Deducing physical properties of substances with physics

Question

Inspired by this question (Why does amount of protons define how matter is?) I’m wondering how one can deduce the physical properties of an element with physics. For example, it is known that sodium will combust in air. How can one predict this with physics? Is it possible to in principle perturbatively solve the schrodinger equation for a sodium-oxygen system and then deduce that the out result will be combustion?

Answer 1

The question is too broad for me, but I can give you an idea about the steps involved to predict thermodynamic properties of your example.

We can use quantum mechanics to obtain the partition function of our system. Statistical thermodynamics tells us then how to calculate the reaction enthalpy or Gibbs free energy change for the reaction of sodium and oxygen. But this is much easier said than done. In particular obtaining the partition function is nontrivial and the equation is misleadingly simple to state,

$$ Z = \text{Tr} (e^{-\beta\hat H}) $$ The exact Hamiltonian is usually already way too difficult to work with and various approximations are invoked to tackle the problem. The most important one(for molecular/chemistry problems) is probably the Born-Oppenheimer Approximation. Within this approximation, we need to solve the electronic Hamilton operator problem, which is the point where electronic structure models enter the stage, like Hartree-Fock or Density functional theory. Lets assume we obtained $H$ within these approximations, we still need to evaluate $Z$. This is possible in closed form for the harmonic oscillator. Thus the harmonic approximation is often invoked in thermochemistry calculations and if we make the harmonic approximation we can evaluate $Z$ and then use the equations from statistical thermodynamics for the properties of interest.

One can write books on each of the steps involved that I have very quickly glanced over but I hope it helps to give a rough idea how it can be done.

Answer 2

Yes. These ard called first principle calculations. This is a study belonging to Density Functional Theory. This is, however, a difficult field of study with a great deal of computational complexity, so it can be a challenge to model even simple systems. There have, however, been significant improvements on this front since the founding of the field.

Answer 3

another name for this is quantum chemistry, in which the different forms of chemical reactions can be deduced/predicted from quantum principles. This field was just getting going in 1970 when I was a freshman in college, and our chem lab teaching assistant and his grad school buddies made jokes about the tragedy of having one's field of study subsumed into just another branch of physics, boo hoo.