Monday, August 15, 2016

Effect of Complex-Valued Optimal Orbitals on Atomization Energies with the Perdew–Zunger Self-Interaction Correction to Density Functional Theory

Susi Lehtola, Elvar Ö. Jónsson, and Hannes Jónsson J. Chem. Theory Comput. in press (2016)
Contributed by David Bowler
Reposted from Atomistic Computer Simulations with permission

One of the biggest problems facing DFT is that of self-interaction: each electron effectively interacts with itself, because the potential derives from the total charge density of the system. This is not an issue for the exact (unknown) density functional, or for Hartree-Fock, but is the cause of significant error in many DFT functionals. Approaches such as DFT+U[1],[2],[3] and hybrid functionals (far too many to reference !) are aimed in part at fixing this problem.
Probably the earliest attempt to remove this error is the self-interaction correction of Perdew and Zunger[4] which corrects the potential for each Kohn-Sham orbital, complicating the calculation considerably over a standard DFT calculation. (Ironically, this paper, which has over 11,000 citations, is best known for its appendix C, where a parameterisation of the LDA XC energy is given.) However, this process is notoriously slow to converge and is not widely used.
A recent paper[5] showed that, even for isolated molecules, complex orbitals were required to achieve convergence, and this approach has now been tested for atomisation energies of a standard set of 140 molecules[6]. The tests compare the new complex SIC implementation against the standard, real implementation, as well as various GGAs, hybrid functionals and meta-GGAs. The complex SIC, when coupled with the PBEsol functional[7], gives good results (though ironically the PBEsol functional was developed to improve PBE for solids). Not surprisingly, the best results are from hybrids, but meta-GGA improves the energies almost as well.
This study highlights the problem with DFT at the moment: there are many different approaches, which often work well for specific problems. SIC is cheaper than hybrid calculations, and can be important for charge transfer problems (and Rydberg states). The results for convergence and complex orbitals are interesting, but based on these results, I would use meta-GGA for atomisation energies, as a good compromise between accuracy and cost (almost the same as GGA).
[1] Phys. Rev. B 52, R5467 (1995) DOI:10.1103/PhysRevB.52.R5467
[2] Phys. Rev. B 57, 1505 (1998) DOI:10.1103/PhysRevB.57.1505
[3] Int. J. Quantum Chemistry 114, 14 (2014) DOI:10.1002/qua.24521
[4] Phys. Rev. B. 23, 5048 (1981) DOI:10.1103/PhysRevB.23.5048
[5] J. Chem. Theory Comput. 12, 3195 (2016) DOI:10.1021/acs.jctc.6b00347
[6] J. Chem. Theory Comput. in press (2016) DOI:10.1021/acs.jctc.6b00622
[7] Phys. Rev. Lett. 100, 136406 (2008) DOI:10.1103/PhysRevLett.100.136406

Wednesday, August 3, 2016

A Total Synthesis of Paeoveitol

Xu, L.; Liu, F.; Xu, L.-W.; Gao, Z.; Zhao, Y.-M. Org. Lett. 2016, ASAP
Contributed by Steven Bacharach
Reposted from Computational Organic Chemistry with permission

Xu, Liu, Xu, Gao, and Zhao report a very efficient synthesis of paeoveitol 1 by the [4+2]-cycloaddition of paeveitol D 2 with the o-quinone methide 3.1 What is interesting here is the selectivity of this reaction. In principle the cyloadditon can give four products (2 different regioisomeric additions along with endo/exo selectivity) and it could also proceed via a Michael addition.

They performed PCM(CH2Cl2)/M06-2x/6-311+G(d,p) computations on the reaction of 2 with 3 and located two different transition states for the Michael addition and the four cycloaddition transition states. The lowest energy Michael and cycloaddition transition states are shown in Figure 1. The barrier for the cycloaddition is 17.6 kcal mol-1, 2.5 kcal mol-1 below that of the Michael addition. The barriers for the other cycloaddition paths are at more than 10 kcal mol-1 above the one shown. This cycloaddition TS is favored by a strong intermolecular hydrogen bond and by π-π-stacking. In agreement with experiment, it is the transition state that leads to the observed product.

Michael TS

[4+2] TS
Figure 1. Optimized geometries of the lowest energy TSs for the Michael and [4+2]cycloaddtion routes. Barrier heights (kcal mol-1) are listed in parenthesis.


(1) Xu, L.; Liu, F.; Xu, L.-W.; Gao, Z.; Zhao, Y.-M. "A Total Synthesis of Paeoveitol," Org. Lett. 2016, ASAP, DOI: 10.1021/acs.orglett.6b01736.
paeoveitol 1: InChI=1S/C21H24O3/c1-5-21-10-14-6-11(2)17(22)8-15(14)13(4)20(21)24-19-7-12(3)18(23)9-16(19)21/h6-9,13,20,22-23H,5,10H2,1-4H3/t13-,20-,21-/m1/s1
paeveitol D 
2: InChI=1S/C9H10O2/c1-3-7-5-8(10)6(2)4-9(7)11/h3-5,10H,1-2H3/b7-3+
3: InChI=1S/C9H10O2/c1-3-7-5-8(10)6(2)4-9(7)11/h3-5,10H,1-2H3/b7-3+

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Saturday, July 30, 2016

Diverse Optimal Molecular Libraries for Organic Light-Emitting Diodes

This paper uses the property-optimizing ACSESS (PO-ACSESS) method to create a set of diverse set of candidates for organic light-emitting diodes (OLEDs) with efficient blue emissions.  There are over 10$^{60}$ synthetically feasible, low molecular eight organic molecules so it is impossible to do an exhaustive search of this so-called small molecule universe looking for better blue OLEDs. Yang and Beratan have therefore developed PO-ACSESS, a stochastic genetic algorithm to extract a set of diverse molecules with a given set of properties.

PO-ACSESS starts with a set of seed molecules (in this case organic molecules that are known blue emitters) that are then randomly mutated and mated. A mutation may be any of a set of elementary steps such a change in bond order, ring formation, atom addition/deletion, etc. and mating is done by randomly fragmenting the molecules at a rotateable bond followed by re-combination of fragments from different parents. The new molecules that do not meet the desired stability, synthetic-feasibility, and electronic criteria are removed. To enforce diversity, molecules that are too close in chemical space are also removed and the entire process is repeated starting with these molecules. The chemical space distance between two compounds is defined as the distance between compounds based on their descriptors, such as atomic number, Gasteiger−Marsili partial charge, atomic polarizability, and topological steric index.

In the case of blue OLEDs the electronic criteria are a vertical singlet excitation energy in the 2.4−4.1 eV range (blue region), an oscillator strength of ≥0.4, and a singlet-triplet gap ≤ 0.3 eV. “Initially, the threshold is set to a less stringent value … to ensure that the population does not collapse to zero, because of the fitness constraint.” The electronic properties were calculated using semiempirical methods such as AM1, ZINDO/S, and DFTB.

The design process was done in two stages: First PO-ACSESS was used to identify 195 molecules with the desired vertical singlet excitation energies and oscillator strengths.  I could not find any details on what seed molecules were used nor the number of iterations. These 195 molecules where then used as seeds for further optimization of the singlet-triplet gap. This PO-ACSESS search was run for 50 iterations where ∼90 molecules were generated per iteration that satisfied the required singlet-triplet gap constraint, which was completed in 7 days on a 16-core CPU. I’d be very curious to know how many molecule were actually screened as part of the process. Anyway, ∼60 structures with a computed singlet-triplet gap-value of ∼0.3 eV that are predicted to emit in the blue region and to have reasonably high oscillator strengths. 

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Friday, July 29, 2016

Dehydro-Diels-Alder Reactions

Contributed by Steven Bacharach
Reposted from Computational Organic Chemistry with permission

I have been delinquent in writing about the dehydro-Diels-Alder reactions, but really can’t put it off any further. These sets of reactions really deserve a fuller analysis than I am going to summarize here, but this post will provide a good jumping off point for anyone interested in further investigation.

So the Diels-Alder reaction is among the most famous and most important reactions in organic chemistry. The reaction creates a 6-member ring and sets up to four stereocenters. In the past couple of years many chemists have expressed interest in the variant where the four-carbon component is more highly unsaturated, i.e. enyne or diyne. I will summarize the results of three recent computational papers dealing with the reaction of a diyne with an yne.

The first paper is by Skraba-Joiner, Johnson, and Agarwal.1 They discuss, among a number of interesting pericyclic reactions, the intramolecular Diels-Alder reaction of triyne 1 to give 2. They examined a concerted and stepwise pathway at (U)M05-2X/6-311+G(d,p) and find the concerted to be favored by 6.0 kcal mol-1. CCSD(T) using these geometries increases the difference to 8.2 kcal mol-1. The T1 diagnostic is fairly large for both the concerted and stepwise transition states, so they also performed CCSD(T)/CBS computations, which had much lower T1 values. The concerted TS remained favorable, but by only 2.7 kcal mol-1.

In the same special issue of the Journal of Organic Chemistry, Cramer, Hoye, and Kuwata examined a reaction closely related to what Johnson examined above.2 They looked at the reaction taking 3 into 4 via both experiments and computations. The M06-2x/6-311+G(d,p) geometries for the concerted and first TS along the stepwise path (with R1=R2=H) are shown in Figure 1. Evaluating the energies at SMD(o-dichlorobenzene)/B3LYP-D3BJ/6-311+G-(d,p)//M06-2X/6-311+G(d,p) find in this case (along with all of the other R1/R2 variants they examined) that the stepwise path has a lower barrier than the concerted path. In the case where R1=R2=H, the stepwise path is favored by 6.0 kcal mol-1. Additionally, these stepwise barriers are in reasonable agreement with the experimentally-derived barriers.

Concerted TS

Stepwise TS
Figure 1. M06-2x/6-311+G(d,p) optimized geometries of the concerted and stepwise TSs for the reaction of 3H going to 4H.

It should be pointed out that the wavefunctions for the concerted TSs were all found to be unstable with regard to a restricted to unrestricted relaxation. Given this problem, they also performed a CASPT2 energy evaluation of the concerted and stepwise transition states for the case R1=R2=H. CASPT2 finds the stepwise barrier to be 3.7 kcal mol-1 lower than the concerted barrier.

The last paper comes from the Houk lab, and examines the simplest set of intermolecular dehdro-Diels-Alder reactions.3 I will focus here on the most unsaturated analogue, the reaction of 1,3-butadiyne 5 with ethyne to give benzyne 6.
The concreted and stepwise transition states for this reaction (at (U)M06-2X/6-311+G(d,p)) are shown in Figure 2. The concerted barrier is 36.0 kcal moml-1 while the stepwise barrier is slightly lower: 35.2 kcal mol-1. The distortion energy for the concerted reaction is large (43.2 kcal mol-1) due mostly to angle changes in the diyne. Its interaction energy is -7.2 kcal mol-1, similar to the interaction energy in other similar Diels-Alder reactions. In contrast, the distortion energy for the stepwise pathway is 27.5 kcal mol-1, but the interaction energy is +7.7 kcal mol-1. These values are very similar to the distortion and interaction energy of the related (but less saturated DA reactions).

Concerted TS

Stepwise TS
Figure 2. (U)M06-2X/6-311+G(d,p) optimized concerted and stepwise TS for the reaction of 1,3-diyne with ethyne.

Molecular dynamics trajectories for both the concerted and stepwise paths reveal interesting differences. The concerted trajectories show an oscillatory behaviour of bending the angles at the C2 and C3 carbons prior to the TS, and then near synchronous formation of the new C-C bonds. The trajectories initiated at the stepwise TS show no systematic motion. Once the bond is formed, the biradical exhibits a long lifetime, on the order of picoseconds, much longer than the trajectory runs.
These three studies indicate the nature of the dehydro Diels-Alder reaction is very sensitive to reaction conditions, substituents, solvation, and all other manner of effects and will likely prove an area of interest for some time. It should keep a number of computational chemists busy for some time!


(1) Skraba-Joiner, S. L.; Johnson, R. P.; Agarwal, J. "Dehydropericyclic Reactions: Symmetry-Controlled Routes to Strained Reactive Intermediates," J. Org. Chem. 201580, 11779-11787, DOI:10.1021/acs.joc.5b01488.
(2) Marell, D. J.; Furan, L. R.; Woods, B. P.; Lei, X.; Bendelsmith, A. J.; Cramer, C. J.; Hoye, T. R.; Kuwata, K. T. "Mechanism of the Intramolecular Hexadehydro-Diels–Alder Reaction," J. Org. Chem. 201580, 11744-11754, DOI: 10.1021/acs.joc.5b01356.
(3) Yu, P.; Yang, Z.; Liang, Y.; Hong, X.; Li, Y.; Houk, K. N. "Distortion-Controlled Reactivity and Molecular Dynamics of Dehydro-Diels–Alder Reactions," J. Am. Chem. Soc. 2016138, 8247-8252, DOI:10.1021/jacs.6b04113.


1: InChI=1S/C9H8/c1-3-5-7-9-8-6-4-2/h1-2H,5,7,9H2
2: InChI=1S/C9H8/c1-2-5-9-7-3-6-8(9)4-1/h1,4H,3,6-7H2
3H: InChI=1S/C8H4O2/c1-3-5-6-7-10-8(9)4-2/h1-2H,7H2
4H: InChI=1S/C10H8O4/c1-6(11)14-8-2-3-9-7(4-8)5-13-10(9)12/h2-4H,5H2,1H3
5: InChI=1S/C4H2/c1-3-4-2/h1-2H
6: InChI=1S/C6H4/c1-2-4-6-5-3-1/h1-4H

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Tuesday, July 19, 2016

Direct Spectroscopic Evidence for an n→π* Interaction

Singh, S. K.; Mishra, K. K.; Sharma, N.; Das, A. Angew. Chem. Int. Ed. 2016, 55, 7801-7805
Contributed by Steven Bacharach
Reposted from Computational Organic Chemistry with permission

The weak n→π* interaction has been proposed to explain some conformational structure. Singh, Mishra, Sharma, and Das have now provided the first spectroscopic evidence of this interactions.1 They examined the structure of methylformate 1. This compound can exist as two conformational isomers, having the carbonyl oxygen pointing towards (cis) or away (trans) from the phenyl ring. They optimized the structures of these two conformers at M05-2X/aug-cc-pVDZ and find that the cis isomer is lower in energy by 1.32 kcal mol-1. Unfortunately, the authors do not provide the structures of these isomers, but since they are so small, I reoptimized them at ωB97XD/6-311g(d) and they are displayed in Figure 1. At this computational level, the cis isomer is lower in enthalpy than the trans isomer by 1.35 kcal mol-1.


Figure 1. ωB97XD/6-311g(d) optimized structures of the cis and trans conformations of 1.

One-color resonant 2-photon ionization (1C-R2PI) spectroscopy followed by UV-VIS hole burning spectroscopy identified two isomers of 1, one present in greater amount that the other. The IR spectra of the dominant isomer showed a carbonyl stretch at 1766 cm-1, in nice agreement with the predicted frequency of 1cis (1770 cm-1). The carbonyl stretch for the minor isomer is at 1797 cm-1, again in nice agreement with the computed frequency for 1trans (1800 cm-1). The cis isomer has the lower carbonyl frequency due to partial donation of the carbonyl oxygen electrons to the π* orbital of the phenyl ring.


(1) Singh, S. K.; Mishra, K. K.; Sharma, N.; Das, A. "Direct Spectroscopic Evidence for an n→π* Interaction,"Angew. Chem. Int. Ed. 201655, 7801-7805, DOI: 10.1002/anie.201511925.


1: InChI=1S/C7H6O2/c8-6-9-7-4-2-1-3-5-7/h1-6H

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Monday, July 11, 2016

Redox Switching of Orthoquinone-Containing Aromatic Compounds with Hydrogen and Oxygen Gas

Urakawa, K.; Sumimoto, M.; Arisawa, M.; Matsuda, M.; Ishikawa, H. Angew. Chem. Int. Ed. 2016, 55, 7432-7436
Contributed by Steven Bacharach
Reposted from Computational Organic Chemistry with permission

In searching for a redox switch, Matsuda, Ishikawa and co-workers1 landed on 13,14-picenedione 1, which could, at least in principle, be reduced by reacting with H2 to form the diol 2. The back reaction could then occur via the reaction with oxygen gas.

They first optimized the geometries of both compounds at B3PW91/6-311+G(2d), and these geometries are shown in Figure 1. TD-DFT computations then predicted that 1 would be yellow (maximum absorption at 412nm) and 2 would be colorless (maximum absorption at 378nm). Furthermore, 1 should have no fluorescence while 2 should fluoresce at 464nm and be blue.


Figure 1. B3PW91/6-311+G(2d) optimized geometries of 1 and 2.

Of particular note is that the geometry of 1 is twisted, with the O-C-C-O dihedral angle being 34.9°, while there is essentially no such twisting in 2 (its O-C-C-O dihedral angle is 0.7°). The twisting in 1 manifests in antiaromatic character of the central ring, with NICS(0)=+13.2ppm, while the central ring of 2 is aromatic, with NICS(0)=-10.0. The redox properties therefore reflect the change in the aromatic character.

They next synthesized 2 and reduced it with hydrogen gas to 1. The x-ray crystal structure of 1 shows a twisted structure (O-C-C-O dihedral of 28.87°). As predicted, 1 is yellow and 2 is colorless, and 1 has no fluorescence while 2 fluoresces blue.


(1) Urakawa, K.; Sumimoto, M.; Arisawa, M.; Matsuda, M.; Ishikawa, H. "Redox Switching of Orthoquinone-Containing Aromatic Compounds with Hydrogen and Oxygen Gas," Angew. Chem. Int. Ed. 201655, 7432-7436, DOI: 10.1002/anie.201601906.


1: InChI=1S/C22H12O2/c23-21-19-15-7-3-1-5-13(15)9-11-17(19)18-12-10-14-6-2-4-8-16(14)20(18)22(21)24/h1-12H
2: InChI=InChI=1S/C22H14O2/c23-21-19-15-7-3-1-5-13(15)9-11-17(19)18-12-10-14-6-2-4-8-16(14)20(18)22(21)24/h1-12,23-24H

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Wednesday, June 29, 2016

Systematic Error Estimation for Chemical Reaction Energies

Gregor N. Simm and Markus Reiher (2016)
Contributed by Jan Jensen

Simm and Reiher present an approach to estimate the error of density functionals parameterized for a specific system.  System-specific parameterization can yield very accurate predictions for the training set but the applicability of the resulting functional to any other systems, including closely related ones, is not guaranteed precisely because the training set is so specific.  However, by Simm and Reiher provide confidence intervals for each result to assess whether the results are reliable. 

Four functional parameters are optimized to best fit 23 CCSD(T) reaction energies of a model system. As one would expect the functional outperforms several other standard functionals for that particular model system. The real question is whether this performance translates to the real system of interest where CCSD(T) benchmarks aren’t available.  To answer this Simm and Reiher generate a set of new values for one of the parameters that lead to a range of predicted reaction energies from which the uncertainty (standard deviations) in the prediction can be computed.  

For the model system the error is within two standard deviations for 21 of the 23 reaction energies. When the functional is then applied to a slightly larger system, for which CCSD(T) reference values also could be computed, the error is within two standard deviations for 17 of the 20 reaction energies. Thus for most of the reaction energies this approach can be used to reliably gauge the accuracy of the results computed using the system dependent density functional.

It should be noted that the current approach only applies to linear parameters, which is the reason the analysis what only performed on one of the four optimized parameters. But it should be possible to extend it to other parameter types, in which case one also needs to address the large number of parameter-combinations that need to be checked.  

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