Fenske-Hall method

The Fenske-Hall method is a modification of crystal held theory. This is done by using a population analysis scheme, then replacing orbital interactions with point charge interactions. This has been designed for the description of inorganic metal-ligand systems. There are both parameterized and unparameterized forms of this method. 

Comparisons between the electronic structures (using a ZINDO analysis) of [Ru(bpy)3] " and [Ru(bpy)(NH3)4], and between related pairs of compounds where bpy is replaced by 2,2 -bipyrazine or 1,2-benzoquinonediimine, show that bpy is unable to accept extra electron density from the metal center whereas the opposite is true for 1,2-benzoquinonediimine. The acceptor properties of the 2,2 -bipyrazine ligand fall between those of bpy and 1,2-benzoquinonediimine. Using the Fenske-Hall method, the electronic structures of [Ru(bpy)3 (ppy) ] "A (Hppy = 2-phenylpyridine) have been investigated. The coordinated ppy is a C,A-donor. The electronic structures of the heteroleptic complexes exhibit a separation of the Ru—C and Ru—N f7-bonding character. It is proposed that the observed preference for cis- over trans- and for fac- over nrer-isomers may arise from the enhanced cr-donating ability of the C atom when it is trans to an N rather than C-donor. ... 

Figure 8-18. Charge densities in the pyridine molecule, calculated using the Fenske-Hall method. The total charge density indicates that pyridine might be expected to react with electrophiles at C(2) and C(4). Also shown are the residual charges associated with the gain or loss of electrons as a result of o- and 7t-bonding at each carbon and nitrogen atom within the molecule.

Further enlarging the set of Coulomb integrals has been done in the Fenske-Hall method practiced more or less widely in the 1970s and 1980s. It takes into account all possible two-electron integrals, but calculates them using the Mulliken approximation eq. (2.29). Nevertheless no decisive success has been achieved in this direction. 

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. 

Some form of MO theory is required to model photoelectron spectrum energies. Representative examples include the application of (1) HF theory to planar dithiophosphonate complexes of Ni", Pd" and Pt" [127], (2) the DVXa model to [M(Cp)2(CO)2] (M = Zr, Ti) [128], (3) the INDO method to halfopen metallocenes of Fe, Ru and Os [129] and (4) the Fenske-Hall method to [CpPt(CH3)3] and [Cp Pt(CH3)3] [130]. In all cases, reasonable qualitative agreement is found. Large but uniform deviations from Koopmans theorem results are noted in the HF calculations while the relaxation accompanying Slater Transition State calculations for the DVXa study show orbital energy changes of 3-4 eV. 

The Fenske-Hall method includes the overlap, and thus solves the Fock Eq. [16c], as does the extended Hiickel models. If there is no charge build-up in the model, Eq. [19b] is identical to extended Hiickel Eq. [16a]. Similarly, Eq. [19d] becomes equal to Eq. [16b], with the proportionality constant K = 2, with the exception of the kinetic energy term already noted. 

Before describing the Fenske-Hall method itself, we will examine an example of the behavior described above. Our example will be ferrocene (Tri -C5H5)2Fe, whose qualitative molecular orbital diagram is shown in Scheme 40.1. The principal bonding... 

Richard Fenske arrived as Assistant Professor at the University of Wisconsin in 1961 after having completed his PhD, with Donald Martin at Iowa State University on applying crystal-field theory to square-planar platinum complexes [19]. Fenske was interested in developing a method more closely tied to the ab initio molecular orbital method described so beautifully by Roothaan [20]. Building on some previous suggestions [21], he and his first students, especially Ken Caulton and Doug Radtke, developed an approximate self-consistent field method that had no empirical or adjustable parameters. With some later refinements by this author, the method became widely known as the Fenske-Hall method [22], and in this form it is still being used today [23]. 

Molecular orbital (MO) theory includes a series of quantum mechanical methods for describing the behavior of electrons in molecules by combining the familiar s, p, d, and / atomic orbitals (AOs) of the individual atoms to form MOs that extend over the molecule as a whole. The accuracy of the calculations critically depends on the way the interactions between the electrons (electron correlation) are handled. More exact treatments generally require more computer time, so the problem is to find methods that give acceptable accuracy for systems of chemical interest without excessive use of computer time. For many years, the extended Hiickel (EH) method was widely used in organometallic chemistry, largely thanks to the exceptionally insightful contributions of Roald Hoffmann. The EH method allowed structural and reactivity trends to be discussed in terms of the interactions of specific molecular orbitals. Fenske-Hall methods also proved very useful in this period. ... 

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