Atomic orbitals, relative energies

The origins of the Finnis-Sinclair potential [Finnis and Sinclair 1984] lie in the density of states and the moments theorem. Recall that the density of states D(E) (see Section 3.8.5) describes the distribution of electronic states in the system. D(E) gives the number of states between E and E - - 8E. Such a distribution can be described in terms of its moments. The moments are usually defined relative to the energy of the atomic orbital from which the molecular orbitals are formed. The mth moment, fi", is given by ... 

No completely general and quantitative theory of the stereochemical activity of the lone-pair of electrons in complex halides of tervalent As, Sb and Bi has been developed but certain trends are discernible. The lone-pair becomes less decisive in modifying the stereochemistry (a) with increase in the coordination number of the central atom from 4 through 5 to 6, (b) with increase in the atomic weight of the central atom (As > Sb > Bi), and (c) with increa.se in the atomic weight of the halogen (F > Cl > Br > 1). The relative energies of the various valence-Ievel orbitals may also be an important factor the F(a) orbital of F lies well below both the s and the p valence... 

Electrons in an atom differ in energy depending on the orbital they occupy— that is, their average location in space relative to the nucleus. 

In this chapter, we focus on electron arrangements in atoms, paying particular attention to the relative energies of different electrons (energy levels) and their spatial locations (orbitals). Specifically, we consider the nature of the energy levels and orbitals available to—... 

The Schrodinger equation can be solved approximately for atoms with two or more electrons. There are many solutions for the wave function, ij/, each associated with a set of numbers called quantum numbers. Three such numbers are given the symbols n, , and mi. A wave function corresponding to a particular set of three quantum numbers (e.g., n = 2, = 1, mi = 0) is associated with an electron occupying an atomic orbital. From the expression for ij/y we can deduce the relative energy of that orbital, its shape, and its orientation in space. 

Relative energies, so far as filling order is concerned, for the molecular orbitals formed by combining 2s and 2p atomic orbitals. 

FIGURE 1.41 The relative energies of the shells, subshells, and orbitals in a many-electron atom. Each of the boxes can hold at most two electrons. Note the change in the order of energies of the 3d- and 4s-orbitals after Z = 20. 

LO Name and explain the relation of each of the four quantum numbers to the properties and relative energies of atomic orbitals (Sections 1.8—1.1 1). 

FIGURE 3.33 A typical d molecular orbital energy-level diagram for a heteronuclear diatomic molecule AB the relative contributions of the atomic orbitals to the molecular orbitals are represented by the relative sizes of the spheres and the horizontal position of the boxes. In this case, A is the more electronegative of the two elements. 

Such an averaging effect of the transition energies of CrMo relative to Crj and Mo is intuitively understandable, as the electronic ground-states of Cr and Mo atoms are both nsHn — l)d and those of Cr and M02 are both considered to be lo-gj 17Tu4 2a-g 18,4. Furthermore, the Cr 4s, 3d and the Mo 5s, 4d atomic orbitals, considered to be the main contributors to the metal-metal bonding in Cr /CrMo/Mo, lu-e known to have similar energies. Further discussion of these bimetallics formed by cryophotoclustering methods will be found in Section III. 

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