Diatomic molecule, orbitals

You will recall that in homonuclear diatomic molecules, orbitals that were unchanged by inversion through the centre of symmetry were labelled g and those that were changed were labelled u. Orbitals of all molecules with a centre of symmetry can be labelled using g or u subscripts. 

A simple example would be in a study of a diatomic molecule that in a Hartree-Fock calculation has a bonded cr orbital as the highest occupied MO (HOMO) and a a lowest unoccupied MO (LUMO). A CASSCF calculation would then use the two a electrons and set up four CSFs with single and double excitations from the HOMO into the a orbital. This allows the bond dissociation to be described correctly, with different amounts of the neutral atoms, ion pair, and bonded pair controlled by the Cl coefficients, with the optimal shapes of the orbitals also being found. For more complicated systems... 

The advantages of INDO over CNDO involve situations where the spin state and other aspects of electron spin are particularly important. For example, in the diatomic molecule NH, the last two electrons go into a degenerate p-orbital centered solely on the Nitrogen. Two well-defined spectroscopic states, S" and D, result. Since the p-orbital is strictly one-center, CNDO results in these two states having exactly the same energy. The INDO method correctly makes the triplet state lower in energy in association with the exchange interaction included in INDO. 

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

We have seen in Chapters 1 and 5 that there is an angular momentum associated with end-over-end rotation of a diatomic molecule. In this section we consider only the non-rotating molecule so that we are concerned only with angular momenta due to orbital and spin... 

Table 7.5 lists the states arising from a few electron configurations in diatomic molecules in which there are two electrons in the same degenerate orbital. 

Promotion of an electron in Hc2 from the (7 15 to a bonding orbital produces some bound states of the molecule of which several have been characterized in emission spectroscopy. For example, the configuration ((J l5 ) ((7 l5 ) ((7 25 ) gives rise to the 2i and bound states. Figure 7.24(a) shows the form of the potential curve for the state. The A-X transition is allowed and gives rise to an intense continuum in emission between 60 nm and 100 nm. This is used as a far-ultraviolet continuum source (see Section 3.4.5) as are the corresponding continua from other noble gas diatomic molecules. 

For the orbital parts of the electronic wave functions of two electronic states the selection rules depend entirely on symmetry properties. [In fact, the electronic selection rules can also be obtained, from symmetry arguments only, for diatomic molecules and atoms, using the (or and Kf point groups, respectively but it is more... 

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. 

Since the vacancy in the nip orbital behaves, in this respect, like a single electron, the states arising are the same as those from nlp) n 2p), since we can ignore electrons in filled orbitals. Equation (7.77), dropping the g and u subscripts for a heteronuclear diatomic molecule, gives... 

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. 

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. 

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. 

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