Elements diatomic molecules

In Chapter IX, Liang et al. present an approach, termed as the crude Bom-Oppenheimer approximation, which is based on the Born-Oppen-heimer approximation but employs the straightforward perturbation method. Within their chapter they develop this approximation to become a practical method for computing potential energy surfaces. They show that to carry out different orders of perturbation, the ability to calculate the matrix elements of the derivatives of the Coulomb interaction with respect to nuclear coordinates is essential. For this purpose, they study a diatomic molecule, and by doing that demonstrate the basic skill to compute the relevant matrix elements for the Gaussian basis sets. Finally, they apply this approach to the H2 molecule and show that the calculated equilibrium position and foree constant fit reasonable well those obtained by other approaches. 

A more useful quantity for comparison with experiment is the heat of formation, which is defined as the enthalpy change when one mole of a compound is formed from its constituent elements in their standard states. The heat of formation can thus be calculated by subtracting the heats of atomisation of the elements and the atomic ionisation energies from the total energy. Unfortunately, ab initio calculations that do not include electron correlation (which we will discuss in Chapter 3) provide uniformly poor estimates of heats of formation w ith errors in bond dissociation energies of 25-40 kcal/mol, even at the Hartree-Fock limit for diatomic molecules. 

Equations are balanced by adjusting coefficients in front of formulas, never by changing subscripts within formulas. On paper, the equation discussed above could have been balanced by writing N6 on the right, but that would have been absurd. Elemental nitrogen exists as diatomic molecules, N2 there is no such thing as an N6 molecule. 

To illustrate molecular orbital theory, we apply it to the diatomic molecules of the elements in the first two periods of the periodic table. 

Among the diatomic molecules of the second period elements are three familiar ones, N2,02, and F2. The molecules Li2, B2, and C2 are less common but have been observed and studied in the gas phase. In contrast, the molecules Be2 and Ne2 are either highly unstable or nonexistent. Let us see what molecular orbital theory predicts about the structure and stability of these molecules. We start by considering how the atomic orbitals containing the valence electrons (2s and 2p) are used to form molecular orbitals. 

Predicted and Observed Properties of Diatomic Molecules of Second Period Elements... 

Table 6-VI lists some properties of the halogens. In the elemental state, the halogens form stable diatomic molecules. This stability is indicated by the fact that it takes extremely high temperatures to disrupt halogen molecules to form the monatomic species. For example, it is known that the chlorine near the surface of the sun, at a temperature near 6000°C, is present as a gas consisting of single chlorine atoms. At more normal temperatures, chlorine atoms react with each other to form molecules ...

The electronic structure of the chlorine atom (3s-3p ) provides a satisfactory explanation of the elemental form of this substance also. The single half-filled 3p orbital can be used to form one covalent bond, and therefore chlorine exists as a diatomic molecule. Finally, in the argon atom all valence orbitals of low energy are occupied by electrons, and the possibility for chemical bonding between the atoms is lost. 

The solar spectrum is, of course, as well studied as our planetary atmosphere will permit. More information will be forthcoming as spectra from man-made satellites are recorded above the atmosphere. At this time, the spectra of many diatomic molecules have been detected. These are not the familiar, chemically stable molecules we find on the stockroom shelf. These are the molecules that are stable on a solar stockroom shelf. Figure 25-3 shows some of these and the location in the periodic table of the elements represented. 

The charges on the atoms in HCI are called partial charges. We show the partial charges on the atoms by writing 8+l I—Cl8. A bond in which ionic contributions to the resonance result in partial charges is called a polar covalent bond. All bonds between atoms of different elements are polar to some extent. The bonds in homonuclear (same element) diatomic molecules and ions are nonpolar. 

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. 

The bond in a heteronuclear diatomic molecule, a diatomic molecule built from atoms of two different elements, is polar, with the electrons shared unequally by the two atoms. We therefore rewrite Eq. I as... 

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. 

The halogens include fluorine, chlorine, bromine and iodine and all have been used in CVD reactions. They are reactive elements and exist as diatomic molecules, i.e., F2, CI2, etc. Their relevant properties are listed in Table 3.2. 

Although the greatest interest in the chemistry of species containing group-IIA-group-IB element bonds is metallurgical, diatomic molecules containing these bonds have been studied for their spectroscopic and thermodynamic properties. 

The first column of the periodic table, Group 1, contains elements that are soft, shiny solids. These alkali metals include lithium, sodium, potassium, mbidium, and cesium. At the other end of the table, fluorine, chlorine, bromine, iodine, and astatine appear in the next-to-last column. These are the halogens, or Group 17 elements. These four elements exist as diatomic molecules, so their formulas have the form X2 A sample of chlorine appears in Figure EV. Each alkali metal combines with any of the halogens in a 1 1 ratio to form a white crystalline solid. The general formula of these compounds s, AX, where A represents the alkali metal and X represents the halogen A X = N a C 1, LiBr, CsBr, KI, etc.). 

C02-0002. Elemental bromine, chlorine, and iodine exist as diatomic molecules. Chlorine is a gas at room temperature, bromine is a liquid, and iodine is a solid. Draw molecular pictures that show the molecular distributions in samples of chlorine, bromine, and iodine. 

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