(Let's assume for the sake of this discussion that computational power were not an issue.) What are the applications to chemistry of quantum mechanics? So far I have only seen the Schrodinger equation being solved for a system with a hydrogen nucleus and 1 electron. Is it possible in theory to find the molecular orbital set, and thus the molecular orbital diagram, for all energetically likely isomers of molecules with a set number and type of atoms and set number of electrons (directly from the information of which and how many atoms there are, and how many electrons there are and which atomic orbitals they originally belonged to)? How do we go about writing the equations to do this (solving them need not be demonstrated, nor the approximations you need to do so, although I don't mind if you care to show these things). Given two molecules and conditions such as temperature and pressure, can you theoretically calculate a) whether they will react and, if so, what product they will form or b) given the product you expect to be formed, the rate constant for the reaction?
The first task is to identify the possible orbitals of the electrons - once you have that, just fill them with electrons. Finding those orbitals can be done approximately with computers, indeed, quantum chemistry does that all the time. Chemistry is "just" applied quantum mechanics. Just the Schroedinger equation. It can be useful to use some approximations to simplify the calculations. If computing power is not an issue: sure.
Although you could say that in principle chemistry should be reducible to QM (I think one could argue but I won't) maybe the student's question is more asking an indication on what is the state of the art in actually doing that? Because many student textbooks will have done the H atom, and maybe the H_{2}^{+} molecule and aspects of the He atom, they leave it there and the rest of chemistry is covered in a qualitative, not to mention somewhat dogmatic, fashion. I don't know if this only indicates how long ago I did any, but for that again I may not be the only one here. Clearly the H atom does throw a flood of light of principles on all atoms, but now good are we at calculating their properties, their spectra let alone their chemistry? Quite a wide question I realise. For what I know a bit more about I would say that protein structure calculations and predictions are not just computational physics.
Protein folding and even multi-protein interactions can be estimated with computers (you can even contribute with your own PC). It is not the only method to evaluate the structure of proteins, sure. Molecules are objects in our universe, so they can in principle be described with physics. That is a direct consequence of the scope of physics. And the laws for the interactions of electrons and nuclei are well understood, and described with quantum mechanics. I mentioned that in my post.
Let's look at this first then. What is the required information we have to input into the Schrodinger equation? e.g. if I wanted to write the equation which will land me up with the structure of water and all of its isomers, alongside values of how energetically likely each isomer is (and thus how prevalent I should expect each to be), how would I specify that? Maybe if you take me through that example (you don't need to list every electron necessarily, I should get the gist!) or send me a link for that example or another one (which is a proper molecule, not just H or H_{2}^{+} or something). So we're talking about finding those orbitals here, i.e. we're going to find an equation/equations which when solved would yield the molecular orbital diagram(s) for the isomers of water, along with estimations of how energetically likely each isomer is? And where do we start seeing the fact that the structure of the same substance in different phases may differ - e.g. PCl_{5} in the gaseous phase has a different structure to what it has in the solid phase unit cell. Then there's complex ions, which exist only in solution or in double salts. How do we get explanations for these structures out of QM?
Electronic structure is very important in chemistry. Most of theoretical chemistry outside of electronic structure is still mostly classical but classical molecular dynamics simulations are starting to involve more quantum corrections. For example, path integral quantum mechanics is used to quantize nuclear motion which is very important in such chemical problems as proton transport.
Any suggestions? At least the name of the field in which this stuff can be found? I would have looked into a book straight away but all the books I have stop after the H nucleus with 1 electron. They don't even begin to consider multiple electrons, much less large molecules. If you do recommend a book or name the field, I'd appreciate being directed to the field which describes how to formulate the method for finding the structures of each isomer and how energetically likely each one is, in terms of writing the equations - i.e. one which is focused on the development of the method for writing the equations needed to specify the molecule, rather than the approximations or computational solution methods.
The field dealing with the electronic structure (and other properties) of molecules on quantum mechanical level is called ``Quantum Chemistry''. If you happen to have a university library around, you could look for introductory textbooks in this topic. If you want to get a detailed insight into how molecular properties are calculated, you could look up "Molecular electronic structure theory" by Helgaker, Jørgensen, and Olsen (but this is not an introductory textbook). Probably the most important aspects to understand if you want to get into this topic are Hartree-Fock and second quantization, because everything else is based on that. And, basically, Hartree-Fock is the picture defining MO theory, and on which the ``conventional'' picture of chemical theory (including DFT, if you are honest) is based.
Do people actually start with "Schrodinger equation" still in such type of calculation? As cgk has mentioned, techniques such as density function theory are very common-place in tackling such problems, especially when they involved many-body interactions. This is one of the most obvious "application" of quantum mechanics in chemistry. Zz.
Yes. At the very least, the Schrödinger equation is used to derive approximations. There is also a large field of electronic structure theory in which real many-body wave functions beyond mean field are routinely calculated (usually when DFT doesn't cut it). But also in other fields, like theoretical vibrational spectroscopy or reaction dynamics many approaches are based on wave function theory (even if they sometimes get lost in the process and replaced by other things, e.g., surface hopping or path integrals). Chemistry is very quantum-y on the theoretical side.
And perhaps, while I wait for some books to arrive, you can humour me by answering an extension question. Could quantum theory predict the properties of a mixture rather than a single pure substance? For instance, if I know that I have an aggregate mixture of certain liquids (in terms of solutions, and also in the broader sense, e.g. crude oil) - including the chemical structure of each liquid and the percentage composition by number of moles of each liquid in the mixture - could I predict the chemical properties of the mixture? Could I predict the physical properties of the mixture (e.g. viscosity, etc.)?
That problem is completely intractable using a full quantum treatment. It is possible to find bulk properties using classical mechanics with quantum mechanical corrections.
Given that computing power is not an issue for my consideration? Is the theoretical method to do it using QM laid out, and just difficult to actually process, or is it little known?
That's the big difference between theory and practice. The required computation power for a full quantum-mechanical solution (based on the Schrödinger equation) grows really fast with the number of involved particles. With a real (and with every realistic) computer, you have to make some approximations.
I just want to look into the method. Ways for actually getting a final answer out of it, I'll look up separately once I've grasped the possibilities in the field. As I asked above, is the theoretical method to consider chemical and physical properties of aggregate mixtures using QM laid out, and just difficult to actually process, or is it unknown? Do such things even lie within the domain of QM?
What do you mean by laid out? In principle we have theories that can get us just about any level of accuracy from solving the schrodinger equation explicitly to a highly coarse grained, numerical, classical mechanics picture. The issue is that the more complete pictures are almost always orders of magnitude more challenging to solve analytical, or orders of magnitude more time consuming to solve numerically. In principle - completely in principle - you could solve for the properties of a mixture by solving the schrodinger equation for it.
And where I can learn how to specify the Schrodinger equation for a mixture? (If you would suggest looking into a book, please also suggest a name with it.) I am assuming the activity of each component in the mixture, as well as what structures each component is, will be the defining factors for how we write the specific Schrodinger equation for the mixture.