Orbital character

The g-value of a free electron is a scalar, ge = 2.00232. In a radical species, g becomes a matrix because of the admixture of orbital angular momentum into S through spin-orbit coupling. The components of the g-matrix thus differ from ge to the extent that p-, d-, or f-orbital character has been incorporated, and they differ from one another, depending on which p-, d-, or f-orbitals are involved. 

Compared with the conducting anion radical salts of metal complexes, the number of molecular conductors based on cationic metal complexes is still limited. Donor type complexes M(dddt)2 (M = Ni, Pd, Pt Fig. 1) are the most studied system. The M(dddt)2 molecule is a metal complex analogue of the organic donor BEDTTTF. Formally, the central C=C bond of BEDT-TTF is substituted by a metal ion. The HOMO and LUMO of the M(dddt)2 molecule are very similar in orbital character to those of the M(dmit)2 molecule. In addition, the HOMO of the M(dddt)2 molecule is also very similar to that of BEDT-TTF. More than ten cation radical salts of M(dddt)2 with a cation (monovalent) anion ratio of 2 1 or 3 2 are reported [7]. A few of them exhibit metallic behavior down to low temperatures. The HOMO-LUMO band inversion can also occur in the donor system depending on the degree of dimerization. In contrast to the acceptor system, however, the HOMO-LUMO band inversion in the donor system leads a LUMO band with the one-dimensional character to the conduction band. 

The interface nature of the states shown in Figure 3 have been corroborated in recent theoretical calculations (8). The calculated energy position of these states is in close agreement with the experimental results. Their orbital character has been determined as well. These results indicate that the interface states at about 1.5 eV are of appropriate character and energy to be active in environmental chemical reactions involving sub- and monolayer copper films on ruthenium. 

The crystal field interacts directly only with the orbital motion of the unpaired electrons and it has an effect on the electronic spins only through the spin orbit coupling. The strongest spin-lattice interaction will therefore occur for ions with ground states having an appreciable orbital character. 

Table I also contains an analysis of the orbital character of these five energy levels. These were determined from the four-component spinors by neglecting the two lower, "small," components, and by assuming that the radial functions depend only upon , i.e. that the radial functions for pi/2 and p3/2> or for da/2 and ds/2> are the same. The orbitals may then be written in "Pauli" form as products of (complex) spherical harmonics and spin functions. Populations are equal to the squares of the absolute magnitudes of the coefficients listed in Table I. [For all but 17e3g, an additional orbital (not shown) is occupied which has the same energy but the opposite spin pattern (i.e. a and 3 are interchanged).]...

Similarly, a simplified 7t-orbital interaction for metal allenylidene complexes of the Fisher-type can be constructed, as shown in Figure 4.2. The LUMO is mainly localized at Q and C.. As a result, nucleophilic attack favors the Q and Cy positions [59-61]. It has been found that the contributions of Q and Cy to the LUMO are similar. Therefore, a dear preference for a nucleophilic attack at either Q or Cy could not be deduced [59]. On the basis of the orbital characters in the HOMO, we can again deduce that electrophilic attack occurs at the P-carbon and/or the metal center. 

These attempts may be called thermodynamic semi-theoretical approaches . They concern mostly the simplest kind of bonding, namely the metallic bond. The underlying hypothesis is that the contributions of different outer orbitals (7 s, 6 d, 5 f) in some chosen thermodynamic or structural property can be linearly combined, the coefficients of this linear combination being related to the degree of participation of the different orbitals in the bonding an approach clearly related to the molecular orbital approach of quantum chemistry and to the hybridization concept, and which had been previously employed in other transition metals and to the rare-earth metallic systems " (for a criticism of this approach, see Ref. 6). The chosen thermodynamic and structural properties are, therefore, bonding indicators , since they will reflect contributions introduced by the fact that the wavefunctions of bonding electrons have mixed orbital characters. 

This treatment aiming to evaluate thermodynamically the orbital character of the bond in actinide metals, follows closely the general features illustrated above and has a particular value inasmuch as it is accompanied by a fairly comprehensive survey of the chemical and physical properties of actinide metals known at that time. In it, the metallic radius and the crystal structures are taken as valence indicators AH nd Tm as the bonding indicators . The metallic valence, however, is not taken as constant throughout the actinide series, but rather allowed to vary. The particular choices are justified by physical and chemical arguments, which are taken in support of the hypothesis chosen. 

The evaluated partial orbital characters of the bond are given in Table 2. 

The first factor will dictate, from the properties of the one-electron wavefunctions, the characteristic dependence of the cross-sections on the initial orbital character of the electron and on the exciting photon energy. 

Figure 9 Construction of the energy bands of undistorted one dimensional chains and two dimensional sheets of (a) the platinum amine halide system where the z2 orbital is used, and (b) the Cu02 sheet where the x2 - y2 orbital is used. Notice the strong similarities in orbital character, and compare with Figure 7b.

Figure 10 (a) Splitting apart of the half-filled band on the asymmetric distortion of Figure 8a. This is the higher of the two bands of Figure 9(a). Notice the change in orbital character as a result of a Peierls distortion for the platinum chain, (b) Plot of orbital energy vs k, showing the orbitals most strongly affected.

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