Calculations of the energies of the excited states of open-shell atoms in the Hartree-Fock approximation

In the framework of the Roothaan-Hartree-Fock atomic theory, the solution of a many-electron problem is considered on the basis of the methods of minimizing a function of many variables. To implement this approach, expressions are obtained for the energy derivatives with respect to the elements of density matrices and the nonlinear parameters of atomic orbitals, that is, orbital exponents. Using the first- and second-order minimization methods, we performed optimization of the orbital exponents of Slater-type atomic orbitals for atoms and ions with several open shells. For them, energies that are close to the data of the numerical solution of the Hartree-Fock equations at a high accuracy of the virial ratio were determined. For a number of atoms the frequencies of the first dipole transitions were calculated, and the results were compared to the data obtained in calculation by the method of random phases and to experimental data. ©2005 Springer Science+Business Media, Inc.