Orbital experiments

How large are orbitals Experiments that measure atomic radii provide information about the size of an orbital. In addition, theoretical models of the atom predict how the electron density of a particular orbital changes with distance from the nucleus, r. When these sources of information are combined, they reveal several regular features about orbital size. 

We know from Maxwell s equations that whenever a charged particle undergoes acceleration, electromagnetic waves are generated. An electron in a circular orbit experiences an acceleration toward the center of the orbit and as a result emits radiation in an axis perpendicular to the motion. 

Other rows in the periodic table follow a similar trend. However, for the third row, there is a general decrease in radius except for the last two or three elements in the transition series. The covalent radii of Fe, Co, Ni, Cu, and Zn are 126, 125, 124, 128, and 133 pm, respectively. This effect is a manifestation of the fact that the 3d orbitals shrink in size as the nuclear charge increases (going to the right), and the additional electrons populating these orbitals experience greater repulsion. As a result, the size decreases to a point (at Co and Ni), but after that the increase in repulsion produces an increase in size (Cu and Zn are larger than Co and Ni). 

In the Ni atom, the 4s orbital contains two electrons. This spatially extended, doubly occupied orbital experiences a large repulsive interaction with the doubly occupied H2 a orbital of the same symmetry. Dissociation of H2 has a large activation energy because electron promotion has to occur from 4s to 3d atomic orbitals in order for dissociation to occur. Coordination by ligands, as in Ni(PH3)2/ decreases the promotion energy. The Ni(PH3)2 complex has linear geometry (Fig. 4.15). 

In the Ni atom, the 4s orbital contains two electrons. This spatially extended, doubly occupied orbital experiences a large repulsive interaction with the doubly... 

The Kohn-Sham construction is a pragmatic one, justified by computational utility. Of special computational utility is the fact that each Kohn-Sham orbital experiences the same potential and that this potential, in turn, is a functional of the electron density alone. This allows us to rewrite the Kohn-Sham energy in terms of the first-order density matrix,... 

Now let us consider the arrangement of the electrons in Li (Z = 3). In the ground state, the H atomic orbital is fully occupied and the third electron could occupy either a 2s or 2p orbital. Which arrangement will possess the lower energy An electron in a 2s or 2p atomic orbital experiences the effective charge, of a nucleus partly shieldedhy the ly... 

To minimize electron-electron repulsions, the last added (sixth) electron of carbon enters one of the unoccupied 2p orbitals by convention, we place it in the m/ = 0 orbital. Experiment shows that the spin of this electron is parallel to (the same as) the spin of the other 2p electron n = 2, I = 1, / / = 0, = +5. 

Figure 22.24 Splitting of d-orbital energies by a tetrahedral field of ligands. Electrons in d y, dy2, and orbitals experience greater repulsions than those h d s y2 and d, so the tetrahedral splitting pattern is the opposite of the octahedral pattern.

An example will show the application of some of the ideas introduced above. Let us start with the simple two-ccntcr-two-orbital problem described exhaustively in Chapter 2. In the language of perturbation theory these two orbitals experience a degenerate interaction for the case of H2 where the energies of each atomic orbital are the same. The result is an in-phase (bonding) combination and an out-of-phase (antibonding) combination, between the centers A and B. A more complicated example arises when there are two orbitals on A and one on B as when the orbitals of linear H3 are constructed from those of II2 + H (3.10). This is shown in Figure 3.1, where the relative phases of the orbitals have been chosen so that Sij and are positive. 

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