In ab initio molecular orbital calculations, two-electron integral computing timesaccount for more than 99 % of the total computing times. We are now developing a special-purpose machine MOEngine, which accelerates the calculations of two-electron integrals with high-performance and cost-effectiveness. Methods for two-electron integral calculations consist of mainly two steps, 1) computing auxiliary s-type integrals (m), 2) computing two-electron integrals by using [O] (m). MOEngine accelerates the step 2) by the Obara's recurrence formula. This is very effective when we compute the integrals in which each orbital has high total angular momentum, like [dd|dd]. However, these recurrence calculation steps 2) is quite less when we compute the integrals in which each orbital has low total angular momentum, like [ss|ss] and [ps|ss]. Here we discuss the efficient and high-performance computing methods for the auxiliary s-type integrals [O](m) by MOEngine.
Society of Computer Chemistry, Japan