With just over a week before 4th year project reports are due in for Natural Sciences, everyone’s quietly busying away attempting to tie everything together. My project has been half computational and half experimental, and although much of my effort is now in writing up I can’t convince myself to stop running simulations to try and backup what I’ve found so far. Given electronic structure theory is used in so many areas of chemistry today, I thought it’d be interesting to give a quick layman’s overview of the main approach to simulating what’s achieved in the lab, especially since it’s not taught at A-level (as far as I know!).
On the level of atoms and molecules, everything starts to behave more like waves than billiard balls, and to find properties of a system (say like it’s total energy) the Schrodinger wave equation is used. This works amazingly well, however, there’s a fundamental problem in that if you have a separate wave equation for each electron and nucleus in an atom, it can’t actually be solved because the energies of each particle are dependent on each other! One way to think about this is part of the energy of each electron will depend on the repulsion of another electron. How do you find out that repulsion? Just calculate the other electron’s energy! ..which includes a repulsion term for that first electron.
Solving this problem is the heart of computational chemistry, where different methods are used to see what you can approximate and still get good results. So often you’ll treat the nuclei as if they’re stationary (they move slow compared to electrons), or you might average out all the repulsion of the electrons. Even with these approximations, most methods have a lot of unknowns, the solution of which is usually to guess some initial values, run those through an algorithm, and then use the results as the initial values and repeat until the results converge. That is, assuming they will converge! Which is a common problem I’m experiencing a lot of right now..
What I’m trying to simulate is the ground and excited states of molecules, and their vibrational spectra. A lot of these molecules have partially filled electron shells, resulting in a lot of these approximation methods breaking down, but progress is slowly being made! This kind of work is becoming more and more expected to compliment and back up experimental data, and as methods get more sophisticated these can be expanded to small biological systems and beyond!
2 responses to “Convergence failures and hidden electronic states: the world of computational chemistry”
[…] the end my project consisted of four components, two of which involved simulating molecules using electronic structure theory to aid in detecting them in the future, while the other two consisted of optimising and using a […]
This often reminds me of the three celestial bodies problem in mathematics which knows no solution, however, the planets and their moons still have (rather) stable orbits around their suns. Several decades ago I tried to put the Huecker Molecular Orbital model into a computer (punch cards back then and you had to “queue” for computing time at the “mainframe” whose capacity was less than any mobile phone or pocket calculator has today … sigh), and I tried to formulate each atom as matrices to feed into “lattices” to let them interact. I never got very far because the complexity seemed to go up exponentially even for simple two-atom molecules of the methane, ethane, propane … series. Nowadays you can afford more “brute force” methods as computing time and esp. memory are no bottle necks anymore. Good luck!