Self-consistent partial charges

Tanford and Roxby introduced the approximation that the average influence of site k on site i is proportional to the average charge of site k. The procedure of Tanford and Roxby iterates to a set of self-consistent partial charges on titrating sites at a given pH. The fractional protonation state, 0 is estimated from the Henderson-Hasselbalch equation... 

In the RISM-SCF theory, the ab initio MO calculation and the RISM equation must be solved in a self-consistent manner. In other words, solvent distribution around the solute molecule is determined by the electronic structure of the solute, and the electronic structure of the solute is affected by the surrounding solvent distribution. To achieve this, the iteration cycle is repeated until mutual convergence between the ab initio MO calculation, which provides the partial charge on the solute, and the RISM equation, which provides PCFs, is attained. As mentioned above, it is noteworthy that the computational cost is drastically reduced by the analytic expression of the theory, compared with the QM/MM method. This means that the combination with more sophisticated (and computationally more expensive) methods such as CASPT2 and MCQDPT can be realized with moderate computational costs. Moreover, solvent distribution at the molecular level can be obtained simultaneously. These are remarkable merits compared with other hybrid-type methods. 

Marenich, A. V. Olson, R. M. Kelly, C. P. Cramer, C. J. Truhlar, D. G. Self-consistent reaction field model for aqueous and nonaqueous solutions based on accurate polarized partial charges, J. Chem. Theor. Comput. 2007, 3, 2011 -2033. 

Table 12. Charges inside the atomic spheres Qy and the ratios Qy VOy of the 1 partial charges for LiTl and NaTl. For both compounds the self consistent scalar relativistic APW calculations have been performed for both structures B2 and B32. The lattice constants are chosen aB32 = 2 agi where aB32(NaTl) = 7.47 A and aB2(Lin) = 3.42 A are the lattice constants found experimentally. The volumes of the muffin-tin sphere are Wu(LiTl) = w-nCLiTI) = 12.47 A and ti)nj(NaTl) = o)Ti(NaTl) = 16.84 A ...

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