Atomic orbitals allocating electrons

The orbitals and electrons of any particular boron atom are allocated to satisfy, as first priority, the requirements of the external B-H single bonds and the bridge B-H-B bonds. The remaining orbitals and electrons are allocated to the skeletal molecular orbitals of the boron framework. 

Remember, the MO method first combines the atomic orbitals to give molecular orbitals, then populates the molecular orbitals with electrons (no more than two paired electrons per orbital). This part of the procedure is similar to the way electrons are allocated to atomic orbitals (Section 6-1). 

Coulson referred to the atomic orbitals as personal wave functions to emphasize that each electron is allocated to an individual orbital in this model [20],... 

The allocation electrons among degenerate orbitals can be formalized as Hand s rule For an atom in its ground state, the term with the highest multiplicity has the lowest energy. 

The only drawback to the NPA methodology is that it rests on allocating electrons to atoms through an orbital occupancy basis, not in terms of the actual locations of the electrons. The latter property is a physical observable, whereas orbital occupancy is not an observable. The NPA method does attempt to define as well as possible localized atomic orbitals, but completely localized atomic orbitals are impossible. Some electrons in an orbital centered on atom A will, in fact, be closer to atom B. Natural orbitals will have tails that penetrate zero-flux surfaces. Therefore, the NPA populations will differ from the rigorous spatially defined topological values. 

Molecular orbital (MO) theory allocates electrons to molecular orbitals formed by the overlap (interaction) of atomic orbitals. 

The next step is to consider multiple bonding character. Each N and O atom has an unused 2p atomic orbital lying perpendicular to the plane of the molecule. Overlap between the 2p atomic orbital on nitrogen with one of those on an oxygen atom gives rise to one localized 7r-bond. The six remaining valence electrons are allocated as follows ... 

In order to be sure that a bond actually forms between two atoms linked by a molecular orbital it is necessary to calculate the energies of the molecular orbitals and then allocate electrons to them. In essence, the approximate Schrodinger equation... 

Suppose we have a molecule with a conjugated carbon atom skeleton. It is assumed that certain electrons, the a electrons, are allocated to certain particular bonds and that they retain their places. Others, the ir electrons, are assigned to molecular orbitals. What this means mathematically is that each is described by a wave function which is constructed tentatively as a sum of atomic orbitals... 

For simplicity, one can allocate 3 electron pairs to nonbonding orbitals on each metal atom, which leaves three AO s on each metal atom for cluster skeletal bonding, and 7 electron pairs to be accommodated in the bonding MO s these AO s generate. This description is reminiscent of that outlined above (Fig. 7) for EgHa ". Each Ru(CO)j unit of H2Rue(CO)i8, like each BH unit of can contribute three... 

It should be stressed that, in this treatment of metal-carbonyl clusters, the number of nonbonding electron pairs allocated to each metal atom [3 pairs for each ruthenium atom of H2Ru8(CO)i8 2 pairs for each rhodium atom of Rhe(CO)i6] is not arbitrary but is chosen with two objectives in mind (o) to reduce the number of electrons formally remaining for skeletal bonding to fewer than the number of orbitals remaining, because only then is it realistic to assume that all these electrons can be accommodated in bonding MO s and (6) to provide a suitable number of electron pairs on each metal atom for metal carbon... 

---