Diatomic molecules molecular orbitals

The molecular orbital (MO) approach to the electronic structure of diatomic, and also polyatomic, molecules is not the only one which is used but it lends itself to a fairly qualitative description, which we require here. 

Figure 7.14 Molecular orbital energy level diagram for first-row homonuclear diatomic molecules. The 2p, 2py, 2p atomic orbitals are degenerate in an atom and have been separated for convenience. (In O2 and F2 the order of

To derive the states arising from a molecular orbital configuration in a diatomic molecule see Sections 7.2.2 and 7.2.4. There are two states, and 11 /2, arising from this configuration and is the lower in energy and, therefore, the ground state. 

Unlike the stable molecule N2O, the sulfur analogue N2S decomposes above 160 K. In the vapour phase N2S has been detected by high-resolution mass spectrometry. The IR spectrum is dominated by a very strong band at 2040 cm [v(NN)]. The first ionization potential has been determined by photoelectron spectroscopy to be 10.6 eV. " These data indicate that N2S resembles diazomethane, CH2N2, rather than N2O. It decomposes to give N2 and diatomic sulfur, S2, and, hence, elemental sulfur, rather than monoatomic sulfur. Ab initio molecular orbital calculations of bond lengths and bond energies for linear N2S indicate that the resonance structure N =N -S is dominant. 

Figure 17.2 Schematic molecular orbital energy diagram for diatomic halogen molecules. (For F2 the order of the upper and 7T bonding MOs is inverted.).

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. 

The diatomic molecule of fluorine does not form higher compounds (such as F3, F4, - ) because each fluorine atom has only one partially filled valence orbital. Each nucleus in Fs is close to a number of electrons sufficient to fill the valence orbitals. Under these circumstances, the diatomic molecule behaves like an inert gas atom toward other such molecules. The forces that cause molecular fluorine to condense at 85°K are, then, the same as those that cause the inert gases to condense. These forces are named van der Waals forces, after the Dutch scientist who studied them. 

Hurley, A. C., Proc. Roy. Soc. [London) A216, 424, The molecular orbital theory of chemical valency. XIII. Orbital wave functions for excited states of a homonuclear diatomic molecule."... 

Wallis, R. F., and Hulburt, H. M., J. Chem. Phys. 22, 1774, "Approximation of molecular orbitals in diatomic molecules by diatomic orbitals."... 

Kotani, M., Texas J. Sci. 8, 135 Proc. of the molecular quantum mechanics conference at Austin Texas, 1955. Electronic structure of some simple diatomic molecules/ Li2, 02 MO-SCF, MO-CI. Slater type orbitals. 

The se the orie s are inevitablj based upem analyse s of the interactions and transformations of molecular orbitals, and consequently the accurate construction and re presentation of molecular orbitals has become essential, furthermore, although the forms of molecular orbitals in diatomics and of delocalized tt orbitals in conjugated systems are familiar, a general, non-computational method for determining the qualitative nature of or and t orbitals in arbitrary molecules has been lacking. 

In the molecular orbital description of homonuclear diatomic molecules, we first build all possible molecular orbitals from the available valence-shell atomic orbitals. Then we accommodate the valence electrons in molecular orbitals by using the same procedure we used in the building-up principle for atoms (Section 1.13). That is,... 

We shall illustrate these rules first with H2 and then with other diatomic molecules. The same principles apply to polyatomic molecules, but their molecular orbitals are more complicated and their energies are harder to predict. Mathematical software for calculating the molecular orbitals and their energies is now widely available, and we shall show some of the results that it provides. 

FIGURE 3.31 Atypical molecular orbital energy-level diagram for the homonuclear diatomic molecules Li2 through N2. Each box represents one molecular orbital and can accommodate up to two electrons. 

The ground-state electron configurations of diatomic molecules are deduced by forming molecular orbitals from all the valence-sbell atomic orbitals of the two atoms and adding the valence electrons to the molecular orbitals in order of increasing energy, in accord ivith the building-up principle. 

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 molecular orbital energy-level diagrams of heteronuclear diatomic molecules are much harder to predict qualitatitvely and we have to calculate each one explicitly because the atomic orbitals contribute differently to each one. Figure 3.35 shows the calculated scheme typically found for CO and NO. We can use this diagram to state the electron configuration by using the same procedure as for homonuclear diatomic molecules. 

FIGURE 3.35 The molecular orbital schemes typical of those calculated for a diatomic oxide molecule, EO (where E = C for CO and E = N for NO). Note that the D-orbitals are formed from mixtures of s- and p/-orbitals on both atoms accordingly, we label them simply Id,... 

The molecular orbital theory of polyatomic molecules follows the same principles as those outlined for diatomic molecules, but the molecular orbitals spread over all the atoms in the molecule. An electron pair in a bonding orbital helps to bind together the whole molecule, not just an individual pair of atoms. The energies of molecular orbitals in polyatomic molecules can be studied experimentally by using ultraviolet and visible spectroscopy (see Major Technique 2, following this chapter). 

Hiroshima, 721 histidine, 443, 774 hole, 195 homeostasis, 386 HOMO, 126, 580 homogeneous alloy, 202 homogeneous catalyst, 565 homogeneous equilibria, 362 homogeneous mixture, F53 homolytic dissociation, 80 homonuclear diatomic molecule, 103 Hooke s law, 92 hormone, 670 horsepower, A4, 791 hour, A4 HPLC, 354 HRF products, 723 HTSC, 192 Humphreys series, 51 Hund, F 35 Hund s rule, 35, 37 Hurricane Rita, 144 hyaluronic acid, 344 hybrid orbital, 109 hybridization bond angle, 131 molecular shape, 111 hydrangea color, 463 hydrate, F32 hydrate isomer, 676 hydration, 178 hydrazine, 627... 

Let us first briefly review the construction of molecular orbitals in simple diatomic molecules, AB, using the linear combination of atomic orbitals (LCAO) scheme. The end product for the first long row of the periodic table is the well-known diagram in Fig. 6-1. We focus on two broad principles that are exploited in the construction of this diagram one has to do with symmetry and overlap, the other concerns energies. 

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