Diatomic molecules bonding orbitals

The three 2p orbitals from each atom can be combined to give o bonding and antibonding orbitals and n bonding and antibonding orbitals. In heteronuclear diatomic molecules, these orbitals are simply labelled c or n and do not have subscripts. The subscripts g and u refer to behaviour under inversion through the... 

In an extension to the labelling used for diatomic molecules, this orbital is referred to as a 7t orbital. We can describe the bonding in ethene as consisting of bonding orbitals in the plane of the molecule formed by overlap of the sp2 hybrid orbitals with each other and with the s orbitals on hydrogen and an out-of-plane Tt-bonding orbital. By analogy with orbitals for diatomic molecules, the orbitals formed by the sp2 hybrid orbitals are called a orbitals. 

Two atomic orbitals on different nuclei must have the same symmetry around the bond axis to form a good bonding LCAOMO. In a diatomic molecule, two orbitals with different symmetry cannot form an eigenfunction of the appropriate symmetry operators. We will assume the same behavior in a polyatomic molecule. 

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... 

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. 

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 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). 

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C09-0047. Hydrogen forms diatomic molecules with elements from Group 1 of the periodic table. Describe the bonding in LiH and include a picture of the overlapping orbitals. 

As their names suggest, molecular orbitals can span an entire molecule, while localized bonds cover just two nuclei. Because diatomic molecules contain just two nuclei, the localized view gives the same general result as molecular orbital theoiy. The importance of molecular orbitals and delocalized electrons becomes apparent as we move beyond diatomic molecules in the follow-ing sections of this chapter. Meanwhile, diatomic molecules offer the simplest way to develop the ideas of molecular orbital theory. 

The data show that bond energies for these three diatomic molecules increase moving across the second row of the periodic table. We must construct molecular orbital diagrams for the three molecules and use the results to interpret the trend. 

The halogens, the elements from Group 17 of the periodic table, provide an introduction to intermolecular forces. These elements exist as diatomic molecules F2, CI2, Bf2, and I2. The bonding patterns of the four halogens are identical. Each molecule contains two atoms held together by a single covalent bond that can be described by end-on overlap of valence p orbitals. 

Figure 6.6 shows the molecular orbital energy diagrams for a few homonudear diatomic molecules. The stability of the molecules can be estimated from the number of electrons occupying bonding orbitals compared with the number of electrons in the antibonding orbitals. (Antibonding orbitals are sometimes denoted with the subscript, as in 2jt. )... 

In diatomic molecules such as N2, O2, and CO the valence electrons are located on the 5cr, Ijt and 2jt orbitals, as shown by Fig. 6.6. [Note that the 5cr level is below the Ijt level due to interaction with the 4cr level, which was not included in the figure.] In general, the Ijt level is filled and sufficiently low in energy that the interaction with a metal surface is primarily though the 5cr and 2jt orbitals. Note that the former is bonding and the latter antibonding for the molecule. We discuss the adsorption of CO on d metals. CO is the favorite test molecule of surface scientists, as it is stable and shows a rich chemistry upon adsorption that is conveniently tracked by vibrational spectroscopy. 

The limitation of the above analysis to the case of homonuclear diatomic molecules was made by imposing the relation Haa = Hbb> as in this case the two nuclei are identical. More generally, Haa and for heteronuclear diatomic molecules Eq. (134) cannot be simplified (see problem 25). However, the polarity of the bond can be estimated in this case. The reader is referred to specialized texts on molecular orbital theory for a development of this application. 

The simplest diatomic molecule consists of two nuclei and a single electron. That species, H2+, has properties some of which are well known. For example, in H2+ the internuclear distance is 104 pm and the bond energy is 268kJ/mol. Proceeding as illustrated in the previous section, the wave function for the bonding molecular orbital can be written as... 

The basic principles dealing with the molecular orbital description of the bonding in diatomic molecules have been presented in the previous section. However, somewhat different considerations are involved when second-row elements are involved in the bonding because of the differences between s and p orbitals. When the orbitals being combined are p orbitals, the lobes can combine in such a way that the overlap is symmetric around the intemuclear axis. Overlap in this way gives rise to a a bond. This type of overlap involves p orbitals for which the overlap is essentially "end on" as shown in Figure 3.5. For reasons that will become clear later, it will be assumed that the pz orbital is the one used in this type of combination. 

For diatomic molecules, there is coupling of spin and orbital angular momenta by a coupling scheme that is similar to the Russell-Saunders procedure described for atoms. When the electrons are in a specific molecular orbital, they have the same orbital angular momentum as designated by the m value. As in the case of atoms, the m value depends on the type of orbital. When the internuclear axis is the z-axis, the orbitals that form a bonds (which are symmetric around the internuclear axis) are the s, pz, and dzi orbitals. Those which form 7r bonds are the px, p, dlz, and dyi orbitals. The cip-y2 an(i dxy can overlap in a "sideways" fashion with one stacked above the other, and the bond would be a 8 bond. For these types of molecular orbitals, the corresponding m values are... 

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