Net Charges of Transition Metal Atoms

Two approaches have been applied to estimate the net charges of atoms from the observed electron-density distribution in crystals. The first method is a direct integration of observed density in an appropriate region around an atom (hereafter abbreviated as DI method) (64). The second is the so-called extended L-shell method (ELS method) (19, 81) in which a valence electron population of an atom is calculated by a least-squares method on the observed and calculated structure amplitudes. 

The number of electrons belonging to an atom is calculated by the integration of electron density in an effective region of the atom, 

Since an a priori definition of the effective region is hardly possible, each atomic region is usually approximated by a spherical region around the atom, where the radius is taken as its ionic, atomic, or covalent bond radius. The radial distribution of electron density around an atom is also useful to estimate the effective radius of an atom, particularly in ionic crystals. In an ionic crystal, the distance from the metal nucleus to the minimum in the radial distribution curve generally corresponds to the ionic radius. As an example, the radial distribution curves around K in o-KvCrO., (85) are shown in Fig. 19a. The radial distributions of valence electrons (2p electrons) exhibit a minimum at 1.60 A for K(l) and 1.52 A for K(2), respectively. These distances correspond to the ionic radii in crystals (1.52-1.65 A) 

Radial distributions of the electron density of a-K2CrO( (85). (a) Observed 

In the case of a-K2Cr04, the estimation was carried out on a crude assumption that the interatomic charge could be assigned equally to the Cr and the four O atoms. Staudenmann et al. (69) have proposed a different method to define the effective region of an atom, where an atomic region is represented by an assembly of many small parallel piped volume elements for computational convenience. This method may enable us to define the effective atomic region more precisely for covalent molecules. From a practical point of view, however, it seems to be difficult to define an exact atomic region in this way. 

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In metal oxides and silicates, the net charges of transition metal atoms are quite different. Table III shows the net charges of metal atoms in these crystals, which are slightly neutralized but almost equal to their oxidation numbers. The ionic characters of these crystals may be demonstrated by the electron population analysis of the CoA1204 crystal. The net charges of Co(II), Al(III), and O(II) atoms were estimated by the ELS method to be +1.5(1), +2.8(1), and -1.8 e, respectively (84). 

There may be a relatively large charge separation, e.g. in MoSj- and almost equal net charges on the metal and sulfur atoms, e.g. in [Mo2S(CN),2]6-. 78a MO calculations on the latter ion show that there are k MOs delocalized over three centers. Resonance Raman studies further indicate that the delocalization extends over the whole linear N—C—Mo—S—Mo—C—N system. The tt(S) -> t/(Mo) donation induces a decrease of electron density on the sulfur and is, therefore, responsible for an unusual charge transfer transition Mo-+S (band at 27100cm-1), quite the reverse assignment to that in examples with terminal sulfide where a considerable p contribution also has to be anticipated (see Table l).3,4... 

Many molecules of acute chemical interest are charged in particular many species containing transition metal atoms are anions. Sometimes these anions are closed-shell, sometimes open-shell. There exists a formal proof that the solutions of the (differential, GUHF) Hartree-Fock equations actually exist for neutral systems and cations. The proof apparently cannot be extended to anions all that can be proved is that a molecule with n -t-1 electrons is stable if the net nuclear charge sum is n 4- where may be small but non-zero. This means that the existence of the solutions of the Hartree-Fock equations for anions is contingent on the particular case in some cases the solutions will exist, in other cases not. Clearly, it is extremely unlikely that the Hartree-Fock equations for multiply charged anions will exist. 

Answer. The [Zr6Cli2X]m+ core charge is —4 — (—5) = +1. If X is a main-group atom then we have 12 + vx — 1 = 14. vx = 3 = B. If X is a transition metal the same sum =18 and vx = 7 = Mn. The utilization of these cluster building blocks to generate nets and three-dimensional networks should be evident. 

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