Predicting the pK_a of a compound from first principles remains a challenge, despite all of the many algorithmic and methodological advantages within the sphere of computational chemistry. Predicting the gas-phase deprotonation energy is relatively straightforward as I detail in Section 2.2 of my book. The difficulty is in treating the solvent and the interaction of the acid and its conjugate base in solution. Considering that we are most interested in acidities in water, a very polar solvent, the interactions between water and the conjugate base and the proton are likely to be large and important!

Baker and Pulay report a procedure for determining acidities with the aim of high throughput.¹ Thus, computational efficiency is a primary goal. Their approach is to compute the enthalpy change for deprotonation in solution using a continuum treatment and then employ a linear fit to predict the pK_a with the equation:

pK_a(c) = α_cΔH + β_c

where c designates a class of compound, such as alcohol, carboxylic acid, amine, etc. Fitting constants α_c and β_c need to be found then for each unique class of compound, where the fitting is to experimental pK_as in water. In their test suite, they employed eleven anilines and amines, seven pyridines, nine alcohols and phenols, and seven carboxylic acids.

They test a number of different computational variants: (a) what functional to employ, (b) what basis set to use for optimizing structures, and (c) what basis set to use for the enthalpy computation. They opt to employ COSMO for treating the solvent and quickly reject the use of gas phase structures (and particularly use of geometries obtained with molecular mechanics. Their ultimate model is OLYP/6-311+G**//3-21G(d) with the COSMO solvation model. Mean deviation is less than 0.4 pK units. They do note that use of HF or PW91 provides similar small errors, but ultimately favor OLYP for its computational performance.

While this procedure offers some guidance for future computation of acidity, I find a couple of issues. First, it relies on fitted parameters for every class of compound. If one is interested in a new class, then one must develop the appropriate parameters – and the experimental values may not be available or perhaps an insufficient number of them are experimentally available. Second, the parameters cover-up a great deal of problematic computational sins, like the solvation energy of the proton, small basis sets, missing correlation energies, missing dispersion corrections etc. A purist might hope for a computational algorithm that allows for systematic correction and improvement in the estimation of pK_as. Further work needs to be done to meet this higher goal.

References

(1) Zhang, S.; Baker, J.; Pulay, P., "A Reliable and Efficient First Principles-Based Method for Predicting pKa Values. 1. Methodology," J. Phys. Chem. A 2010, 114 , 425-431, DOI: 10.1021/jp9067069

The recent synthesis and characterization of the quadrannulene 1 once again stretches
our notions of aromaticity.¹

The core of this system is a four-member ring with four fused-phenyl rings, forming the very small circulene (see this earlier post on circulenes). One might write other resonance structures for the molecule, which could include a central cyclobutadienyl fragment. However, the X-ray structure and computational analysis rejects any significant contribution of the cyclobutadienyl character. First, the four C-C bond of this central ring are 1.45 Å long, with an NBO bond order of 1.08, signifying single bonds. The bonds from the central 4-member ring are 1.36 Å long with bond order of 1.77 – these are double bonds. NICS computations attest to the central ring (+4.5 ppm) being more like [4]radialene (with a NICS value of -2.6 ppm) than like cyclobutadiene (with a NICS value of +16.5 ppm). The 6-member rings fused to the central ring have NICS values of -2.33 ppm, suggesting a non aromatic character, while the outer rings have NICS values of -10.7ppm, similar to that of benzene. The structure is clearly of radialene form. Nonetheless, the central ring possess extremely pyramidalized carbons, as seen in Figure 1, and their π-orbital axis vector, a measure of the pyramidalization, is 107°, which is similar to the idealized tetrahedral value of 109.47°. Despite this stain, the molecule is thermally stable to 170°C and reacts only slowly with air or base. This molecule will surely inspire further work in the small circulenes.

1

1a

Fig 1. B3LYP/6-311G** structures of 1 and its parent 1a (lacking the TMS groups).¹

References

(1) Bharat, R. B.; Bally, T.; Valente, A.; Cyranski, M. K.; Dobrzycki, L.; Spain, S. M.; Rempala, P.; Chin, M. R.; King, B. T., "Quadrannulene: A Nonclassical Fullerene Fragment," Angew. Chem. Int. Ed. 2009, DOI: 10.1002/anie.200905633

InChIs

1: InChI=1/C44H48Si4/c1-45(2,3)33-21-29-30(22-34(33)46(4,5)6)38-27-19-15-16-20-28(27)40-32-24-36(48(10,11)12)35(47(7,8)9)23-31(32)39-26-18-14-13-17-25(26)37(29)41-42(38)44(40)43(39)41/h13-24H,1-12H3
InChIKey=CDVRNAINHDQBCN-UHFFFAOYAM

1a: InChI=1/C32H16/c1-2-10-18-17(9-1)25-19-11-3-4-12-20(19)27-23-15-7-8-16-24(23)28-22-14-6-5-13-21(22)26(18)30-29(25)31(27)32(28)30/h1-16H
InChIKey=QTVPEOVCCYEZNL-UHFFFAOYAK

The conformational preference of α-β-unsaturated carbonyl compounds is well established: the two π-bonds prefer to be in conjugation with the oxygen and three carbon atoms (nearly) coplanar. Now, what about the conformational preference of vinyl sulfoxides? Since the S-O π-bond is weak, alternate conformations might be favorable. Podlech has prepared some 1,3-dithian-1-oxides that should be conformationally static and thereby offer some insight into this question.¹ The dithiane oxides 1 and 2 can exist with the S-O bond in the axial (a) or equatorial (e) positions.

The B3LYP/6-31++G(d,p) geometries are shown in Figure 1. The equatorial structure has the two π bonds close to coplanar (the C-C-S-O dihedral is 14°), while in the axial isomers, the C-C-S-O dihedral is about -122°.

1a	1e
2a	2e

Figure 1. B3LYP/6-31++G(d,p) optimized structures of 1 and 2.

Podlech argues for a π_C=C → σ*_S-O stabilization in the axial isomer on the basis of two observations. First, the UV maximum absorbance in 1a is at 266nm, 12 nm greater than in 1e and similarly, the UV maximum in 2a is 2 nm higher than in 2e. Second, NBO analysis indicates a much larger contribution for this interaction in 1a (3.05 kcal mol^-1) than in 1e (0.07 kcal mol^-1).

However, I am unconvinced that this interaction is really dominant. Oxidation of the precursor dithiane with MCPBA gives a 42:58 ratio of 1e:1a and a 76:24 ratio of 2e:2a, which indicates a preference for the equatorial form of 1 and only a small preference for the axial form of 2. Unreported by Podlech (even in the supporting materials) is the relative computed energy difference of the two stereoisomers. At B3LYP/6-31++G(d,p) with ZPE, 1e is 2.6 kcal mol^-1 lower in energy than 1a and 2e is 0.05 kcal mol^-1 lower than 2a. So, in the gas-phase, it appears that the vinyl sulfoxides prefer the equatorial orientation, just as in α-β-unsaturated carbonyl compounds. The π_C=C → σ*_S-O interaction is stronger in the axial conformation, but it is doubtful that this alone manifests in any diastereomeric selectivity.

References

(1) Ulshöfer, R.; Podlech, J., "Stereoelectronic Effects in Vinyl Sulfoxides," J. Am. Chem. Soc. 2009, 131, 16618-16619, DOI: 10.1021/ja904354g

The standard model for explaining enzyme activation is that the active site is designed to stabilize the transition state, thereby reducing the activation barrier. Jonathan Goodman offers a very compelling argument for an alternative explanation for at least some enzymes.¹

He examined enzymes that coordinate the substrate through what’s called an “oxyanion hole”, a region in the active site where an incipient oxyanion can be stabilized through 2 or three hydrogen bonds. This usually involves nucleophilic attack at a carbonyl. Analysis of the protein data bank turned up several hundred such structures where a carbonyl is coordinated to the enzyme by 2 or more hydrogen bonds. Also examined were several hundred small molecule x-ray structures that also exhibit this sort of hydrogen bonding scheme. The geometry about the carbonyl oxygen was examined – distances angles and dihedral angles – and the only significant difference between the enzyme and small molecule set is for the dihedral angle formed between the O=C-R plane of the carbonyl and the C=O^…H angle to the hydrogen bond donor. For the small molecules, the preferred value is about 0°, but for the enzymes, the preferred angle is about 90°.

MPWB1K/6-311++G**//B3LYP/6-31G(d,p) computations of a model enzyme active site (see Scheme 1) were performed where the two waters are arranged at different dihedral angles. For both reactant and transition state, the coordinating waters stabilize the structures – and there is a stabilization for all dihedral angles.

Scheme 1

But the best arrangement, i.e. the maximum stabilization, occurs when the waters are arranged with a dihedral angle of 0° for both the reactant and transition state. At 0°, the reactant is significantly stabilized, more so than the stabilization of the TS. At 90° stabilization of both species is less than at 0° but the stabilization is much less for the reactant than for the TS. Thus, at 90° the activation barrier is lowered not by preferential stabilization of the TS but by lesser stabilization of the reactant! The active site is set up not to stabilize the TS but rather to minimize the activation barrier through differential stabilization of the reactant vs the TS. This new model offer another approach towards creating artificial catalysts, ones designed not to maximize binging, but rather to minimize the activation barrier through judicious stabilization of the TS and destabilization of the reactant.

References

(1) Simon, L.; Goodman, J. M., "Enzyme Catalysis by Hydrogen Bonds: The Balance between Transition State Binding and Substrate Binding in Oxyanion Holes," J. Org. Chem. 2010, DOI: 10.1021/jo901503d

Hard to believe but here’s another approach to dealing with intramolecular basis set super position error (BSSE). (I blogged on a previous approach here.) Jensen’s approach¹ is to define the atomic counterpoise correction as

ΔE_ACP = Σ E_A(basisSet_A) – E_A(basisSet_AS)

where this sum runs over all atoms in the molecule and E_A(basisSet_A) is the energy of atom A using the basis set centered on atom A. The key definition is of the last term E_A(basisSet_AS), where this is the energy of atom A using the basis set consisting of those function centered on atom A and some subset of the basis functions centered on the other atoms in the molecule. The key assumption then is just how to select the subset of ghost functions to include in the calculation of the second term.

For intermolecular basis set superposition error, Jensen suggests using the orbitals on atom A along with all orbitals on the other fragment, but not include the orbitals on other atoms in the same fragment where atom A resides. He demonstrates that this approach gives essentially identical superposition corrections as the traditional counterpoise correction for N₂, ethylene dimer and benzene dimer.

For intramolecular corrections, Jensen suggests keeping only the orbitals on atoms a certain bonded distance away from atom A. So for example, ACP(4) would indicate that the energy correction is made using all orbitals on atoms that are 4 or more bonds away from atom A. Jensen suggests in addition that orbitals on atoms that are farther than some cut-off distance away from atom A may also be omitted. He demonstrates the use of these ideas for the relative energies of tripeptide conformational energies.

So while the ACP method is conceptually simple, and also computationally efficient, it does require some playing around with the assumptions of which orbitals will comprise the appropriate subset. And it may be that one has to tune this selection for the individual system of interest.

References

(1) Jensen, F., "An Atomic Counterpoise Method for Estimating Inter- and Intramolecular Basis Set Superposition Errors," J. Chem. Theory Comput. 2010, 6, 100–106, DOI: 10.1021/ct900436f.

I have recently finished reading Free: The Future of a Radical Price by Chris Anderson (buy it here). The premise of the book is that giving things away is not only a serious business plan, it might just be the only business plan for the new economy. I found the book interesting, but ultimately disappointing. All of the models that are in practice or ones he proposes rest upon analogy to the old Gillette razor blade model: give away the razor and sell the blades. The perhaps most successful modern example is giving away search services and browsers and email services all supported by ad placement (Google). Perhaps less successful universally, but certainly working for some, are those bands who give away songs and albums, hoping it leads to concert visits where fans will not just buy tickets but also t-shirts and other paraphernalia.

Giving away stuff is a nice idea, and in the field of science, particularly computational science, we have lots of examples, like free operating systems, free technical software, and free databases. But in reality they’re not truly free.

The problem ultimately is that money needs to be made somewhere; people got to eat and put a roof over their heads and get clothes and that requires real cash. So virtually all of the people developing the computational tools are being paid in some other way - say off of an NSF grant, or by the university or by their commercial employer. Or one produces some code in the hope that it attracts attention that can lead to real paying employment; one might think of this as “reputation payment” that might sometime soon be cashed in for real currency!

Now some stuff, and that can include valuable stuff, is produced truly for free. A great example are the thousands of people who contribute to Wikipedia in their free time. Those chemists who have volunteered to clean up wikipedia entries have done a great job (like this one on the recently infamous PETN) and they not only don’t get paid, they largely contribute anonymously - so they don’t even get a “reputation payment”. The same goes for the many contributors to ChemSpider. But this work is done piecemeal and infrequently and must by definition be a personal low priority because of the need to do work that puts cash in hand.

So, that leads me to ask the question “why Blog? especially why blog in chemistry?” Not an easy one to really figure out, because unless one is just doing it on a lark or very infrequently, the time necessary to blog in a serious way is quite an investment. One has to figure out how to make the blog pay off in some way. Given that our community has not adopted blogging as a means for publishing original research, though Henry Rzepa is attempting to push on this course of action (see his blog), blogging must serve some other purpose, and one that can either directly pay cash or directly raise one’s reputation.

So I’ll answer the question for myself. I blog not for altruistic reasons. While I hope that the blog provides solid information and leads people to interesting articles, that’s not why I do it. Rather the blog serves to meet two goals, both directly related to potential cash. First, the blog is an ongoing update of my monograph Computational Organic Chemistry and so the blog serves as both a way to make the book more valuable to its owners and as a great advertisement for the book - hopefully leading to continuing new sales (like right here!). Second, the systematic blogging builds up materials for a new edition of the book that I hope to begin serious work on in 2011. These blog posts will certainly help reduce the time I anticipate needing to invest in the revisions. I hope the next edition can be as successful as the first has been so far.

So, I’d really like to encourage more people to be creative about making chemical blogs viable. I enjoy many of my colleagues’ blogs, and I wish they would blog more often and that others would also step into the breach. I moved the blog and the book website off of the university campus not just to take advantage of the services that the web host provides (like back-up and 24/7 availability, etc.), but to allow for the possibility of making the sites more commercial - like by including fixed ads or Google ads. I haven’t done this because the blog is really self-sustaining right now, but this route might be a way for more people to think about starting their own blogs.

And I’d like to see more serious scientific blogging that acts to push the boundaries of how we can use this technology to enhance our scientific communication. Remember, we are the chemistry community and if enough of us make this technology our own, others will have to take it seriously and adopt new communication modes. Otherwise, we are stuck kowtowing to the whims and fears of publishers and scientists afraid of the new.

Following up on his previous studies of isotope effects on the ring opening of cyclopropylcarbinyl radical 1 to give 2 (see my previous post), Borden now reports on its kinetic isotope effect (KIE).¹

Using the small-curvature tunneling approximation along with structures and frequencies computed at B3LYP/6-31G(d), he finds a negligible KIE at C₁, consistent with little motion of C₁ in the transition vector. The KIE for substitution at C₄ is large (k(¹²C/¹⁴C)=5.46), also consistent with its large motion in the transition vector. What is surprising is the KIE for deuterium substitution at C₁: 0.37. This is a large inverse isotope effect!

Analysis of the vibrational frequencies that involve the C₁ hydrogens provides an explanation. In going to the TS for the ring opening, both the torsional motion about the C₁-C₂ bond (making the double bond) and the pyramidal motion increase in frequency. This leads to a higher activation barrier for H than D, and the inverse isotope effect.

References

(1) Zhang, X.; Datta, A.; Hrovat, D. A.; Borden, W. T., “Calculations Predict a Large Inverse H/D Kinetic Isotope Effect on the Rate of Tunneling in the Ring Opening of Cyclopropylcarbinyl Radical,” J. Am. Chem. Soc., 2009, 131, 16002-16003, DOI: 10.1021/ja907406q.

Coming on the heels of the very nice combined computational/experimental study of the enantioselective Strecker reaction by Jacobsen (see this post), there’s this JACS communication that really disappoints in its use of computational chemistry. Cobb uses yet another chiral thiourea to produce the enantioselective intramolecular Michael addition of nitronoates (Reaction1).¹ The reaction goes with excellent diastereoselectivity and eneatioselectivity, and can even be done with a substrate to produce three chiral centers. This is very nice synthetic chemistry.

The lack of reactivity of the Z ester suggested that the thiourea must associate with both the nitro group and the ester carbonyl. The authors provide a B3LYP/3-21G complex of thiourea with a simple nitroester (once again without providing coordinates in the supporting materials!) to demonstrate this sort of association. But this single structure, at this very low computational level, with these simplified reagents, and lacking solvent (see Rzepa’s comment) really makes one wonder just what value this computation provides. It also goes to demonstrate just how much effort Jacobsen went through to provide substantive computational support for his proposed mechanism of action.

References

(1) Nodes, W. J.; Nutt, D. R.; Chippindale, A. M.; Cobb, A. J. A., "Enantioselective Intramolecular Michael Addition of Nitronates onto Conjugated Esters: Access to Cyclic γ-Amino Acids with up to Three Stereocenters," J. Am. Chem. Soc. 2009, 131, 16016-16017, DOI: 10.1021/ja9070915

The competition between Bergman cyclization and Myers-Saito cyclization of ene-ynes and related species is discussed in Chapter 3.3 of my book and also in these posts. Yet another variation, the Garratt-Braverman cyclization^1-3 has now been examined in terms of competition with the Myers-Saito cyclization for 1 using both experiments and computations.⁴ Subjecting 1 to base should cause the rearrangement to either GB1 or MS2. These can undergo either the Garratt-Braverman cyclization to give GB2 or the Myers-Saito cyclization to MS2.

B3LYP/6-31G(d) predicts that GB1 is only slightly higher in energy than MS1 (by 0.7 kcal mol^-1). The transition states (GB1toGB2 or MS1toMS2 - see Figure 1) each lie 24.4 kcal mol^-1 above their respective reactants. However, the diradical GB2 is 7.2 kcal mol^-1 below GB1 but MS2 is only 0.3 kcal mol^-1 below MS1. So while the two reactions are of similar kinetic probability, having identical activation barriers, the GB route leads to the more thermodynamically stable intermediate. Furthermore, the GB route ultimately results in GBP, via an intramolecular cyclization of the diradical, while the MS route, which ends with MSP, requires intermolecular abstraction of 4 hydrogens. Thus, the unimolecularity of the GB path further favors the GB route over the MS pathway. In fact, experimental studies of 1 and related compounds all give rise to the GB product only.

GB1	GB1toGB2
GB2
MS1	MS1toMS2
MS2

Figure 1. B3LYP/6-31G(d) optimized structures.⁴

References

(1) Braverman, S.; Segev, D., "Novel cyclization of diallenic sulfones," J. Am. Chem. Soc. 2002, 96, 1245-1247, DOI: 10.1021/ja00811a060

(2) Garratt, P. J.; Neoh, S. B., "Strained heterocycles. Properties of five-membered heterocycles fused to four-, six-, and eight-membered rings prepared by base-catalyzed rearrangement of 4-heterohepta-1,6-diynes," J. Org. Chem. 2002, 44, 2667-2674, DOI: 10.1021/jo01329a016

(3) Zafrani, Y.; Gottlieb, H. E.; Sprecher, M.; Braverman, S., "Sequential Intermediates in the Base-Catalyzed Conversion of Bis(π-conjugated propargyl) Sulfones to 1,3-Dihydrobenzo- and Naphtho[c]thiophene-2,2-dioxides," J. Org. Chem. 2005, 70, 10166-10168, DOI: 10.1021/jo051692i

(4) Basak, A.; Das, S.; Mallick, D.; Jemmis, E. D., "Which One Is Preferred: Myers-Saito Cyclization of Ene-Yne-Allene or Garratt-Braverman Cyclization of Conjugated Bisallenic Sulfone? A Theoretical and Experimental Study," J. Am. Chem. Soc. 2009, 131, 15695-15704, DOI: 10.1021/ja9023644

The longstanding unknown oxyallyl diradical (1) singlet-triplet gap has now been addressed with a very nice photoelectron spectroscopy study by Lineberger with interpretation greatly aided by computations provided by Hrovat and Borden.¹

The photoelectron detachment spectrum of oxyallyl radical anion shows 5 major peaks, one at 1.942 eV and a series of four peaks starting at 1.997 eV separated by 405 cm^-1.

B3LYP/6-311++G(d,p) computations indicate that the energy for electron detachment from the radical anion to triplet oxyallyl diradical is 1.979 eV. (The structure of triplet 1 is shown in Figure 1.) Further, the computed vibrational frequency of the C-C-C bend is 408 cm^-1. These computations suggest that the four peak sequence represents a vibrational progression in the C-C-C bend of the triplet oxyallyl diradical.

1A1

3B2

Figure 1. Structures of the singlet and triplet oxyallyl diradical 1.¹

CASPT2 computations on singlet oxyallayl diradical indicate that it lies in a very shallow well, lower than the zero-point energy. (This structure is shown in Figure 1.) In fact, the singlet diradical can collapse without a barrier to cyclopropanone. Interestingly, the C-O stretching frequency of 1 is computed to be 1731 cm^-1, and close inspection of the photoelectron spectrum does show a progression of this magnitude originating from peak A. Therefore, both the singlet and triplet states of 1 are identified and their gap is extraordinarily small – the singlet is only 0.055 eV lower in energy than the triplet.

References

(1) Ichino, T.; Villano, S. M.; Gianola, A. J.; Goebbert, D. J.; Velarde, L.; Sanov, A.; Blanksby, S. J.; Zhou, X.; Hrovat, D. A.; Borden, W. T.; Lineberger, W. C., "The Lowest Singlet and Triplet States of the Oxyallyl Diradical," Angew. Chem. Int. Ed., 2009, 48, 8509-8511, DOI: 10.1002/anie.200904417