Quantum mechanics in chemistry

[DrDu]

These are all quite complicated topics and I suggest you to read a book or article on quantum chemistry and physical chemistry.

Just one point: The temperature does not enter the hamiltonian but is taken into account via a thermal ensemble where the occupation probability of an excited state of a molecule is given by Boltzmann factors exp (-E/kT), where E is the energy relative to the ground state.
Pressure effects, at least in gasses, are often calculated starting from a virial expansion, i.e. interactions of the molecules are considered according to the number of interacting molecules (2, 3, 4 etc.).

 

[Big-Daddy]

As for isomers, what you specify in the SE are, as was mentioned above, potentials. These will depend on distances between nuclei and how many electrons there are and, when you're done, you'll have a set of solutions for each electron with an energy and a sense of where they're located. If you move the nuclei around, you'll change the potential and change the solutions for the electrons. Usually in quantum chemistry, you get rid of this issue by making the "Born-Oppenheimer approximation" that says that the nuclei are essentially fixed and you can compute the solutions for the electrons with that in mind. What you generally DO in quantum chemistry (as opposed to what you could do, in principle) is to look at a number of snapshots of nuclear positions (isomers) and see what their energy and Gibbs Free Energies are, see what barriers exist between them and then discuss the thermodynamics and kinetics of possible "reactions" that take you from one isomer to the other. This can be visualized in terms of an "energy surface".

Thanks for the argument, very interesting and new way of considering what isomers actually are. Looking at this bit particularly:

As for isomers, what you specify in the SE are, as was mentioned above, potentials. These will depend on distances between nuclei and how many electrons there are and, when you're done, you'll have a set of solutions for each electron with an energy and a sense of where they're located. If you move the nuclei around, you'll change the potential and change the solutions for the electrons.

From the Schrodinger equation will in theory arise the wave-function solutions for this set of nuclei and electrons, I grasp, which I will then restrict with statistical mechanics to the correct wave-function that represents correctly the electrons in my molecule under these statistical mechanical conditions.

Does this wave-function refer to a single isomer? If not, how do we find the different "isomers" from the wave-function - because, after all, if one wave-function refers to more than one isomer, then there should be no concept of inter-conversion between isomers as the isomers would fundamentally be the same (which could be the case for resonance structures but not normal molecular isomers)?

 

[DrDu]

Most of quantum chemistry is built upon the Born Oppenheimer approximation as has been pointed out by Einstein Mcfly already.
http://en.wikipedia.org/wiki/Born_Oppenheimer
Concepts like molecular structure and isomers have no meaning at a fully quantum mechanical level but are emergent properties in the Born_Oppenheimer approximation which is the result of the vast difference of electronic and nuclear masses.

 

[Big-Daddy]

Concepts like molecular structure and isomers have no meaning at a fully quantum mechanical level but are emergent properties in the Born_Oppenheimer approximation which is the result of the vast difference of electronic and nuclear masses.

I've read the page you linked on the Born-Oppenheimer approximation. However, I'm still confused as to what you mean by "molecular structure and isomers have no meaning at a fully quantum mechanical level" - surely there must be something to distinguish isomers from each other at the most fundamental level, since they are indeed different species and we can isolate them separately from one another in the lab?

 

[Einstein Mcfly]

I've read the page you linked on the Born-Oppenheimer approximation. However, I'm still confused as to what you mean by "molecular structure and isomers have no meaning at a fully quantum mechanical level" - surely there must be something to distinguish isomers from each other at the most fundamental level, since they are indeed different species and we can isolate them separately from one another in the lab?

Each arrangement of nuclei for a given number of electrons will have its own wave functions (solutions to the SE for that particular potential). That wave function doesn't "know" anything about any other wave function based on any other potential (due to different coordinates for the nuclei or numbers of electrons). If you want to compare properties of isomers at the quantum mechanical level, you must do separate calculations for each system and then compare their properties. If one of them has a lower total energy than another (all else being equal), then you can say that this structure should be found more readily in nature than the higher energy one. It's not exactly that simple (there are factors like kinetics and further reactions and whatnot) but that's the general idea. Quantum mechanics and quantum chemistry don't solve everything all at once; you need to do quite a bit of work yourself to investigate the possibilities.

 

[DrDu]

I've read the page you linked on the Born-Oppenheimer approximation. However, I'm still confused as to what you mean by "molecular structure and isomers have no meaning at a fully quantum mechanical level" - surely there must be something to distinguish isomers from each other at the most fundamental level, since they are indeed different species and we can isolate them separately from one another in the lab?

Isomers can isomerize. On a most fundamental level, the eigenstates of the full hamiltonian are superpositions of different isomers.
The question why we really observe isomers is far from trivial. Probably it is due to interactions with neighbouring molecules, so it is a colligative effect. You may want to google for Hund's paradox.

 

[Einstein Mcfly]

Isomers can isomerize. On a most fundamental level, the eigenstates of the full hamiltonian are superpositions of different isomers.
The question why we really observe isomers is far from trivial. Probably it is due to interactions with neighbouring molecules, so it is a colligative effect. You may want to google for Hund's paradox.

Doesn't Hund's paradox just apply to chiral systems? I thought his question was more about non-degenerate isomers (boat versus chair and all that).

 

[DrDu]

Doesn't Hund's paradox just apply to chiral systems? I thought his question was more about non-degenerate isomers (boat versus chair and all that).

Yes, but as always, for degenerate states the consideration of superpositions is most relevant.