Non-Standard Optimizations Of S4-Symmetry Molecules In DMol3

A little bit of procedure and a little bit of error-checking, all provided to point out that a chemistry program without chemical intuition is a rodent maze without savory cheese.

An important aspect of any solid-state density functional theory analysis of molecular crystals, such as the high explosives HMX and PETN onsidered in some previous posts, is identifying just how those molecules change in the solid-state. This is accomplished by simply performing an isolated-molecule calculation at the same level of theory on a single molecule to identify where the structural and vibrational differences from the solid-state results lie, the vibrational aspect being the focus of the terahertz studies considered in those previous HMX and PETN posts. The comparisons of the low-frequency isolated-molecule and solid-state vibrational modes make obvious (1) how much the external vibrational modes BETWEEN molecules (the rotational and translational modes ignored in isolated-molecule normal mode analyses) contribute to structure in solid-state THz spectra and (2) how much the crystal environment affects the geometries of single molecules through electrostatic interactions (this is obvious in periodic hydrogen-bonding systems, but even non-polar molecules like dodecahedrane are deformed from their icosahedral symmetry due to weak intermolecular interactions between neighboring molecules in its crystal packing environment, as observed in neutron spectra and solid-state simulations).

Any good quantum chemist knows that symmetry is better than no symmetry when performing optimizations and normal mode analyses. In the case of PETN, this molecular symmetry is S4, which reduced the four-armed beast to a one-armed beast, thereby reducing the number of steps in the vibrational calculation by 3/4. Application of symmetry in the DMol3 isolated-molecule calculation of PETN yielded the results I summarize below. This oddity of symmetry, removed when the symmetry option was turned off, was repeated with a second S4 symmetry system. Long-short, something wrong with (at least) the S4-optimization of single molecules. Details are provided below.


The molecule figure shows superimposed views of PETN (left) and 1,3,5,7-tetrafluorocyclooctatetraene (right, C8F4H4 from now on) using both S4 symmetry (red) and no symmetry (blue). The difference in the PETN molecule optimizations is obvious. The arms of the molecule are flattened upon optimization such that the central carbon becomes planar, taking 50 steps to not optimize in this case. The energy difference upon "optimization" is 1133 kJ/mol in favor of the asymmetric form. As expected, optimization of the S4 symmetry molecule without the symmetry restrictions yields an S4 minimum energy form, doing so in 5 steps. In short, there is something wrong with the symmetrized Hessian matrix of the potential energy being used in the optimization of this S4 molecule (you can follow this in the .hessian file or take my word for it). This same test was performed in C8F4H4 to confirm that the problem was the symmetry and not the molecule. Here, 50 steps yields a 44 kJ/mol difference in energy favoring the non-symmetrized form, which also optimizes to S4 symmetry. This smaller energy difference is due to the greater flex available in the 8-member ring (no rehybridization of a central atom necessary). The optimization without symmetry restriction takes 10 steps to achieve an accurate, S4 minimum energy form.

The two plots (click for the larger image) are for show, summarizing the total energies (with some scaling thrown in to get everything to fit in the image), energy changes, displacements, and maximum forces associated with each optimization. The lower plots show optimizations with the symmetry turned off, which clearly are easier to look at.


To summarize, there's a problem with S4 symmetry molecule optimizations in DMol3 (this problem has been reported to Accelrys, who apparently have fixed the Mulliken population analysis issue described in a previous post) and it behooves the user to know that and take appropriate steps (like posting to a blog). I've not tried the other Sn groups, but I do know S2 (that is, Ci) seems to work fine.

Speaking of improper rotations, what's purple and commutes?

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