Atomic monopole "point charges" are routinely determined through a least squares fit to molecular electrostatic potentials [potential-derived (PD) charges]. Previously, it has been shown that these charges vary with variation in molecular conformation. Also, it has been observed that these swings in charges are highly correlated between neighboring atoms. Here, we examine the least squares variance-covariance data matrices for a set of data in the literature and find further indications of high colinearity within the data. These colinearities effectively reduce the dimensionality of the data to a value well below the number of atoms in the molecules. This suggests that the data is not of sufficient dimensionality to support calculation of the charges for all of the atoms in a statistically significant way. We experiment with fixing the charges of atoms whose PD charges reflect large errors in the fit. The resulting estimates of fit of the remaining charges are little degraded from the estimates of fit when the charges of all of the atoms are fit. In addition, the charges that are fit take what would be considered more reasonable and "chemically intuitive" values, often of smaller magnitude. Although most of the free charges continue to vary with molecular conformation, their range is no larger than when all charges were fit and, in some cases, the ranges of the charges for the fit atoms is actually reduced over those that are found when all of the atoms take part in the fitting procedure. The errors of fit are lower and the unconstrained charges appear more reasonable when more chemically "reasonable" charges are used for the fixed values. This suggests that in many cases charges are transferable between molecules. Further, it shows a way to justifiably reduce the large fluctuations in PD charges that occur with variations in conformation. 0 1993 by John Wiley & Sons, Inc.
METHODOLOGY
The data was the same as used in our previous studyz5 and consisted of 11 different conformations