Structural Chemistry by Mihai V. Putz Fanica Cimpoesu & Marilena Ferbinteanu

Author:Mihai V. Putz, Fanica Cimpoesu & Marilena Ferbinteanu
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

5.2.3 Are the Hybrids with s, p, and d Composition Realistic?

Following the title question, we will check the validity of hybridization ideas in respect with d-type transition compounds. It is learnt in basic courses that the octahedral pattern is associated with the d2sp3 hybrids. However, this statement does not descend from calculations, let us say of VB type, to which the hybrids were associated as appropriate basis. The d2sp3 composition is suggested by symmetry reasons. Namely, the vertices of an octahedron, or a collection of orbitals capable of σ bonding, pointing toward the symmetry center, are behaving in the O h point group like the a 1g + e g + t 1u representation. The atomic orbitals (or, more specifically, the corresponding sets of spherical harmonics) are behaving as follows: s = a 1g , p = t 1u , d = e g + t 2g , d = a 2u + t 1u + t 2u . Then, the hybrids, as a set of central equivalent orbitals isomorphous with the octahedron σ bonding representation can be produced picking from atomic representations the needed components, namely one s orbital (the a 1g ), three p functions (the t 1u triple degenerate set), and two d-type AOs (the e g doublet). One arrives in this way to the d2sp3 set. The spelling order of orbitals is meant to suggest their energy order (e.g. concerning the 3d, 4s, and 4p shells, in elements from the first transition series). However, the symmetry reasoning does not determine, in itself, this composition. Just formally, a d2sf3 set could be an equally good option, since the f orbitals are also incorporating the needed t 1u representation. Or, if we consider octahedral lanthanide units, it may seem that the 4f, 5d, and 6s orbitals are acting on equal footing, which cannot be true. Actually this symmetry filtering is the way in which all the hybridization sets are assigned with respect of the symmetry of the geometric figure having the same number of vertices like the orbital count, projected on the available valence shells. Thus, the tetrahedral sp3 set results considering that the tetrahedron has the a 1 + t 2 representation, matched by s as a 1 and the three p AOs represented by t 2 in the T d point group. However, t 2 can be also found in the d orbital set, behaving as e + t 2. Therefore, the tetrahedral hybrids can also be presented as the sd3 denomination, a fact considered for transition metal complexes with such geometry.

To be distinguished from the s–p type hybrids, that receive validation at computational level, or by the other reasons, debated in the previous section, the s–p–d mixing has a rather limited support. We will show in the following that it is not fit for the coordination compounds, systems for which the d2sp3 are sometimes invoked. Figure 5.5a concludes the result of the NBO procedure applied to the results of a DFT calculation of the [CrF6]3− complex anion.

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