MO Theory, sp Hybridization question

[sgoodrow]

Recently I begun learning about molecular orbitals and the geometry of an sp orbital. It is my understanding that in the creation of an sp orbital with the combination of an s orbital and p orbital, one gets something that resembles half of a p-orbital (although larger). My professor noted that the other lobe exists infinitesimally small, in opposite phase. She said it was beyond the scope of our course to discuss how this lobe would affect the geometry of MOs, but I was curious regardless. When I asked her she said she would get back to me, and hasn't yet, so I thought I'd ask around on my own!

Why/when do these infinitesimally small lobes affect the geometry of an MO? Probabilistically speaking, what is the math behind it? Basically, if anyone knows anything about the relationship/importance of maintaining the infinitesimally small lobe of an sp-orbital, do tell!

Thanks, I look forward to hearing from you!

 

[JPRitchie]

The out-of-phase lobe of an sp hybrid is smaller than the in-phase lobe, but not infinitesimally small. It's needed to maintain orthogonality between different hybrids on the same atom. That is, the properly normalized sum and difference of an s and p orbital gives two sp hybrids that are orthogonal to one another. If the hybrids were somehow positive everywhere, the overlap integral couldn't be zero. Maintaining orthogonality ensures the orbitals span the orbital space most effectively.
-Jim

 

[ravenprp]

Thank you for your question! The infinitesimally small lobes of an sp orbital do play a role in the geometry of molecular orbitals, as they contribute to the overall shape and symmetry of the orbital. The concept of phase is important in molecular orbital theory, as it determines whether the lobes of the orbital are constructive (in-phase) or destructive (out-of-phase). This, in turn, affects the energy and stability of the orbital.

The math behind this is based on the wave function, which describes the probability of finding an electron in a given region of space. The sign of the wave function determines the phase of the orbital, with positive sign representing in-phase and negative sign representing out-of-phase. This is why the infinitesimally small lobes, although they may seem insignificant, are actually important in determining the geometry and properties of the MO.

As for the relationship/importance of maintaining the infinitesimally small lobe, it primarily affects the bonding and antibonding interactions between atomic orbitals. In an sp hybridized orbital, the s and p orbitals combine to form two molecular orbitals - one bonding and one antibonding. The infinitesimally small lobes contribute to the overall shape and symmetry of these orbitals, which can affect the strength and stability of the bond formed.

In summary, the infinitesimally small lobes of an sp orbital do have an impact on the geometry and properties of MOs, and their maintenance is important in understanding the bonding and interactions between atomic orbitals. I hope this helps answer your question, and if you have any further inquiries, please don't hesitate to ask!