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I know that Gaussian (or other quantum chemical packages) assumes the molecule is alone in vacuum, that is, the molecule doesn't interact with anything, when optimizing the molecule.

But I've found that optimization at HF or DFT levels results are almost the same as experimental data, which were from the solid state by X-ray diffraction. Everyone knows that the solid state is quite different from the vacuum, for molecules interact with each other in the solid state.

Then why do the two generate nearly the same results? Or have I looked at so few samples that I neglect occasions when the two give quite different results?

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2 Answers 2

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You raise an excellent question and the short answer is "yes, quantum chemistry calculations are intrinsically in vacuum".

Approximate methods like semiempirical (AM1, PM6, PM7) and hybrid DFT methods (e.g., B3LYP) use experimental data, which often comes from crystal structures.

For many years, single-crystal x-ray diffraction studies were the gold standard of "what is the geometry of a molecule." Performing gas-phase measurements of bond angles and bond lengths are extremely difficult, since they typically require a molecular beam of the intended target and then very high resolution IR, rotational spectroscopy, or gas electron diffraction.

I once heard a talk by an extremely talented theorist, who asked the question "is an experimental crystal structure accurate enough?" He showed that in many cases, the answer is "no." (Consider that establishing the position of hydrogen atoms is difficult if not impossible with many single crystals.) The method he was proposing (geometry optimization with CCSD(T) and a basis set limit) isn't really appropriate for large molecules.

Until there's some huge database of gas-phase molecular geometry measurements and CCSD(T) calculations, most methods are compared with crystal structures.

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    $\begingroup$ I'll point out that for bond lengths and angles of non-hydrogen atoms, the geometry in the solid state often is not that different from the gas phase. Packing effects tend to alter dihedral angles (e.g., flattening the inter-ring biphenyl torsion). $\endgroup$
    – Geoff Hutchison
    Commented Jun 16, 2015 at 15:10
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    $\begingroup$ I'm not well enough versed in the method to evaluate it critically, but Neese's DLPNO-CCSD(T) claims excellent accuracy relative to 'canonical' CCSD(T), but with linear scaling with system size. It's implemented for closed-shell species in the current version of ORCA, and might be a first step toward such a practical theoretical database. $\endgroup$
    – hBy2Py
    Commented Jun 16, 2015 at 15:33
  • $\begingroup$ In fact, performing a gas-phase measurement is not so difficult, analysis is the tough part: the procedure which spits out geometrical parameters from the experimental data is usually quite cumbersome. With respect to the methods used for gas-phase structural determination @GeoffHutchison definitely forgot to mention GED (Gas Electron Diffraction) technique which is quite frequently used jointly with MW spectroscopy to give the most reliable results. $\endgroup$
    – Wildcat
    Commented Jun 16, 2015 at 15:41
  • $\begingroup$ Oh, yes, yes, yes. Establishing the position of hydrogen atoms in X-ray crystallography always looks like a straight cheating to me. :D Good-ol' "Everybody believes in experimental results, except the one who did it." On the other hand, "Nobody believes in theoretical calculations, except the one who did it." :D $\endgroup$
    – Wildcat
    Commented Jun 16, 2015 at 15:47
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    $\begingroup$ @GeoffHutchison, I did GED in the past. The most interesting part of analysis is that you anyway need quantum chemical calculations (basically, you need a force field to perform the GED results analysis). So usually what is done is a combined analysis of electron diffraction data, rotational constants and ab initio calculations. Anyway, this joint analysis provides quite reliable gas phase geometric parameters. I usually benchmark DFT functionals against such data if available. $\endgroup$
    – Wildcat
    Commented Jun 16, 2015 at 16:03
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It is possible to do crystal structure optimizations in Gaussian by adding translation vectors (DFT isn't as good with intermolecular reactions, but it will probably be a better approximation than optimizing without PBC, which is akin to a gas phase molecule). Whether or not solid behavior and gas behavior are similar will depend on the material, and the properties you're measuring, so could you tell us more specifically what you're studying?

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  • $\begingroup$ Hi Felipe, I'm not talking about a specific molecule. Yesterday I suddenly realised that I used Gaussian to optimise molecules in gas phase but got the same results as by X-ray diffraction. And I remember once in class a teacher talked about a molecule optimised at HF level, he said,"look, the bond length and bond angle are exactly the same as experimental data in this paper, so this level and basis set are suitable for this type of molecule." Since then I've been using solid state data to choose the best method to optimise molecules in gas phase. Now I question this way of studying chemistry. $\endgroup$
    – OhLook
    Commented May 4, 2015 at 6:59

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