How to think of molecular orbitals quantum mechanically

[Sophrosyne]

The electrons in a molecule are said to be in a quantum superposition state in terms of their position/spin/momentum. But when you look at a molecule like water at a chemical level, it has a very specific shape corresponding to the P orbitals of the outer shell of the Oxygen atom. The two hydrogen atoms definitely line up at angles to match up with two of the lobes of the P orbital on the outer shell of the oxygen atom. This angular structure of the water molecule is why it has the chemical properties it has- like its electrical polarization, easy dissolving of charged ions, surface tension, etc...

But this means that those electrons can't be in a complete superposition. There is definitely a favored position they are concentrated in. So how should one think of this? Here are possibilities that I can come up with:

A) The hydrogen atoms are acting as sort of "observers" of the position of the electrons around the oxygen atom, and so they are constantly "collapsing the wave function", at least for position, to give those electrons their particular favored positions around the Oxygen nucleus (within limits of the uncertainty principle). They are basically bringing out the shape of the P orbital by being there and forcing the electrons to interact with them (ie, "observing them") in a chronic way.

B) There is no collapse of the electron wave functions. They are still in a superposition state, but there is a sort of entanglement phenomenon going on between the electrons and the atomic nuclei forming the molecule (I am not sure how this would work exactly, but I have heard it explained this way once. I wasn't able to get details).

C) Something else entirely (please explain).

Thank you in advance.

 

[ZapperZ]

When you "look" at the water molecule, you are not actually looking at where the electrons forming the bonds are! The location of the electrons forming the bonds between each H atom and the O atom are not precisely determined. It is spread out between the two atoms.

Zz.

 

[A. Neumaier]

those electrons can't be in a complete superposition.

In water at room temperature, the electrons of a a water molecule will be approximately in a mixed thermal state such that the region where the electron density is significant has the shape usually drawn for a water molecule.

 

[jfizzix]

The electrons in a molecule are said to be in a quantum superposition state in terms of their position/spin/momentum. But when you look at a molecule like water at a chemical level, it has a very specific shape corresponding to the P orbitals of the outer shell of the Oxygen atom...

...But this means that those electrons can't be in a complete superposition. There is definitely a favored position they are concentrated in. So how should one think of this?

In this case, I would point out that just as atomic orbitals describe the electron wavefunction for energy/angular momentum eigenstates of a single atom, molecular orbitals, are (approximate) solutions to the Schrodinger equation that describe the wavefunction of an electron in a molecule. Molecular orbitals can be described in terms of contributions from orbitals of various atoms (e.g., hybridized orbitals), and have been exceedingly useful in describing a quantum-mechanical origin of chemical bonds, but it is not entirely necessary to do this.

The Schrodinger equation for an electron in a molecule has a different hamiltonian with different potential energy due to the charges of the other nuclei among other factors, but the solutions are orbitals in their own right. Describing them as superpositions of atomic orbitals is an often convenient approximation, but is not fundamental to the actual nature of the electron wavefunction.

My best guess is that water molecules have the shape they do because that's what the lowest energy bonding molecular orbitals of the valence electrons in a water molecule look like:
https://en.wikipedia.org/wiki/Molecular_orbital_diagram

 

[Sophrosyne]

In water at room temperature, the electrons of a a water molecule will be approximately in a mixed thermal state such that the region where the electron density is significant has the shape usually drawn for a water molecule.

But for electrons to have a "density", it means that you are "measuring" their location, ie, repeatedly collapsing the wave function, doesn't it? Otherwise, why would the orbital be in one particular orientation vs. another random one? You won't know where they are dense unless you are "looking". (I am putting the words in quotes because I understand these words mean something different in the quantum realm). I am thinking the hydrogen atoms here are acting as the "observers" and repeatedly collapsing the position wave function in that area.
The Schrodinger equation simply predicts where the electron locations will be most dense *when measured repeatedly*.

And has anyone heard about entanglement to explain this? I heard it once, here on this forum. But I was never able to pursue that conversation.

 

[ZapperZ]

But for electrons to have a "density", it means that you are "measuring" their location, ie, repeatedly collapsing the wave function, doesn't it? Otherwise, why would the orbital be in one particular orientation vs. another random one? You won't know where they are dense unless you are "looking". (I am putting the words in quotes because I understand these words mean something different in the quantum realm). I am thinking the hydrogen atoms here are acting as the "observers" and repeatedly collapsing the position wave function in that area.
The Schrodinger equation simply predicts where the electron locations will be most dense *when measured repeatedly*.

And has anyone heard about entanglement to explain this? I heard it once, here on this forum. But I was never able to pursue that conversation.

See, this is another example where, if you try to pick up QM right in the middle, without first learning and understanding the very basic, simplest level, you end up with this kind of situation. Your question here is no longer about "superposition" and "water molecules", but rather on the very basic understanding of what the solution to the Schrodinger equation means.

When we solve for, say, the hydrogen atoms, we get all these various quantum numbers corresponding to the various quantities such as energy, angular momentum, etc. I do not need to know where each electrons are located to verify their validity, because measuring the location of an electron "destroys" all other info about it other than its position value. And I will need to make many more measurements to get any kind of an average or spread.

Instead, I measure something else, and in this case, I can measure the energy state, etc... which is not the position, but rather an observable that does not commute with the position observable. This is where the understanding of the mathematics of commuting operators matter, something we teach in intro QM very early on. Measuring the energy state (i.e. the energy spectrum that you see when you look at light coming from an excited atom), will verify that (i) the solution to the Schrodinger equation is valid and (ii) that the position of the electrons are spread out the way the mathematics described.

The superposition of 10¹¹ particles in the Delft/Stony Brook experiment did not directly measure that these particles are in a superposition of current directions, but rather, they measured the presence of the coherence energy gap, which can only be there if superposition exists. It is practically impossible to measure what each electron in the supercurrent is doing, and in this case, it isn't necessary, the same way it isn't necessary to know where the electrons are in the H-O bond. The superposition can be detected via another channel rather than making numerous direct measurements of position.

While advancement in STM and AFM have given us "images" of these bondings, and verify what we know, it is still the mathematics and the experiments that verify the mathematics that are still the foundation of all this.

Zz.

 

[Sophrosyne]

See, this is another example where, if you try to pick up QM right in the middle, without first learning and understanding the very basic, simplest level, you end up with this kind of situation. Your question here is no longer about "superposition" and "water molecules", but rather on the very basic understanding of what the solution to the Schrodinger equation means.

When we solve for, say, the hydrogen atoms, we get all these various quantum numbers corresponding to the various quantities such as energy, angular momentum, etc. I do not need to know where each electrons are located to verify their validity, because measuring the location of an electron "destroys" all other info about it other than its position value. And I will need to make many more measurements to get any kind of an average or spread.

Instead, I measure something else, and in this case, I can measure the energy state, etc... which is not the position, but rather an observable that does not commute with the position observable. This is where the understanding of the mathematics of commuting operators matter, something we teach in intro QM very early on. Measuring the energy state (i.e. the energy spectrum that you see when you look at light coming from an excited atom), will verify that (i) the solution to the Schrodinger equation is valid and (ii) that the position of the electrons are spread out the way the mathematics described.

The superposition of 10¹¹ particles in the Delft/Stony Brook experiment did not directly measure that these particles are in a superposition of current directions, but rather, they measured the presence of the coherence energy gap, which can only be there if superposition exists. It is practically impossible to measure what each electron in the supercurrent is doing, and in this case, it isn't necessary, the same way it isn't necessary to know where the electrons are in the H-O bond. The superposition can be detected via another channel rather than making numerous direct measurements of position.

While advancement in STM and AFM have given us "images" of these bondings, and verify what we know, it is still the mathematics and the experiments that verify the mathematics that are still the foundation of all this.

Zz.

I see. This makes a little more sense. Thanks.

 

[A. Neumaier]

for electrons to have a "density", it means that you are "measuring" their location, ie, repeatedly collapsing the wave function, doesn't it?

No. The density is the expectation value of the 1-particle charge density operator. No collapse is involved, not even measurement.