Advances in Quantum Chemistry 28 , 171-188 (1997)
Tatiana Korona, Robert Moszynski, and Bogumil Jeziorski
Department of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
Convergence of Symmetry-Adapted Perturbation Theory for the Interaction between Helium Atoms and between a Hydrogen Molecule and a Helium Atom
Convergence properties of perturbation expansions for the
interaction energy are investigated by performing high-order
for the interaction between helium atoms and
between a hydrogen molecule and a helium atom.
It is shown that for small intermonomer distances the standard
Rayleigh-Schrödinger (polarization) expansion converges to a
state of the dimer. At large separations
the exchange component of the interaction energy is not
recovered in a practically low order and
an apparent convergence to the Coulomb part of the interaction energy
Rayleigh-Schrödinger (SRS) theory
provides in low
order very accurate values of both the Coulomb and the exchange
parts of the interaction energy for the physical, Pauli allowed state.
In the region of the van der Waals minimum already the second-order treatment
reproduces the full configuration interaction (FCI) energy with
an error of a few percent. In very high orders the convergence of the SRS
theory becomes extremely slow and the series appears to converge to a
nonphysical limit very close to the exact interaction energy.
The symmetry-adaptation characteristic of the Hirschfelder-Silbey
(HS) theory is shown to correct this pathological behavior although
the improved convergence is observed only in very high orders, so from the
practical point of view the HS theory is not superior to the SRS approach.
The HS series converges to the FCI interaction
energy only if the latter is corrected for the basis set superposition
error using the full counterpoise correction of Boys and Bernardi.
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