D -p hybrid orbitals

The inclusion of d orbitals into the hybridization scheme leads to no change in the maximum directions of the hybrids. The mixing of d character into the sp hybrids enhances the directional character of the hybrids towards the four corners of a tetrahedral structure. The complementary (d-p) hybrid orbitals are ... 

If metalhc bonding does not contribute to the ground state properties of oxides, it is possible however, that the outer orbitals of the actinide atom might form hybridized bonds with the 2p orbitals of oxygen atom. Brooks and Kelly have calculated the ground state properties of by including only d-p hybridization. They found a relevant... 

In this discussion the orbital moments (along the orbital axes) have been assumed to be equal for bond orbitals and unshared-pair orbitals. Calculation of the moment (average value of cosine of angle with bond axis) for the %p hybrid orbitals leads to a value only half as great for the bond orbital as for the unshared-pair orbital. However, equality is found when the d-character (4 percent) and... 

In symmetries lower than cubic the (/-orbitals mix with the donor atom s—p hybrid orbitals to varying extents in molecular orbitals of appropriate symmetry. However, the mixing is believed to be small and the ligand field treatment of the problem proceeds upon the basis that the effective d-orbitals still follow the symmetry requirements as (/-orbitals should. There will be separations between the MOs which can be reproduced using the formal parameters appropriate to free-ion d-orbitals. That is, the separations may be parameterized using the crystal field scheme. Of course, the values that appear for the parameters may be quite different to those expected for a free ion (/-orbital set. Nevertheless, the formalism of the CFT approach can be used. For example, for axially distorted octahedral or tetrahedral complexes we expect to be able to parameterize the energies of the MOs which house the (/-orbitals using the parameter set Dq, Ds and Dt as set out in Section 6.2.1.4 or perhaps one of the schemes defined in equations (11) and (12). 

The valence ns and np electrons play important roles in the chemistry of main group elements, in contrast to the d electrons in the chemistry of transition metals. In Figure 1 are shown the radii of atomic orbitals (maximal electron-density), which are calculated for group 14 elements. It should be noted that the valence ns and np atomic orbitals show great difference in their sizes for the heavier atoms (Si, Ge, Sn, Pb), though the size of the 2s atomic orbital of carbon is almost equal to that of the 2p atomic orbitals. Therefore, the heavier atoms have a lower tendency to form s-p hybrid orbitals with high p character and they prefer to retain the ns np valence electronic configuration, in contrast to the case of carbon. 

Another factor which affects the most stable arrangeinent of the atom in a molecule is the vanationof bond energy with hybridization. The directed lobes ofs-p hybrid orbitals overlap more eKctively than the undirected s orbitak, the two-lobed p Qibitak, or the difiiise d orbitals. The increased overlap results in stronger bonds... 

With a coordination number of four, the tetrahedral configuration arises by the formation of sp or dh hybrid orbitals. The remaining electrons form TT bonds which may be strong hybridization), or weak (rf or p hybridization). The planar configuration, due to either dsp or d p hybridization may have four stable tt bonds between the central atom and the surrounding atoms, depending on the number of available electrons. 

In the third row K uses a doubly occupied 4s band of bonding orbitals, and Ca uses two s-p hybrid orbitals. In Sc the 3d-electron is comparable in energy to the 4s, and the d orbitals form a five-fold degenerate band. The free atoms of the first transition series all have high spin d-electrons in accordance with Hund s rule. We expect similar behavior in the solid state, so that only 2 1/2 electrons will fill the bonding d levels without double occupancy. This is the case for Sc, Ti and V. 

The d block of the M-L fragment therefore contains five low-energy orbitals that are all likely to be occupied. The rare stable complexes do indeed have a electronic configuration (2-97). They are therefore 12-electron complexes with three empty nonbonding orbitals on the metal, an s-p hybrid orbital (cr symmetry) and two pure p orbitals of n symmetry that are higher in energy (2-100). 

In cesium chloride, CsC , where each atom is surrounded by eight equivalent neighbors, the orbitals of the elementary cells are built from the four p and p orbitals of chlorine atom, as well as from the eight sp d f hybrid orbitals of the neighboring cesium atoms, pointing toward the chlorine atom. 

Alabugin, I. V., Bresch, S., Gomes, G. d. P. (2014). Orbital hybridization a key electronic factor in control of structure and reactivity. Journal of Physical Organic Chemistry, 28, 147-162. 

These three orbitals maximize their electron densities towards the directions of the four vacant corners of the cube and correspond to a rotation of 45° of the tetrahedral structure along the z axis (see (1)). Figure 3 illustrates the nodal characteristics of the p -d y hybrid orbital. 

For the trigonal bipyramid the d y and d i yi orbitals transform according to the same representations of the D31, point group as and Py. Therefore the limiting hybridization schemes are either sp d or spd. The optimum hybrids can be obtained using the same methodology as that developed above for the tetrahedron. The in-phase d-p hybrids... 

In a trigonal prismatic transition metal complex (16), in addition to the six a hybrids which form M-L bonds there are three non-bonding orbitals which include one pure d 2 and two e d-p hybrid non-bonding orbitals (see Table 3). As discussed above, it can be concluded that capping the square faces is preferred to the triangular faces in the mono- and bi-capped trigonal prismatic transition metal complexes because of the two d-p hybrid non-bonding orbitals which maximize their electron density towards the square faces. The existence of structures such as [Mo(CNR)gI] (mono-capped) [39] and ZrFf" (bicapped) [40] supports the conclusions above. 

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