I’m hoping someone will help me fill in some holes in my understanding of the electronic wavefunction.(adsbygoogle = window.adsbygoogle || []).push({});

I understand the electronic wavefunction to be a *complex valued* function of the positions of all electrons in the system. But, most descriptions of atomic orbitals refer to the various “lobes” of high probability amplitude as being of positive or negative sign, and the nodes as being loci where the sign changes.

It is tempting to think that this is just shorthand for a description of some projection (e.g. the real part) if a complex phasor, and the nodes are those locations where the phase angle is 90 or 270 degrees. But this can’t be the case, since the probability density (which is the square of the phasor’s amplitude) also goes to zero at these locations. So the vector magnitude of the wavefunction must vary smoothly with position, and it must be this magnitude that is zero at the nodes. Is that correct?

So, my first question is, should the wavefunction generally, and orbitals specifically, be thought of as scalar fields which have positive and negative regions, or as complex numbers with smoothly varying phase vs. position. If they are complex numbers, what accounts for spatial nodes of the probability density – zero vector magnitude, or some particular phase?

From there I’d like to understand what happens to the sign/phase of the orbital when an atomic bond forms. If for example two singly-occupied 2p orbitals form a bond, does the initial sign/phase of the lobes of the orbitals that are closest to each other affect the interaction in any way? Is there meaning associated with whether a positive-valued lobe happens to abut a negative valued lobe of the other atom, vs. positive-to-positive? Is this in any way related to the bonding and antibonding orbitals that Molecular Orbital theorists talk about?

Thanks in advance for any insight you can impart.

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# The meaning of the sign of the wavefunction in electronic structure

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