Monday, December 11, 2017

Heavy-Atom Tunneling Calculations in Thirteen Organic Reactions: Tunneling Contributions are Substantial, and Bell’s Formula Closely Approximates Multidimensional Tunneling at ≥250 K

Doubleday, C.; Armas, R.; Walker, D.; Cosgriff, C. V.; Greer, E. M., Angew. Chem. Int. Ed. 2017, 56, 13099-13102
Contributed by Steven Bacharach
Reposted from Computational Organic Chemistry with permission

Though recognized to occur in organic systems, the breadth of involvement of heavy-atom tunneling has not been established. Doubleday, Greer and coworkers have examined 13 simple organic reactions sampling pericyclic reactions, radical rearrangements and SN2 reactions for heavy-atom tunneling.1 A few of these reactions are shown below.

Reaction rates were obtained using the small curvature tunneling approximation (SCT), computed using Gaussrate. Reaction surfaces were computed at B3LYP/6-31G*. The tunneling correction to the rate was also estimated using the model developed by Bell: kBell = (u/2)/sin(u/2) where u = hν/RT and ν is the imaginary frequency associated with the transition state. The temperature was chosen so as to give a common rate constant of 3 x 10-5 s-1. Interestingly, all of the examined reactions exhibited significant tunneling even at temperatures from 270-350 K (See Table 1). The tunneling effect estimated by Bell’s equation is very similar to that of the more computationally demanding SCT computation.

Table 1. Tunneling contribution to the rate constant
% tunneling
CN + CH3Cl → CH3CN + Cl (aqueous)

This study points towards a much broader range of reactions that may be subject to quantum mechanical tunneling than previously considered.


1. Doubleday, C.; Armas, R.; Walker, D.; Cosgriff, C. V.; Greer, E. M., "Heavy-Atom Tunneling Calculations in Thirteen Organic Reactions: Tunneling Contributions are Substantial, and Bell’s Formula Closely Approximates Multidimensional Tunneling at ≥250 K." Angew. Chem. Int. Ed. 2017, 56, 13099-13102, DOI: 10.1002/anie.201708489.

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

Sunday, November 26, 2017

Understanding and Breaking Scaling Relations in Single-Site Catalysis: Methane-to-methanol Conversion by Fe(IV)=O

Highlighted by Jan Jensen

This is the first study I have come across that locates TS structures as part of a "high-throughput" single-site catalyst design study. Furthermore, the catalyst contains iron, which is not the easiest of elements to work with computationally. 

The study locates 76 and 43 TSs for the oxo formation (TS1) and hydrogen atom transfer (HAT, TS2) steps of the catalytic cycle. These are relatively small numbers compared to high throughput studies of other properties (hence the quotation marks), but they are roughly an order of magnitude larger than the number of TSs found in typical computational study of catalysts. The number is smaller for HAT due to difficulties in locating TSs for this step.

The TSs were located using either NEB implemented in DL-FIND or Q-CHEM where initial guess structures were generated using a locally modified version of molSimplify.

The studies show that there is a good correlation between reaction energy and barrier for the HAT step (R2 = 0.99) but a poor correlation for the oxo formation (R2 = 0.50 - 0.81). The authors conclude "Overall, our work shows that LFERs can be leveraged in single-site catalyst screening only when the coordination geometry is held fixed. Reliance solely on LFERs for single-site catalysis will thus miss rich areas of chemical space accessible through scaffold distortion."

Tuesday, November 14, 2017

Tunneling Control of Chemical Reactions: The Third Reactivity Paradigm

Schreiner, P. R., J. Am. Chem. Soc. 2017, 139, 15276-15283
Contributed by Steven Bacharach
Reposted from Computational Organic Chemistry with permission

Over the past nine years the Schreiner group, often in collaboration with the Allen group, have produced some remarkable studies demonstrating the role of tunneling control. (I have made quite a number of posts on this topics.) Tunneling control is a third mechanism for dictating product formation, in tandem with kinetic control (the favored product is the one that results from the lowest barrier) and thermodynamic control (the favored product is the one that has the lowest energy). Tunneling control has the favored product resulting from the narrowest mass-considered barrier.
Schreiner has written a very clear perspective on tunneling control. It is framed quite interestingly by some fascinating quotes:
It is probably fair to say that many organic chemists view the concept of tunneling, even of hydrogen atoms, with some skepticism. – Carpenter 19832
Reaction processes have been considered as taking place according to the laws of classical mechanics, quantum mechanical theory being only employed in calculating interatomic forces. – Bell 19333
Schreiner’s article makes it very clear how critical it is to really think about reactions from a truly quantum mechanical perspective. He notes the predominance of potential energy diagrams that focus exclusively on the relative energies and omits any serious consideration of the reaction coordinate metrics, like barrier width. When one also considers the rise in our understanding of the role of reaction dynamics in organic chemistry (see, for example, these many posts), just how long will it take for these critical notions to penetrate into standard organic chemical thinking? As Schreiner puts it:
It should begin by including quantum phenomena in introductory textbooks, where they are, at least in organic chemistry, blatantly absent. To put this oversight in words similar to those used much earlier by Frank Weinhold in a different context: “When will chemistry textbooks begin to serve as aids, rather than barriers, to this enriched quantum-mechanical perspective?”4


1) Schreiner, P. R., "Tunneling Control of Chemical Reactions: The Third Reactivity Paradigm." J. Am. Chem. Soc. 2017139, 15276-15283, DOI: 10.1021/jacs.7b06035.
2) Carpenter, B. K., "Heavy-atom tunneling as the dominant pathway in a solution-phase reaction? Bond shift in antiaromatic annulenes." J. Am. Chem. Soc. 1983105, 1700-1701, DOI: 10.1021/ja00344a073.
3) Bell, R. P., "The Application of Quantum Mechanics to Chemical Kinetics." Proc. R. Soc. London, Ser. A1933139 (838), 466-474, DOI: 10.1098/rspa.1933.0031.
4) Weinhold, F., "Chemistry: A new twist on molecular shape." Nature 2001411, 539-541, DOI: 10.1038/35079225.

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

Tuesday, November 7, 2017

The Cope Rearrangement of 1,5-Dimethylsemibullvalene-2(4)-d1: Experimental Evidence for Heavy-Atom Tunneling

Schleif, T.; Mieres-Perez, J.; Henkel, S.; Ertelt, M.; Borden, W. T.; Sander, W., Angew. Chem. Int. Ed. 2017, 56, 10746-10749
Contributed by Steven Bacharach
Reposted from Computational Organic Chemistry with permission

Another prediction made by quantum chemistry has now been confirmed. In 2010, Zhang, Hrovat, and Borden predicted that the degenerate rearrangement of semibullvalene 1 occurs with heavy atom tunneling.1 For example, the computed rate of the rearrangement including tunneling correction is 1.43 x 10-3 s-1 at 40 K, and this rate does not change with decreasing temperature. The predicted half-life of 485 s is 1010 shorter than that predicted by transition state theory.
Now a group led by Sander has examined the rearrangement of deuterated 2.2 The room temperature equilibrium mixture of d42 and d22 was deposited at 3 K. IR observation showed a decrease in signal intensities associated with d42 and concomitant growth of signals associated with d22. The barrier for this interconversion is about 5 kcal mol-1, too large to be crossed at this temperature. Instead, the interconversion is happening by tunneling through the barrier (with a rate about 10-4 s-1), forming the more stable isomer d22 preferentially. This is exactly as predicted by theory!


1. Zhang, X.; Hrovat, D. A.; Borden, W. T., "Calculations Predict That Carbon Tunneling Allows the Degenerate Cope Rearrangement of Semibullvalene to Occur Rapidly at Cryogenic Temperatures." Org. Letters 2010, 12, 2798-2801, DOI: 10.1021/ol100879t.
2. Schleif, T.; Mieres-Perez, J.; Henkel, S.; Ertelt, M.; Borden, W. T.; Sander, W., "The Cope Rearrangement of 1,5-Dimethylsemibullvalene-2(4)-d1: Experimental Evidence for Heavy-Atom Tunneling." Angew. Chem. Int. Ed. 2017, 56, 10746-10749, DOI: 10.1002/anie.201704787.


1: InChI=1S/C8H8/c1-3-6-7-4-2-5(1)8(6)7/h1-8H
d42: InChI=1S/C10H12/c1-9-5-3-7-8(4-6-9)10(7,9)2/h3-8H,1-2H3/i5D
d22: InChI=1S/C10H12/c1-9-5-3-7-8(4-6-9)10(7,9)2/h3-8H,1-2H3/i7D

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

Tuesday, October 31, 2017

An automated transition state search and its application to diverse types of organic reactions

Highlighted by Jan Jensen

Copyright 2017 American Chemical Society

Finding transition states remains one of the most labor intensive pursuits in computational chemistry.  While interpolation methods are becoming increasingly robust, they usually require that the atom order for reactant and product are identical (atom mapping) and can be sensitive the starting conformations and relative orientation in case of bi-molecular reactions.  Furthermore, one still has to check whether the right TS is found and formulate a strategy if it is not.  All these things to do not immediately lend themselves to automation but this paper proposes solutions for all these problems.

In particular the paper offers a very elegant solution for the atom mapping problem: bonds are broken in both reactants and products until the connectivity of the fragments are identical after which the atoms in the fragments can be easily matched. Both the comparison and atom mapping of fragments can be easily done with modern cheminformatics toolkits such as RDKit using canonical smiles and  maximum common substructure searchers (after atom order and charge has been removed).  Cases where this fails due to equivalent atoms (e.g. the hydrogens in a methylene group) can then be dealt with by searching for the solution with the lowest RSMD between reactant and product.

The study focussed on relatively small and rigid molecules and issues due to multiple conformations is left for a future publication.

This work is licensed under a Creative Commons Attribution 4.0 International License.

Saturday, October 28, 2017

How To Arrive at Accurate Benchmark Values for Transition Metal Compounds: Computation or Experiment?

Y. A. Aoto, A. P. de Lima Batista, A. Köhn, A. G. S. de Oliveira-Filho, J. Chem. Theor. Comput., 2017
Contributed by Theo Keane

Copyright 2017 American Chemical Society 

When performing calculations of any kind, it is important to establish how accurate a method one intends to use is for a given application. Transition metals (TMs) are often problematic systems for computational chemists, because they exhibit “strong correlation”, i.e. either static or dynamic correlation is significant in systems that contain TMs (usually both). This paper adds to the existing literature of benchmark results for TM compounds by performing some rather high-level calculations on 60 diatomic TM compounds. I believe this is intended to improve upon the recent 3dMLBE20 set of Truhlar and co-workers,[1] which was criticised in a pair of papers published in early 2017.[2,3]

In this new benchmarking set, 43 molecules contain first row TMs, 7 contain Ru, Rh or Ag, and the remaining 10 contain Ir, Pt and Au. The multiplicities range from 1 to 7. For these molecules they have assembled experimental data, including bond length, harmonic vibrational frequency and bond dissociation energies. Single reference benchmark values were obtained via (RO/U)CCSD(T)/aug-cc-pwCVnZ-PP[4d, 5d metals]aug-cc-pwCVnZ[else], with n = T, Q, 5, and were extrapolated to the Complete-Basis-Set (CBS) limit. They also investigated the effect of core-valence correlation on the single-reference values. Furthermore, internally contracted Multi-Reference CCSD(T) (icMRCCSD(T)) calculations were performed in the aug-cc-pwCVTZ(-PP) basis, based on full-valence CASSCF reference wavefunctions to investigate the effect of static correlation – the full details of the chosen active spaces are provided in the SI (Table S6). Finally, relativistic effects were considered: scalar relativistic corrections were obtained by comparing frozen core CCSD(T)/aug-cc-pwCVTZ(-PP) calculations with and without the 2nd-order Douglas-Kroll-Hess (DKH2) Hamiltonian. For the 4d and 5d TM containing molecules, Spin-Orbit corrections were obtained from CASSCF calculations with full valence active spaces and the full, 2 electron Breit-Pauli operator. It is important to note that, with the exception of the SO correction, these corrections were not merely calculated for the equilibrium geometry, rather these were calculated at multiple points along the bond length. Overall, the authors have clearly spent a great deal of care ensuring that their ‘benchmark level’ calculations are truly deserving of the title.

An interesting thing to note is that multi-reference, spin-orbit and core-valence correlation corrections all appear to be very weak and sometimes do not improve the agreement with experiment (Table 3). CBS extrapolation is by far the major way to reduce error. This is very important to bear in mind when looking at previous benchmarking results. The authors also note that the usual ‘multireference’ diagnostics are practically useless: there is weak correlation between diagnostics and, more critically, there is very weak correlation between any of the diagnostics and the magnitude of any MR corrections. The M diagnostic[4] is the best performing one; however, it still fails for approximately 30% of cases and yields both false positives and false negatives. The authors also briefly investigate the effect of including 4f orbitals into the correlation treatment for Ir and Pt and find that this has a very weak effect on their results (SI, Table S5).

Finally, the authors use their new benchmark set to rank some functionals. Overall, at the DFT/aug-cc-pVQZ + DKH2 correction level, it appears that hybrid functionals performs on average the best for bond-dissociation energies and equilibrium distances, when compared to the fully corrected results (Table 7). On the other hand, pure functionals perform better for harmonic frequencies. In agreement with the conclusions of the original 3dMLBE20 paper, it is clear that many functionals beat plain CCSD(T)(FC)/aug-cc-pwCVTZ. This reinforces the critical need for CBS extrapolation when performing CC calculations.

(1) Xu, X.; Zhang, W.; Tang, M.; Truhlar, D. G. Do Practical Standard Coupled Cluster Calculations Agree Better than Kohn–Sham Calculations with Currently Available Functionals When Compared to the Best Available Experimental Data for Dissociation Energies of Bonds to 3 D Transition Metals? J. Chem. Theory Comput. 2015, 11 (5), 2036–2052 DOI: 10.1021/acs.jctc.5b00081.
(2) Cheng, L.; Gauss, J.; Ruscic, B.; Armentrout, P. B.; Stanton, J. F. Bond Dissociation Energies for Diatomic Molecules Containing 3d Transition Metals: Benchmark Scalar-Relativistic Coupled-Cluster Calculations for 20 Molecules. J. Chem. Theory Comput. 2017, 13 (3), 1044–1056 DOI: 10.1021/acs.jctc.6b00970.
(3) Fang, Z.; Vasiliu, M.; Peterson, K. A.; Dixon, D. A. Prediction of Bond Dissociation Energies/Heats of Formation for Diatomic Transition Metal Compounds: CCSD(T) Works. J. Chem. Theory Comput. 2017, 13 (3), 1057–1066 DOI: 10.1021/acs.jctc.6b00971.
(4) Tishchenko, O.; Zheng, J.; Truhlar, D. G. Multireference Model Chemistries for Thermochemical Kinetics. J. Chem. Theory Comput. 2008, 4 (8), 1208–1219 DOI: 10.1021/ct800077r.

Tuesday, October 24, 2017

An Atomistic Fingerprint Algorithm for Learning Ab Initio Molecular Force Fields

Yu-Hang Tang, Dongkun Zhang, and George Em Karniadakis, arXiv:1709.09235
Contributed by Jesper Madsen

Modeling potential energy landscapes of complex atomic environments is challenging. Conventional interatomic potentials are very useful because the potential energy surface is well approximated by some appropriate smooth function of nuclear coordinates. However, choosing the functional form too simple and closed comes with severe limitations because the true potential energy surface may not be (easily) decomposable. 

Instead of sticking with an explicit functional form, one can use continuous density-fields, formed by superimposition of a smoothing kernel on the atoms of the atomic configuration, in order to represent and compare atomistic neighborhoods. Herein, I highlight a recent example of such a method called Density-Encoded Canonically Aligned Fingerprint (DECAF). 

Figure 1: (A) “Two 1D density profiles, ρ1 and ρ2, are generated from two different atomistic configurations using atom-centered smoothing kernel functions. The ‘distance’ between them is measured as the L2 norm of their difference, which corresponds to the highlighted area in the middle plot.” (B) “Shown here is a 2D density field using smoothing kernels whose widths depend on the distances of the atoms from the origin. Darker shades indicate higher density.” 

The preprint by Tang et al. describes the DECAF algorithm (Fig. 1) and also briefly reviews and critically compares with the recent literature of similar methods [such as Smooth Overlap of Atomic Positions (SOAP), Coulomb Matrix, Graph Approximated Energy (GRAPE), and Atom-Centered Symmetry Functions].

The work rests on the key idea of splitting up conventional functional forms into two separate problems, one of representation and one of interpolation, which appears particularly powerful. Molecular fingerprint algorithms such as DECAF are promising in representing atomic neighborhoods faithfully using kernel regression methods. All the beneficial tools and analyses from modern statistics come into play, but there are still open questions that remain. For instance, it is not clear which smoothing kernel, distance metric (and so on) is superior in relating atomic configurations to one-another -- both in general and in specific situations. It is conceivable that there does not exist a best one-size-fits-all option. Furthermore, there will as always be tradeoffs between resolution and computational costs. For an introductory discussion on these topics, the preprint by Tang et al. (and the references within) is a good place to start.