Page 199 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

182 Y. G. SMEYERS ET AL.

where ,.. are the matrix representations of the corresponding oper-
ators. In particular, is defined as , where A is now the inverse diagonal
matrix of the overlap between the occupied corresponding orbitals, and and
_ and the coefficient matrices of two set of occupied orbitals. Finally, s is the
overlap matrix between the basis functions.
For the excited states, with an orthogonal orbital pair, we have:

where is defined as before except for the diagonal element, of the , corre-
sponding to the orthogonal orbitals which is missing, and where
are the column vectors of the coefficients of the and orbitals, respectively.

3.1. THE METHYLENE MOLECULE
As well known, the methylene lowest state is a triplet, with electronic configu-
ration which lies somewhat below the fundamental
singlet state, In addition, the companion singlet state, is also known. To

in degrees, r in and energy in Hartrees.

study the potential energy functions of both states, as a function of the bending