Relativistic spin-orbit

The spin—orbit coupling constants f4f and fsd, which represent the relativistic spin—orbit interaction in the 4f and 5d shells, also determined by means of the radial wave functions Rrd of the 4f and 5d Kohn—Sham orbitals of the lanthanide ions.23... 

Figure 1. The relation between central density and the mass of various degenerate star models. Chandrasekhar s curve is for white dwarfs with a mean molecular weight 2 of atomic mass units. Rudkjobing s curve is the same except for inclusion of the relativistic spin-orbit effects Rudkjobing (1952). The curve labeled Oppenheimer and Volkoff is for a set of neutron star models. The solid line marked Wheeler is a set of models computed with a generalized equation of state, from Cameron (1959).

The nonrelativistic limit of this operator yields the paramagnetic spin-orbit (PSO) contribution of Ramsey s theory. The remaining terms in eq. (4.10b) result in the ZORA relativistic spin-orbit Hamiltonian,... 

In his theoretical treatment, Nugent (5(5) has pointed out that the relativistic spin-orbit coupling would not contribute considerably towards the tetrad effect, and he based his explanation of the tetrad theory on Russell-Saunders states for the lantha-... 

The eigenfunctions of the zeroth order Hamiltonian define the projection of the DCB equation onto the subspace of electronic solutions. This is a first and necessary step to apply QED theory in quantum chemistry. The resulting second quantized formalism is compatible with the non-relativistic spin-orbital formalism if the connection (unbarred spinors <-> alpha-spinorbitals) and (barred spinors beta spinorbitals) is made. This correspondence allows transfer to the relativistic domain of non-relativistic algorithms after the differences between the two formalism are accounted for. 

We start with the relativistic energy expectation value (492) in terms of the occupied relativistic spin orbitals tpi. Then we use the relation... 

A full relativistic theory for coupling tensors within the polarization propagator approach at the RPA level was presented as a generalization of the nonrelativistic theory. Relativistic calculations using the PP formalism have three requirements, namely (i) all operators representing perturbations must be given in relativistic form (ii) the zeroth-order Hamiltonian must be the Dirac-Coulomb-Breit Hamiltonian, /foBC, or some approximation to it and (iii) the electronic states must be relativistic spin-orbitals within the particle-hole or normal ordered representation. Aucar and Oddershede used the particle-hole Dirac-Coulomb-Breit Hamiltonian in the no-pair approach as a starting point, Eq. (18),... 

The value of coefficient B is defined by crystalline fields originated from equilibrium positions of lattice ions. Magnetic spins are coupled with these fields via weak relativistic spin-orbit interaction (giving rise to above magnetic anisotropy energy), while electric dipoles are coupled with electric crystalline field electrostatically. In ferroelastics, the elastic dipoles constituting order parameter interact with elastic strain or gradients of crystalline field. 

In W2-F12, the Hartree-Fock component is calculated with the VQZ-F12 basis set. The valence CCSD-F12 correlation energy is extrapolated from the VTZ-F12 and VQZ-F12 basis sets, using the above two-point extrapolation formula with a = 5.94. The quasiperturbative triples, (T), corrections are obtained from standard CCSD(T)/VTZ-F12 calculations (i.e., without inclusion of F12 terms) and scaled by the factor f = 0.987 x mp2-fi2/-Emp2- This approach has been shown to accelerate the basis set convergence [31, 49]. The CCSD inner-shell contribution is calculated with the core-valence weighted correlation-consistent A PWCVTZ basis set, while the (T) inner-shell contribution is calculated with the PWCVTZ(no Q basis set. The scalar relativistic, spin-orbit coupling, DBOC, and ZPVE corrections are obtained in the same way as in W1-F12 theory. 

When relativistic spin-orbit coupling effects are omitted, the single-site matrix t 6i) describing the scattering from a site with local moment orientated in the direction ii becomes... 

Kanpp M, Malkina O (1998) Density functional analysis of C and H chemical shifts and bonding in mercrtrimethanes and organomercury hydrides The role of scalar relativistic, spin-orbit and substituent... 

A reliable prediction of spectroscopic phenomena in heavy-element compounds requires a balanced description of scalar-relativistic, spin-orbit and electron-correlation effects. In some cases one or more of these effects can be dominant, requiring an elaborate method to take this into account, whereas the others may be treated in a more approximate way or can even be completely neglected. The choice of the Hamiltonian is a crucial issue in relativistic calculations of spectroscopic quantities. Four-component methods employing the Dirac-Coulomb or Dirac-Coulomb-Breit Hamiltonian offer the most... 

Isotope Shifts. - Oxygen-induced isotope shifts on Tc shielding in the pertechnetate ion have been explored by Cho et a/. The variations in the Tc shielding in isotopomers involving 0, 0 and 0 have been predicted by making use of a relativistic spin-orbit density functional theory combined with a solvated ion approach. A single atom substitution, for example, 0 0 in... 

Arbuznikov, A. V., Vaara, J., Kaupp, M. (2004). Relativistic spin-orbit effects on hyperfine coupling tensors by density-functional theory. Journal of Chemical Physics, 120, 2127. 

Let us note that after the decay i - kpe the symmetry of the ion field may change, and therefore the electron wave function acquires on admixture of another angular momentum. It may change the anisotropy parameter, which even for vacancy will deviate from being equal to 2. However, in the Ar 1s-vacancy case, it is necessary to have in mind that relativistic (spin-orbit) corrections to an e p-wave function and an admixture of quadrupole transition, which is essential in this frequency region, also leads to... 

Nichols P, Govind N, Bylaska EJ and de Jong WA 2009 Gaussian basis set and planewave relativistic spin-orbit methods in nwchem. J. Chem. Theory Comput. 5(3), 491 99. 

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