Atomic charges molecular mechanics schemes

This exercise will examine other ways of computing charges other than Mulliken population analysis. Since atomic charge is not a quantum mechanical observable, all methods for computing it are necessarily arbitrary. We ll explore the relative merits of various schemes for partitioning the electron density among the atoms in a molecular system. 

Das D, KP Eurenius, EM Billings, P Sherwood, DC Chatfield, M Hodoscek, BR Brooks (2002) Optimization of quantum mechanical molecular mechanical partitioning schemes Gaussian delocalization of molecular mechanical charges and the double link atom method. J. Chem. Phys. 117 (23) 10534-10547... 

The treatment of charges in molecular mechanics calculations remains a central question. The exact computational scheme used to obtain charges has been under considerable review. One obvious way is to obtain the charges from quantum mechanics calculations. Since quantum mechanically derived point charges are based on various population analyses, the level of accuracy required and how the charges should be distributed between the atoms have not been universally accepted. One final check on the charge distribution in a molecule is the comparison of the... 

In order to transform the quantum mechanical language and observables, equations (6) and (7), into empirical force field language and parameters, we first have to partition the molecule into atoms , and then reproduce the moments and their derivatives that appear in equations (6) and (7) from those of the atoms. There is, of course, no unique way of doing so, and in the following we adopt the scheme in which the molecule is a collection of point charges, dipoles, quadrupoles etc. centered on the nuclei. Furthermore, we assume that the first molecular moment - the dipole moment - is completely reproduced by the atomic charges ... 

For example, the fact that ions of m/z [90 + R]+ and [104 + R]+ arise directly from the molecular ions of sulfones (Scheme 5.20) confirms a transformation with a new C-C bond formation between carbon atoms of the small ring and of the second benzene ring prior to the fragmentation of the M+. In this case the cyclopropyl moiety (maybe iso-merized) retains the charge and unpaired electron and attacks the second aromatic ring by a nucleophilic or radical mechanism. 

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