Basics of Quantum Chemistry, especially entanglement

[darkmatter(s)]

Chemical bonds and quantum entanglement

I have a very basic understanding of quantum mechanics and chemistry, so please bear with any misunderstandings I may have. My question is this: what does QM have to do with the bonding between atoms in a molecule or compound? Can these bonds be labelled as "existing in an entangled state?" For example, in a water molecule, there are two H atoms bonded to an O atom. Are these two H atoms "entangled" with the O atom, thereby creating a molecule, which is then itself in an entangled state? (BTW I wish I had my chem 1010 book here, as I hope I didn't screw up any definitions).

 

[darkmatter(s)]

After several hours of searching the net and 5 books in my library, I am fairly certain I was thinking WAY too broadly in forming my question. I suppose in my defense though, I have nothing on quantum chemistry as of yet. In any case, what exactly is a chemical bond from the viewpoint of QM?

 

[DeShark]

After several hours of searching the net and 5 books in my library, I am fairly certain I was thinking WAY too broadly in forming my question. I suppose in my defense though, I have nothing on quantum chemistry as of yet. In any case, what exactly is a chemical bond from the viewpoint of QM?

Well, for something simple, such as a proton-proton system, with one electron kicking about (A hydrogen molecular ion), the attractive term comes from the exchange of the electron. Feynman deals with it in his 3rd volume. Basically, one assumes that the system can be modeled by the electron being "near" one nucleus or the other. So we can have state |1> where the electron is by nucleus 1 and state |2> where the electron is by nucleus two (we assume enough distance between them to be able to distinguish between the two states). Thus a two state system is set up leading to a splitting of the energy levels. That is to say, if the nuclei are separated by an infinite distance, the energy of the system is just that of the ground state, E_0, but due to the exchange effects the energy is split into two levels E_0 + A and E_0 - A where A is the probability amplitude for the electron to switch positions between the two nuclei. Now the lowest energy level possible will be that for which the electron spends an equal amount of time about each nucleus. This lowest energy state corresponds to a certain distance between the nuclei and thus a "bonding" of the system. A "one electron bond". Note that there are many factors involved and a more complex study would be necessary to find the actual values for separation distances and bonding energies, but it is possible. My point was to give a qualitative explanation, that's all.

 

[darkmatter(s)]

Well, for something simple, such as a proton-proton system, with one electron kicking about (A hydrogen molecular ion), the attractive term comes from the exchange of the electron. Feynman deals with it in his 3rd volume. Basically, one assumes that the system can be modeled by the electron being "near" one nucleus or the other. So we can have state |1> where the electron is by nucleus 1 and state |2> where the electron is by nucleus two (we assume enough distance between them to be able to distinguish between the two states). Thus a two state system is set up leading to a splitting of the energy levels. That is to say, if the nuclei are separated by an infinite distance, the energy of the system is just that of the ground state, E_0, but due to the exchange effects the energy is split into two levels E_0 + A and E_0 - A where A is the probability amplitude for the electron to switch positions between the two nuclei. Now the lowest energy level possible will be that for which the electron spends an equal amount of time about each nucleus. This lowest energy state corresponds to a certain distance between the nuclei and thus a "bonding" of the system. A "one electron bond". Note that there are many factors involved and a more complex study would be necessary to find the actual values for separation distances and bonding energies, but it is possible. My point was to give a qualitative explanation, that's all.

Thank you very much for your reply. It was a good qualitative explanation for what a chemical bond actually is, at the most fundamental level, and is precisely what I was hoping for. As for the book you recommended, is the title: The Feynman Lectures on Physics, Vol. 3?

 

[Renge Ishyo]

Feynamn's Lectures are great, but if you really want the best book you can probably get on this topic, try Linus Paulings "The Nature of the Chemical Bond." It explores tons of applications on this topic.

 

[darkmatter(s)]

Alright, I sure will. Thanks to you both for your insight, I can't wait to learn more concerning this topic.

Chad