Overlapping atoms

M + e + hv). The structured background is produced by partially or completely overlapping atomic, ionic, or in some cases, molecular emission. To obtain precision better than 10% the concentration of an element must be at least 5 times the detection limit. 

There are two complementary lines of approach to examining the part played by 3d orbitals in molecular orbital theory and to appreciating current doubts as to their role. On the one hand, there is the question of 3d orbitals in relation to the basic formulation of molecular orbitals by overlapping atomic orbitals on the other hand, there is the question of the effect of including or excluding 3d functions in molecular orbital calculations, particularly of the ab initio type. We shall consider each of these briefly in turn. 

To determine the geometry of a molecule, we need to know how atoms bond with each other three dimensionally, so it makes sense for our discussion to start with orbitals. After all, bonds come from overlapping atomic orbitals. 

In this chapter, we develop a model of bonding that can be applied to molecules as simple as H2 or as complex as chlorophyll. We begin with a description of bonding based on the idea of overlapping atomic orbitals. We then extend the model to include the molecular shapes described in Chapter 9. Next we apply the model to molecules with double and triple bonds. Then we present variations on the orbital overlap model that encompass electrons distributed across three, four, or more atoms, including the extended systems of molecules such as chlorophyll. Finally, we show how to generalize the model to describe the electronic structures of metals and semiconductors. 

The option "Modify precursor" (Process menu) permits you to modify the position of the atoms in any precursor on the synthesis tree. It has been introduced because, when the program disconnects a molecule, partially overlapping atoms may appear, or the precursor generated may come up in an impossible conformation. 

The formation of bonding molecular orbitals by an overlap of atomic orbitals applies not only to the Is orbitals of hydrogen, but also to other atomic orbitals. When the atomic orbitals overlap along the axis of the bond, a covalent bond, called a sigma (a) bond, results. This is normally referred to as end-on overlap. Some examples of the formation of a bonds from overlapping atomic orbitals are shown in the diagrams. 

A theoretical approach in molecular orbital studies to formulate an expression for the wave function of a molecular orbital (both for bonding and antibonding orbitals) by linear combinations of the overlapping atomic orbitals with appropriate weighting factors. 

Every part of the electron density of the crystal must belong to at least one atom. The definition of atoms must ensure a complete coverage of the space occupied by the crystal in order to ensure electroneutrality. However, atoms may overlap, since the electron density in an overlap region can be partitioned in any convenient way between the overlapping atoms. 

Making the usual assumption that the crystalline potential, V, is given by the sum of overlapping atomic potentials, v, we have... 

So, while derivations of SCRF theory using ideal cavities are very useful for conceptual purposes, they are insufficiently accurate for all but the most crude analyses. Modem applications of continuum models almost invariably use arbitrary cavity shapes, typically constmeted from overlapping atomic spheres, and we turn to examples of these models next. 

The fluorine atom has five overlapping atomic orbitals that contain its nine electrons, which are not shown. 

There are several qualitative approaches to bonding in polyatomic molecules, but we shall discuss here the most widely used and currently popular approach. This approach involves setting up appropriate atomic orbitals for the atoms and considering that each bond arises from the attractive electrical forces of two or more nuclei for a pair of electrons in overlapping atomic orbitals, with each orbital on a different atom. The geometry of the bonds is assumed to be determined by the geometry of the orbitals and by the repulsive forces between the electrons. In the course of showing how this approach... 

In writing the conventional Lewis structures for molecules, we assume that a covalent chemical bond between two atoms involves sharing of a pair of electrons, one from each atom. Figure 6-5 shows how atomic orbitals can be considered to be used in bond formation. Here, we postulate that a single bond is formed by the pulling together of two atomic nuclei by attractive forces exerted by the nuclei for the two paired electrons in overlapping atomic orbitals. 

Because two atomic orbitals can hold a maximum of four electrons, it is reasonable to ask why it is that two rather than one, three, or four electrons normally are involved in a bond. The answer is that two overlapping atomic... 

Explicit formulas and numerical tables for the overlap integral S between AOs (atomic orbitals) of two overlapping atoms a and b are given. These cover all the most important combinations of AO pairs involving ns, npSlater type, each containing two parameters i [equal to Z/( - 5)], and n — S, where n — S is an effective principal quantum number. The S formulas are given as functions of two parameters p and t, where p = p- + p,s)R/ao, R being the interatomic distance, and t = — Mb)/(ma + Mb)- Master tables of... 

This description of a covalent bond in terms of overlapping atomic orbitals stems from the desire to retain and use the atomic orbital concept. Atomic orbitals were designed to describe electron distributions in isolated atoms however, one might expect distortions of the isolated atom electron cloud when it is in close proximity to the positive charge of another atom. A more detailed description of the covalent bond would have to include this distortion. 

Figure 6.8. Approximate charge density prior to bonding in overlapping atomic orbitals that form <7-type molecular orbitals in ML6 (a) (b) eg, (c) e g. The actual charge density in the molecule...

Fig. 5. Idealized, close-packed structures for (a) niobium and (b) rhodium penta-fluorides. Atoms in the first, second, third, and fourth layers are shown as single, double, crossed, and hatched circles, respectively. The symbols for overlapped atoms are shown dashed. The bridge bonds are shaded.

For analyzing noncovalent interactions, we typically evaluate V(r) on a three-dimensional surface of the molecule. For this purpose, we use the 0.001 au (electrons/bohr3) contour of its electronic density, as suggested by Bader et al. [51]. This surface encompasses at least 96% of the electronic charge of the molecule, and reflects its specific features, such as lone pairs, n electrons, strained bonds, etc., which is not true of surfaces created by overlapping atomic spheres. 

---