Abstract for the Annual meeting of Japan Society for Molecular Science 2012

2E01

Molecular calculations with the Slater-type orbitals(No affiliation1 and Universidad Autónoma de Madrid2)
Kazuhiro Ishida,1 Rafael López,2 and Jaime Fernández Rico2
Introduction In recent molecular physics and theoretical chemistry, most people use
basis sets consisting of Gaussian-type orbitals (GTO). However, it is well known that2GTO, exp(−α r ) , have, at least, two serious defects; i.e., (a) they have no cusp atr = 0 and (b) decay too fast at r → ∞ . In contrast with GTO, the Slater-type orbitals(STO) have the right cusp and long distance behavior. It is clear that STO should be thenatural choice for molecular calculations, but the fact that they lead to difficult integrals
have seriously hindered their use in this field. Recently, two of us (R.L. and J. F. R)
showed that the difficult integrals (which are the four-center electron-repulsion integrals,
ERI) can be calculated with using the so-called STO-NG expansion with an enoughprecision [1]. They developed a computer program named as SMILES2003 for themolecular calculations with using STO as basis functions [2]. The accompanying
coordinate expansion (ACE) algorithm developed by one of us (K. I.) is capable tocompute such integrals extremely fast [3]. We revised the SMILES2003 toSMILES2007 with using the ACE algorithm for the four-center ERI.
Table I. Speeding up ratio for the individual ERI by the ACE algorithm
ERI type

SMILES 2003

SMILES 2007

Parallel

Total effect(1s1s|1s1s)

1 .62 ms

992 μs117 μs

14 times faster(2p2p|2p2p)

20 .8 ms

4 .74 ms

212 μs98 times faster(3d3d|3d3d)

454 ms

18 .6 ms

614 μs

740 times faster(4f4f|4f4f)

18 .8 s50 ms

4 .0 ms 4700 times faster(5g5g|5g5g)

68 .7 s

84 ms

27 ms

2500 times faster(6h6h|6h6h)

260 s

236 ms

149 ms1700 times faster

Computation time was measured with a HITAC sr11000 computer.
The 64 processors were used for the parallel computation
For all four-center computation, the STO-12G expansion is used for 1s-, 2p-, and 3d-type
STO, the STO-11G is used for 4f- and 5g-type STO, and the STO-10G is for 6h-type STO.

Table I shows that the speeding-up ratio in the computation time from as inSMILES2003 to as in SMILES2007. The parallel version of SMILES2007 is extremely
efficient, as seen in Table I.
Table II shows the total computation time for several molecules with using the parallelversion of SMILES2007. We are now tractable to the computation of middle-sizedmolecules like adenine with the STO as basis functions, as seen in Table II.
Table II. Total computation time of the four-center ERIs over STOs for several molecules
Molecule

SMILES 2007

Parallel 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)Benzene C6H6 (42 electrons D2h)
VB1 (150 STOs)

789 sec.

44 sec.

(18 times faster)VB2 (300 STOs)

8699 sec.

410 sec.

(21 times faster)

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

19490 sec.

1095 sec. (19 times faster)VB2 (425 STOs)

201128 sec.

8698 sec. (23 times faster)

The basis set of VB1 is a “triple-zeta + polarization”
The VB2 is a “quadruple zeta + double polarization”
The VB3 is a “quintuple zeta + triple polarization”
We may conclude that we have now an efficient tool to compute molecules with STO.
The next will be the geometry optimization of molecules. We need derivatives ofmolecular integrals for such purpose. We derive the derivatives of one-electron integrals
and present them at the meeting.
References[1] J. Fernández Rico, R. López, A. Aguado, I. Ema, and G. Ramírez, J. Comput. Chem.
19, 1284-1293 (1998)[2] J. Fernández Rico, R. López, I. Ema, and G. Ramírez, J. Comput. Chem. 25,1987-1994 (2004)[3] K. Ishida, J. Chem. Phys. 109, 881-890 (1998)