A program system for ab initio mo calculations on vector and parallel processing machines I. Evaluation of integrals

Abstract 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.

[1]  Michel Dupuis,et al.  Molecular symmetry and closed‐shell SCF calculations. I , 1977 .

[2]  Martin Head-Gordon,et al.  A method for two-electron Gaussian integral and integral derivative evaluation using recurrence relations , 1988 .

[3]  Shigeru Obara,et al.  General recurrence formulas for molecular integrals over Cartesian Gaussian functions , 1988 .

[4]  Shigeru Obara,et al.  Efficient recursive computation of molecular integrals over Cartesian Gaussian functions , 1986 .

[5]  S. Huzinaga,et al.  A systematic preparation of new contracted Gaussian‐type orbital sets. III. Second‐row atoms from Li through ne , 1980 .

[6]  S. Huzinaga,et al.  A systematic preparation of new contracted Gaussian type orbital set. I. Transition metal atoms from Sc to Zn , 1979 .

[7]  E. Davidson,et al.  One- and two-electron integrals over cartesian gaussian functions , 1978 .

[8]  V. R. Saunders,et al.  Applications of the CRAY-1 for quantum chemistry calculations , 1982 .

[9]  R. Wiest,et al.  The metal-carbon triple bond in Cl(Co)4crCH: A CAS SCF study of neutral carbyne complexes , 1986 .

[10]  I. Shavitt,et al.  Vectorizing a sequence of conditional branches: The calculation of the class index of two-electron repulsion integrals on cray computers , 1988 .

[11]  Dermot Hegarty,et al.  Integral evaluation algorithms and their implementation , 1983 .

[12]  Clifford E. Dykstra,et al.  Advanced theories and computational approaches to the electronic structure of molecules , 1984 .