Wednesday, April 25, 2012

Enzymatic catalysis of anti-Baldwin ring closure in polyether biosynthesis

Hotta, K.; Chen, X.; Paton, R. S.; Minami, A.; Li, H.; Swaminathan, K.; Mathews, I. I.; Watanabe, K.; Oikawa, H.; Houk, K. N.; Kim, C.-Y. Nature2012483, 355 (Paywall)
Contributed by Steven Bachrach.
Reposted from Computational Organic Chemistry with permission

Biosynthesis of ladder polyethers is the topic of a very nice experimental/computational study by Chen and Houk.1 The x-ray structure of the enzyme that catalyzes the nucleophilic attack on epoxides to create the 6-member ring ether was determined, but the geometry did not completely indicate the mechanism.

Gas phase computations of the 5-exo-tet and 6-endo-tet ring openings of 1 were examined for both the acid and base catalyzed routes at B2PLYP/6-311++G(d,p)//B2PLYP/6-31G(d).
The results are summarized in Figure 1. Basically, as expected by Baldwin’s rules, the closure to the tetrahydrofuran (5-exo-tet) is favored under both catalyzed conditions. However, the preference is small under base conditions, with the difference in the free energy of activation of only 1.2 kcal mol-1.
Figure 1. Gas phase energies (kcal mol-1) for the acid an base catalyzed reactions of 1 to 2 or 3.

The enzyme Lsd19B produces just the analogue of 3. So, the two regioisomeric TSs were reoptimized with an aspartic acid group and a tyrosine group in the positions they occupy in the active site of the enzyme Lsd19b. The two resulting transition states, evaluated at B2LYP/6-311++G(d,p)//MO6-2x/6-31G(d), are shown in Figure 2. The activation energy for the 6-endo-tet reaction is 18.0 kcal mol-1, 2.5 kcal mol-1 lower than for the 5-exo-tet route. This energy difference would give rise to a 100:1 selectivity for the tetrahydropyran product, in accord with experiment. The enzyme preorganizes for and favors the base catalyzed path that leads to 3.

5-exo-tet TS model
ΔG‡ = 20.5

6-endo-tet TS model
ΔG‡ = 18.0
Figure 2. Transition state models of the active site. Activation energies in kcal mol-1.


(1) Hotta, K.; Chen, X.; Paton, R. S.; Minami, A.; Li, H.; Swaminathan, K.; Mathews, I. I.; Watanabe, K.; Oikawa, H.; Houk, K. N.; Kim, C.-Y., "Enzymatic catalysis of anti-Baldwin ring closure in polyether biosynthesis," Nature, 2012, 483, 355-358, DOI: 10.1038/nature10865.

1: InChI=1/C8H16O2/c1-6(9)4-5-8(3)7(2)10-8/h6-7,9H,4-5H2,1-3H3/t6-,7?,8+/m0/s1
2: InChI=1/C8H16O2/c1-6-4-5-8(3,10-6)7(2)9/h6-7,9H,4-5H2,1-3H3/t6-,7-,8-/m0/s1
3: InChI=1/C8H16O2/c1-6-4-5-8(3,9)7(2)10-6/h6-7,9H,4-5H2,1-3H3/t6-,7-,8+/m0/s1

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Tuesday, April 24, 2012

Fast and Accurate Modeling of Molecular Atomization Energies with Machine Learning

M. Rupp, A. Tkatchenko, K.-R. Müller, and O. A. von Lilienfeld Phys. Rev. Lett., 108, 058301 (2012)                                                                                  

In this study, regression algorithms from machine learning are used to create a model predicting atomization energies of a large class of organic molecules. Training the model with hybrid DFT data yields a prediction error of ~10 kcal/mol.

The power of this technique lies not in improving upon existing DFT approximations, but rather enabling extremely fast calculation of a particular large class of molecules at a near-DFT accuracy. Applications include chemical design, where one attempts to solve the inverse electronic structure problem (i.e. which molecule gives the desired property?), molecular dynamics, and chemical reactions.

We thought the choice of the Coulomb matrix in representing a molecule was an elegant and natural way to satisfy the requirements of invariance under symmetry operations. It would be interesting to know how sensitive the results are to the authors' choice of the diagonal of the Coulomb matrix, as well as the type of kernel used in the kernel ridge regression.
(Summary prepared by John Snyder).

Thursday, April 19, 2012

Resolution of identity approach for the Kohn-Sham correlation energy within exact-exchange random-phase approximation

Hesselman and Gorling recently introduced exact-exchange random phase approximation (EXXRPA) methods. These Kohn Sham (KS) based methods treat the correlation energy via the random phase approximation (RPA) based on TDDFT using the exact frequency-dependent exchange kernel (Mol. Phys. 108, 359 (2010) and PRL 106, 093001 (2011)). Results from these EXXRPA methods for closed shell organic molecules showed results with accuracy on par with CCSD for total energies and slightly less accurate for reaction energies compared to CCSD but better than MP2.

In this paper, the authors report the development and implementation of the resolution of the identity EXXRPA. This results in two new methods: RI-EXXRPA and RI-EXXRPA+. Both methods make use of RI and auxiliary basis sets to reduce the formal scaling from N6 to N5. The computational speedup allows the inclusion of previously neglected terms giving rise to RI-EXXRPA+.

Results for total energies for 21 molecules show RMSD values of around 10 kcal/mol for RI-EXXRPA and CCSD, and below 10 kcal/mol for RI-EXXRPA+ (using CBS extrapolated CCSD(T) as reference). RMSD for 16 reaction energies gives values around 1.7 kcal/mol compared to 2.5 for MP2 using the same reference. Overall, this proof of principle paper presents two methods that employ RI to reduce the computational scaling. These methods, albeit more computationally costly than conventional DFT, could provide alternatives to post-HF methods using a Kohn-Sham based approach after more extensive testing. 

Monday, April 16, 2012

Steric Crowding Can Stabilize a Labile Molecule: Solving the Hexaphenyethane Riddle

In the special issue “90 Years of Chemical Bonding”1 I expressed the opinion2 that despite of the historians’ characterization of chemistry as a “science without territory”, the chemical bond has been the traditional chemical territory and the heartland of chemistry ever since the chemical community amalgamated in the 17th Century.  While historians seem to ignore this “chemical territory”, the good news is that chemists have kept it fertile and teaming with activity, generating new bonding motifs and news (see for example, the recent highlight in CCH, April 4, 2012). One of the recent new and exciting bonding motifs, was found by Peter R. Schreiner and his group3 who have synthesized molecules with very long C-C bonds, 1.647-1.704 Å by Wurtz coupling of so-called diamondoid molecules (nanodiamonds), e.g., 1 which results from diamantane-diamantane coupling.  

                        1                                                                                                    2
Schreiner et al.3 used also DFT calculations to show that ~ 40% of the bond dissociation energy (BDE) of these long C-C bonds is due to the dispersion interactions, and argued that the sticky dispersion interactions are due to short H---H contacts (1.94 and 2.28 Å) that are maintained between the CH---HC faces of the diamondoid moieties.
In a subsequent study, which is described in the highlighted paper,4 Stefan Grimme and Peter R. Schreiner teamed to solve the riddles exhibited by hexaarylethanes.  The parent molecule, hexaphenylethane, is experimentally unknown as it dissociates readily into two Gomberg radicals, 2Ph3C•. Similarly, hexa-(para-tert-butylphenyl)-ethane dissociates into its corresponding radicals. By contrast, the apparently much more crowded hexa-(3,5-di-tert-butylphenyl)ethane (2) is a stable molecule with a very long C-C bond of 1.67 Å. Structure 2 is the only one that maintains attractive H---H interactions between the meta-di-substituted phenyl groups. Grimme and Schreiner showed that in all the hexaarylethanes, the BDE is negative in the absence of dispersion interactions, but becomes positive upon addition of dispersion. However, only 2 has a positive dissociation free energy. Furthermore, computational removal of the dispersion contributions of the tert-butyl groups would have made 2 unstable with BDE<0. Therefore, the sticky fingers that hold the C-C bond in 2 are the H---H interactions, which contribute 40 kcal/mol to the total BDE (>50%). These sticky fingers create a second minimum in the bond dissociation energy curve of 2. This minimum, so-called 2vdw, lies at a C-C distance of ~5.2 Å and its binding energy is purely dispersive and amounts to 26.6 kcal/mol. That is, 2vdw is held exclusively by the sticky H---H fingers!
The role of the sticky H---H fingers was subsequently probed by Fokin, Schreiner et al., to stick together layers of graphanes.5 The potential practical applications of these dispersion-supported bonds are wide ranging. There is something new and potable in chemical bonding!
(1) G. Frenking, S. Shaik, “90 Years of Chemical Bonding”, J. Comput. Chem. 2007, 28, 1-455.
(2) S. Shaik, “The Lewis Legacy: The Chemical Bond-A Territory and Heartland of Chemistry”, J. Comput. Chem. 2007, 28, 51-61.
(3) P. R. Schreiner, L. V. Chernish, P. A. Gunchenko, E. Y. Tikhonchuk, H. Hausman, M. Serafin, S. Schlecht, J. E. P. Dahl, R. M. K. Carlson, A. A. Fokin, “Overcoming Lability of Extremely Long Carbon-Carbon Bonds Through Dispersion Forces”, Nature, 2011, 477, 308-312.
(4) S. Grimme, P. R. Schreiner, “Steric Crowding Can Stabilize a Labile Molecule: Solving the Hexaphenylethane Riddle:, Angew. Chem. Int. Ed. 2011, 50, 12639-12642.
(5) A. A. Fokin, D. Gerbig, P. R. Schreiner, “ss- and p/p-Interactions Are Equally Important: Multilayered Graphanes”, J. Am. Chem. Soc. 2011, 133, 20036-20039.

Contributed by Sason Shaik

Saturday, April 14, 2012

Hydrogen-bond stabilization in oxyanion holes: grand jeté to three dimensions

Luis Simón and Jonathan M. Goodman, Organic and Biomolecular Chemistry, 2012, 10, 1905

Simón (University of Salamanca) and Goodman (University of Cambridge) have in recent years focussed on hydrogen-bonding catalysts in synthetic organic chemistry, examining the origins of rate enhancement and stereoinduction (e.g. J Am Chem Soc 2009, 131, 4070-4077). The use of low molecular weight hydrogen-bonding catalysts derived from organic rather than transition-metal based compounds, or "organocatalysis", has grown rapidly and considerably in recent years, in particular using chiral amines and phosphoric acids, along with mechanistic and predictive computational studies.

Simón and Goodman now direct their attention to hydrogen bonding motifs found in enzymatic catalysis.  Their recent article in RSC journal OBC reveals a rather unexpected geometric preference for nature's hydrogen bonds, that seems to contradict much of the dogma surrounding enzymatic catalysis: namely that transition states in so-called "oxyanion holes" are not optimally stabilised, rather, it is the activation barrier relative to the bound substrate that is minimised instead.

The computational approach employed by the authors is multi-faceted: data-mining is used to compare crystallographic hydrogen-bonding motifs found in PDB and CSD structures, cluster models of enzyme active sites are computed with DFT (often termed "theozyme" calculations, an approach advanced by Himo and Houk), QM:MM calculations are performed to locate a transition state for a rather larger active site model, and classical MD simulations are performed on an oxyanion hole containing enzyme.

A comparison of small molecule (CSD) and protein (PDB) crystal structures reveals different empirical distributions for the dihedral angle between a bound carbonyl group and two H-bond donors. Whilst CSD structures reveal a preference for planar coordination, the two polar hydrogen atoms lying more-or-less where students of organic chemistry are tought to envisage the sp2 "rabbit ear" lone pairs, the PDB structures tell a different story: the H-bond donors are more likely to be found in a plane perpendicular to the carbonyl. MD simulations reveal that this angular distribution is well maintained and not easily distorted even with the application of large constraining forces, so any kind of induced fit is extremely unlikely to alter the hydrogen-bonding geometry.

The key effect of having two hydrogen bond donors perpendicular to the plane of a carbonyl group is suboptimal substrate binding, which results in an overall reduction of the activation barrier to achieve the oxyanion transition state (presumably due a greater electrostatic component to binding, the oxyanion transition state is less fussy about coordination geometry). The contrast between a traditional depiction of carbonyl in-plane H-bonds (here represented by Da Vinci's Vitruvian man) and the authors' current model, which is likened to a ballerina's grand jeté, that gives this paper its title. On the basis of activation barriers computed with DFT, the authors estimate this effect to have an impact of around 2 kcal/mol in barrier lowering, which while only a small fraction of the overall barrier height, is comparable in importance with other contributions to catalysis such as tunnelling.

Wednesday, April 11, 2012

Conformations and Fluorescence of Encapsulated Stilbene

D. Tzeli, G. Theodorakopoulos, I. D. Petsalakis, D. Ajami, J. Rebek Journal of the American Chemical Society 2012, 134, 4346-4354 (Paywall)
Contributed by Steven Bachrach.
Reposted from Computational Organic Chemistry with permission

Petsalakis and Rebek have explored the fluorescence of stilbene inside a couple of different kinds of capsules. trans-Stilbene exhibits weak fluorescence in solution, but when placed inside a small capsule, the fluorescence disappears almost entirely, while in a large capsule, the fluorescence returns to normal. They examined stilbene inside two different capsules using a variety of DFT and ONIOM techniques.

The optimized geometries of trans- and cis-stilbene optimized at CAM-B3LYP/6-31G(d,p) are displayed in Figure 1. As expected, the trans conformer is planar and the cis conformer is twisted to avoid clashes between the phenyl rings. The optimized structure of the 1.1 capsule is also shown in Figure 1. All of these structures are fairly insensitive to computational method. (They have also looked at an even larger capsule, but I have omitted displaying its structure here.)





Figure 1. CAM-B3LYP/6-31G(d,p) optimized structures of (a) trans-stilbene, (b) cis-stilbene , (c) the 1.1 capsule, and (d) trans-stilbene inside the 1.1 capsule.

The structure of trans- stilbene inside the 1.1 capsule is shown in Figure 1. Of particular note is that the stilbene is no longer planar. (This twisting is perhaps better observed by an end-on view, which the reader can obtain by clicking on the picture and then manipulating the full 3-D structure using the Jmol applet.) The different computational methods give slightly different encapsulated structures, and vary a bit in their binding energies, but the twisting of the stilbene is reproduced by each method. Though not shown here, trans-stilbene in the larger capsule is again a nearly planar structure.

The structure of the S1 state of trans-stilbene in the large capsule is the same as for free trans-stilbene. However, the geometry of the S1 state in the smaller 1.1 capsule is twisted and corresponds to the conical intersection geometry.

The absorption spectra and the emission spectra were computed for the free and encapsulated structures. The absorption and emission spectra for free stilbene and stilbene in the larger capsule are nearly identical, corresponding to the experimental observation of similar fluorescence behavior. The absorption spectra of stilbene in the 1.1 capsule has a small blue shift of 8 nm due to the twisted geometry. But the major result is that the S1 state of stilbene inside the 1.1 capsule distorts to the conical intersection, allowing for radiationless return to the ground state. This means that there would be no fluorescence, and that is exactly what is observed.

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Wednesday, April 4, 2012

Quadruple bonding in C2 and analogous eight-valence electron species

Sason Shaik, David Danovich, Wei Wu, Peifeng Su, Henry S. Rzepa, Philippe C. Hiberty, Nature Chemistry 2012, 4, 195 (Paywall)
Contributed by Steven Bachrach.
Reposted from Computational Organic Chemistry with permission

Inspired by a blog post of Henry Rzepa (see here) Shaik and co-workers examined the C2 species with an eye towards the nature of the bond between the two carbon atoms. Using both a valence bond approach and a full CI approach, they end up at the same place: there is a quadruple bond here!

The argument rests largely on a definition of of an in situ bond energy. For the VB approach, this requires choosing as a reference a non-bonding interaction between the atoms with regards to a pair of electrons. For the CI approach, the bond energy is half the energy of the singlet-triplet gap. So, for C2, the VB/6-31G* estimate of the bond energy of the putative fourth bond is 14.3 kcal mol-1. For the full CI/6-31G* computations of the singlet-triplet gap, the bond energy estimate is 14.8 kcal mol-1, and using the experimental value of the gap, the estimate is 13.2 kcal mol-1. Not a strong bond, but certainly meaningful!

In the VB approach, the fourth bond is a weighted sum of the antibonding 2σu and bonding 3σg orbitals – a combination that gives rise to small constructive overlap between the two C atoms. In the CI model, the wavefunction is dominated by the first two configurations; the first configuration, with a coefficient of C0=0.828 has 2σu doubly occupied and the second coefficient, with CD=0.324, has the 3σg orbital doubly occupied. Considering that 3σg is a bonding orbital, the significant contribution of this configuration gives rise to the fourth bond.

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Monday, April 2, 2012

Exchange-Enhanced Open-Shell States: Hund's rule for Bioinorganic Species Applied to H-Abstraction

D. Janardanan, D. Usharani, S. Shaik Angewandte Chemie International Edition 2012, 51, 4421-4425 (Paywall)

In a Perspective in Nature Chemistry last year1 Sason Shaik and co-workers described bond activation by metal-oxo enzymes and synthetic reagents. In it, they argued that Hund's rule of maximum multiplicity (valid for atoms) has an analogue for reactions and kinetics of (bio)inorganic species: the exchange-enhanced reactivity (EER). Pathways that increase the number of unpaired and spin-identical electrons on a metal center will be favored by exchange interactions, and hence are favored over pathways that keep the same number (or less) of exchange interactions.

In this recent paper in Angewandte Chemie International Edition Shaik and co-workers apply their EER principle on H-abstraction reactions, and show how dramatic axial ligand effects can be explained by it. The systems under study are [(Cz)(X)MnVO] (Cz: corrolazinato3-, X=None, F-, CN-) complexes (see Figure below), which probably have a singlet ground state (X=None) or a triplet ground state (X=F-, CN-).

More important than the ground state of the reactant is however the spin state of the transition states (TSs). The hydrogen abstraction involves a proton-coupled electron transfer (PCET): the migrating H· radical transfers its radical to the d-block of the metal, while at the same time the proton makes the O-H bond. For the singlet state, one obtains at the TS an open-shell singlet with an alpha electron on the metal and a beta electron on the substrate. In the exchange-enhanced triplet state, there are now three alpha electrons on the metal (with favorable exchange interactions) that gives the dramatic decrease in barrier (from 32 kcal·mol-1 for the singlet to 23.0 kcal·mol-1 for the triplet).

The axial ligand effect has two origins: the exchange interactions become stronger (11.1, 12.4 and 12.9 kcal·mol-1 for the three complexes) while at the same time the d-orbitals become closer in energy (smaller excitation energy).


(1) S. Shaik, H. Chen, D. Janardanan, "Exchange-enhanced reactivity in bond activation by metal-oxo enzymes and synthetic reagents", Nature Chem. 2011, 3, 19-27, DOI: 10.1038/NChem.943

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Editorial: First indication of impact

This figure shows a plot of cumulative views per month for the PLoS ONE paper "The Energy Computation Paradox and ab initio Protein Folding" by Faver et al.   Month 12 corresponds to March 2012, the month in which the paper was highlighted in Computational Chemistry Highlights.  During March the paper was viewed 345 times - a significant increase compared to the 86 views the previous month and second only to the first month where it was viewed 346 times.

 PLoS ONE is one of the few journals that publish such metrics so similar analyses are not possible for the other highlighted paper.  Never-the-less, the numbers are strong indication that Computational Chemistry Highlights is having an impact already.

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