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COUPLED HARTREE-FOCK APPROACH 289
Since the transformation belongs to the group G one has
and the second-order density matrices transform according to
Owing to permutational symmetry, at most six second-order matrices are indepen-
dent. To account for point molecular symmetry let us introduce the symmetrized
Kronecker square of T, with matrix elements [4]
Eventually one finds the final transformation law for the second-order density matrices
Hence, according to the present method, only the symmetry-distinct density matrices
need to be computed.
Within our approach the entire molecular symmetry is exploited to increase the ef-
ficiency of the code in every step of the calculation. For a molecule belonging to
a group G of order |G|, only symmetry-distinct two-electron integrals
over a basis set of Gaussian atomic functions are calculated and processed at each
iteration within SCF, first- and second-order CHF procedures. A skeleton Coulomb
repulsion matrix is obtained by processing the non-redundant list of unique two-
electron integrals, then the actual repulsion matrices are obtained via
the equation
This method turns out to be a major computer saver, as (i) the iterative steps become
much faster, owing to the reduced number of integrals, and (ii) the occupancy of the
mass storage gets smaller. Accordingly, one can afford large problems which would
be otherwise intractable.