Vectorized Calculations and Use of Fast Semiconductor Memories in the Dv-Xα Method

Abstract

Two types of vectorized programs of the discrete variational Xα method with the basis set of Slater-type orbitals have been developed. The first type calculates a basis function every time that it is used and the second type reads a basis function from outside memories.They are examined for the most efficient way of performing calculations with the HITAC S-810/20 supercomputer (630 MFLOPS at peak) and its available outside memory devices. The acceleration factor of computation by the first type of program over scalar processing is more than 12. The second type of program has no advantage over the first in small electron systems of atomic clusters with primitive basis functions. But in larger systems such as Si 2 O 7 H 6 with complex basis functions, the second type of program, used with semiconductor memories, results in 11 times less CPU time than the first type of program.

Estimation of the Solubility Dependence of Aluminate Salts of Alkali Metals on Ion Radii of Alkali Metals by LDF Molecular Orbital Calculations

“…Methods To Estimate the Binding Energy by Molecular Orbital Calculations. The LDF molecular orbital calculation method applied in our investigation was ESPAC-DF developed by Kobayashi et al, − on the basis of the Kohn−Sham self-consistent-field method. In this calculation method, the local density-functional method is applied to the determination of cluster structures, and the generalized gradient approximation is applied to the energy calculations.…”

“…(mol/mol solvent) (3) In eq 4a, the free energy in the solid phase is considered as the sum of the free energy of one salt molecule and the electric interaction energy between the salt molecules because the crystal structure of the lithium aluminate preservation film on the surface layer facing the solvent is not known exactly. The above interpretation of the free energy in the solid phase allows molecular orbital calculation to be applied to the salt molecule clusters and to estimate the electric interaction energy in the ionic crystal as the electric interaction energy between the salt molecules.…”

“…To estimate the difference in the binding energy among the aluminate salts caused by the difference in the alkali metal ion radius, LDF molecular orbital calculations [3][4][5][6] were applied to multiatomic clusters of aluminate salt molecules (LiAl(OH) 4 , NaAl(OH) 4 , and KAl(OH) 4 ), hydrated alkali metal ions, and aluminate ions. The discussion then focused on how this difference in the binding energy leads to the difference in their solubility, by using some classical theories of solvation, entropy, and electric interaction.…”

“…The purpose of this study is to relate theoretically the low solubility of lithium aluminate with its structure, as reflected by the ion radius. For this purpose, local density functional (LDF) molecular orbital calculations − were applied to the aluminate salts of alkali metals to estimate the difference in their binding energy as reflected by the difference in the alkali metal ion radius. In section 2.2, methods used to estimate the binding energy by molecular orbital calculation are explained.…”