Application of rigorous bounds for efficient evaluation of molecular electrostatic potentials

Rigorous upper bounds to electrostatic potential integrals over Gaussian basis sets have been exploited for accurate and speedy evaluation of molecular electrostatic potentials (MESP). These bounds are applied to eliminate those pairs of Gaussians which contribute insignificantly to the total MESP. An efficient algorithm for MESP mapping has been developed with the help of these bounds. Further, rigorous inequalities to the auxiliary functions Fm(t), were derived. Some of these bounds are so tight that they are employed as a good approximation to Fm(t). The algorithm developed by incorporation of the above aspects is tested on trans-butadiene, cyclopropane and 1,2,3,4,5,6,7-octa-heptene molecules using 4-31G and 3G basis sets. A factor of six and more in terms of CPU time is obtained for all the test cases studied over the usual straightforward computation. A parallel version of this algorithm has also been developed