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220. PCILO: Perturbation Configuration Interaction
Using Localized Orbital Method in the CNDO Hypothesis
by P. Claverie, J. P. Daudey, S. Diner, Cl. Giessner-
Prettre, M. Gilbert, J. Langlet, J. P. Malrieu, U.
Pincelli, and B. Pullman, Laboratoire de Chimie
Quantique, Institut de Biologie Physicochimique, 13 rue
P. et M. Curie, Paris 53, France
PCILO is an automatic program intended for the
calculation of electronic ground state properties of a
molecular system in the framework of semiempirical
methods for all valence electrons. In its present
form, it calculates the electronic ground state energy
and the one-particle density matrix in an approximation
which lies beyond the SCF one using the CNDO/2
hypothesis for the integrals. Due to its speed and
accuracy, compared with the SCF calculations by the
CNDO/2 method of Pople and Segal, PCILO is especially
fitted for conformation analysis. The number of
valence electrons of the system (limited here to 120)
can easily reach 200 or 250, the computing time
remaining reasonable. The only limitation comes from
the precision of the computer.
PCILO was born during the study of the perturbation
treatment of configuration interaction using SCF
localized orbitals. This gives a definition of its
technical framework. From a conceptual point of view,
PCILO is equivalent to a method which views the
molecule as an assembly of "two-center, two-electron
molecules" (chemical bonds) in the interaction, the
interaction being treated by perturbation theory on an
antisymmetrized basis. Classical theoretical chemistry
and the studies on the localization of SCF orbitals
provide a large justification for this conception: the
chemical formula is a very good order approximation for
the study of a molecule.
The method relies on four fundamental steps:
1. The first is a building of bonding and antibonding
orbitals orthogonalized in some way.
2. Bonding orbitals are used to construct a Slater
determinant which is the zeroth order wave
function for the molecule.
3. Antibonding orbitals allow the construction of
Slater determinants corresponding to excited
configurations. These configurations are
characterized by the bonds involved in the
excitations and can be classified according to the
two different possibilities: excitations with or
without electron transfer from one bond to
another.
4. In the basis of all these determinants, the
molecular Hamiltonian is represented by a
"configuration interaction matrix". The lowest
eigenvalue and the corresponding eigenvector are
calculated by a Rayleigh-Schrdinger perturbation
series. Ground state properties are obtained in
this way. Excited states could be studied in an
analogous way, but technical difficulties due to
degeneracy appear and such a calculation is not
included in the standard version of PCILO. The
total molecular Hamiltonian is split according to
the Epstein-Nesbet procedure, which is equivalent
to taking the diagonal part of the interaction
configuration matrix as representation of the non-
perturbed Hamiltonian and the non-diagonal part as
perturbation. The absence of diagonal terms in
the perturbation ensures a faster convergence of
the series. At the same time, the first-order
correction to the energy is zero.
FORTRAN IV (IBM 360/75)
Symbolic Cards: 2411
Recommended Citation: B. Pullman et al., QCPE 11, 220
(1972).
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