Thursday, October 19, 2017

Analyzing Reaction Rates with the Distortion/Interaction-Activation Strain Model

Bickelhaupt, F. M.; Houk, K. N.,  Angew. Chem. Int. Ed. 2017, 56, 10070-10086
Contributed by Steven Bacharach
Reposted from Computational Organic Chemistry with permission

Bickelhaupt and Houk present a nice review of their separately developed, but conceptually identical model for assessing reactivity.1 Houk termed this the “distortion/interaction” model,2 while Bickelhaupt named it “activation strain”.3 The concept is that the activation barrier can be dissected in a distortion or stain energy associated with bringing the reactants into the geometry of the transition state, and the interaction energy is the stabilization energy afforded by the molecular orbital interactions of the reactant components with each other in the transition state.

The review discusses a broad range of applications, including SN2 and Ereactions, pericyclic reactions (including Diels-Alder reactions of enones and the dehdydro Diels-Alder reaction that I have discussed in this blog), a click reaction, a few examples involving catalysis, and the regioselectivity of indolyne (see this post). They also discuss the role of solvent and the relationship of this model to Marcus Theory.

I also want to mention in passing a somewhat related article by Jorgensen and co-authors published in the same issue of Angewandte Chemie as the above review.4 This article discusses the paucity of 10 electron cycloaddition reactions, especially in comparison to the large number of very important cycloaddition reactions involving 6 electrons, such as the Diels-Alder reaction, the Cope rearrangement, and the Claisen rearrangement. While the article does not focus on computational methods, computations have been widely used to discuss 10-electron cycloadditions. The real tie between this paper and the review discussed above is Ken Houk, whose graduate career started with an attempt to perform a [6+4] cycloaddition, and he has revisited the topic multiple times throughout his career.


1. Bickelhaupt, F. M.; Houk, K. N., "Analyzing Reaction Rates with the Distortion/Interaction-Activation Strain Model." Angew. Chem. Int. Ed. 201756, 10070-10086, DOI: 10.1002/anie.201701486.
2. Ess, D. H.; Houk, K. N., "Distortion/Interaction Energy Control of 1,3-Dipolar Cycloaddition Reactivity." J. Am. Chem. Soc. 2007, 129, 10646-10647, DOI: 10.1021/ja0734086
3. Bickelhaupt, F. M., "Understanding reactivity with Kohn-Sham molecular orbital theory: E2-SN2 mechanistic spectrum and other concepts." J. Comput. Chem. 1999, 20, 114-128
4. Palazzo, T. A.; Mose, R.; Jørgensen, K. A., "Cycloaddition Reactions: Why Is It So
Challenging To Move from Six to Ten Electrons?" Angew. Chem. Int. Ed. 2017, 56, 10033-10038, DOI: 10.1002/anie.201701085.

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

Monday, October 9, 2017

Benzophenone Ultrafast Triplet Population: Revisiting the Kinetic Model by Surface-Hopping Dynamics

Marco Marazzi, Sebastian Mai, Daniel Roca-Sanjuán, Mickaël G. Delcey, Roland Lindh, Leticia González, and Antonio Monari (2016)
Highlighted by Ravi Kumar Venkatraman

In 1967, Norrish and Porter were honoured with Nobel prize for their seminal work on understanding the fast chemical reactions using flash photolysis technique.1 Since then benzophenone (Bzp) serves as an archetypal system for understanding the photochemistry of various aromatic ketones. Aromatic ketones find their use in various technologically significant applications like sunscreen, photocatalysis, etc., apart from their fundamental interest.2 Efficacy of aromatic ketones for use in various applications relies upon their photophysics and photochemistry. Therefore, understanding the photophysics and photochemistry of Bzp has attracted several experimental and theoretical investigations.2 Despite these myriads of investigations, pathways for populating the lowest triplet state (T1) after photoexcitation to the S1 state remains still elusive. There are two plausible pathways: i) a direct ISC from S1(nπ*) to T1(nπ*); or ii) an indirect process, involving ISC from S1(nπ*) to T1(ππ*) with subsequent internal conversion (IC) to T1(nπ*). The latter pathway is more efficient, according to El-Sayed’s rule, because it entails a change in the orbital character during the spin-orbit coupling mediated process.3

Reproduced with permission from Marco Marazzi, Sebastian Mai, et. al., J. Phys. Chem. Lett., 7, 622 (2016) under Creative Commons Attribution (CC-BY) License

In this work, authors have employed ab initio surface-hopping dynamics simulation for Bzp in gas phase to explore the pathways for the lowest triplet state (T1) population after photo-excitation to the S1 state. This study clearly demonstrates that the dominant mechanism for populating the T1 state is the indirect pathway invoking T2 state as an intermediate. This study urges reinvestigation of spectroscopic assignment for Bzp in various time-resolved spectroscopic techniques. Furthermore, the mechanism for the photoinduced energy transfer in photocatalysis and DNA damage studies must be revisited as in principle now both channels involving T2 and T1 states are available.

1.) F. Ariese, K. Roy, V. R. Kumar, H. C. Sudeeksha, S. Kayal, S. Umapathy, Time-Resolved Spectroscopy: Instrumentation and Applications in Encyclopedia of Analytical Chemistry, edited by R. A. Meyers, 1-55, (2017) John Wiley & Sons, Ltd.
2.) M. C. Cuquerella, V. L-Vallet, J. Cadet, and M. A. Miranda, Benzophenone Photosensitized DNA Damage, Acc. Chem. Res., 45, 1558 (2012).
3.) Elsayed, M. A., Spin-Orbit Coupling and Radiationless Processes in Nitrogen Heterocyclics. J. Chem. Phys., 38, 2834 (1963).

Friday, October 6, 2017

More applications of computed NMR spectra

Grimblat, N.; Kaufman, T. S.; Sarotti, A. M., "Computational Chemistry Driven Solution to Rubriflordilactone B." Org. Letters 2016, 18, 6420-6423
Reddy, D. S.; Kutateladze, A. G., "Structure Revision of an Acorane Sesquiterpene Cordycepol A." Org. Letters 2016, 18, 4860-4863
Contributed by Steven Bacharach
Reposted from Computational Organic Chemistry with permission

In this post I cover two papers discussing application of computed NMR chemical shifts to structure identification and (yet) another review of computational techniques towards NMR structure prediction.
Grimblat, Kaufman, and Sarotti1 take up the structure of rubriflordilactone B 1, which was isolated from Schisandra rubriflora. The compound was then synthesized and its x-ray structure reported, however its NMR did not match with the natural extract. It was suggested that there were actually two compounds in the extract, the minor one was less soluble and is the crystallized 1, and a second compound responsible for the NMR signal.
The authors looked at all stereoisomers of this molecule keeping the three left-most rings intact. The low energy rotamers of these 32 stereoisomers were then optimized at B3LYP/6-31G* and the chemical shifts computed at PCM(pyridine)/mPW1PW91/6-31+G**. To benchmark the method, DP4+ was used to identify which stereoisomer best matches with the observed NMR of authentic 1; the top fit (92.6% probability) was the correct structure.

The 32 stereoisomers were then tested against the experimental NMR of the natural extract. DP4+ with just the proton shifts suggested structure 2 (99.8% probability); however, the 13C chemical shifts predicted a different structure. Re-examination of the reported chemical shifts identifies some mis-assigned signals, which led to a higher C-DP4+ prediction. When all 128 stereoisomers were tested, structure 2 had the highest DP4+ prediction (99.5%), but the C-DP4+ prediction remained problematic (10.8%). Analyzing the geometries of all reasonable alternative for agreement with the NOESY spectrum confirmed 2. These results underscore the importance of using all data sources.
Reddy and Kutateladze point out the importance of using coupling constants along with chemical shifts in structure identification.2 They examined cordycepol A 3, obtained from Cordyceps ophioglossoides. They noted that the computed chemical shifts and coupling constants of originally proposed structure 3adiffered dramatically from the experimental values.

They first proposed that the compound has structure 3b. The computed coupling constants using their relativistic force field.3 The experimental coupling constants for the proton H1 are 13.4 and 7.1 Hz. The computed values for 3a are 8.9 and 1.6 Hz, and this structure is clearly incorrect. The coupling constants are improved with 3b, but the 13C chemical shifts are in poor agreement with experiment. So, they proposed structure 3c, the epimer at both C1 and C11 of the original structure.

They optimized four conformations of 3c at B3LYP/6-31G(d) and obtained Boltzmann-weighted chemical shifts at mPW1PW91/6-311+G(d,p). The RMS deviation of the computed 13C chemical shifts relative to the experiment is only 1.54 ppm, and more importantly, the computed coupling constants of 13.54 and 6.90 Hz are in excellent agreement with the experiment values.

Lastly, Grimblat and Sarotti present a review of a number of methods for using computed NMR chemical shifts towards structure prediction.4 These methods include CP3DP4DP4+ (all of which I have posted on in the past) and an artificial neural network approach of their own design. They discuss a number of interesting cases where each of these methods has been crucial in identifying the correct chemical structure.


1. Grimblat, N.; Kaufman, T. S.; Sarotti, A. M., "Computational Chemistry Driven Solution to Rubriflordilactone B." Org. Letters 201618, 6420-6423, DOI: 10.1021/acs.orglett.6b03318.
2. Reddy, D. S.; Kutateladze, A. G., "Structure Revision of an Acorane Sesquiterpene Cordycepol A." Org. Letters 201618, 4860-4863, DOI: 10.1021/acs.orglett.6b02341.
3. (a) Kutateladze, A. G.; Mukhina, O. A., "Minimalist Relativistic Force Field: Prediction of Proton–Proton Coupling Constants in 1H NMR Spectra Is Perfected with NBO Hybridization Parameters." J. Org. Chem.201580, 5218-5225, DOI: 10.1021/acs.joc.5b00619; (b) Kutateladze, A. G.; Mukhina, O. A., "Relativistic Force Field: Parametrization of 13C–1H Nuclear Spin–Spin Coupling Constants." J. Org. Chem. 201580, 10838-10848, DOI: 10.1021/acs.joc.5b02001.
4. Grimblat, N.; Sarotti, A. M., "Computational Chemistry to the Rescue: Modern Toolboxes for the Assignment of Complex Molecules by GIAO NMR Calculations." Chem. Eur. J. 201622, 12246-12261, DOI: h10.1002/chem.201601150.


1: InChI=1S/C28H30O6/c1-13-9-20(32-26(13)30)25-14(2)24-17-6-5-15-12-28-21(8-7-16(15)18(17)10-19(24)31-25)27(3,4)33-22(28)11-23(29)34-28/h5-9,14,19-22,24-25H,10-12H2,1-4H3/t14-,19+,20-,21-,22+,24-,25-,28+/m0/s1
2: InChI=1S/C28H30O6/c1-13-9-20(32-26(13)30)25-14(2)24-17-6-5-15-12-28-21(8-7-16(15)18(17)10-19(24)31-25)27(3,4)33-22(28)11-23(29)34-28/h5-9,14,19-22,24-25H,10-12H2,1-4H3/t14-,19-,20-,21-,22+,24+,25-,28+/m0/s1
3c: InChI=1S/C16H28O2/c1-6-11(2)9-14-16(5)12(3)7-8-13(16)15(4,17)10-18-14/h9,12-14,17H,6-8,10H2,1-5H3/b11-9-/t12-,13-,14-,15-,16+/m0/s1

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Saturday, September 30, 2017

Efficient DLPNO−CCSD(T)-Based Estimation of Formation Enthalpies for C‐, H‐, O‐, and N‐Containing Closed-Shell Compounds Validated Against Critically Evaluated Experimental Data

Copyright 2017 American Chemical Society

A computationally methodology is truly robust when it can be used independently and successfully by other groups.  So Frank Neese was understandably delighted when he saw this paper using his DLPNO-CCSD(T) method, as he mentioned during his talk at WATOC2017.

The paper shows tha that DLPNO-CCSD(T)/quadruple zeta//DFT-D3/triple zeta can be used to predict enthalpies of formation as accurate as you can measure them!  It is actually more accurate than G4, but considerably more computationally efficient. 

DLPNO-CCSD(T) cannot handle open shell systems so the energy of H, C, N, and O are replaced by empirical parameters.  This means that enthalpies of formation for molecules containing other elements cannot be computed without similar parametrisation, but usually atom energies/enthalpies of formation are used "only" to validate the method and are not needed to compute reaction energies.

The largest molecule considered is biphenyl and it is not clear to me that B3LYP-D3 is he optimum choice for more complex molecules requiring a conformer search. But, on the other hand, I also doubt the accuracy is very sensitive to the choice of functional for the small molecules used in the study.  It's easy enough to find out: the most time-consuming calculation (biphenyl) required only 10 hours using 10 CPUs. 

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Tuesday, September 19, 2017

The Parameter Uncertainty Inflation Fallacy

Pascal Pernot (2017)
Highlighted by Jonny Proppe

In a recent study on uncertainty quantification, Pernot(1) discussed the effect of model inadequacy on predictions of physical properties. Model inadequacy is a ubiquituous feature of physical models due to various approximations employed in their construction. Along with data inconsistency (e.g., due to incorrect quantification of measurement uncertainty) and parameter uncertainty, model inadequacy only acquires meaning by comparison against reference data. For instance, a model is inadequate if it cannot reproduce reference data within their uncertainty range (cf. Figure 1), given all other sources of error are negligible. While parameter uncertainty is inversely proportional to the size of the reference set, systematic errors based on data inconsistency and model inadequacy remain without explicit identification and elimination.

Figure 1. Illustration of model inadequacy. (a) Reference versus calculated (CCD/6-31G*) harmonic vibrational frequencies reveal a linear trend in the data (red line), which is not the unit line. In this diagram, the uncertainty of the reference data is too small to be visible. (b) Residuals of temperature-dependent viscosity predictions based on a Chapman–Enskog model reveal an oscillating trend, even if the 2 confidence intervals of the reference data are considered. Reproduced from J. Chem. Phys. 147, 104102 (2017), with the permission of AIP Publishing.

In related work, Pernot and Cailliez(2) demonstrated the benefits and drawbacks of several Bayesian calibration algorithms (e.g., Gaussian process regression, hierarchical optimization) in tackling these issues. These algorithms approach model inadequacy either through a posteriori model corrections or by parameter uncertainty inflation (PUI). While a posteriori corrected models cannot be transferred to observables not included in the reference set, PUI ensures that the corresponding covariance matrices are transferable to any model comprising the same parameters. However, the resulting predictions may not reflect the correct dependence on the input variable(s), which is determined by the sensitivity coefficients of the model (the partial derivatives of a model prediction at a certain point in input space with respect to the model parameters at their expected values). Pernot referred to this issue as the “PUI fallacy”1 and illustrated it at three examples: (i) linear scaling of harmonic vibrational frequencies, (ii) calibration of the mBEEF density functional against heats of formation, and (iii) inference of Lennard–Jones parameters for predicting temperature-dependent viscosities based on a Chapman–Enskog model (cf. Figure 2). In these cases, PUI resulted in correct average prediction uncertainties, but uncertainties of individual predictions were systematically under- or overestimated.

Figure 2. Illustration of the PUI fallacy for different algorithms (VarInf_Rb, Margin, ABC) at the example of temperature-dependent viscosity predictions based on a Chapman–Enskog model. In all cases, the centered prediction bands (gray) cannot reproduce the oscillating trend in the residuals. Reproduced from J. Chem. Phys. 147, 104102 (2017), with the permission of AIP Publishing

Pernot’s paper presents a state-of-the-art study for rigorous uncertainty quantification of model predictions in the physical sciences, which only recently started to gain momentum in the computational chemistry community. His study can be seen as an incentive for future benchmark studies to rigorously assess existing and novel models. Noteworthy, Pernot has made available the entire code employed in his study ( 

(1) Pernot, P. The Parameter Uncertainty Inflation Fallacy. J. Chem. Phys. 2017, 147 (10), 104102.
(2) Pernot, P.; Cailliez, F. A Critical Review of Statistical Calibration/Prediction Models Handling Data Inconsistency and Model Inadequacy. AIChE J. 2017, 63 (10), 4642–4665.

Friday, September 15, 2017

Spectroscopic Observation of the Triplet Diradical State of a Cyclobutadiene

Kostenko, A.; Tumanskii, B.; Kobayashi, Y.; Nakamoto, M.; Sekiguchi, A.; Apeloig, Y., Angew. Chem. Int. Ed. 2017, 56, 10183-10187
Contributed by Steven Bacharach
Reposted from Computational Organic Chemistry with permission

Cyclobutadiene has long fascinated organic chemists. It is the 4e analogue of the 6e benzene molecule, yet it could hardly be more different. Despite nearly a century of effort, cyclobutadiene analogues were only first prepared in the 1970s, reflecting its strong antiaromatic character.

Per-trimethylsilylcyclobutadiene 1 offers opportunities to probe the properties of the cyclobutadiene ring as the bulky substituents diminish dimerization and polymerization of the reactive π-bonds. Kostenko and coworkers have now reported on the triplet state of 1.1 They observe three EPR signals of 1 at temperatures above 350 K, and these signals increase in area with increasing temperature. This is strong evidence for the existence of triplet 1 in equilibrium with the lower energy singlet. Using the variable temperature EPR spectra, the singlet triplet gap is 13.9 ± 0.8 kcal mol-1.

The structures of singlet and triplet 1 were optimized at B3LYP-D3/6-311+G(d,p) and shown in Figure 1. The singlet is the expected rectangle, with distinctly different C-C distance around the ring. The triplet is a square, with equivalent C-C distances. Since both the singlet and triplet states are likely to have multireference character, the energies of both states were obtained at RI-MRDDCI2-CASSCF(4,4)/def2-SVP//B3LYPD3/6-311+G(d,p) and give a singlet-triplet gap of 11.8 kcal mol-1, in quite reasonable agreement with experiment.


Figure 1. Optimized geometries of singlet and triplet 1.


1. Kostenko, A.; Tumanskii, B.; Kobayashi, Y.; Nakamoto, M.; Sekiguchi, A.; Apeloig, Y., "Spectroscopic Observation of the Triplet Diradical State of a Cyclobutadiene." Angew. Chem. Int. Ed. 201756, 10183-10187, DOI: 10.1002/anie.201705228.


1: InChI=1S/C16H36Si4/c1-17(2,3)13-14(18(4,5)6)16(20(10,11)12)15(13)19(7,8)9/h1-12H3

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Wednesday, August 30, 2017

How Large is the Elephant in the Density Functional Theory Room?

Frank Jensen (2017)
Highlighted by Jan Jensen

Having highlighted this paper it is only right that I highlight Frank Jensen's response. To recap, the previous study used wavelets to compute benchmark energies for PBE and PBE0 functionals and showed that even aug-cc-pV5Z failed to reach chemical accuracy for some atomization energies.

In this paper Jensen shows that this problem goes away when one uses basis sets specifically designed for DFT calculations. At the pentuple-zeta level the maximum errors are reduced by factors of 5 and 10 for segmented contracted and uncontracted basis sets, respectively and the MAE for atomization energies are well below 1 kcal/mol.

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Tuesday, August 22, 2017

Is the Accuracy of Density Functional Theory for Atomization Energies and Densities in Bonding Regions Correlated?

Brorsen, K. R.; Yang, Y.; Pak, M. V.; Hammes-Schiffer, S., J. Phys. Chem. Lett. 2017, 8, 2076-2081
Contributed by Steven Bacharach
Reposted from Computational Organic Chemistry with permission

I recently blogged about a paper arguing that modern density functional development has strayed from the path of improving density description, in favor of improved energetics. The Medvedev paper1 was met with a number of criticisms. A potential “out” from the conclusions of the work was that perhaps molecular densities do not fare so poorly with more modern functionals, following the argument that better energies might reflect better densities in bonding regions.

The Hammes-Schiffer group have now examined 14 diatomic molecules with the goal of testing just this hypothesis.2 They subjected both homonuclear diatomics, like N2, Cl2, and Li2, and heteronuclear diatomics, like HF, LiF, and SC, to 90 different density functionals using the very large aug-cc-pCVQZ basis set. Using the CCSD density as a reference, they examined the differences in the densities predicted by the various functional both along the internuclear axis and perpendicular to it.

The 20 functionals that do the best job in mimicking the CCSD density are all hybrid GGA functionals, along with the sole double hybrid functional included in the study (B2PLYP). These functionals date from 1993 to 2012. The 20 functionals that do the poorest job include functionals from all rung-types, and date from 1980-2012. A very slight upward trend can be observed in the density error increasing with development year, while the error in the dissociation energy clearly is decreasing over time.

They note that six functionals of the Minnesota-type, those that are highly parameterized and of recent vintage, perform very poorly at predicting atomic densities, but do well with the diatomic densities.

Hammes-Schiffer concludes that their diatomic results support the general trend noted by Medvedev’s atomic results, that density description is lagging in more recently developed functionals. I’d add that this trend is not as dramatic for the diatomics as for atoms.
They pose what is really the key question: “Is the purpose to approximate the exact functional or simply to provide chemists with a useful tool for exploring chemical systems?” Since, as they note, the modern highly parameterized functionals have worked so well for predicting energies and geometries, “the observation that many modern functionals produce incorrect densities could be of no great consequence for many studies”. Nonetheless, “the ultimate goal is still to obtain both accurate densities and accurate energies”.


1) Medvedev, M. G.; Bushmarinov, I. S.; Sun, J.; Perdew, J. P.; Lyssenko, K. A., "Density functional theory is straying from the path toward the exact functional." Science 2017, 355, 49-52, DOI: 10.1126/science.aah5975.
2) Brorsen, K. R.; Yang, Y.; Pak, M. V.; Hammes-Schiffer, S., "Is the Accuracy of Density Functional Theory for Atomization Energies and Densities in Bonding Regions Correlated?" J. Phys. Chem. Lett. 2017, 8, 2076-2081, DOI: 10.1021/acs.jpclett.7b00774.

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Tuesday, August 8, 2017

Mechanisms and Origins of Periselectivity of the Ambimodal [6 + 4] Cycloadditions of Tropone to Dimethylfulvene

Yu, P.; Chen, T. Q.; Yang, Z.; He, C. Q.; Patel, A.; Lam, Y.-h.; Liu, C.-Y.; Houk, K. N., J. Am. Chem. Soc. 2017, 139 (24), 8251-8258
Contributed by Steven Bacharach
Reposted from Computational Organic Chemistry with permission

Bispericyclic transition states arise when two pericyclic reactions merge to a common transition state. This leads to a potential energy surface with a bifurcation such that reactions that traverse this type of transition state will head towards two different products. The classic example is the dimerization of cyclopentadiene, involving two [4+2] Diels-Alder reactions. Unusual PESs are discussed in my book and in past blog posts.

Houk and coworkers have now identified a bispericyclic transition state involving two [6+4] cycloadditions.1 Reaching back to work Houk pursued as a graduate student with Woodward for inspiration, these authors examined the reaction of tropone 1 with dimethylfulvene 2. Each moiety can act as the diene or triene component of a [6+4] allowed cycloaddition:

The product with fulvene 2 as the 6 π-e component and tropone as the 4 π-e component [6F+4T] is 3, while reversing their participation in the [6T+4F] cycloaddition leads to 4. A variety of [4+2] reactions are also possible. All of these reactions were investigated at PCM/M06-2X/6-311+G(d,p)//B3LYP-D3/6-31G(d). The reaction leading to 3 is exothermic by 3.0 kcal mol-1, while the reaction to 4 endothermic by 1.3 kcal mol-1.

Interestingly, there is only one transition state that leads to both 3 and 4, the first known bispericyclic transition state for two conjoined [6+4] cycloadditions. The barrier is 27.9 kcal mol-1. The structures of the two products and the transition state leading to them are shown in Figure 1. 3 and 4 can interconvert through a Cope transition state, also shown in Figure 1, with a barrier of 26.3 kcal mol-1 (for 4 → 3).



TS [6+4]

TS Cope
Figure 1. B3LYP-D3/6-31G(d) optimized geometries.

Given that a single transition leads to two products, the product distribution is dependent on the molecular dynamics. A molecular dynamics simulation at B3LYP-D3/6-31G(d) with 117 trajectories indicates that 4 is formed 91% while 3 is formed only 9%. Once again, we are faced with the reality of much more complex reaction mechanisms/processes than simple models would suggest.


1) Yu, P.; Chen, T. Q.; Yang, Z.; He, C. Q.; Patel, A.; Lam, Y.-h.; Liu, C.-Y.; Houk, K. N., "Mechanisms and Origins of Periselectivity of the Ambimodal [6 + 4] Cycloadditions of Tropone to Dimethylfulvene." J. Am. Chem. Soc. 2017, 139 (24), 8251-8258, DOI: 10.1021/jacs.7b02966.


1: InChI=1S/C7H6O/c8-7-5-3-1-2-4-6-7/h1-6H
2: InChI=1S/C8H10/c1-7(2)8-5-3-4-6-8/h3-6H,1-2H3
4: InChI=1S/C15H16O/c1-9(2)14-10-7-8-11(14)13-6-4-3-5-12(10)15(13)16/h3-8,10-13H,1-2H3

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Monday, July 31, 2017

A Robust and Accurate Tight-Binding Quantum Chemical Method for Structures, Vibrational Frequencies, and Noncovalent Interactions of Large Molecular Systems Parametrized for All spd-Block Elements (Z = 1−86)

Stefan Grimme, Christoph Bannwarth, and Philip Shushkov (2017)
Highlighted by Jan Jensen

Copyright American Chemical Society (2017)

Inspired by the success of the sTDA-xTB method for predicting electronic spectra, Grimme and co-workers present the tight binding DFT method GFN-xTB for predicting Geometries, vibrational Frequencies and Noncovalent interactions ("x" stands for extensions in the AO basis set and the form of the Hamiltonian).  

The method is implemented in a new program called xtb which includes shared memory parallelization, angeometry optimizer, MD, conformational searches, reaction path optimisation modules, and a GB solvation model supplemented with analytical nuclear gradients.  The software is free to academics and can be obtained by writing to the authors.

Importantly, the method is parameterized for all spd elements, so finally there is an alternative to PM6 for heavier elements. A Fermi smearing technique helps convergence for molecules with small HOMO-LUMO gaps and GFN-xTB gives structures organometallic compounds that are in good agreement with DFT.

As implied by the name, GFN-xTB is not parameterized against reaction energies but the methods gives reasonable results for properties like heats of formation.  However, as the authors write

A key premise of the present method is its special purpose character. In our view, low-cost semiempirical QM methods cannot describe simultaneously very different chemical proper- ties, such as structures and chemical reaction energies, and the GFN-xTB method (as the name conveys) focuses on structural properties. The efficiently computed structures and vibrational frequencies or the conformers obtained from global search procedures can (and should) be used subsequently for more accurate DFT or WFT refinements. We hope that the method can serve as a general tool in quantum chemistry and in particular recommend GFN-xTB optimized structures (and thermostatistical corrections) in a multilevel scheme together with PBEh-3c single-point energies. Large-scale molecular dynamics, screening of huge molecular spaces (libraries), parametrization of force-fields, or providing input for novel machine learning techniques are obvious other fields of application.
I thank Anders Christensen for bringing this paper to my attention

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Thursday, July 27, 2017

A few review articles

Contributed by Steven Bacharach
Reposted from Computational Organic Chemistry with permission

A few nice review/opinion pieces have been piling up in my folder of papers of interest for this Blog. So, this post provides a short summary of a number of review articles that computationally-oriented chemists may find of interest.

Holy Grails in computational chemistry

Houk and Liu present a short list of “Holy Grails” in computationally chemistry.1 They begin by pointing out a few technical innovations that must occur for the Grails to be found: development of a universal density functional; an accurate, generic force field; improved sampling for MD; and dealing with the combinatorial explosion with regards to conformations and configurations. Their list of Grails includes predicting crystal structures and structure of amorphous materials, catalyst design, reaction design, and device design. These Grails overlap with the challenges I laid out in my similarly-themed article in 2014.2

Post-transition state bifurcations and dynamics

Hare and Tantillo review the current understanding of post-transition state bifurcations (PTSB).3 This type of potential energy surface has been the subject of much of Chapter 8 of my book and many of my blog posts. What is becoming clear is the possibility of a transition state followed by a valley-ridge inflection leads to reaction dynamics where trajectories cross a single transition state but lead to two different products. This new review updates the state-of-the-art from Houk’s review4 of 2008 (see this post). Mentioned are a number of studies that I have included in this Blog, along with reactions involving metals, and biochemical systems (many of these examples come from the Tantillo lab). They close with the hope that their review might “inspire future studies aimed at controlling selectivity for reactions with PTSBs” (italics theirs). I might offer that controlling selectivity in these types of dynamical systems is another chemical Grail!
The Hase group has a long review of direct dynamics simulations.5 They describe a number of important dynamics studies that provide important new insight to reaction mechanism, such as bimolecular SN2 reactions (including the roundabout mechanism) and unimolecular dissociation. They write a long section on post-transition state bifurcations, and other dynamic effects that cannot be interpreted using transition state theory or RRKM. This section is a nice complement to the Tantillo review.

Benchmarking quantum chemical methods

Mata and Suhm look at our process of benchmarking computational methods.6 They point out the growing use of high-level quantum computations as the reference for benchmarking new methods, often with no mention of any comparison to experiment. In defense of theoreticians, they do note the paucity of useful experimental data that may exist for making suitable comparisons. They detail a long list of better practices that both experimentalists and theoreticians can take to bolster both efforts, leading to stronger computational tools that are more robust at helping to understand and discriminate difficult experimental findings.


1) Houk, K. N.; Liu, F., "Holy Grails for Computational Organic Chemistry and Biochemistry." Acc. Chem. Res. 2017, 50 (3), 539-543, DOI: 10.1021/acs.accounts.6b00532.
2) Bachrach, S. M., "Challenges in computational organic chemistry." WIRES: Comput. Mol. Sci. 2014, 4, 482-487, DOI: 10.1002/wcms.1185.
3) Hare, S. R.; Tantillo, D. J., "Post-transition state bifurcations gain momentum – current state of the field." Pure Appl. Chem. 2017, 89, 679-698, DOI: 0.1515/pac-2017-0104.
4) Ess, D. H.; Wheeler, S. E.; Iafe, R. G.; Xu, L.; Çelebi-Ölçüm, N.; Houk, K. N., "Bifurcations on Potential Energy Surfaces of Organic Reactions." Angew. Chem. Int. Ed. 2008, 47, 7592-7601, DOI: 10.1002/anie.200800918
5) Pratihar, S.; Ma, X.; Homayoon, Z.; Barnes, G. L.; Hase, W. L., "Direct Chemical Dynamics Simulations." J. Am. Chem. Soc. 2017, 139, 3570-3590, DOI: 10.1021/jacs.6b12017.
6) Mata, R. A.; Suhm, M. A., "Benchmarking Quantum Chemical Methods: Are We Heading in the Right Direction?" Angew. Chem. Int. Ed. 2017, ASAP, DOI: 10.1002/anie.201611308.

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Wednesday, July 26, 2017

Intrinsic map dynamics exploration for uncharted effective free-energy landscapes

Eliodoro Chiavazzo, Roberto Covino, Ronald R. Coifman, C. William Geard, Anastasia S. Georgiou, Gerhard Hummer, and Ioannis G. Kevrekidis. PNAS June 20, 2017
Contributed by Jesper Madsen

The desire to use enhancing sampling to save computational expense in simulations has been there from the beginning. Broadly speaking, there are two main approaches of enhancing molecular dynamics (MD) simulations in order to determine the free-energy surface (FES) of a computationally expensive Hamiltonian: 1) Trajectory-based enhanced sampling (e.g. temperature replica-exchange) and 2) collective variable (CV)-based methods (e.g. umbrella sampling). It is worth noting that the “zoo” of actual techniques to date is rather large. Either type of method, trajectory-based or CV-based, comes with its own set of advantages and disadvantages and mixing-and-matching is popular. 

Here I highlight a newcomer that is spun off from the rapidly growing field of Machine Learning – a field that most of us is keeping a keen eye on these days. 

The algorithm is called intrinsic map dynamics (iMapD) and it is conceptually simple (See Fig. 1 from the paper). 
1. Run a MD trajectory
2. Figure out, in some abstract sense, what region of configuration space you have sampled.
3. Determine the (non-linear) boundary of the sampled region in the abstract space
4. Initialize new MD trajectories in these boundary areas and explore the uncharted territories of the FES.

It is with the concretization of each step above that machine learning has contributed its ideas and tools. Specifically, the map of the configuration space is data mined and a d-dimensional manifold learning technique called diffusion maps (DMAPs) is applied to find the appropriate manifold and its dimensionality. The (d-1)-dimensional boundary manifold of the explored region is determined by a “wrapping” algorithm (here they use alpha shapes). Outward extrapolation is done by performing local principal component (LPC) analysis in ambient space. New simulations are seeded from these extended initial configurations and the algorithm loops back to the beginning. 

Fig.1: Pictorial illustration of the iMapD exploration procedure with (Left) 1D and (Right) 2D effective FESs. In Left Inset, a good collective coordinate is already available—the collective coordinates in Left and Right are not a priori known. "Copyright (2017) National Academy of Sciences

Since iMapD is a trajectory-based approach, absolutely no prior knowledge about the mechanistics of the process we study is required, which is appealing. One can think of the method as a clever hybrid MD/Monte Carlo algorithm and time will show how it stacks up against other alternative approaches in terms of practical usefulness. 

WInote that the algorithm is pedagogically presented in the paper and if you fancy Indiana Jones, well then there’s a little treat for you in the main text. Enjoy.

Wednesday, July 19, 2017

The Structure of the Elusive Simplest Dipeptide Gly-Gly

Cabezas, C.; Varela, M.; Alonso, J. L., Angew. Chem. Int. Ed. 2017, 56, 6420-6425
Contributed by Steven Bacharach
Reposted from Computational Organic Chemistry with permission

Continuing their application of laser ablation molecular beam Fourier transform microwave (LA-MB-FTMW) spectroscopy and computational chemistry to biochemical molecules (see these previous posts), the Alonso group reports on the structure of the glycine-glycine dipeptide 1.1 The microwave spectrum shows three different conformers. MP2/6-311++G(d,p) computations, the same method they have previously utilized for predicting geometries, revealed a number of different conformations. By matching the spectroscopic parameters obtained from the spectrum with those of the computed structures, they proposed the three conformations 1a1b, and 1c, shown in Figure 1.



Figure 1. ωb97xd/6-31G(d) optimized structures of the three conformers of 1.
Note that the authors did not report their structures in their supporting materials(!) so I have optimized them.

The structures of conformers 1a and 1b are nearly planar. MP2 predicts a non-planar rotomer of 1a, which brings the carboxyl group out of plane, to be the lowest conformation in terms of electronic energy. With the M06-2x functional, this non-planar rotomer is about isoenergetic with 1a. With all computational levels 1a is the lowest in free energy. The barrier for rotation between the non-planar rotomer and 1a is very small, and this explains why it is not observed in the supersonic expansion.


1) Cabezas, C.; Varela, M.; Alonso, J. L., "The Structure of the Elusive Simplest Dipeptide Gly-Gly." Angew. Chem. Int. Ed. 2017, 56, 6420-6425, DOI: 10.1002/anie.201702425.


1: InChI=1S/C4H8N2O3/c5-1-3(7)6-2-4(8)9/h1-2,5H2,(H,6,7)(H,8,9)

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Tuesday, July 18, 2017

Development of a 13C NMR Chemical Shift Prediction Procedure Using B3LYP/cc-pVDZ and Empirically Derived Systematic Error Correction Terms: A Computational Small Molecule Structure Elucidation Method

Xin, D.; Sader, C. A.; Chaudhary, O.; Jones, P.-J.; Wagner, K.; Tautermann, C. S.; Yang, Z.; Busacca, C. A.; Saraceno, R. A.; Fandrick, K. R.; Gonnella, N. C.; Horspool, K.; Hansen, G.; Senanayake, C. H., J. Org. Chem. 2017, ASAP
Contributed by Steven Bacharach
Reposted from Computational Organic Chemistry with permission

Here’s another take on automating a procedure for using computer 13C chemical shifts to assess chemical structure.1 (Have a look at these previous posts for some alternative methods and applications.) The approach here is to benchmark a few computational methods against a conformationally flexible drug-like molecule, in this case 1. A variety of conformations were optimized using the different computational methods, and 13C chemical shifts evaluated from a Boltzmann-weighted distribution. While the best agreement with the experimental chemical shifts (based on the root-mean-squared deviation) is with ωB97XD/cc-pVDZ, the authors opt for B3LYP/cc-pVDZ for its computational efficiency with only slightly poorer performance. (It should be note that WC04/cc-pVDZ, a functional designed for computing 13chemical shifts,2 is almost as good as ωB97XD/cc-pVDZ. Also, not mentioned in the article is the dramatically poorer performance of the pcS-2 basis set, despite the fact that it was parametrized3 for NMR computation!)
They apply the procedure to a number of test cases. For example, the HIV-1 reverse transcriptase inhibitor nevirapine hydrolyzes to a compound whose structure has been difficult to identify. The four proposed structures 2a-d were subjected to the computational method, and the 13C chemical shift RMSD for 2d is only 2.3ppm, significantly smaller than for the other 3 structures. Compound 2d was then synthesized and its NMR matches that of the nevirapine hydrolysis product.


1) Xin, D.; Sader, C. A.; Chaudhary, O.; Jones, P.-J.; Wagner, K.; Tautermann, C. S.; Yang, Z.; Busacca, C. A.; Saraceno, R. A.; Fandrick, K. R.; Gonnella, N. C.; Horspool, K.; Hansen, G.; Senanayake, C. H., "Development of a 13C NMR Chemical Shift Prediction Procedure Using B3LYP/cc-pVDZ and Empirically Derived Systematic Error Correction Terms: A Computational Small Molecule Structure Elucidation Method." J. Org. Chem. 2017, ASAP, DOI: 10.1021/acs.joc.7b00321.
2) Wiitala, K. W.; Hoye, T. R.; Cramer, C. J., “Hybrid Density Functional Methods Empirically Optimized for the Computation of 13C and 1H Chemical Shifts in Chloroform Solution,” J. Chem. Theory Comput. 20062, 1085-1092, DOI: 10.1021/ct6001016.
3) Jensen, F., “Basis Set Convergence of Nuclear Magnetic Shielding Constants Calculated by Density Functional Methods,” J. Chem. Theory Comput.20084, 719-727, DOI: 10.1021/ct800013z.


1: InChI=1S/C24H26F4N2O4S/c1-4-35(33,34)18-7-8-20-15(10-18)9-17(30-20)13-23(32,24(26,27)28)22(2,3)12-14-5-6-16(25)11-19(14)21(29)31/h5-11,30,32H,4,12-13H2,1-3H3,(H2,29,31)/t23-/m0/s1
2d: InChI=1S/C15H16N4O2/c1-9-6-8-17-14(18-10-4-5-10)12(9)19-13-11(15(20)21)3-2-7-16-13/h2-3,6-8,10H,4-5H2,1H3,(H,16,19)(H,17,18)(H,20,21)

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Monday, July 10, 2017

Does Proton Conduction in the Voltage-Gated H+ Channel hHv1 Involve Grotthuss-Like Hopping via Acidic Residues?

Siri C. van Keulen, Eleonora Gianti, Vincenzo Carnevale, Michael L. Klein, Ursula Rothlisberger, and Lucie Delemotte (2017)
Contributed by Dries Van Rompaey

Voltage gated proton channels are membrane channels that are are regulated by both the pH gradient and the voltage. In most cases these channels only open when the electrochemical proton gradient is outwards, functioning as a passive acid extrusion mechanism. They have an exquisite selectivity for protons, prompting Delemotte and coworkers to investigate the mechanism of proton transport and the origin of this selectivity.

The mechanism for proton transport was explored using an integrative approach, combining classical simulations with QM/MM. Three separate cation binding sites can be observed in the channel, each consisting of a pair of negatively charged residues. QM/MM simulations were used to examine binding and unbinding of the proton, while conformational rearrangements were sampled using classical simulation. In contrast to the classic Grotthus mechanism, where the proton is transported through a water wire by subsequent bond formation and bond breaking, simulations indicated that the proton may traverse the channel by jumping between the acidic residues, assisted by a water molecule. As shown by classical MD, structural rearrangements occur upon proton binding, orienting the residues for the next proton jump, allowing for the proton to move through the channel. This integrative modelling study provides an interesting and novel mechanism for the transfer of a proton across a membrane. It will be interesting to see where future work on this channel leads.