Molecular orbital Mixing coefficient

CM2(r 3) as well as physical constants. The term CM is the molecular orbital mixing coefficient for the platinum 5d orbital, and the r"3 average is taken over the platinum d radial function. The differences in energy of the ground and first excited A2g and Eg states are given in terms of the transition wavelengths, A. 

In this equation, the coefficients c j are called the molecular orbital expansion coefficients, and are optimized during the computational procedme. In chemical terms, one can think of the basis functions as the sets of constituent atomic orbitals, which mix to form the molecular orbitals of the molecule. In order to approach the exact solution to the Schrodinger equation, an infinite set of basis functions would be required, as this would introduce sufficient mathematical... 

The relative magnitudes of the resulting average mixing coefficients Ay and Ay per and Bi average AO, respectively, give a measure of the polarity of the Bi — Bi MOs. In simple cases (say, HC1) the concepts of orbital polarity and electron polarity (as a measure of ionicity) coincide. The extension of the latter inference to more complicated molecular systems is far from trivial, although such a conclusion is commonly accepted for qualitative purposes. 

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. 

The first and most influential molecular-orbital calculation on metal-alkynyl complexes is that of Kostin and Fenske, who applied the Fenske-Hall method to the complexes FeCp(C=CH)(PH3)2 and FeCp-(C=CH)(C0)2 (11). They concluded that the M-CCH bonds in these complexes are nearly pure a in character. The large energy gap (ca. 15 eV) between the occupied metal orbitals and ir (C=CH) levels severely limits the ir-accepting quality of the latter, with the total electron population for the pair of tt orbitals being 0.22 e for FeCp(C=CH)(PH3)2 and 0.14 e" for FeCp(C=CH)(CO)2. The filled ir(C=CH) orbitals, in contrast, mix extensively with the higher-lying occupied metal orbitals these filled-filled interactions result in the destabilization of the metal-based orbitals. The HOMOs of both complexes possess substantial coefficients at the alkynyl jS-carbon this was noted to be consistent with the alkynyl-localized reactivity of these complexes. 

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