Mean-field spin-orbit method

Mean-Field Spin-Orbit Method Applicable to Correlated Wavefunctions. 

O. Gropen. A mean-field spin-orbit method applicable to correlated wave-functions. Chem. Phys. Lett., 251 (1996) 365-371. 

A Mean-Field Spin-Orbit Method Applicable to Correlated Wavefunctions. (b) M. Ilias, V. Kello, L. Visscher, and B. Schimmelpfennig, J. Chem. Phys., 115, 9667 (2001). Inclusion of Mean-Field Spin-Orbit Effects Based on All-Electron Two-Component Spinors Pilot Calculations on Atomic and Molecular Properties. 

Brownridge S et al (2003) Efficient calculation of electron paramagnetic resonance g-tensors by multireference configuration interaction sum-over-state expansions, using the atomic mean-field spin-orbit method. J Chem Phys 118 9552-9562... 

Hess BA, Marian CM, Wahlgren U, Gropen O. A mean-field spin-orbit method apphcable to correlated wavefunctions. Chem Phys Lett. 1996 251 365. 

Sun Q, Xiao Y and Liu W 2012 Exact two-component relativistic theory for NMR parameters General formulation and pilot application. J. Chem. Phys. 137(17), 174105—20. van Lenthe E 1996 The ZORA Equation PhD thesis Vrije Universiteit Amsterdam, Netherlands. He6 BA, Marian CM, Wahlgren U and Gropen O 1996 A mean-field spin-orbit method applicable to correlated wavefunctions. Chem. Phys. Lett. 251, 365—371. 

An alternative is represented by methods where one mixes one-electron configurations to obtain a many-determinant wave function. [12] These configurations are generated by distributing the electrons among the mean field spin orbitals. If one takes all the possible substitutions (single, double, triple, etc.) into account, one obtains in principle the exact solution to the Schrddinger equation. 

In most of the connnonly used ab initio quantum chemical methods [26], one fonns a set of configurations by placing N electrons into spin orbitals in a maimer that produces the spatial, spin and angular momentum syimnetry of the electronic state of interest. The correct wavefimction T is then written as a linear combination of tire mean-field configuration fimctions qj = example, to describe the... 

Relativistic mean field (RMF) models have been applied successfully to describe properties of rinite nuclei. In general ground state energies, spin-orbit splittings, etc. can be described well in terms of a few parameters ref. [18]. Recently it has lead to the suggestion that the bulk SE is strongly correlated with the neutron skin [19, 20] (see below). In essence the method is based upon the use of energy-density functional (EDF) theory. 

The HF method treats electron-electron interactions at a mean field level, with the Hartree and exchange interactions exactly written. The method can be implemented either in its spin restricted form (RHF), for closed shell systems, or in the unrestricted form (UHF) for open-shell or strongly correlated systems. In the first case, the one-electron orbitals are identical for electrons of both spin directions, while UHF can account for a non-uniform spin density. The one electron orbitals, which are determined in the course of the self-consistent resolution of the HF equations, are expanded on an over-complete basis set of optimized variational functions. 

Instead of using the traditional LS-representation for the spin-orbit coupling we return to more fundamental representation (Eq. 7) and note that since all basis-set oriented mean-field methods expand the singleelectron wavefunctions according to Eq. (3), it is only necessary to determine matrix elements of the form ... 

One fundamental aspect in the understanding of the photochemical behaviour of transition metal complexes is the role of the triplet states on the photoreactivity. The calculation of Spin-Orbit Coupling (SOC) effects is mandatory and should be performed in connection with highly correlated methods. The zero-field splitting of triplet molecular states can be calculated by the means of perturbation theory until the spin-orbit effects are not of... 

Theory can now provide much valuable guidance and interpretive assistance to the mechanistic photochemist, and the evaluation of spin-orbit coupling matrix elements has become relatively routine. For the fairly large molecules of common interest, the level of calculation cannot be very high. In molecides composed of light atoms, the use of effective charges is, however, probably best avoided, and a case is pointed out in which its results are incorrect. It seems that the mean-field approximation is a superior way to simplify the computational effort. The use of at least a double zeta basis set with a method of wave function computation that includes electron correlation, such as CASSCF, appears to be imperative even for calculations that are meant to provide only semiquantitative results. The once-prevalent degenerate perturbation theory is now obsolete for quantitative work but will presumably remain in use for qualitative interpretations. 

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