Solving the Hydrogen Molecule computationally

1. Apr 3, 2013

dipole

Hi, I'm interested in solving the Hydrogen Molecule for a school project (computational physics course) WITH electron interactions included. I'm thinking of calculating the bond length using some kind of variational method, but I'd also like to calculate the energy levels of the two-electron wave function and compare to experiment.

What I need are some good references to get me started. I need an approach which isn't overly sophisticated so the code can be written from scratch over the course of a few weeks (i.e. please don't suggest using a DFT approach or something very complicated like that...). I'm open to Monte Carlo or some kind of relaxation method or other! I've tried searching in the American Journal of Physics, but I didn't find much there so I'm hoping maybe some people here can post some info and some references to point me in the right direction.

Again, this isn't really so much about understanding the physics as it is understanding how to actually do the numerical computation since this is a three-body problem (well four technically, but I plan on treating the protons as being fixed) and analytical methods are out of the question.

Thanks.

2. Apr 4, 2013

Staff: Mentor

Nice, ambitious project!

As a good starting point, I suggest you look at Atkins and Friedman, Molecular Quantum Mechanics, 5th ed. (OUP, 2011). Fourth edition will also do, not sure about the ealier ones. Chapter 9 pretty much spells out the recipe (see especially Fig. 9.1).

Usually, the main difficulty is making the equations converge. But for a two-electron system, you basically end up having to solve only a quadratic equation, so it should be doable without having to learn about optimization methods.

Good luck!

3. Apr 4, 2013

dipole

Great, thanks for the tip!

If anyone else out there has additional resources I'd love to hear them!