Orbitals of lithium

The weakness of the covalent bond in dilithium is understandable in terms of the low effective nuclear charge, which allows the 2s orbital to be very diffuse. The addition of an electron to the lithium atom is exothermic only to the extent of 59.8 kJ mol-1, which indicates the weakness of the attraction for the extra electron. By comparison, the exother-micity of electron attachment to the fluorine atom is 333 kJ mol-1. The diffuseness of the 2s orbital of lithium is indicated by the large bond length (267 pm) in the dilithium molecule. The metal exists in the form of a body-centred cubic lattice in which the radius of the lithium atoms is 152 pm again a very high value, indicative of the low cohesiveness of the metallic structure. The metallic lattice is preferred to the diatomic molecule as the more stable state of lithium. 

It is fairly well understood that alkyl lithiums form rather stable aggregates in which carbon-lithium bond order is maximized by the utilization of all valence orbitals of lithium.(1) Polystyryl lithium molecules are mostly dimeric in solution.(1.3,4) This has been generally accepted by all the investigators.TlT However, association numbers of two(6) and four(Z T has been reported for polydienes. Two methods were used in determining these values, viz., light scattering measurements (in vacuo) and viscosity measurements. 

Fig. 1. Radial distribution functions of the most highly occupied spin-up (above) and spin-down (below) natural orbitals of lithium.

The zeroth-order perturbation wave function (10.40) uses the full nuclear charge (Z = 3) for both the Is and 2s orbitals of lithium. We expect that the 2y electron, which is partially shielded from the nucleus by the two Is electrons, will see an effective nuclear charge that is much less than 3. Even the Is electrons partially shield each other (recall the treatment of the helium ground state). This reasoning suggests the introduction of two variational parameters and 2 into (10.40). 

Dinitrogen has a dissociation energy of 941 kj/mol (225 kcal/mol) and an ionisation potential of 15.6 eV. Both values indicate that it is difficult to either cleave or oxidize N2. For reduction, electrons must be added to the lowest unoccupied molecular orbital of N2 at —7 eV. This occurs only in the presence of highly electropositive metals such as lithium. However, lithium also reacts with water. Thus, such highly energetic interactions ate unlikely to occur in the aqueous environment of the natural enzymic system. Even so, highly reducing systems have achieved some success in N2 reduction even in aqueous solvents. 

Because each lithium atom has one valence electron and each molecular orbital can hold two electrons, it follows that the lower half of the valence band (shown in color in Figure 5) is filled with electrons. The upper half of the band is empty. Electrons near the top of the filled MOs can readily jump to empty MOs only an infinitesimal distance above them. This is what happens when an electrical field is applied to the crystal the movement of electrons through delocalized MOs accounts for the electrical conductivity of lithium metal. 

The energy of the one-electron bond in the lithium molecule ion is calculated with consideration of the s-p separation to be 1.19 e. v and the hybrid bond orbital involved is shown to involve about equal contributions from the 25 and 2p orbitals of the lithium atom. 

Let us consider lithium as an example. In the usual treatment of this metal a set of molecular orbitals is formulated, each of which is a Bloch function built from the 2s orbitals of the atoms, or, in the more refined cell treatment, from 2s orbitals that are slightly perturbed to satisfy the boundary conditions for the cells. These molecular orbitals correspond to electron energies that constitute a Brillouin zone, and the normal state of the metal is that in which half of the orbitals, the more stable ones, are occupied by two electrons apiece, with opposed spins. 

For the inner shells the outermost contour is again 0.025 Bohr 3/2. They are much steeper and, therefore, the increment is here 0.2 Bohr-3/2. Three of these inner shell contours are drawn. If the remaining inner shell contours were drawn, the inner part would be solid black. For this reason, the inner shell contours are not drawn beyond the third one and, instead, the value of the inner shell orbital at the position of the nucleus has been written into the diagram. From the figure, it is obvious that the inner shell of lithium is very similar in Li2 and LiH, and in a very practical sense transferable. However, note that the localized inner shell orbital of the lithium atom has a slight negative tail towards the other atom which yields a very small amount of antibinding. 

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