Different methods of averaging of energy over the states of electronic configurations yN (nr = I , 2, 3 and N = 1, 2 , . . . , 2n, -1) leading to Roothaan' energy expression are considered. The consequent values of vector coupling coefficients (vcc) in energy functionals for various states as well as for average values of energy are presented.It is shown also that in molecular systems of cubic and tetragonal symmetry having electronic configurations tN (N = 2-4) and e z there exist states for which vcc are dependent on the choice of basis set of degenerate open-shell molecular orbitals. The origin of such "non-Roothaan" terms and peculiarities of its calculation by the restricted Hartree-Fock method are discussed.

AbstractsThe Fock generating function method is employed for the separation of spin variables into two-particle transition density matrices. Their spatial components introduced by McWeeny are expressed through Schrodinger's coordinate wave functions. Some nontrivial integral relations between these components and the charge and transition spin density matrices are obtained. The interrelation between the mentioned spatial components and the Matsen-Poshusta symmetrized density matrices of an arbitrary spatial function is found.

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AbstractsThe two-particle spatial density matrix components introduced by McWeeny are expressed in terms of the Fock coordinate wave function, which is constructed from an arbitrary function of N spatial coordinates. The integral relations for these components are verified. The necessary matrix elements of a standard representation of the S, group are calculated.

Explicit equations for the constants a and b of the energy as the average expectation value for the minimal domain of states giving the Roothaan energy functional are derived in terms of the total spin value and the "seniority" quantum number. The state with off-diagonal long-range order can appear in the framework of the Roothaan scheme for the quasidegenerate system as an alternative to the Hund rule. Admissible many-electron states are established for all configurations of the icosahedral symmetry group systems, and corresponding a and b coefficients are calculated.