Boron atom orbital energies

Boron is unique among the elements in the structural complexity of its allotropic modifications this reflects the variety of ways in which boron seeks to solve the problem of having fewer electrons than atomic orbitals available for bonding. Elements in this situation usually adopt metallic bonding, but the small size and high ionization energies of B (p. 222) result in covalent rather than metallic bonding. The structural unit which dominates the various allotropes of B is the B 2 icosahedron (Fig. 6.1), and this also occurs in several metal boride structures and in certain boron hydride derivatives. Because of the fivefold rotation symmetry at the individual B atoms, the B)2 icosahedra pack rather inefficiently and there... 

At infinite separation, one arrives at two boron atoms each having a donut-like cylindrical density as indicated in Figure 5-3. However, such a density cannot be obtained from real atomic p-orbitals. In other words, the density that results from the supermolecule is simply inaccessible from calculations on the isolated atoms. Whatever we do, we will never generate the correct charge density (and therefore energy) of the dissociated B2 molecule by calculations of the isolated boron atoms and the requirement of size-consistency is violated. Only if one switches to complex orbitals such as lpx rpyl, are cylindrical atomic densities possible. But even then, we are still in trouble and face a different problem. Just as... 

In each of the B-H-B bridges, only two electrons bond the three atoms together by having the orbitals on the boron atoms simultaneously overlap the hydrogen Is orbital. A bond of this type is known as a two-electron three-center bond. In terms of molecular orbitals, the bonding can be described as the combination of two boron orbitals and one hydrogen orbital to produce three molecular orbitals, of which only the one of lowest energy is populated ... 

The decision to add an unoccupied orbital with a large weighting factor to the prototype carbene in the case of BA and an occupied one for XA is easily made. The boron atom introduces a low energy unoccupied orbital and the oxygen a high energy occupied one into the aromatic n-system. The choice is less clear for FL and its derivatives. Providence, however, provides the same conclusion from either choice. 

Energy changes during the formation of sp2 hybrid orbitals in the boron atom. 

A boron atom, B (atomic number 5), in its lowest energy state has four of its five electrons filling the Is and 2s orbitals. Its fifth electron may reside in any one of the 2p orbitals, all of which are at the same energy level ... 

The one-electron molecular-orbital energies resulted from the calculations when the oxygen atom of the cluster is replaced by substitution boron was show in Fig. 2 on the right side. 

The electronic structure of the boron atom is 1 s2 2s2 Ip1. It might be expected that boron would lose the outer electrons and be present in compounds as B3+ ions. This ionization, however, requires more than 6700 kJ mol-1, and this amount of energy precludes compounds that are strictly ionic. Polar covalent bonds are much more likely, and the hybridization can be pictured as follows. Promoting a 2s electron to one of the vacant 2p orbitals can be accomplished followed by the hybridization to produce a set of sp2 hybrid orbitals ... 

A molecular orbital diagram for a three-center B-H-B bond in diborane. In this diagram, represents an atomic orbital and and represent the bonding and antibonding three-center wave functions, respectively. Note the relative energies of the atomic orbitals on boron and hydrogen atoms (ionization potentials 8.3 eV and 13.6 eV, respectively). 

The expected MO energy-level diagram for the combination of the 2p orbitals on two boron atoms. 

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