Describing Noncovalent Interactions beyond the Common Approximations: How Accurate Is the “Gold Standard,” CCSD(T) at the Complete Basis Set Limit?

Řezáč, J.; Hobza, P.  J. Chem. Theor. Comput., 2013, 9, 2151
Contributed by Steven Bachrach.
Reposted from Computational Organic Chemistry with permission

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.

This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.

The Optical Rotation of Methyloxirane in Aqueous Solution: A Never Ending Story?

Lipparini, F.; Egidi, F.; Cappelli, C.; Barone, V. J. Chem. Theor. Comput. 2013, 9, 1880
Contributed by Steven Bachrach.
Reposted from Computational Organic Chemistry with permission

Computing the optical rotation of simple organic molecules can be a real challenge. One of the classic problems is methyloxirane. DFT typically gets the wrong sign, let alone the wrong value. Cappelli and Barone¹ have developed a QM/MM procedure where methyloxirane is treated with DFT (B3LYP/aug-cc-pVDZ or CAM-B3LYP/aubg-cc-pVDZ). Then 2000 arrangements of water about methyloxirane were obtained from an MD simulation. For each of these configurations, a supermolecule containing methyloxirane and all water molecules with 16 Å was identified. The waters of the supermolecule were treated as a polarized force field. This supermolecule is embedded into bulk water employing a conductor-polarizable continuum model (C-PCM). Lastly, inclusion of vibrational effects, and averaging over the 2000 configurations, gives a predicted optical rotation at 589 nm that is of the correct sign (which is not accomplished with a gas phase or simple PCM computation) and is within 10% of the correct value. The full experimental ORD spectrum is also quite nicely matched using this theoretical approach.

References

(1) Lipparini, F.; Egidi, F.; Cappelli, C.; Barone, V. "The Optical Rotation of Methyloxirane in Aqueous Solution: A Never Ending Story?," J. Chem. Theor. Comput. 2013, 9, 1880-1884, DOI:10.1021/ct400061z.

InChIs

(R)-Methyloxirane:
InChI=1S/C3H6O/c1-3-2-4-3/h3H,2H2,1H3/t3-/m1/s1
InChIKey=GOOHAUXETOMSMM-GSVOUGTGSA-N

This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.

Corrected small basis set Hartree-Fock method for large systems

Rebecca Sure and Stefan Grimme Journal of Computational Chemistry, early view

Contributed by +Jan Jensen 

Steven Bachrach recently highlighted Kruse and Grimme's geometric counterpoise scheme (gCP) - an add on term that corrects for BSSE in the same spirit as Grimme's dispersion correction.  One of the many interesting observations in this paper is that gCP- and dispersion-corrected HF minimal basis set calculations can yield very accurate binding energies.

The paper by Sure and Grimme investigates this particular issue further and presents the so-called HF-3c method.  "3c" stands for the 3 different corrections: gCP, dispersion, and a short-range basis incompleteness (SRB) correction for "systematically overestimated bond lengths for electronegative elements (e.g. N,O,F) when employing small basis sets."  HF-3c uses a minimal basis set for H, C, N, and O and a split valence basis for heavier elements.  In all only 9 empirically adjusted parameters are needed.

Being an HF/minimal basis set calculation the method can be applied to rather large molecules, but will be slower than corresponding semi-empirical calculations on a single core.  However, the HF-3c can of course be run in parallel. HF-3c interaction energies computed for the S22, S66, and X40 datasets are of similar accuracy to PM6-DH2 and significantly better than PM6.

HF-3c geometry optimizations and vibrational frequency calculations are found to significantly more numerically stable and offer more accurate structures (including protein structures) than PM6, as implemented in MOPAC2012.  HF-3c thus offers an attractive alternative when MOPAC2012 is giving imaginary frequencies.  If HF-3c can produces accurate transition state geometries, the method might also be a viable alternative to QM/MM calculations.

HF-3c is implemented in the ORCA package, which is available free of charge.

This work is licensed under a Creative Commons Attribution 3.0 Unported License.

  

The solution to the challenge in "Time-Reversible Random Number Generators" by Wm. G. Hoover and Carol G. Hoover

Federico Ricci-Tersenghi arXiv:1305.1805
Contributed by Dan Gezelter
Reposted from The OpenScience Project with permission

William G. Hoover (of the Nosé-Hoover Thermostat) and Carol G. Hoover issued a $500 challenge on arXiv to generate a time-reversible random number generator.  The challenge itself would be quite remarkable news.  What’s even better is that the challenge (including the source code for an implementation) was solved in 6 days by Frederico Ricci-Tersenghi.

Why is this a big deal?  Most of the equations in physics that govern time evolution of particles obey time-reversal symmetry; the same differential equations that govern molecular or planetary motion will take you back to your starting point if you suddenly reverse the time variable.  This is a usually a fantastic way to check to see if you are doing the physics correctly in your simulations, and also means that collections of  starting points that are related to each other behave in certain predictable ways when they evolve.

Stochastic approaches to physical motion introduce an aspect of randomness to mimic the behavior of complex phenomena like the motion of solvent surrounding the moleculewe’re interested in, or to mimic the transitions between different electronic states of a molecule.   The introduction of random numbers has meant we had to give up time-reversibility, and we’ve been willing to live with that for a long time because we can study more complicated phenomena.

If we have access to a time-reversible pseudo-random number generator, however, we get that very powerful tool back in our toolbox.

Now, the Langevin equation,

md2xdt2=F–γ(t)dxdt+R(t)

has two things that prevent it from being time-reversible.  Besides the stochastic or random force, R(t), there’s also a drag or friction force, −γ(t)dxdt, that depends on the velocities of the particles.  There’s no solution yet to time reversibility for this piece (and I have my doubts that there ever will be a way to reverse this).