Hybrid Atomic Orbitals

 

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For those who are interested, we'll attempt to give a slightly deeper explanation of what hybrid orbitals are in the context of wave behavior.

 
We'll use the hydrogen atom in its ground electronic state as a way to start the discussion.

  
It shouldn't be surprising that the discussion is based on the premise that wave behavior underlies the description of where electrons are expected to be found and what energies they might have.

  

This is the 1s "pure" atomic orbital.		 The (electronic) ground state of an isolated hydrogen atom is intimately familiar to you. At least at some level; certainly pictorial. The electron is subject to the spherically symmetric electrostatic attraction to the positive nucleus. (That is, all directions out from the nucleus map the same electrostatic force acting on an electron.) Putting such an arrangement into the (Schrödinger) wave equation gives an infinite number of allowed solutions...wave functions and their associated energy values. The ground state is the familiar spherical shape.
Suppose we had a hydrogen atom next to a hypothetical positively charged plate (shown as blue) and were interested in the ground electronic state in this situation. The wave equation would incorporate the forces acting on the electron -- the attraction to the nucleus and the attraction to the positive plate. The resulting wave function for the ground state would look qualitatively as indicated to the right.
This is the ground state atomic orbital for an electron held strongly to the hydrogen nucleus, yet affected by a second nearby positive charge.
How do we describe the electron's ground state atomic orbital here? It turns out that the exact answer (pictured) can be very closely approximated by saying that if you took a simple mixture of wave functions you already know, perhaps 90% 1s and 10% 2pz, the combination would look almost perfectly like the true answer. That combination is like breeding a hybrid from mixed parentage... and the approximate result is referred to as a hybrid atomic orbital. It would appear nearly identical to what is already displayed as the exactly correct result, but now we can talk about it using existing vocabulary (although giving it a name in this example would be awkward).


  
Now about atoms in complex chemical structures. When a carbon atom with its 2s and 2p valence orbitals (four valence electrons in all) about the carbon nucleus (plus inner core electrons) is moved into an atomic environment that has two additional positive charges arranged in a linear fashion with carbon at the center, the wave equation no longer produces pure 2s and 2p atomic orbitals, but rather orbitals that look very much like what you get by taking 50:50 mixtures (that is, equal parts) of the 2s and 2pz (leaving the other two 2p's almost unaltered). The mixture, being equal part s and p, is abbreviated an "sp" orbital, so we have a name for it. One mixture adds 2s+2p and the other subtracts (2s-2p). Each of these mixtures is again a hybrid atomic orbital, very closely approximating the exact result. Each such hybrid orbital can contain up to two electrons.


  
These are the pure 2s (left) and pure 2p (right) atomic orbitals that would be expected if carbon (or any other atom or ion) were under consideration.
The above pictures representing visualizations of the 2s and 2p wave functions would be incorrect if the attraction of electrons were from other than a single, centrally located nucleus. We'll consider a simple pictorial example below.
  
These two illustrations have placed the carbon atom between two positive charges (which could be other nuclei or atoms with affinities for drawing electrons). These are two equal energy hybrid solutions that can be synthesized by adding and subtracting, respectively, the previous pure atomic orbitals on the central atom. In this one, the electron distribution around the carbon is pulled toward the right positive charge. (In this arrangement, the remaining two valence orbitals are barely changed from their original description, pure 2p's (since they are not directed at the perturbing electrostatic forces). For convenience, they are considered to remain pure atomic orbitals.


 In this hybrid combination, the electron distribution is pulled toward the left positive charge.
In summary, depending on the environment around valence electrons of an atom, different wave forms are generated by quantum mechanics. The directional character of these revised atomic orbitals is determined by the symmetry with which the perturbing forces are geometrically distributed around the originally isolated atom. Here we have looked at just a linear geometry of external influences on the valence electrons. In class, we look at trigonal planar, tetrahedral, trigonal bipyramidal, and octahedral environments as well. A tetrahedrally dispersed geometric arrangement about an atom would necessitate that the s and all three p valence orbitals be abandoned and be replaced instead by four new orbitals. These four valence orbitals are very closely mimicked by hybrids that are each one part s and three parts p; that is, each is a sp3 hybrid atomic orbital.

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