Molecular potential global

The second symmetry requirement that the expression for the inter-molecular potential has to meet is that it must be invariant under any rotation of the global coordinate frame. The transformation properties of the symmetry-adapted functions Gj Hw) under such a rotation are easily obtained from Eqs. (10) and (5) ... 

The macroscopic property of interest, e.g., heat of vaporization, is represented in terms of some subset of the computed quantities on the right side of Eq. (3.7). The latter are measures of various aspects of a molecule s interactive behavior, with all but surface area being defined in terms of the electrostatic potential computed on the molecular surface. Vs max and Fs min, the most positive and most negative values of V(r) on the surface, are site-specific they indicate the tendencies and most favorable locations for nucleophilic and electrophilic interactions. In contrast, II, a ot and v are statistically-based global quantities, which are defined in terms of the entire molecular surface. II is a measure of local polarity, °fot indicates the degree of variability of the potential on the surface, and v is a measure of the electrostatic balance between the positive and negative regions of V(r) (Murray et al. 1994 Murray and Politzer 1994). 

The most serious problem with MM as a method to predict molecular structure is convergence to a false, rather than the global minimum in the Born-Oppenheimer surface. The mathematical problem is essentially still unsolved, but several conformational searching methods for approaching the global minimum, and based on either systematic or random searches have been developed. These searches work well for small to medium-sized molecules. The most popular of these techniques that simulates excitation to surmount potential barriers, has become known as Molecular Dynamics [112]. 

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