[Traumatic Acid]

Hi there
Doing some pericyclic chemistry right now, but this is more of a physical chemistry question.
With pericyclic chemistry the arangement of molecular P orbitals is important, HOMO, LUMO, suprafacial, antarafacial and all that jazz affecting the steriochemistry of the product.
My question is why do molecular P orbitals have two lobes, and how are they discerned? P orbitals (of one orientation) are usually depicted as two lobes of different colours representing zones where electrons are most probable to be found. So, why differentiate the two lobes? And why do the lobes have to be in symmetry with one another to form Pi bonds?

If the differentiation between the two lobes comes down to electron density, one lobe having higher electron density than the other that would cause polarity and it would make more sense for the lobes (Py & Pz) to be inverted to bond?

Basically: What makes the lobes different? And why to they have to be symmetrically aligned to bond?

Cheers

[Corribus]

The sign refers to the wavefunction amplitude, which may be positive or negative. Positive and negative regions are separated by a node, where the electron density is zero. The wavefunction alone does define the electron density, rather the probability distribution function does, which is typically related to the square of the wave function. The probability distribution function is therefore always positive.

That said, the amplitude of the wave function is important because mixing of atomic orbitals (wavefunctions) to form molecular orbitals (wavefunction) is accomplished by taking linear combinations of the atomic wavefunctions - in the LCAO-MO approximation. So for example if you have two P orbitals being brought together to form a pi orbital, they can be oriented in the same direction (the positive and negative regions being oriented in parallel) or in the opposite direction (antiparallel). In the former case the wavefunction constructively add, forming a strong molecular bonding orbital. In the latter case the positive and negative amplitude regions cancel out, basically, leading to an antibonding pi orbital with no electron density (the square of the molecular orbital wavefunction) between the two atomic centers. In physical organic chemistry, these same considerations come into play when determining rotation of certain groups during bond formation. In order for a bond to form the "+" regions have to overlap, otherwise the wavefunctions cancel each other out.

[Traumatic Acid]

Perfect explanation, that makes a lot of sense.
Thank you!