Archive for the 'Grimme' Category

A record short H…H non-bonding interaction

Following on previous work (see these posts on ladderane and hexaphenylethane), Schreiner, Grimme and co-workers have examined the structure of the all-meta tri(di-t-butylphenyl)methane dimer 12.1 In the study of hexaphenylethane,2 Schreiner and Grimme note that t-butyl groups stabilize highly congested structures through dispersion, identifying them as “dispersion energy donors”.3 The idea here is that the dimer of 1 will be stabilized by these many t-butyl groups. In fact, the neutron diffraction study of the crystal structure of 12 shows an extremely close approach of the two methane hydrogens of only 1.566 Å, the record holder for the closest approach of two formally non-bonding hydrogen atoms.

To understand the nature of this dimeric structure, they employed a variety of computational techniques. (Shown in Figure 1 is the B3LYPD3ATM(BJ)/def2-TZVPP optimized geometry of 12.) The HSE-3c (a DFT composite method) optimized crystal structure predicts the HH distance is 1.555 Å. The computed gas phase structure lengthens the distance to 1.634 Å, indicating a small, but essential, role for packing forces. Energy decomposition analysis of 12 at B3LYP-D3ATM(BJ)/def2-TZVPP indicates a dominant role for dispersion in holding the dimer together. While 12 is bound by about 8 kcal mol-1, the analogue of 12 lacking all of the t-butyl groups (the dimer of triphenylmethane 22) is unbound by over 8 kcal mol-1. Topological electron density analysis does show a bond critical point between the two formally unbound hydrogen atoms, and the noncovalent interaction plot shows an attractive region between these two atoms.

Figure 1. ATM(BJ)/def2-TZVPP optimized geometry of 12, with most of the hydrogens suppressed for clarity. (Selecting the molecule will launch Jmol with the full structure, including the hydrogens.)


1) Rösel, S.; Quanz, H.; Logemann, C.; Becker, J.; Mossou, E.; Cañadillas-Delgado, L.; Caldeweyher, E.; Grimme, S.; Schreiner, P. R., "London Dispersion Enables the Shortest Intermolecular Hydrocarbon H···H Contact." J. Am. Chem. Soc. 2017, 139, 7428–7431, DOI: 10.1021/jacs.7b01879.

2) Grimme, S.; Schreiner, P. R., "Steric Crowding Can Stabilize a Labile Molecule: Solving the Hexaphenylethane Riddle." Angew. Chem. Int. Ed. 2011, 50 (52), 12639-12642, DOI: 10.1002/anie.201103615.

3) Grimme, S.; Huenerbein, R.; Ehrlich, S., "On the Importance of the Dispersion Energy for the Thermodynamic Stability of Molecules." ChemPhysChem 2011, 12 (7), 1258-1261, DOI: 10.1002/cphc.201100127.


1: InChI=1S/C43H64/c1-38(2,3)31-19-28(20-32(25-31)39(4,5)6)37(29-21-33(40(7,8)9)26-34(22-29)41(10,11)12)30-23-35(42(13,14)15)27-36(24-30)43(16,17)18/h19-27,37H,1-18H3

Grimme &Schreiner Steven Bachrach 21 Jun 2017 No Comments

Fractional occupancy density

Assessing when a molecular system might be subject to sizable static (non-dynamic) electron correlation, necessitating a multi-reference quantum mechanical treatment, is perhaps more art than science. In general one suspects that static correlation will be important when the frontier MO energy gap is small, but is there a way to get more guidance?

Grimme reports the use of fractional occupancy density (FOD) as a visualization tool to identify regions within molecules that demonstrate significant static electron correlation.1 The method is based on the use of finite temperature DFT.2,3

The resulting plots of the FOD for a series of test cases follow our notions of static correlation. Molecules, such as alkanes, simple aromatics, and concerted transition states show essentially no fractional orbital density. On the other hand, the FOD plot for ozone shows significant density spread over the entire molecule; the transition state for the cleavage of the terminal C-C bond in octane shows FOD at C1 and C2 but not elsewhere; p-benzyne shows significant FOD at the two radical carbons, while the FOD is much smaller in m-benzyne and is negligible in o-benzyne.

This FOD method looks to be a simple tool for evaluating static correlation and is worth further testing.


(1) Grimme, S.; Hansen, A. "A Practicable Real-Space Measure and Visualization of Static Electron-Correlation Effects," Angew. Chem. Int. Ed. 2015, 54, 12308-12313, DOI: 10.1002/anie.201501887.

(2) Mermin, N. D. "Thermal Properties of the Inhomogeneous Electron Gas," Phys. Rev. 1965, 137, A1441-A1443, DOI: 10.1103/PhysRev.137.A1441.

(3) Chai, J.-D. "Density functional theory with fractional orbital occupations," J. Chem. Phys 2012, 136, 154104, DOI: doi: 10.1063/1.3703894.

Grimme Steven Bachrach 20 Jan 2016 2 Comments

Host-guest complexes

Grimme and coworkers have a featured article on computing host-guest complexes in a recent ChemComm.1 They review the techniques his group has pioneered, particularly dispersion corrections for DFT and ways to treat the thermodynamics in moving from electronic energy to free energy. they briefly review some studies done by other groups. They conclude with a new study of eight different host guest complexes, three of which are shown in Figure 1.




Figure 1. TPSS-D3(BJ)/def2-TZVP optimized structures of 1-3.

These eight host-guest complexes are fairly large systems, and the computational method employed means some fairly long computations. Geometries were optimized at TPSS-D3(BJ)/def2-TZVP, then single point energy determined at PW6B95-D3(BJ)/def2-QZVP. Solvent was included using COSMO-RS. The curcurbituril complex 2 includes a counterion (chloride) along with the guest adamantan-1-aminium. Overall agreement of the computed free energy of binding with the experimental values was very good, except for 3 and the related complex having a larger nanohoop around the fullerene. The error is due to problems in treating the solvent effect, which remains an area of real computational need.

An interesting result uncovered is that the binding energy due to dispersion is greater than the non-dispersion energy for all of these complexes, including the examples that are charged or where hydrogen bonding may be playing a role in the bonding. This points to the absolute necessity of including a dispersion correction when treating a host-guest complex with DFT.

As an aside, you’ll note one of the reasons I was interested in this paper: 3 is closely related to the structure that graces the cover of the second edition of my book.


(1) Antony, J.; Sure, R.; Grimme, S. "Using dispersion-corrected density functional theory to understand supramolecular binding thermodynamics," Chem. Commun. 2015, 51, 1764-1774, DOI: 10.1039/C4CC06722C.

Grimme &host-guest Steven Bachrach 12 May 2015 1 Comment

Testing for method performance using rotational constants

The importance of dispersion in determining molecular structure, even the structure of a single medium-sized molecule, is now well recognized. This means that quantum methods that do not account for dispersion might give very poor structures.

Grimme1 takes an interesting new twist towards assessing the geometries produced by computational methods by evaluating the structures based on their rotational constants B0 obtained from microwave experiments. He uses nine different molecules in his test set, shown in Scheme 1. This yields 25 different rotational constants (only one rotational constant is available from the experiment on triethylamine). He evaluates a number of different computational methods, particularly DFT with and without a dispersion correction (either the D3 or the non-local correction). The fully optimized geometry of each compound with each method is located to then the rotational constants are computed. Since this provides Be values, he has computed the vibrational correction to each rotational constant for each molecule, in order to get “experimental” Be values for comparisons.

Scheme 1.

Grimme first examines the basis set effect for vitamin C and aspirin using B3LYP-D3. He concludes that def2-TZVP or lager basis sets are necessary for reliable structures. However, the errors in the rotational constant obtained at B3LYP-D3/6-31G* is at most 1.7%, and even with CBS the error can be as large as 1.1%, so to my eye even this very small basis set may be completely adequate for many purposes.

In terms of the different functionals (using the DZVP basis set), the best results are obtained with the double hybrid B2PLYP-D3 functional where the mean relative deviation is only 0.3%; omitting the dispersion correction only increases the mean error to 0.6%. Common functionals lacking the dispersion correction have mean errors of about 2-3%, but with the correction, the error is appreciably diminished. In fact B3LYP-D3 has a mean error of 0.9% and B3LYP-NL has an error of only 0.6%. In general, the performance follows the Jacob’s Ladder hierarchy.


(1) Grimme, S.; Steinmetz, M. "Effects of London dispersion correction in density functional theory on the structures of organic molecules in the gas phase," Phys. Chem. Chem. Phys. 2013, 15, 16031-16042, DOI: 10.1039/C3CP52293H.

Grimme Steven Bachrach 11 Feb 2014 No Comments

Acene dimers – open or closed?

The role of dispersion in large systems is increasingly recognized as critical towards understanding molecular geometry. An interesting example is this study of acene dimers by Grimme.1 The heptacene and nonacene dimers (1 and 2) were investigated with an eye towards the separation between the “butterfly wings” – is there a “stacked” conformation where the wings are close together, along with the “open” conformer?



The LPNO-CEPA/CBS potential energy surface of 1 shows only a single local energy minima, corresponding to the open conformer. B3LYP-D3 and B3LYP-NL, two different variations of dealing with dispersion (see this post), do a reasonable job at mimicking the LPNO-CEPA results, while MP2 indicates the stacked conformer is lower in energy than the open conformer.

B3LYP-D3 predicts both conformers for the nonacene dimer 2, and the optimized structures are shown in Figure 2. The stacked conformer is slightly lower in energy than the open one, with a barrier of about 3.5 kcal mol-1. However in benzene solution, the open conformer is expected to dominate due to favorable solvation with both the interior and exterior sides of the wings.



Figure 1. B3LYP-D3/ef2-TZVP optimized structures of the open and stacked conformations of 2.


(1) Ehrlich, S.; Bettinger, H. F.; Grimme, S. "Dispersion-Driven Conformational Isomerism in σ-Bonded Dimers of Larger Acenes," Angew. Chem. Int. Ed. 2013, 41, 10892–10895, DOI: 10.1002/anie.201304674.


1: InChI=1S/C60H36/c1-2-10-34-18-42-26-50-49(25-41(42)17-33(34)9-1)57-51-27-43-19-35-11-3-4-12-36(35)20-44(43)28-52(51)58(50)60-55-31-47-23-39-15-7-5-13-37(39)21-45(47)29-53(55)59(57)54-30-46-22-38-14-6-8-16-40(38)24-48(46)32-56(54)60/h1-32,57-60H

2: InChI=1S/C76H44/c1-2-10-42-18-50-26-58-34-66-65(33-57(58)25-49(50)17-41(42)9-1)73-67-35-59-27-51-19-43-11-3-4-12-44(43)20-52(51)28-60(59)36-68(67)74(66)76-71-39-63-31-55-23-47-15-7-5-13-45(47)21-53(55)29-61(63)37-69(71)75(73)70-38-62-30-54-22-46-14-6-8-16-48(46)24-56(54)32-64(62)40-72(70)76/h1-40,73-76H

Aromaticity &Grimme Steven Bachrach 28 Oct 2013 2 Comments

A computationally inexpensive approach to correcting for BSSE

Basis set superposition error plagues all practical computations. This error results from the use of incomplete basis sets (thus pretty much all computations will suffer from this problem). The primary example of this error is in the formation of a supermolecule AB from the monomers A and B. Superposition occurs when in the computation of the supermolecule, basis functions centered on B are used to supplement the basis set of A, not to describe the bonding or interaction between the two monomers, but simply to better the description of the monomer A itself. Thus, BSSE always serves to increase the binding in the supermolecule. Recently, this concept has been extended to intramolecular BSSE, as discussed in these posts (A and B).

The counterpoise correction proposed by Boys and Bernardi corrects for the superposition by computing the energy of each monomer using the basis sets centered on both monomers, often referred to as ghost orbitals because the functions are used but not the nuclei upon which they are centered. This can overcorrect for superposition but is the only widely utilized approach to treat the problem. A variation on this approach is what has been suggested for the intramolecular
BBSE problem.

A major discouragement for wider use of counterpoise correction is its computational cost. Kruse and Grimme offer a semi-empirical approach that is extremely cost effective and appears to strongly mimic the traditional counterpoise correction.1

They define the geometric counterpoise scheme (gCP) that provides an energy correction EgCP that can be added onto the electronic energy. This term is defined as

Eq. (1)

where σ is an empirically fitted scaling term. The atomic contributions are defined as

Eq. (2)

where emiss are the errors in the energy of an atom with a particular target basis set, relative to the energy with some large basis set:

Eq. (3)

(On a technical matter, the atomic terms are computed in an electric field of 0.6a.u. in order to get some population into higher energy orbitals.) The fdec term is a decay function that relates to the distance between the atoms (Rnm) and the overlap

Eq. (4)

where Nvirt is the number of virtual orbitals on atom m, and α and β are fit parameters. Lastly, the overlap term comes from the integral of a single Slater orbital with coefficient

ξ = η(ξs + ξp)/2

Eq. (5)

where ξs and ξp are optimized Slater exponents from extended Huckel theory, and η is the last parameter that needs to be fit.

There are four parameters and these need to be fit for each specific combination of method (functional) and basis set. Kruse and Grimme provide parameters for a number of combinations, and suggest that the parameters devised for B3LYP are suitable for other functionals.

So what is this all good for? They demonstrate that for a broad range of benchmark systems involving weak bonds, the that gCP corrected method coupled with the DFT-D3 dispersion correction provides excellent results, even with B3LYP/6-31G*! This allows one to potentially run a computation on very large systems, like proteins, where large basis sets, like TZP or QZP, would be impossible. In a follow-up paper,2 they show that the B3LYP/6-31G*-gCP-D3 computations of a few Diels-Alder reactions and computations of strain energies of fullerenes match up very well with computations performed at significantly higher levels.

Once this gCP method and the D3 correction are fully integrated within popular QM programs, this combined methodology should get some serious attention. Even in the absence of this integration, these energy corrections can be obtained using the web service provided by Grimme at


(1) Kruse, H.; Grimme, S. "A geometrical correction for the inter- and intra-molecular basis set superposition error in Hartree-Fock and density functional theory calculations for large systems," J. Chem. Phys 2012, 136, 154101-154116, DOI: 10.1063/1.3700154

(2) Kruse, H.; Goerigk, L.; Grimme, S. "Why the Standard B3LYP/6-31G* Model Chemistry Should Not Be Used in DFT Calculations of Molecular Thermochemistry: Understanding and Correcting the Problem," J. Org. Chem. 2012, 77, 10824-10834, DOI: 10.1021/jo302156p

BSSE &Grimme Steven Bachrach 15 Jan 2013 No Comments

Benchmarked Dispersion corrected DFT and SM12

This is a short post mainly to bring to the reader’s attention a couple of recent JCTC papers.

The first is a benchmark study by Hujo and Grimme of the geometries produced by DFT computations that are corrected for dispersion.1 They use the S22 and S66 test sets that span a range of compounds expressing weak interactions. Of particular note is that the B3LYP-D3 method provided the best geometries, suggesting that this much (and justly) maligned functional can be significantly improved with just the simple D3 fix.

The second paper entails the description of Truhlar and Cramer’s latest iteration on their solvation model, namely SM12.2 The main change here is the use of Hirshfeld-based charges, which comprise their Charge Model 5 (CM5). The training set used to obtain the needed parameters is much larger than with previous versions and allows for treating a very broad set of solvents. Performance of the model is excellent.


(1) Hujo, W.; Grimme, S. "Performance of Non-Local and Atom-Pairwise Dispersion Corrections to DFT for Structural Parameters of Molecules with Noncovalent Interactions," J. Chem. Theor. Comput. 2013, 9, 308-315, DOI: 10.1021/ct300813c

(2) Marenich, A. V.; Cramer, C. J.; Truhlar, D. G. "Generalized Born Solvation Model SM12," J. Chem. Theor. Comput. 2013, 9, 609-620, DOI: 10.1021/ct300900e

Cramer &DFT &Grimme &Solvation &Truhlar Steven Bachrach 14 Jan 2013 No Comments

Dispersion leads to long C-C bonds

Schreiner has expanded on his previous paper1 regarding alkanes with very long C-C bonds, which I commented upon in this post. He and his colleagues report2 now a series of additional diamond-like and adamantane-like sterically congested alkanes that are stable despite have C-C bonds that are longer that 1.7 Å (such as 1! In addition they examine the structures and rotational barriers using a variety of density functionals.



For 2, the experimental C-C distance is 1.647 Å. A variety of functionals all using the cc-pVDZ basis predict distances that are much too long: B3LYP, B96, B97D, and B3PW91. However, functionals that incorporate some dispersion, either through an explicit dispersion correction (Like B3LYP-D and B2PLYP-D) or with a functional that address mid-range or long range correlation (like M06-2x) or both (like ωB97X-D) all provide very good estimates of this distance.

On the other hand, prediction of the rotational barrier about the central C-C bond of 2 shows different functional performance. The experimental barrier, determined by 1H and 13C NMR is 16.0 ± 1.3 kcal mol-1. M06-2x, ωB97X-D and B3LYP-D, all of which predict the correct C-C distance, overestimate the barrier by 2.5 to 3.5 kcal mol-1, outside of the error range. The functionals that do the best in getting the rotational barrier include B96, B97D and PBE1PBE and B3PW91. Experiments and computations of the rotational barriers of the other sterically congested alkanes reveals some interesting dynamics, particularly that partial rotations are possible by crossing lower barrier and interconverting some conformers, but full rotation requires passage over some very high barriers.

In the closing portion of the paper, they discuss the possibility of very long “bonds”. For example, imagine a large diamond-like fragment. Remove a hydrogen atom from an interior position, forming a radical. Bring two of these radicals together, and their computed attraction is 27 kcal mol-1 despite a separation of the radical centers of more than 4 Å. Is this a “chemical bond”? What else might we want to call it?

A closely related chemical system was the subject of yet another paper3 by Schreiner (this time in collaboration with Grimme) on the hexaphenylethane problem. I missed this paper somehow near
the end of last year, but it is definitely worth taking a look at. (I should point out that this paper was already discussed in a post in the Computational Chemistry Highlights blog, a blog that acts as a journals overlay – and one I participate in as well.)

So, the problem that Grimme and Schreiner3 address is the following: hexaphenylethane 3 is not stable, and 4 is also not stable. The standard argument for their instabilities has been that they are simply too sterically congested about the central C-C bond. However, 5 is stable and its crystal structure has been reported. The central C-C bond length is long: 1.67 Å. But why should 5 exist? It appears to be even more crowded that either 3 or 4. TPSS/TZV(2d,2p) computations on these three compounds indicate that separation into the two radical fragments is very exoergonic. However, when the “D3” dispersion correction is included, 3 and 4 remain unstable relative to their diradical fragments, but 5 is stable by 13.7 kcal mol-1. In fact, when the dispersion correction is left off of the t-butyl groups, 5 becomes unstable. This is a great example of a compound whose stability rests with dispersion attractions.

3: R1 = R2 = H
4: R1 = tBu, R2 = H
5: R1 = H, R2 = tBu


(1) Schreiner, P. R.; Chernish, L. V.; Gunchenko, P. A.; Tikhonchuk, E. Y.; Hausmann, H.; Serafin, M.; Schlecht, S.; Dahl, J. E. P.; Carlson, R. M. K.; Fokin, A. A. "Overcoming lability of extremely long alkane carbon-carbon bonds through dispersion forces," Nature 2011, 477, 308-311, DOI: 10.1038/nature10367

(2) Fokin, A. A.; Chernish, L. V.; Gunchenko, P. A.; Tikhonchuk, E. Y.; Hausmann, H.; Serafin, M.; Dahl, J. E. P.; Carlson, R. M. K.; Schreiner, P. R. "Stable Alkanes Containing Very Long Carbon–Carbon Bonds," J. Am. Chem. Soc., 2012, 134, 13641-13650, DOI: 10.1021/ja302258q

(3) Grimme, S.; Schreiner, P. R. "Steric Crowding Can tabilize a Labile Molecule: Solving the Hexaphenylethane Riddle," Angew. Chem. Int. Ed., 2011, 50, 12639-12642, DOI: 10.1002/anie.201103615

Grimme &Schreiner Steven Bachrach 25 Sep 2012 4 Comments

Review of DFT with dispersion corrections

For those of you interested in learning about dispersion corrections for density functional theory, I recommend Grimme’s latest review article.1 He discusses four different approaches to dealing with dispersion: (a) vdW-DF methods whereby a non-local dispersion term is included explicitly in the functional, (b) parameterized functional which account for some dispersion (like the M06-2x functional), (c) semiclassical corrections, labeled typically as DFT-D, which add an atom-pair term that typically has an r-6 form, and (d) one-electron corrections.

The heart of the review is the comparison of the effect of including dispersion on thermochemistry. Grimme nicely points out that reaction energies and activation barriers typically are predicted with errors of 6-8 kcal mol-1 with conventional DFT, and these errors are reduced by up to 1.5 kcal mol-1 with the inclusion fo the “-D3” correction. Even double hybrid methods, whose mean errors are much smaller (about 3 kcal mol-1), can be improved by over 0.5 kcal mol-1 with the inclusion of the “-D3” correction. The same is also true for conformational energies.

Since the added expense of including the “-D3” correction is small, there is really no good reason for not including it routinely in all types of computations.

(As an aside, the article cited here is available for free through the end of this year. This new journal WIREs Computational Molecular Science has many review articles that will be of interest to readers of this blog.)


(1) Grimme, S., "Density functional theory with London dispersion corrections," WIREs Comput. Mol. Sci., 2011, 1, 211-228, DOI: 10.1002/wcms.30

DFT &Grimme Steven Bachrach 06 Dec 2011 20 Comments

Origin of DFT failures – part III

The much publicized failure of common DFT methods to accurately describe alkane isomer energy and bond separation reactions (which I have blogged about many times) has recently been attributed to long-range exchange1 (see this post) or simply just DFT exchange2 (see this post). Grimme now responds by emphatically claiming that it is a failure in accounting for medium-range electron correlation.3

First, Grimme notes that the bond separation energy for linear alkanes (as defined in
Reaction 1) is underestimated by HF, and slightly overestimated by MP2, but SCS-MP2 provides energy in nice agreement with CCSD(T)/CBS energies. Since MP2 adds in coulomb correlation to the HF energy (which treats exchange exactly within a one determinant wavefunction), the traditional wavefunction approach strongly suggests a correlation error.

CH3(CH2)mCH3 + mCH4 → (m+1)CH3CH3        Reaction 1

Next, bond separation energies computed with PBE and BLYP (which lack exact exchange), PBE0 (which has 25% non-local exchange) and BHLYP (which has 50% non-local exchange) are all similar and systematically too small. So, exchange cannot be the culprit. It must be correlation.

He also makes two other interesting points. First, inclusion of a long-range correction – his recently proposed D3 method4 – significantly improves results, but the bond separation energies are still underestimated. It is only with the double-hybrid functional B2PLYP and B2GPPLYP that very good bond separation energies are obtained. And these methods do address the medium-range correlation issue. Lastly, Grimme notes that use of zero-point vibrational energy corrected values or enthalpies based on a single conformation are problematic, especially as the alkanes become large. Anharmonic corrections become critical as does inclusion of multiple conformations with increasing size of the molecules.


(1) Song, J.-W.; Tsuneda, T.; Sato, T.; Hirao, K., "Calculations of Alkane Energies Using Long-Range Corrected DFT Combined with Intramolecular van der Waals Correlation," Org. Lett., 2010, 12, 1440–1443, DOI: 10.1021/ol100082z

(2) Brittain, D. R. B.; Lin, C. Y.; Gilbert, A. T. B.; Izgorodina, E. I.; Gill, P. M. W.; Coote, M. L., "The role of exchange in systematic DFT errors for some organic reactions," Phys. Chem. Chem. Phys., 2009, DOI: 10.1039/b818412g.

(3) Grimme, S., "n-Alkane Isodesmic Reaction Energy Errors in Density Functional Theory Are Due to Electron Correlation Effects," Org. Lett. 2010, 12, 4670–4673, DOI: 10.1021/ol1016417

(4) Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H., "A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu," J. Chem. Phys., 2010, 132, 154104, DOI: 10.1063/1.3382344.

DFT &Grimme Steven Bachrach 08 Nov 2010 No Comments

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