The gold standard in quantum chemistry is the method that is considered to be the best, the one that gives accurate reproduction of experimental results. The CCSD(T) method is often referred to as the gold standard, especially when a complete basis set (CBS) extrapolation is utilized. But is this method truly accurate, or simply the highest level method that is within our reach today?
Řezáč and Hobza1 address the question of the accuracy of CCSD(T)/CBS by examining 24 small systems that exhibit weak interactions, including hydrogen bonding (e.g. in the water dimer and the water…ammonia complex), dispersion (e.g. in the methane dimer and the methane…ethane complex) and π-stacking (e.g. as in the stacked ethene and ethyne dimers). Since weak interactions result from quantum mechanical effects, these are a sensitive probe of computational rigor.
A CCSD(T)/CBS computation, a gold standard computation, still entails a number of approximations. These approximations include (a) an incomplete basis set dealt with by an arbitrary extrapolation procedure; (b) neglect of higher order correlations, such as complete inclusion of triples and omission of quadruples, quintuples, etc.; (c) usually the core electrons are frozen and not correlated with each other nor with the valence electrons; and (d) omission of relativistic effects. Do these omissions/approximations matter?
Comparisons with calculations that go beyond CCSD(T)/CBS to test these assumptions were made for the test set. Inclusion of the core electrons within the correlation computation increases the non-covalent bond, but the average omission is about 0.6% of the binding energy. The relativistic effect is even smaller, leaving it off for these systems involving only first and second row elements gives an average error of 0.1%. Comparison of the binding energy at CCSD(T)/CBS with those computed at CCSDT(Q)/6-311G** shows an average error of 0.9% for not including higher order configuration corrections. The largest error is for the formaldehyde dimer (the complex with the largest biding energy of 4.56 kcal mol-1) is only 0.08 kcal mol-1. If all three of these corrections are combined, the average error is 1.5%. It is safe to say that the current gold standard appears to be quite acceptable for predicting binding energy in small non-covalent complexes. This certainly gives much support to our notion of CCSD(T)/CBS as the universal gold standard.
An unfortunate note: the authors state that the data associated with these 24 compounds (the so-called A24 dataset) is available on their web site (www.begdb.com), but I could not find it there. Any help?
References
(1) Řezáč, J.; Hobza, P. "Describing Noncovalent Interactions beyond the Common Approximations: How Accurate Is the “Gold Standard,” CCSD(T) at the Complete Basis Set Limit?," J. Chem. Theor. Comput., 2013, 9, 2151–2155, DOI: 10.1021/ct400057w.
Henry Rzepa responded on 29 May 2013 at 7:31 am #
I would add that even very very small and simple molecules may not respond to the Gold standard. Thus C2 itself needs to be handled by multi-reference procedures. Bartlett has indeed recently developed these (see 10.1063/1.3567115), although I am not sure what the state of 1st/2nd energy derivatives is for the computer codes. So one other decision that has to be made is whether multireference character induces significant errors in non-covalent interactions. Does anyone know of any examples?
Steven Wheeler responded on 30 May 2013 at 8:29 pm #
I’ve always found the term “gold standard” rather misleading, for some of the reasons that Henry mentions. In particular, I think it gives the false impression that CCSD(T)/CBS will always give accurate results. Of course, we know this not to be the case for multireference systems.
On the other hand, I think it also implies, to some extent, that CCSD(T)/CBS is necessary to achieve high accuracy. For example, there are plenty of systems for which you can get very accurate results using just Hartree-Fock theory. In these cases, CCSD(T)/CBS will be a waste of time.
The point is that different problems require different tools, and always reaching for the “gold standard” can either give you a false sense of confidence in the face of daunting multireference character or it can lead you to waste perfectly good CPU time on system that are adequately treated at much lower levels of theory.
Steven: I believe I heard at the ACS meeting in New Orleans that A24 will be available on BEGDB at some later date, although I would have expected it to be there by now.
Steven Bachrach responded on 31 May 2013 at 9:01 am #
Do not take my post as saying that I believe that CCSD(T)/CBS is the gold standard. It does appear to be used as the de facto gold standard, and as Henry and Steven point out, there are issues with that stance. There are cases where CCSD(T) will fail – though increased incorporation of configurations will address the multi-configuration problem, though perhaps quite slowly. And Steven is absolutely correct that one does not always need to wield the sledgehammer when a small ball peen hammer will suffice. The right tool for the right problem!
Nonetheless, CCSD(T) is often our source of best approximation for the exact answer, useful for testing much more efficient computational tools, like a new density functional. This study does give us some hope that CCSD(T) is serving adequately for that purpose.
Lastly, Thanks Steven for the news about the A24 set. Last I looked at the site, the benchmark was still not there.