A PROGRAM SYSTEM FOR ABINITIO MO CALCULATIONS ON VECTOR AND PARALLEL PROCESSING MACHINES .1. EVALUATION OF INTEGRALS

We present a program system for ab initio molecular orbital calculations on vector and parallel computers. The present article is devoted to the computation of one- and two-electron integrals over contracted Gaussian basis sets involving s-, p-, d- and f-type functions. The McMurchie and Davidson (MMD) algorithm has been implemented and parallelized by distributing over a limited number of logical tasks the calculation of the 55 relavant classes of integrals. All sections of the MMD algorithm have been efficiently vectorized, leading to a scalar/vector ratio of 5.8. Different algorithms are proposed and compared for an optimal vectorization of the contraction of the "intermediate integrals" generated by the MMD formalism. Advantage is taken of the dynamic storage allocation for tunning the lenght of the vector loops (i.e. the size of the vectorization buffer) as a function of (i) the total memory available for the job, (ii) the number of logical tasks defined by the user (≤13), and (iii) the storage requested by each specific class of integrals. Test calculations carried out on a CRAY-2 computer show that the average number of finite integrals computed over a (s,p,d,f) CGTO basis set is about 118000 per second and per processor. The combination of vectorization and parallelism on this 4-processor machine reduces the CPU time by a factor larger than 20 with respect to the scalar and sequential performance. © 1990.