 So this entire approach to modeling is called molecular modeling, or molecular mechanics, in contrast to quantum mechanics, of course. The key idea with molecular mechanics is that we forego the quantum world, we forego the electrons, and we treat molecules consisting of point-like particles, so each atom is a point that has a partial charge, it's participating in bonds, angles, and torsions, and it has Reynolds parameters. There is no question that that's an approximation, but it's an approximation that biases some other things. In particular, we're using semi-empiric parameters. That sounds strange, that's another approximation, that's not something that should improve things. Well, it does, in the following way. Remember those Lenard-Jones interactions? You had two atoms interacting. And I said that, in principle, we know that the repulsion here, for instance, is exponential, and that's something that you can calculate from quantum mechanics. But if we try to calculate this from quantum mechanics and use it in a simulation, the result would be lousy. And I even think there's a plot of that in one of the figures in previous lectures, although I didn't tell you at the time. Why is that lousy? Well, I calculate the parameter exactly, but that parameter does not just apply to pairwise interactions. In general, in quantum mechanics, I also have three-body interactions between all three particles here, and four-body, and five-body, and six-body, all the way up to n-body interactions. And there is no way I can calculate that in a classical simulation. If I 100,000 for each step, I would need to calculate something involving all 100,000 atoms, and 99,999, and 99,998, forget about it. But if I instead choose to approximate that with a pairwise interaction, if I still use the parameters that I derived theoretically that would apply to the n-body interactions, I have introduced an error. So what I instead do is that I stick to my pairwise interaction. I only look at that pair. But instead, I fit a model that only takes the pairs to come and makes sure that I reproduce the density and heat of aberration. And fascinatingly, that means that my end result here, when I simulate the liquid, is going to be better than if I applied the correct quantum mechanical parameters between incorrect number of interactions. So take home message here. Be careful about assuming that things are by definition better just because there is a quantum prefix. There are frequently other approximations that you did not think of.