LAUSR

Rational drug design involves a vast amount of computations to get thermodynamically reliable results and often relies on atomic charges as a means to model electrostatic interactions within the system. Computational inefficiency often hampers the development of new and wider dissemination of the known methods; thus, any source to speed up the calculations without a sacrifice in quality is warranted. At the heart of many empirical methods of calculating atomic charges is the solution of a system of linear algebraic equations (SLAE). The classical method of solving SLAE-the Gauss method-has in general case a cubic computational complexity. It is shown that the use of iterative methods for solving SLAE, characteristic to typical empirical atomic charge calculation methods, makes it possible to significantly reduce the amount of calculations and to obtain a computational complexity approaching a quadratic one. Despite the fact that this phenomenon is well-known in numerical methods, iterative solvers surprisingly do not seem to have been systematically applied to calculation of atomic charges via empirical schemes. Another finding is the relative values of the matrix elements, determined by the physical grounds of the interactions within the empirical system, generally lead to SLAE's with well-defined matrices, suited to use with iterative solvers to fasten computation compared to using the noniterative solvers. This finding broadens the applicability range of atomic charges obtained with empirical methods for such cases as, e.g., account of polarizability via "on-the-fly" recalculation of charges in changing surroundings within the force fields in molecular dynamics settings.