Empty orbital

All the atoms of butadiene lie in a plane defined by the s p hybrid orbitals. Each carbon atom has one remaining p orbital that points perpendicular to the plane, in perfect position for side-by-side overlap. Figure 10-42 shows that all four p orbitals interact to form four delocalized molecular orbitals two are bonding MOs and two are antibonding. The four remaining valence electrons fill the orbitals, leaving the two p orbitals empty. 

For metal ions having configurations d°, d1, d1, or d. there will always be two of the d orbitals empty to form a set of d2sp3 hybrids. Therefore, we expect complexes of these metal ions to be octahedral in which the hybrid orbital type is d2sp3. If we consider Cr3+ as an example, the formation of a complex can be shown as follows ... 

Answer. The eve count for [Al77R2o]2 is 253 so it is an odd electron cluster. Considering the inner two clusters with full radial and tangential bonding (the smaller one with an interstitial A1 atom) yields a count of 50 + 178 = 228. If the outer AIR fragments are attached by radial bonding alone the total count is 228 + 20 x 2 = 268 which is 15 more than observed and perhaps 14 more than a probable even electron species. Hence, one would have to assume seven tangential orbitals empty. 

The m.o. diagram is shown in Fig. 7.10, which also depicts the various ambinations of a.o.s in the formation of m.o.s. The non-bonding tt orbital empty, which explains the Lewis acid character of BH3. There are six mding electrons shared by all the atoms, giving an average of two iectrons per formal BH bond ... 

The choice of reference space for MRCI calculations is a complex problem. First, a multieonfigurational Hartree-Fock (MCSCF) approach must be chosen. Common among these are the generalized valence-bond method (GVB) and the complete active space SCF (CASSCF) method. The latter actually involves a full Cl calculation in a subspace of the MO space—the active space. As a consequence of this full Cl, the number of CSFs can become large, and this can create very long Cl expansions if all the CASSCF CSFs are used as reference CSFs. This problem is exacerbated when it becomes necessary to correlate valence electrons in the Cl that were excluded from the CASSCF active space. It is very common to select reference CSFs, usually by their weight in the CASSCF wave function. Even more elaborate than the use of a CASSCF wave function as the reference space is the seeond-order Cl, in which the only restriction on the CSFs is that no more than two electrons occupy orbitals empty in the CASSCF wave function. Such expansions are usually too long for practical calculations, and they seldom produce results different from a CAS reference space MRCI. 

The same holds true for the five orbitals in a d-subshell. Adding three electrons to a d-subshell will place one electron in three of the five orbitals, leaving two orbitals empty. No pairing would take place until more than five electrons are added to the d-subshell. 

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