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Yoshimine sort : ウィキペディア英語版
Yoshimine sort
The Yoshimine
sort〔M. Yoshimine, The use of direct access devices in problems requiring the reordering of long lists of data, report RJ-555, IBM Research Laboratory, San Jose, California, 1969.

is an algorithm that is used in quantum chemistry
to order lists of two electron repulsion integrals. It is implemented in the IBM Alchemy program
suite 〔A.D. McLean, M. Yoshimine, B.H. Lengsfield, P.S. Bagus, B. Liu:
ALCHEMY II, A Research Tool for Molecular Electronic Structure and Interactions,
in: Modern Techniques in Computational Chemistry (MOTECC-91),
(E. Clementi, ed.) ESCOM Science Publishers Leiden, 1991, ISBN 90-72199-10-3〕
and in the UK R-matrix package for electron and positron scattering by molecules

L.A. Morgan, J. Tennyson and C.J. Gillan,
The UK molecular R-matrix codes,
Computer Physics Communications,
Volume 114, Issues 1-3, November 1998, Pages 120-128

which is based on the early versions of the IBM Alchemy program suite.
== Use of basis set expansions in quantum chemistry ==
In quantum chemistry, it is common practice to represent one electron functions in terms of an
expansion over a basis set, \chi_i. The most common choice for this basis set is Gaussian orbitals (GTOs) however for linear molecules Slater orbitals (STOs) can be
used.
〔A. D. McLean and M. Yoshimine,
Computation of Molecular Properties and Structure,
IBM Journal of Research and Development, Volume 12, Number 3, May, 1968
pages 206--233

The Schrödinger equation, for a system with two or more electrons, includes the Coulomb repulsion
operator. In the basis set expansion approach this leads to the requirement to compute two electron
repulsion integrals involving four basis functions. Any given basis set may be ordered so that
each function can assigned a unique index. So, for any given basis set, each two electron
integral can be described by four indices, that is the indices of the four basis functions involved.
It is customary to denote these indices as p,q,r and s and the integral as (pq|rs). Assuming that
\chi_i are real functions, the (pq|rs) are defined by
:
(pq|rs) = \int\int \frac_1 ) \;
\chi_r( \mathbf_2 ) \;
\chi_s( \mathbf_2 ) \;
}
_2 \mid
}
\;\; d\mathbf_1 \; d\mathbf_2

The number of two electron integrals that must be computed for any basis set depends on the
number of functions in the basis set and on the symmetry point group of the molecule being studied.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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