Open-shell Orbitals Research Articles

Electronic Structure and Spectrum of the NiF6−4Cluster: Results of Calculations Based on Self-Consistent-Field Models

Restricted and unrestricted Hartree-Fock molecular-orbital self-consistent-field calculations were performed on the cluster Ni$\mathrm{F}_{6}^{}{}_{}{}^{\ensuremath{-}4}$ with a fixed internuclear distance appropriate to KNi${\mathrm{F}}_{3}$. A slightly extended multicenter atomic-orbital basis was used. In contrast to the approach of earlier calculations which sought to describe $10{D}_{q}$ as a single electron promotion between ${t}_{2g}$ and ${e}_{g}$ antibonding (LCAO) molecular orbitals, we obtained the spectra as the difference in energy between various many-electron open-shell states. The results obtained with limited configuration interaction are in good agreement with the five observed optical absorption bands. We find that the earlier orbital picture can be approximately maintained only if the covalency parameters are obtained from the open-shell orbitals of excited states, which are solutions of the Hartree-Fock-Roothaan Hamiltonians. In these orbitals we find considerable $\ensuremath{\sigma}$ bonding and a smaller $\ensuremath{\pi}$ bonding, significant fluoride $s\ensuremath{-}p$ hybridization, and a small expansion of the $3d$ orbitals which is greater in the ${t}_{2g}$ than in the ${e}_{g}$ orbitals. Allowing for spin-polarization correlation in the unrestricted calculations, however, adds important contributions to transferred hyperfine interactions and neutron form factors.

Electronic absorption spectra and dipole moments for hydrazyl radicals

The paper gives the results of the calculations of transition energies, dipole moments and bond lengths for some hydrazyl radicals carried out by the SCF LCAO MO method with restricted configuration interaction on self-consistent open-shell orbitals. The calculated transition energies for the radicals considered are in a good agreement with the locations of the long-range wave absorption maxima. It is shown that the DPPH dipole moment is the π-electronic moment. On introducing different substitutents in the molecule the σ-moment contribution may be quite considerable. The estimated values for the bond lengths in the substituted radicals show little alteration in the molecular structure.

Study of the electronic structure of radicals by the CI method

There are presented the results in the π-electronic approximation for some properties of the excited doublet states of the benzyl radical obtained by the CI method on the SCF closed and open shell orbitals taking into account all singly and some doubly excited configurations. Also the first quartet and sextet states were computed by the SCF open shell theory in the one-configurational approximation. The energies and transition moments agree well with the available experimental data. The classification and the assignment of the excited terms are given. The calculated spectrum is strongly distorted when the set of all singly excited configurations is truncated. The inclusion of the doubly excited configurations leads also to a significant distortion of the spectrum changing the mutual order of the neighbouring terms in some cases. The transition from the closed shell orbitals to the open shell ones results in a considerable lowering of all terms. As in the case of the triplet molecular terms the decrease of the electronic interaction brings together the lowest excited term of the radical with its ground state term. The electronic and spin density distributions in the excited states of the benzyl radical are computed.

Self-Consistent-Field Theory. I. General Treatment

A general method is described for obtaining SCF orbitals for electronic systems without restriction on the number or the symmetry of open-shell orbitals. A separation on the basis of symmetry designation is made at the beginning. The pseudo-eigenvalue equations are obtained from the SCF equations by the introduction of a new form of coupling operator. The new equations must be solved individually for orbitals of a separate symmetry designation. Some examples are given.