Spin-orbit coupling perturbative handling

Appendix A Perturbative Handling of the Renner—Teller Effect and Spin-Orbit Coupling in n Electronic States of Tetraatomic Molecules... 

The first theoretical handling of the weak R-T combined with the spin-orbit coupling was carried out by Pople [71]. It represents a generalization of the perturbative approaches by Renner and PL-H. The basis functions are assumed as products of (42) with the eigenfunctions of the spin operator conesponding to values E = 1/2. The spin-orbit contribution to the model Hamiltonian was taken in the phenomenological form (16). It was assumed that both interactions are small compared to the bending vibrational frequency and that both the... 

APPENDIX A PERTURBATIVE HANDLING OF THE RENNER-TELLER EFFECT AND SPIN-ORBIT COUPLING IN n ELECTRONIC STATES OF TETRAATOMIC MOLECULES... 

We introduce the dimensionless bending coordinates qr = t/XrPr anti qc = tAcPc ith Xt = (kT -r) = PrOir, Xc = sJ kcPc) = Pc nc. where cor and fOc are the harmonic frequencies for pure trans- and cis-bending vibrations, respectively. After integrating over 0, we obtain the effective Hamiltonian H = Ho + H, which is employed in the perturbative handling of the R-T effect and the spin-orbit coupling. Its zeroth-order pait is of the foim... 

General relationships between AOM and crystal field parameters are shown in Table 23. Using the AOM one can easily compute the electronic energy levels, inclusive of spin-orbit coupling, without any symmetry assumption or perturbation procedure, and it is also easy to account for the different chemical natures of the ligands and for differences in bond distances. It is also possible to handle anisotropic n interactions, which can be expected to occur with pyridine or pyridine iV-oxide ligands.366,367 General review articles on the AOM and its applications have already appeared.364,368-371... 

The methods of choice must be adequate for manifolds of electronic states that are localized around a lanthanide ion in a solid host. The combination of a solid environment, a heavy element, and 4/, 5d, and other open-shells, demands the consideration of the effects of the solid host, the use of relativistic Hamiltonians up to spin-orbit coupling, the correct treatment of static and dynamic correlation, and handling large manifolds of quasi-degenerate excited states. We decided to use embedded-cluster wavefunction theory-based (EC-WFT) methods, with a two-component relativistic Hamiltonian to be used in two-steps, a multi-configurational variational treatment of static correlation, and a multireference second-order perturbation theory treatment of dynamic correlation. 

---