Page 306 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer
P. 306

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.
   301   302   303   304   305   306   307   308   309   310   311