1E03

Parallel computation of the four-center molecular
integral over the Slater-type orbitals(Tokyo Univ. of Science1 and Universidad Autónoma de Madrid2)
Kazuhiro Ishida,1 Rafael López,2 and Jaime Fernández Rico2
1. Introduction
Up to present, we have developed efficient algorithms [1-2] for the calculation of all of
the one-electron as well as the two-electron integrals with the Slater-type orbitals (STO).
Especially, one of us (K.I.) has developed the ACE-b3k3 algorithm [2] for the four-center
two-electron integrals with the STO-NG expansions. The ACE-b3k3 algorithm has been
implemented in our program for the molecular integrals with STO (SMILES 2007) [1].
Recently, one of us (K.I.) has developed a parallel version of his ACE-b3k3 algorithm.
We have already presented a part of the present efficiency of the parallel calculation for
the four-center (two-electron) electron-repulsion integrals (ERIs) at the 13th
International Congress of Quantum Chemistry (ICQC) held at the Helsinki University
during June 22-27, 2009 [3]. A part of the present results is shown in Table I. As seen inTable I, we may conclude that ab initio calculation for middle size molecules with a good
STO basis sets are currently an actual possibility. The next step is clearly the parallel
computation of the derivatives of the four-center ERIs over STOs. The derivatives withrespect to the nuclear coordinates are necessary, for example, for the geometry
optimization of a molecule, for the calculation of the intrinsic reaction coordinates (IRC),and so on. In this report, we show a new algorithm for the derivatives.
2. A new algorithm special for the derivatives
A part of the results of the present new algorithm is shown in Table II. As seen in Table
II, the total computer time for ERI + 12 kinds of derivatives is only slightly more thanthat for ERI only.
3.

References[1] Fernández Rico, J.; López, R.; Ema, I.; Ramírez, G. Int. J. Quantum Chem. 2008, 1081415-1421.
[2] Ishida, K. J. Chem. Phys. 2000, 113, 7818-7829.
[3] Ishida, K; López, R.; Fernández Rico, J. Abstract #B49, 13th ICQC.

Table I. Computer time of all four-center ERIs over STOs for several molecules
Molecule

SMILES 2007Parallel computation

Basis (# of STOs)

single processor

with 64 processors

Methanol CH3OH (18 electrons; Cs)
VB1 (62 STOs)

79 sec.

3.6 sec. (22 times faster)VB2 (130 STOs)

990 sec.

35 sec.

(28 times faster)

VB3 (244 STOs)

7928 sec.

270 sec.

(29 times faster)Naphthalene C10H8 (68 electrons; C-C=1.40 and C-H=1.01; D2h)
VB1 (238 STOs)

9293 sec.

591 sec. (16 times faster)

Adenine C5H5N5 (70 electrons; Cs)
VB1 (220 STO2)

19490 sec.

1095 sec. (19 times faster)

Di-silicon hexa-chloride Si2Cl6 (130 electrons; D3d)
ZVB2 (336 STOs)

2652 sec.

231 sec. (11 times faster)

The basis set VB1 is a “triple-zeta + polarization”
Each basis set of VB2 and ZVB2 is a “quadruple zeta + double polarization”
The basis set VB3 is a “quintuple zeta + triple polarization”
Table II. Comparison of the present parallel algorithm with a new parallel algorithm forthe four-center ERIs and its first derivatives over STOs in the case of (2p2p|2p2p)
The parallel

New parallel for bothfor 81 ERIs

81x(ERI + 12 Derivatives)

Preparation time

41 !sec.

28 !sec.

Computation 1 time

121 !sec.

190 !sec.

Communication time

42 !sec.

31 !sec.

Computation 2 time

8 !sec.

34 !sec.

212 !sec.

283 !sec.

Total time

For all parallel computation, 64 processors were used.
Computation time was measured with a HITAC sr11000 computer.
The communication time depends on the computer hardware used.