By Per-Olov Löwdin
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Ferrocene—the prototypical metallocene—is a desirable molecule. although it was once first found over fifty years in the past, study into ferrocene-containing compounds maintains apace, mostly motivated through their winning purposes in catalysis, fabrics technological know-how and bioorganometallic chemistry.
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Kecent reviews have been given, for example, by I'Haya (1964) and Fischer-Hjalmars (1964). Section II,A gives a brief review of the self-consistent field method. Zero Differential Overlap 27 The assumptions, typical for the ZDO approximation, are given in Eqs. (7)-(11). , by application of the Mulliken approximation to the energy expressions in the MO basis and by introduction of a basis of orthogonalized atomic orbitals (OAO's). It is pointed out that such justifications are only valid in a certain approximation.
Eq. (59)] on the atom p should be taken into account by the following adjustment of the a value : a, = - #Q,Y,,. , Streitwieser, 1961, where further references are given): + a, = u,” w/3’Q,. (67) A comparison of Eqs. 4. This value is somewhat higher than those used in recent calculations, in line with the obvious fact that a theoretical w value must be too high due to neglect of polarization of the 0 core. Equation (52) also indicates a possible modification of up when there are considerable charges (2, on the neighboring atoms.
The effect of Y 2on energy quantities is smaller still since the latter involve squares of the spinor components. Y 2may be eliminated between Eqs. (22) to yield an equation for Ylalone. rr]Y1 = 0 (25) which we may write HeffY1= EY1. (254 We shall now forget entirely about Y 2 and regard (25) as the fundamental wave equation in a two-component theory. 02 % u / c for an atomic electron), Y is equivalent to the Pauli-Schrodinger wave function. We have improved upon the original Pauli-Schrodinger formulation in that ( i ) we have arrived at it by a consistent, unified approach and (ii) Ifeff contains certain terms missing from the original theory, in which k(r) is simply replaced by 1.