D atomic orbitals

We will limit ourselves here to transition metals. It is well known that in these metals, the cohesive properties are largely dominated by the valence d electrons, and consequently, sp electrons can be neglected save for the elements with an almost empty or filled d valence shelP. Since the valence d atomic orbitals are rather localized, the d electronic states in the solid are well described in the tight-binding approximation. In this approximation, the cohesive energy of a bulk crystal is usually written as ... 

Similarly, if an atom contributes d atomic orbitals to the SOMO,... 

Semi-empirical methods (e.g. CNDO, MNDO or PM3), which had been successfully applied to elements of the second period, failed for the heavier elements. This is probably due to the determination of the parameters for the d-atomic orbitals which turned... 

Figure 1.1 Surface plots of representative s, p, and d atomic orbitals (from the Kr valence shell).

Figure 10.4 Shapes of the s, p, and d atomic orbitals. The s orbital (a) is spherically symmetrical about the nucleus. The three p orbitals (b) are figure-of-eight lobes orientated along the three orthogonal axes (only z axis shown). The five d orbitals (c, d, and e) are four quatrefoil lobes, one orientated along the x-y axes, three between the axes, and the fifth (e) a figure-of-eight along the z axis with an additional donut around the nucleus. The orbitals are not drawn to the same scale.

Functions Obtained from s, p, and d Atomic Orbitals Using the Operators lxy lyy and lz... 

In the columns on the right are some of the basis functions which have the symmetry properties of a given irreducible representation. R, Ry, and R. stand for rotations around the specified axes. The binary products on the far right indicate, for example, how the d atomic orbitals will behave ( transform ) under the operations of the group. 

Fig. 6.19 Directional properties of hybrid ortuals From j. p, and d atomic orbitals. [From Kasha, M., adapted from Kimball, G. Arm. Rev. Phys. Chem. 1951, 2. 177. Reproduced with permission.)...

CHARACTERISTIC SHAPES AND SPATIAL ORIENTATIONS OF s, p, AND d ATOMIC ORBITALS THE ORIGIN OF THE COORDINATE AXIS SYSTEM IS THE ATOMIC NUCLEUS... 

Figure 10.89. Qualitative molecular orbital diagram for FeF, involving the fluorine 2p and iron 4.v. 3 d atomic orbitals [244], The energies of the iron non-bonding orbitals (15, 9 a, 4 it) are very close to that of the 10cr antibonding orbital.

All p and d atomic orbitals are symmetrical about rotation and reflection axis. However, the hybridised orbitals are highly asymmetric because they do not have any reflection plane of symmetry, rotational axis of symmetry. 

STO-3G computations were aimed at examining the role of the d atomic orbital of Si, and although they have led to somewhat different electron structures for adsorption complexes (e.g., the electron charge on Si decreased by 0.3e), the binding energy remained practically the same. Thus, consideration of the d AO did not reveal any new qualitative effect. 

Position vectors pointing toward the ligands d Atomic orbitals... 

There are many texts that make the point very clearly that the bonding in a molecule such as SFfi has very little to do with the availability of d atomic orbitals, but this is normally done in the context of MO theory, whereas the general ideas of utilizing d orbitals are much more closely allied with the ideas of classical valence bond theory. This, perhaps, is one of the reasons for the continued survival of such models. The purpose of this Chapter is to describe various calculations which have been performed using modern valence bond theory, in its spin-coupled form, resulting in a useful aide memoire which we term the democracy principle. We argue that there are no significant qualitative differences between the hypercoordinate nature of first-row, second-row and noble gas atoms in appropriate chemical environments. 

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