Atomic Natural Spinor

The DC-CASCI (12, 4) calculation was performed to construct reference functions. The active space includes the molecular spinors, which have atomic nature of 6s1/2, 6p1/2, 6py2 of T1 and 1 s1/2 of H, and two virtual molecular spinors. The DC-CASPT2 (10, 12, 110) calculation followed and this choice of active space provided smooth potential curves for four low-lying states of T1H at the DC-CASPT2 level. 

The fully relativistic (four-component) LCAO calculations of molecular systems use contracted Gaussian-type spinors as the basis two scalar wavefunctions within a two-component basis spinor are multiplied by a common expansion coefficient, for dimensions n of both the large and small components the total number of variational parameters (the scalar expansion coefficients) is equal to 2n [496]. In the relativistic correlated calculations the atomic basis sets should be optimized in the atomic correlated calculations. As Almlof and Taylor showed [538], atomic basis sets optimized to describe correlations in atoms also describe correlation effects in molecules very well. The two main types of basis sets are used in correlation calculations of molecules basis of atomic natural orbitals (ANO) suggested by Ahnlof and Taylor [538] correlation-consistent (CC) basis set suggested by Dunning [462]. 

A natural choice for the expansion of the wave function would be the atomic 2-spinors of the form... 

All electrons, protons and neutrons, the elementary constituents of atoms, are fermions and therefore intrinsically endowed with an amount h/2 of angular momentum, known as spin. Like mass and charge, the other properties of fermions, the nature of spin is poorly understood. In quantum theory spin is treated purely mathematically in terms of operators and spinors, without physical connotation. 

The representation of operators by spinors is a rather more delicate matter. By 1935 only one detailed application of Kramers s symbolic method to atomic spectroscopy appears to have been carried out that of Wolfe (1932) to the atomic configuration k. Some of the difficulties of the method are discussed below in section 5.1. For the moment we need only say that the abstract nature of the method did not prove appealing to most theoretical spectroscopists. No one in the 1930 s or since, as far as the writer is aware, has used the functions... 

In order to describe the one-electron spinors of molecules that enter the Slater determinants to approximate the total electronic wave function it is natural to be inspired by the fact that molecules are composed of atoms. It should be noted that this at first sight obvious fact is not obvious at all as we describe only the ingredients, i.e., the elementary particles (electrons and atomic nuclei) and not individual atoms of a molecule. To define what an atom in a molecule shall be is not a trivial issue in view of the continuous total electron distribution p r) of a molecule. Nonetheless, we may utilize what we have... 

From the standpoint of chemical reactivity, the 5s and 5p shells of lanthanides can be considered to be core electrons. Indeed arguments to this effect could be made for Ln 4f orbitals, given their extremely contracted nature. Shown in Figure 3 is a plot from a DHF calculation of a 4f spinor for Gd(III). Note the maximum in the wavefunction at 0.57 A that is, a value comparable to a hydrogen Is orbital Dolg et al. - examined various lanthanide core sizes and found essentially no difference in state splittings of the Ce atom between all-electron calculations and those in which a 28-electron core ([Ar]3d °) is used, Satisfactory results are also obtained for a 46-electron core ([Kr]4di°). Inclusion of 5s and 5p into the core (i.e, a 54-electron [Xe] core)... 

Abstract This chapter aims to present QTAIM and ELF topological analyzes in the framework of two-component relativistic computations. Attention is focused on spin-orbit coupling (SOC) effects on the chemical bond in systems containing heavy atoms. The emblematic At2 and uranyl species have been studied as a relevant test set. The presented methodology appears particularly suitable for evidencing relativistic effects on bonding schemes. The influence of SOC was found to depend, not only of the involved heavy atoms, but also of the bond nature. Furthermore, the robustness of QTAIM and ELF for analyzing wave functions built from spinors has been verified. 

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