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Internet Electronic Journal of Molecular Design - IEJMD, ISSN 1538-6414, CODEN IEJMAT
| ABSTRACT - Internet Electron. J. Mol. Des. July 2005, Volume 4, Number 7, 527-536 |
Use of Lanczos Tau Method to Derive Polynomial Approximate from
the Addition Theorem of Slater Type Orbitals
Ahmed Bouferguene and Hassan Safouhi
Internet Electron. J. Mol. Des. 2005, 4, 527-536
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Abstract:
Multi-center integrals are certainly the building blocks of
quantum chemistry packages ranging from semi-empirical
to the so-called ab initio. The efficiency (accuracy and
speed) of the numerical methods used for the computation
of such integrals is therefore of extreme importance since
millions of these need to be computed for molecules of
practical interest. In this work, the Lanczos τ method is
applied to derive a polynomial approximate to the so-called
one-center expansion of Slater Type Orbitals (STOs). The
procedure is applied to the three-center nuclear attraction
integrals, which are essential not only in quantum
chemistry but also to model electron-molecule scattering.
Starting with a spherical Slater Type Orbital a differential
equation governing such functions is elaborated. The
application of the Lanczos τ to the differential equation
enables us to obtain a polynomial approximate, and more
importantly the corresponding absolute error. Such an
approximate is afterwards used in the master formula
allowing the computation of multi-center integrals over
STOs. Numerical values for three-center nuclear attraction
integrals are reported. Comparison with previous work is
performed. Multi-center integrals over STOs are still a
challenging problem. The case of nuclear attraction integral
is among the problems that can be tackled with various
approaches including the one presented in this work.
However for fully functional quantum chemistry software
using STOs to be efficient it is necessary to combine the
best of all methods by selecting the most appropriate tool
for each case.
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