Homonuclear diatomic molecules, electron distribution

In Section 2.12, we saw that a polar covalent bond in which electrons are not evenly distributed has a nonzero dipole moment. A polar molecule is a molecule with a nonzero dipole moment. All diatomic molecules are polar if their bonds are polar. An HC1 molecule, with its polar covalent bond (8+H—Clfi ), is a polar molecule. Its dipole moment of 1.1 D is typical of polar diatomic molecules (Table 3.1). All diatomic molecules that are composed of atoms of different elements are at least slightly polar. A nonpolar molecule is a molecule that has no electric dipole moment. All homonuclear diatomic molecules, diatomic molecules containing atoms of only one element, such as 02, N2, and Cl2, are nonpolar, because their bonds are nonpolar. 

Fig. 5.41 The distribution of the electron density (charge density) p for a homonuclear diatomic molecule X2. One nucleus lies at the origin, the other along the positive z-axis (the z-axis is commonly used as the molecular axis). The xz plane represents a slice through the molecule along the z-axis. The —p = f(x, z) surface is analogous to a potential energy surface E = /(nuclear coordinates), and has minima at the nuclei (maximum value of p) and a saddle point, corresponding to a bond critical point, along the z axis (midway between the two nuclei since the molecule is homonuclear)...

Fig. 5.42 Contour lines for p, the electron density distribution, in a homonuclear diatomic molecule X2. The lines originating at infinity and terminating at the nuclei and at the bond critical point C are trajectories of the gradient vector field (the lines of steepest increase in p two trajectories also originate at C). The line S represents the dividing surface between the two atoms (the line is where the plane of the paper cuts this surface). S passes through the bond critical point and is not crossed by any trajectories...

Hoffmann-Ostenhof and Morgan (1981) were able to prove that the ground-state charge distribution of a one-electron homonuclear diatomic molecule can exhibit maxima in p only at the positions of the nuclei. In this proof an important inequality is used (Hoffmann-Ostenhof and Hoffman-Ostenhof 1977),... 

The electron distributions for the homonuclear diatomic molecules of the first and second periods are shown in Table 9-1 together with their bond orders, bond lengths, and bond energies. 

Which homonuclear diatomic molecules or ions of the second period have the following electron distributions in MOs In other words, identify X in each. 

The homonuclear diatomic molecules discussed Section 5.2 are nonpolar molecules. The electron density within the occupied molecular orbitals is evenly distributed over each atom. A discussion of heteronuclear diatomic molecules provides an introduction into how molecular orbital theory treats molecules that are polar, with an unequal distribution of the electron density in the occupied orbitals. 

Fig. 8.9 (a) Illustration of the variables R, 0, and (p in the interaction potential V R,0,(p). (b) Schematic electron cloud distribution for excited homonuclear diatomic molecules in a 77 state. Also shown are the two directions of cp for a i7-type and a /7-type interaction potential... 

Just as we treated the bonding in H2 by using molecular orbital theory, we can consider the MO description of otiier diatomic molecules. Initially we will restrict our discussion to homonuclear diatomic molecules (those composed of two identical atoms) of elements in flie second row of the periodic table. As we will see, die procedure for determining the distribution of electrons in these molecules closely follows the one we used for H2. 

In a free atom, the electron density distribution is spherical, and centred on the nucleus, with the number of electrons equal to the nuclear charge. So diagrams often represent an atom by a point at its nucleus, the atom bearing a net charge of zero. In a homonuclear diatomic molecule, bonding electrons are shared equally between the... 

Studies on molecular charge distributions and chemical binding due to Bader and co-workers include the first-row homonuclear diatomics (Bader et al., 1967a), the first-row diatomic hydrides (Bader et al., 1976b), the first-row 12- and 14-electron diatomic series (Bader and Bandrauk, 1968a), the second-row diatomic hydrides (Cade et al., 1969), and the excited, ionized, and electron-attached states of several diatomic molecules (Cade et al., 1971). Bader (1970, 1975,1981), Deb (1973), and Mulli-ken and Ermler (1977) review their works in some detail. 

There are many other indications that the electrostatic effects of non-spherical features of the charge distribution, such as lone pairs and n electrons, can be important in determining molecular crystal structures. At the extreme of homonuclear diatomics (X2), the electrostatic potential outside the molecule arises from the non-spherical distribution of the valence electrons. Just as there are considerable variations in the bonding orbitals in the diatomics, there are also considerable variations in the lowest temperature ordered crystal structure. 

In this chapter, we will require that the orbitals we form are symmetry orbitals, so that each orbital wave function corresponds to an irreducible representation in the molecule s point group. For the homonuclear diatomic MOs, we combine only orbitals of the same n, I and m/1 values on each of the two atoms, because the electron distributions around identical nuclei in the same molecule must be identical if the symmetry is to be preserved. We will not mix a Is orbital on nucleus A with a Ip orbital on nucleus B, for example. 

Unlike the homonuclear diatomic F2, which has a symmetrical distribution of radial electron density, the het-eronuclear diatomic GIF has an asymmetric distribntion as predicted due to the unequal sharing of electron density. When Cl (at y = 0 bohr) and F (at y = 3.050 bohr) combine to form CIF, the single core shell in the F atom and both core shells in the Cl atom remain mostly nnchanged in the bonded molecule as shown in Fig. 2b. This hgnre also shows that the RBCP is skewed toward the flnorine nucleus. This feature makes sense because F is more electronegative than chlorine, and Cl is fairly polarizable. In Fig. 2d, the cross section of the GIF molecnle depicts the two core shells for Cl and the single core shell for F. 

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