Canonical spinors

Solving the canonical Hartree-Fock equations for a particular molecule directly yields the canonical spinors of that molecule. How the equations can be solved is discussed from a technical point of view in the next section, while their explicit solution procedures are presented in chapters 9 and 10. The terms "Dirac-Hartree-Fock", "Dirac-Fock", and "four-component Hartree-Fock" are used synonymously in research papers. 

Canonical ensemble, multiparticle collision dynamics, single-particle friction and diffusion, 116-118 Cartesian Gaussian spinors ... 

N. Cufaro-Petroni, P. Gueret, and J. P. Vigier, Second-order wave equation for spin /2 Fields 8-Spinors and canonical formulation, Found. Phys. 18(11) (1988). 

In this expression the fundamental la), /3) spinor resembles a quark state three quarks are coupled together to form the quartet result. The use of the quartet spin bases does not mean that our /g really corresponds to a quartet spin. It only means that we can introduce a fictitious spin operator, S, which acts on the /g components in the same way as the real spin momentum would act on the components of a spin quartet. The transformations of the /g spinor under the elements of the group O may be obtained by combining the transformation matrices for the fundamental (la) 1/3)) spins with the quartet coupling scheme in Eq. (7.69). In the group O, this irrep is denoted as ie- In Table 7.7 the results are shown for two generators of the octahedral group. These matrices can be taken as the canonical basis relationships... 

Quiney (2000)]. The quadratically convergent NR algorithm for relativistic MCDF SCF calculations has been discussed in detail in previous work [Vilkas et al. (1998a)] and is not discussed further. To remove the arbitrariness of the MC SCF spinors and density weighting, the canonical SCF spinors are transformed into natural spinors for subsequent pertur-... 

While seminal works intended to reveal SOC effects on the bonding schemes were discussed in term of spinors [9-13], canonical molecular spinors are not suited for the bonding analysis in complex systems, as opposed to small and/or symmetric model systems. Some have promoted the use of localized spinors [14], and in order to recover some chemical significance in terms of bonding, lone pairs and core orbitals, natural spinors similar to natural orbitals in the non-relativistic firameworks have been derived and implemented [15, 16]. It is worth noting that the concept of bond order in the context of multiconfigurational wave functions have been extended recently to two-step spin-orbit coupling approaches [17]. 

Our first experience with levels involved the 4/ states of Pr + and the levels of 11" + [86]. Excellent agreement with experiment was obtained, with an MAE of 222 cm for the Pr + levels and 114 cm for 11 +. The error for Pr + was four times smaller than that of the MCDF calculation [87], demonstrating the more comprehensive inclusion of dynamic correlation by CC. More recently, a larger basis set was employed, extending the analysis to include the excited states of U + and the 5/, Sfls, and Sfbd states of U +, which are important in interpreting the electronic spectrum of the neutral UO2 molecule [25]. Results are presented and compared with experiment [88] and other calculations in Table 2.13. It should be noted that we use one set of canonical SCF spinors for all states in... 

---