[spirochete]

I'm interested in understanding MO theory so I can eventually apply it to organic reactions, but I've got a long way to go.  This sentence in my book makes is really confusing me.  It is in reference to the plus/minus sign in a orbital diagrams:

"The plus sign and the minus sign are not charges.  The plus or minus sign is the instantaneous sign of the constantly changing wave function"

Could somebody clarify that for me?  For example in the first harmonic which represents the P orbital, I understand that when you square that function each peak/trough represents a maximum probability of finding an electron.  So how are they different exactly?

[kryptoniitti]

The plus/minus sign doesn't really have a physical meaning (e.g. charge or whatever). It roots from the fact that mathematics of oscillating wave is used to describe the electron. However, when you start combining atomic orbitals to molecular orbitals (lcao-mo theory), the sign of the wavefunction is crucial, because what you do is square the sum of the individual wave functions to get the probability density for the MO. Hence you will have constructive interference between two wave functions of the same sign and destructive interference between different signs. Here's a neat picture:

The square of the w.f. is easy to understand, probability of finding an electron somewhere. Understanding the w.f. is another question. When I finished physical chemistry course few years back, my conclusion was that w.f. is something thoroughly abstract and complex and doesn't give you much concrete until you use operators on it or square it You might want to check the Copenhagen interpretation.