[lillybeans]

Hey everyone,

This question has bothered me for a long time. I understand that 2 orbitals can either interfere constructively/in phase (and thus form a bonding orbital) or destructively/out of phase (an antibonding orbital), but how can they interfere BOTH constructively and destructively at the same time? Two waves are either in phase or out of phase, I don't see how both can happen.

By "existing at the same time", I'll give an example. Electrons in bonding first occupy the bonding orbitals, then the antibonding ones. Antibonding orbitals are at a higher energy level than bonding orbitals. Examples would be some common diatomic molecules like H2 (only occupies bonding orbital), O2 (bonding and antibonding orbitals). Clearly, the electrons involved in bonding are sitting in both types of orbitals, suggesting that they both exist at the same time. How can this be? Am I misunderstanding something here?

Please elaborate and thanks in advance.

Lilly

[juanrga]

Hey everyone,

This question has bothered me for a long time. I understand that 2 orbitals can either interfere constructively/in phase (and thus form a bonding orbital) or destructively/out of phase (an antibonding orbital), but how can they interfere BOTH constructively and destructively at the same time? Two waves are either in phase or out of phase, I don't see how both can happen.

By "existing at the same time", I'll give an example. Electrons in bonding first occupy the bonding orbitals, then the antibonding ones. Antibonding orbitals are at a higher energy level than bonding orbitals. Examples would be some common diatomic molecules like H2 (only occupies bonding orbital), O2 (bonding and antibonding orbitals). Clearly, the electrons involved in bonding are sitting in both types of orbitals, suggesting that they both exist at the same time. How can this be? Am I misunderstanding something here?

Please elaborate and thanks in advance.

Lilly

Orbitals are not waves (as EM waves) but representation of quantum states.

The wavefunction for two-electrons is

In a first approximation you can do where are the coordinates of electron j.

In a better model the electrons are not considered independent and then the state is built over a linear combination of one-particle states and you can combine them as a+b or like a-b. One combination given bonding and other antibonding. I would not say interference of waves, but it is merely a linear combination of states in a vector space. Those combinations also exist in classical physics, where you can obtain the classical phase space state from a linear combination of the classical states of independent classical particles. The main difference being that in classical physics you obtain a continuum of states.

The interference of EM waves and happens when both waves exist at the same position and time . It is different.

[fledarmus]

In non-mathematical, hand-waving terms, orbitals are mathematical representations of states in which electrons can exist. A single atom, with one nucleus and a multiplicity of electrons, will have the electrons in orbitals which provide the lowest energy for the entire system. You are familiar with those types of orbitals, obviously.

When you add a second nucleus at an appropriate distance, you can imagine a new set of orbitals which are vector sums of the orbitals on a single nucleus system. As Juanrga said, they are the a + b and a - b sums. One set will be slightly lower in energy than any of the orbitals they were summed from (stabilizing, bonding orbitals), and the other will be slightly higher (de-stabilizing, anti-bonding). In general, the antibonding orbitals are somewhat more destabilizing than the bonding ones are stabilizing (due to entropy).

The orbitals are occupied in the usual way, from lowest to highest energy. This means the electrons will be occupying the bonding orbitals first, then the anti-bonding. If there are more electrons in bonding orbitals than in anti-bonding orbitals, the result will be that the two-nucleus system is more stable than the separate single-nucleus systems, and the nuclei will be bonded. The most stable bond would be when all of the bonding orbitals are filled and all of the anti-bonding orbitals are empty - that would be the highest level of stabilization possible from the combination. However, if there are as many electrons in anti-bonding orbitals as there are in binding orbitals, then the slight excess of destabilization energy means that the net energy of the system is higher than it would be if the two nuclei were separate, the bond is not stabilized, and the nuclei go their separate ways.