Li to Ne, computed with σ = 0.3 in 1s2-core and 2-el clouds
|In general the Kimball non overlapping model does not do badly with the total energies, a bit less with the ionization potentials. The ionization process of an atom connects two spherically symmetric eigenstates. |
For these the Aufbauprinciple requests and explains the blue IP sequence. For the pink Kimball values this is definitely incorrect. Ok. But, what do you try to understand? Lewis' and Kimballs chemical atoms are meant to be used in a chemical context, which is never spherically symmetric. For this the spherical eigenstates of an isolated atom are inadequate and don't apply. The four-"valent" Lewis/Kimball C-atom has later been replaced by the physicists spherical 2s2p2 atom. This caused a problem for every chemistry teacher: Why does the C-atom with two half filled p-orbitals form four and not only two electron pair bonds? The problem does not exist if the cart is not put before the horse. Symmetry comes before the eigenstates because the symmetry of the external perturbing field creates the correct eigenstates and not the other way round: If the isolated, spherical C-atom with 2s2p2 3P senses ligands nearing, the valence electron shell spontaneously responds. If it's one ligand only, a cylindrical deformation happens (e.g. CO formation), if there are four equivalent ligands, a tetrahedral field may distort the shell. This is a completely new situation with a broken-up relation to the original spherical environment. The C-atom is now forming symmetry-adapted incipient molecular orbitals
|with, perhaps, Td symmetry. s2p2 splits into a11+t23 orbitals, decoupling the pair of s2, with s going down in energy into a1 and p going up into three t2 orbitals. This does not cost energy since the energy loss for s is equal to the sum of the gains of the p electrons. But it is NOT sp3 but a1+t23. The energy gap between the two subshells is clearly observable by photoelectron spectroscopy and two different ionization potentials (Mulliken 1935), wheras the degenerate s and p orbitals (only accidentally valid for the H-atom) would not show an energy difference. The usual cheap jargon "sp3 hybrid orbitals" is wrong (only true in spherical symmetry which we explicitly don't have)! It makes believe, that a structure is caused by clever combination of orbitals instead of teaching, that the symmetry of the external field creates appropriate eigenstates and electron distributions. The innocent student gets deluded with jargon, he is apparently not supposed to understand (because he does not yet have the physics and mathematics necessary). If a knowledgeable scientist talks about "sp3" he probably means this as a shortcut label for the deeper truth sketched above. But, sp3 does not explain anything to an untrained mind and destroys scientific education with esoterics. Of course, a beginner does not understand a1t23 as well. Furthermore, a good QC computation does not show any sign of hybridization, see the canonical G3MP2 orbitals of methane here:
So, why not just state: When a C-atom is exposed to a tetrahedral ligandfield it deforms its spherical shape observably into a tetrahedron deploying four chemically equivalent bonds, period? Kimballs four equivalent single spheres or Lewis' four equivalent dots of the C atom are meant to represent this experience, and not C's ionization potential. Variations of this story can now be developed for other symmetries, no symmetries, and any atom.
|However, I'm not as stubborn as all this: If a colleague talks about "sp" or "sp2" ... I assume that he means "cylindrical, i.e. digonal" or "trigonal" symmetry, but please, not in the inverted sense. I am less happy if chemists use e.g. the label sp3 for any||four-bonded carbon (or other atom), even when the structure is far from tetrahedral, say CH2F(OH). Sorry, but this misuse (in textbooks and even research literature) should not be tolerated by a responsible reviewer!|