Spin-orbit coupling 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... 

Matrix elements for the valence functions were taken with the effective core potential the coulomb and exchange terms were handled exactly, numerically, without any parameterization and a Phillips-Kleinman projection operator term was also used. Spin-orbit coupling effects amongst the valence orbitals were treated semi-empirically using the operator... 

The accuracy of ab initio geometries is astonishing, in view of the approximations present the 3-21G( ) basis set is small and the 6-31G is only moderately large, and so these probably cannot approximate closely the true wavefunction the HF method does not account properly for electron correlation, and the MP2 method is only the simplest approach to handling electron correlation the Hamiltonian in both the HF and the MP2 methods used here neglects relativity and spin-orbit coupling. Yet with all these approximations the largest error (Table 5.7) in bond... 

Older versions of SOCI programs are very I/O intensive because they used to store the Hamiltonian matrix on disk and read it in every iteration step.52,141 Integral-driven direct methods for spin-orbit coupling came up in the mid 1980s123,142 following the original fomulation of direct Cl methods for spin-independent Hamiltonians.143-146 Modern direct SOCI programs can easily handle several million determinants.108,147-151... 

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