# How much does the initial geometry affect the final geometry in optimization calculations?

This might be a stupid question but to what extent will the initial configuration of a bulk phase geometry optimization calculation affect the final geometry? Most places say to start with experimental data but if there isn't any then is there a next best way of starting?

Would populating your initial configuration with a molecule repeated along the x y and z directions yield a different final geometry than populating it with molecules in random locations? or will this only effect the run time?

• @CharlieCrown Thank you! I did mean energy minimization, and your response makes a lot of sense. – Cavenfish May 29 '20 at 23:24

## Alot

Optimizations are all about finding the minimum in something. Typically in geometry optimization, it is about finding the minimum in energy. At a minimum the derivative of energy with respect to changing position should be zero, or better put, the jacobian should be positive definite.

Your question is about bulk systems, however, single molecules are problematic enough.

A single molecule by itself can take on many different conformations, each with a different energy. Given a starting configuration, a geometry optimization changes atomic coordinates to minimize energy. In practice, this usually means you find the nearest local minimum.

It is therefore important, and often ignored, to do a conformer search for a single molecule and find the lowest energy conformer prior to doing a geometry optimization. I can't stress the importance of conformer searches enough.

## Now

You are interested in a system of many molecules. For a single molecule the actual x,y,z position does not really matter. For a system of them however it does. Each molecule will relax to some conformer, possibly not the best one, and they will relax to certain orientations and centers of mass x,y,z most likely not the best ones, but representing the nearest local minimum in energy from the initial starting guess.

Finding a best geometry for a single molecule is tough, I would say, currently, it is impossible for a bulk system, you find the best one that you can, and live with it.

You can of course generate many initial guesses and take the lowest energy final geometry. You can try simulated annealing techniques, you can try all sorts of numerical methods really, but, finding the global minumum is an unsolved problem for an N-body problem such as a bulk phase of molecules.

Courtesy of Andrew Rosen, this paper has a nice example of zeolite structures depending on initial configuration.

• Just to tack onto this: here is a nice example where the initial configuration of various zeolites greatly impacts the resulting structure. – Andrew Rosen May 30 '20 at 4:50
• I can bump that up into the response. I felt like I was cheaping out without posting an image... this can kind of add a little heft to it – B. Kelly May 30 '20 at 5:11

I won't go over what Charlie Crown already described in his answer, but if you don't have experimental data, you can try starting off with the experimental structure of a similar compound that has the same crystal structure (i.e. ZrO2 and HfO2). If there are several options, try them and choose the relaxation that gives you the lowest energy. Just to add a quick anecdote, I've relaxed a single adsorbate atom on top of a slab structure, and the initial position had a very strong effect on the final relaxed position of both the adsorbate atom and the elastic distortions beneath the adsorbate. Try multiple arrangements!