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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