I'm currently exploring a method called Nudge Elastic Band to find the minimum energy pathway in a reaction involving a large metal cluster. While the NWChem documentation isn't bad, it could be clearer for happy amateurs like myself, which is the impetus for this post.
As usual, this is how I understand it --
which may be wrong.
The NEB method is described
here.
So...
There are a number of ways of modelling reaction pathways computationally.
Brute force PES scan (g09 or nwchem)
The fastest, cheapest, least accurate one would be to make a simple Potential Energy Surface (PES) scan by keeping all coordinates frozen with the exception of the ones directly involved in a reaction
e.g. for Me-OH -> Me + OH you'd simply vary the C-O distance.
If you don't let the structures relax for each change in bond length you will overestimate the activation energy. If you do let the structures relax you run the risk of every single snapshot relaxing back to either pure methanol or pure Me and OH, rather than giving you a series of transitional energies.
Transition state search e.g. QST2 (g09)
A somewhat more sophisticated method is to try to identify a proper transition state (TS). You can do this by making a lucky guess and try to do a transition state optimisation. You can improve your chances by using e.g. QST2 (or QST3, which also uses a specific TS guess), which takes the product and the starting material and interpolates the coordinates to generate a transition state guess. This has worked pretty well for me for cases where a simple transition state is expected (i.e. a hydride transfer). You can then model the reaction path by doing an IRC calc.
Minimum energy pathway methods (chain-of-states) e.g. Nudge Elastic Band (nwchem)
A more sophisticated method is to use a chain-of-state method such as
Nudge Elastic Band (NEB). There's a nice page about it here:
http://theory.cm.utexas.edu/henkelman/research/saddle/
NEB generates a series of structures based on the starting point and the product. These are initially generated a simple interpolations between the coordinates of the starting point and the end point -- this is very similar to a brute for PES scan and gives an unnaturally high transition energy. However, the individual structures are then optimised in passes.
 |
| 10 passes. Structural convergence is not achieved. |
Not clear? Well, here's a rough algorithm:
1. Generate a series of linearly interpolated structures (
beads) based on the Starting Point (SP) and End Point (EP) structures. In the simplest case, for N structures, each structure
n is SP+(n/N)*(EP-SP).
Now, typically you're more interested in structures in the middle than at the ends (i.e. to get better resolution for the transition) and that is manipulated using the spring constant,
kbeads. See figure 3 in
http://theory.cm.utexas.edu/henkelman/pubs/jonsson98_385.pdf for an example of varying the spring constant. 1.0 seems to be reasonably safe.
The number of structures is set by
nbeads. Make sure to use a reasonable number so that you get enough resolution.
2. Each structure thus generated is submitted to a single geometry optimisation step i.e. it's not optimised until convergence, but only takes a single step along the energy gradient. The speed at which it is decending along the energy gradient is set using the
stepsize.
The largest possible stepsize will give the fastest descent (which is good), but too large a stepsize may cause issues due to the atoms being moved too far (which is bad) and in turn cause SCF convergence failures due to the structures becoming unreasonable. So try 1.0 and hope for the best.
Rule of thumb: if you
decrease the stepsize by a factor of 10 from 1.0 to 0.1, you should
increase maxiter by a factor of 10.
3. The energies of the new structures are calculated and a reaction profile is generated.
4. Repeat step 2 and 3 until structural convergence or
maxiter steps.
5. If you're lucky your calculation will end due to structural convergence. If not, and if you want to restart your calculation you can read in the last set of structures using
xyz_path.
But make sure that you do print the intermediate structures in the first place by using
print_shift 1.
