AM1. ° In this model a term was added to MNDO to correct for the excessive repulsions at van der Waals distances. Toward this end, each atom was assigned a number of spherical gaussians, which were intended to mimic long range correlation effects. The core-core repulsion term was modified and became... 

Barriers calculated using MNDO are frequently too high. This may be due in pan to the excess repulsions between atoms separated by distances just greater than normal covalent bond distances. These are largely corrected by... 

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