Another two benchmarking studies of the performance of DFT have appeared.

The first is an examination by Csonka and French of the ability of DFT to predict the relative energy of carbohydrate conformation energies.¹ They examined 15 conformers of α- and β-D-allopyranose, fifteen conformations of 3,6-anydro-4-O-methyl-D-galactitol and four conformers of β-D-glucopyranose. The energies were referenced against those obtained at MP2/a-cc-pVTZ(-f)//B3LYP/6-31+G*. (This unusual basis set lacks the f functions on heavy atoms and d and diffuse functions on H.) Among the many comparisons and conclusions are the following: B3LYP is not the best functional for the sugars, in fact all other tested hybrid functional did better, with MO5-2X giving the best results. They suggest the MO5-2X/6-311+G**//MO5-2x/6-31+G* is the preferred model for sugars, except for evaluating the difference between ¹C₄ and ⁴C₁ conformers, where they opt for PBE/6-31+G**.

The second, by Korth and Grimme, describes a “mindless” DFT benchmarking study.²
This is really not a “mindless” study (as the term is used by Schaefer and Schleyer³ and discussed in this post, where all searching is done in a totally automated way) but rather Grimme describes a procedure for removing biases in the test set. Selection of “artificial molecules” is made by first deciding how many atoms are to be present and what will be the distribution of elements. In their two samples, they select systems having 8 atoms. The two sets differ by the distribution of the elements. The first set the atoms Na-Cl are one-third as probable as the elements Li-F, which are one-third as probable as H. The second set has the probability distribution similar to those found in naturally occurring organic compounds. The eight atoms, randomly selected by the computer, are placed in the corners of a cube and allowed to optimize (this is reminiscent of the “mindless” procedure of Schaefer and Schleyer³). This process generates a selection of random bonding environments along with open- and closed shell species, and removes (to a large degree) the biases of previous test sets, which are often skewed towards small molecules, ones where accurate experiments are available or geared towards a select group of molecules of interest. Energies are then computed using a variety of functional and compared to the energy at CCSD(T)/CBS. The bottom line is that the functional nicely group along the rungs defined by Perdew:⁴ LDA is the poorest performer, GGA does much better, the third rung of meta-GGA functionals are slightly better than GGA functionals, hybrids do better still, and the fifth rung functionals (double hybrids) perform quite well. Also of interest is that CCSD(T)/cc-pVDZ gives quite large errors and so Grimme cautions against using this small basis set.

References

(1) Csonka, G. I.; French, A. D.; Johnson, G. P.; Stortz, C. A., "Evaluation of Density Functionals and Basis Sets for Carbohydrates," J. Chem. Theory Comput. 2009, ASAP, DOI: 10.1021/ct8004479.

(2) Korth, M.; Grimme, S., ""Mindless" DFT Benchmarking," J. Chem. Theory Comput. 2009, ASAP, DOI: 10.1021/ct800511q.

(3) Bera, P. P.; Sattelmeyer, K. W.; Saunders, M.; Schaefer, H. F.; Schleyer, P. v. R., "Mindless Chemistry," J. Phys. Chem. A 2006, 110, 4287-4290, DOI: 10.1021/jp057107z.

(4) Perdew, J. P.; Ruzsinszky, A.; Tao, J.; Staroverov, V. N.; Scuseria, G. E.; Csonka, G. I., "Prescription for the design and selection of density functional approximations: More constraint satisfaction with fewer fits," J. Chem. Phys. 2005, 123, 062201-9, DOI: 10.1063/1.1904565

Singleton has again found a great example of a simple reaction that displays unmistakable non-statistical behavior.¹ The hydroboration of terminal alkenes proceeds with selectivity, preferentially giving the anti-Markovnikov product. The explanation for this selectivity is given in all entry-level organic textbooks – who would think that such a simple reaction could in fact be extraordinarily complex?

Reaction 1, designed to minimize the role of hydroboration involving higher order boron-hydrides (RBH₂ and R₂BH), the ratio of anti-Markovnikov to Markovinkov product is 90:10. Assuming that this ratio derives from the difference in the transition state energies leading to the two products, using transition state theory gives an estimate of the energy difference of the two activation barriers of 1.1 to 1.3 kcal mol^-1.

The CCSD(T)/aug-cc-pVDZ optimized structures of the precomplex between BH₃ and propene 1, along with the anti-Markovnikov transition state 2 and the Markovnikov transition state 3 are shown in Figure 2. The CCSD(T) energy extrapolated for infinite basis sets and corrected for enthalpy indicate that the difference between 2 and 3 is 2.5 kcal mol^-1. Therefore, transiitn state theory using this energy difference predicts a much greater selectivity of the anti-Markovnikov product, of about 99:1, than is observed.

1
2	3

Figure 1. CCSD(T)/aug-cc-pVDZ optimized geometries of 1-3.¹

In the gas phase, formation of the precomplex is exothermic and enthalpically barrierless. (A free energy barrier for forming the complex exists in the gas phase.) When a single THF molecule is included in the computations, the precomplex is formed after passing through a barrier much higher than the energy difference between 1 and either of the two transition states 2 or 3. (2 is only 0.8 kcal mol^-1 above 1 in terms of free energy.) So, Singleton speculated that there would be little residence time within the basin associated with 1 and the reaction might express non-statistical behavior.

Classical trajectories were computed. When trajectories were started at the precomplex 1, only 1% led to the Markovnikov product, consistent with transition state theory, but inconsistent with experiment. When trajectories were initiated at the free energy transition state for formation of the complex (either with our without a single complexed THF), 10% of the trajectories ended up at the Markovnikov product, as Singleton put it “fitting strikingly well with experiment”!

Hydroboration does not follow the textbook mechanism which relies on transition state theory. Rather, the reaction is under dynamic control. This new picture is in fact much more consistent with other experimental observations, like little change in selectivity with varying alkene substitution² and the very small H/D isotope effect of 1.18.³ Singleton adds another interesting experimental fact that does not jibe with the classical mechanism: the selectivity is little affect by temperature, showing 10% Markovnikov product at 21 °C and 11.2% Markovnikov product at 70 °C. Dynamic effect rears its ugly complication again!

References

(1) Oyola, Y.; Singleton, D. A., “Dynamics and the Failure of Transition State Theory in Alkene Hydroboration,” J. Am. Chem. Soc. 2009, 131, 3130-3131, DOI: 10.1021/ja807666d.

(2) Brown, H. C.; Moerikofer, A. W., “Hydroboration. XV. The Influence of Structure on the Relative Rates of Hydroboration of Representative Unsaturated Hydrocarbons with Diborane and with Bis-(3-methyl-2-butyl)-borane,” J. Am. Chem. Soc. 1963, 85, 2063-2065, DOI: 10.1021/ja00897a008.

(3) Pasto, D. J.; Lepeska, B.; Cheng, T. C., “Transfer reactions involving boron. XXIV. Measurement of the kinetics and activation parameters for the hydroboration of tetramethylethylene and measurement of isotope effects in the hydroboration of alkenes,” J. Am. Chem. Soc. 1972, 94, 6083-6090, DOI: 10.1021/ja00772a024.

Sheppard and Acevedo¹ have reported a careful re-examination of the ene reaction of singlet oxygen with alkenes that points out inherent difficulties in examining high-dimension potential energy surfaces by reducing the dimensionality.

Their work begins by careful reassessment of the computational study of Singleton, Foote and Houk.² These authors looked at the reaction of singlet oxygen with cis-2-butene by creating a 15×15 gird of optimized geometries holding the C-O distance fixed to specific values while letting the other geometric variables completely relax (see 1). These geometries were obtained at B3LYP/6-31G* and single-point energies were then obtained at CCSD(T)/6-31G*. They find two transiti0n states, one corresponding to symmetric addition of oxygen to the alkene 2 which leads to the pereperoxide 3. However, this pereperoxide 3 is not an intermediate, but rather a transition state for interconversion of the ene products 4 and 5. These structures and mechanism appear consistent with the experimental kinetic isotope effects. The authors characterize the reaction as “two-step no-intermediate”. Essentially, the reactants would cross the first transition state 1, encounter a valley-ridge inflection point that bifurcates reaction paths that go to either 3 or 4 and avoid ever reaching the second transition state 2.

Sheppard and Acevedo¹ tackle two major issues with this work. First, they are concerned about the role of solvent and so perform QM/MM computations with either DMSO, water of cyclohexane as solvent. The second factor is the choice of scanning just a 2-D grid as a projection of the multidimensional potential energy surface. Sheppard and Acevedo point out that since all other variable are optimized in this process, the hydrogen atom that is involved in the ene process must be bonded to either C or O and is therefore removed from the reaction coordinate. So they have performed a 3-D grid search where in addition to the two C-O distances they use the O-C-C angle as a variable. They find that this PES provides the more traditional stepwise pathway: a transition state that leads to formation of the pereperoxide intermediate and then a second transition state that leads to the ene product. In addition, solvent effects are significant, a not unexpected result given the large dipole of the pereperoxide.

But the main point here is that one must be very careful in reducing the dimensionality of the hypersurface and drawing conclusions from this reduced surface. It appears that the valley-ridge inflection point in the single oxygen ene reaction is an artifact of just this reduced dimensionality.

References

(1) Sheppard, A. N.; Acevedo, O., “Multidimensional Exploration of Valley-Ridge Inflection Points on Potential-Energy Surfaces,” J. Am. Chem. Soc. 2009, 131, 2530-2540, DOI: 10.1021/ja803879k.

(2) Singleton, D. A.; Hang, C.; Szymanski, M. J.; Meyer, M. P.; Leach, A. G.; Kuwata, K. T.; Chen, J. S.; Greer, A.; Foote, C. S.; Houk, K. N., “Mechanism of Ene Reactions of Singlet Oxygen. A Two-Step No-Intermediate Mechanism,” J. Am. Chem. Soc. 2003, 125, 1319-1328, DOI: 10.1021/ja027225p.

InChIs

Pereperoxide: InChI=1/C4H9O2/c1-3-4(2)6(3)5/h3-5H,1-2H3/t3-,4+
InChIKey=FRFPREFIPHRMOI-ZXZARUISBV

3: InChI=1/C4H8O2/c1-3-4(2)6-5/h3-5H,1H2,2H3/t4-/m1/s1
InChIKey=KRKIWMRTOODQMQ-SCSAIBSYBR

4: InChI=1/C4H8O2/c1-3-4(2)6-5/h3-5H,1H2,2H3/t4-/m0/s1
InChIKey=KRKIWMRTOODQMQ-BYPYZUCNBC

Tetraphenylene 1 has a saddle-shape. The barrier for interconverting the two mirror image saddles has been estimated to range from about 5 kcal mol^-1 to as much as 220 kcal mol^-1. These estimates were made either experimentally, by placing a substituent on the ring and measuring the energy needed to racemize the compound or by fairly primitive computation (CNDO).

Bau, Wong and co-workers have prepared the dideutero and dimethyl derivations 2 and 3.¹ The optical activity of 2 turns out to be far too small to be useful (and the effort expended to determine if 2 is enantiopure is truly heroic). 3 proved to have significant optical activity and so could be used to determine if enantiopure 3 racemized under heating. Amazingly, there was no measurable loss of optical activity upon heating at 550 °C for 4 hours. Rather, heating at higher temperature lead to decomposition and no noticeable racemization. To corroborate this very high barrier for racemization, they optimized the structure of 1 in its ground state saddle geometry 1s and in its planar form 1p, presumably the transition state for racemization. These two geometries (B3LYP/6-31G(d,p) are shown in Figure 1. The barrier is an astounding 135.8 kcal mol^-1, consistent with the experiment.

They apparently did not perform a frequency computation to confirm that 1p is a true transition state. In fact, Müllen, Klärner, Roth and co-workers demonstrated that the transition state for the ring flip of 1 is not planar.² They located a C₁ TS using MM2 that is some 66 kcal mol^-1 above the tub-shaped ground state.

I have just published a follow up study on 1 and the related benzannulated cyclooctatetraenes.³ The true transition state for the ring flip of 1 has D₄ symmetry (1ts) and is shown in Figure 1. The barrier for ring flip through 1ts is 76.5 kcal mol^-1 at B3LYP/6-31G(d,p) (78.6 kcal mol^-1 at MP2/6-31G(d,p)). This barrier is too large to be overcome by heating, and so Bau and Wong are correct in concluding that decomposition proceeds racemization.

1	1p
1ts

Figure 1. B3LYP/6-31G(d,p) structures of 1,¹ 1p,¹ and 1ts.³

References

(1) Huang, H.; Stewart, T.; Gutmann, M.; Ohhara, T.; Niimura, N.; Li, Y.-X.; Wen, J.-F.; Bau, R.; Wong, H. N. C., “To Flip or Not To Flip? Assessing the Inversion Barrier of the Tetraphenylene Framework with Enantiopure 2,15-Dideuteriotetraphenylene and 2,7-Dimethyltetraphenylene,” J. Org. Chem. 2009, 74, 359-369, DOI: 10.1021/jo802061p.

(2) Müllen, K.; Heinz, W.; Klärner, F.-G.; Roth, W. R.; Kindermann, I.; Adamczk, O.; Wette, M.; Lex, J., “Inversionsbarrieren ortho,ortho’-verbücketer Biphenyle,” Chem. Ber. 1990, 123, 2349-2371.

(3) Bachrach, S. M., “Tetraphenylene Ring Flip Revisited,” J. Org. Chem. 2009, DOI: 10.1021/jo900413d.

InChIs

1: InChI=1/C24H16/c1-2-10-18-17(9-1)19-11-3-4-13-21(19)23-15-7-8-16-24(23)22-14-6-5-12-20(18)22/h1-16H/b19-17-,20-18-,23-21-,24-22-
InChIKey=KTQYWNARBMKMCX-LEYBOLSUBU

2: InChI=1/C24H16/c1-2-10-18-17(9-1)19-11-3-4-13-21(19)23-15-7-8-16-24(23)22-14-6-5-12-20(18)22/h1-16H/b19-17-,20-18-,23-21-,24-22-/i1D,3D
InChIKey=KTQYWNARBMKMCX-UEXWXQHBFR

3: InChI=1/C26H20/c1-17-11-13-23-24-14-12-18(2)16-26(24)22-10-6-4-8-20(22)19-7-3-5-9-21(19)25(23)15-17/h3-16H,1-2H3/b20-19-,24-23-,25-21-,26-22-
InChIKey=XIGXQJCZIXRTIQ-CURPJEMVBV

Molecular structures can differ depending on phase, particularly between the gas and solution phase. Kass has looked at the protonation of 4-aminobenzoic acid. In water, the amino is its most basic site, but what is it in the gas phase? The computed relative energies of the protonation sites are listed in Table 1. If one corrects the B3LYP values for their errors in predicting the proton affinity of aniline and benzoic acid, the carbonyl oxygen is predicted to be the most basic site by 5.0 kcal mol^-1, in nice accord with the G3 prediction of 4.1 kcal mol^-1. Clearly, the structure depends on the medium.

Table 1. Computed relative proton affinities (kcal mol^-1) of 4-aminobenzoic acid.

Electrospray of 4-aminobenzoic acid from 3:1 methanol/water and 1:1 acetonitrile/water solutions gave different CID spectra. H/D exchange confirmed that electrospray from the emthanol/water solution gave the oxygen protonated species while that from the acetonitrile/water solution gave the ammonium species.

References

(1) Tian, Z.; Kass, S. R., “Gas-Phase versus Liquid-Phase Structures by Electrospray Ionization Mass Spectrometry,” Angew. Chem. Int. Ed., 2009, 48, 1321-1323, DOI: 10.1002/anie.200805392.

InChIs

4-aminobenzoic acid: InChI=1/C7H7NO2/c8-6-3-1-5(2-4-6)7(9)10/h1-4H,8H2,(H,9,10)/f/h9H
InChIKey=ALYNCZNDIQEVRV-BGGKNDAXCD

One more nail in the coffin of the widely disputed Le Clair structure of hexacyclinol is provided by the B97-2/cc-pVTZ/B3LYP/6-31G(d,p) computed proton and ¹³C NMR for the two “structures” (see my previous blog post for structures and background). These computations¹ are at a more rigorous level than those performed by Rychnovsky, and the addition of the proton spectrum helps clearly settle this issue. Rychnovsky’s structure is the correct one – the mean absolute error between the experimental and computed structure is half that for Rychnovsky structure. The computed coupling constants also are in much better agreement with the Rychnovsky structure. So, Bagno’s contribution accomplishes, I hope, two things: (1) convinces everyone that DFT NMR spectra can be an important tool in identifying natural product structure and (2) closes the book on hexacylinol!

References

(1) Saielli, G.; Bagno, A., "Can Two Molecules Have the Same NMR Spectrum? Hexacyclinol Revisited," Org. Lett. 2009, 11, 1409-1412, DOI: 10.1021/ol900164a.

The paper I will discuss here is a bit afield from computational organic chemistry, but it raises some interesting issues that tangentially touch on the main theme of my blog.

Roger Sayle of OpenEye describes a software tool for translating chemical names from one language into another, for example a name in English to the corresponding name in German or Japanese or Chinese.¹ One might imagine the many difficulties in this process – the strong dependency on very minor changes in the name can mean substantially different chemicals (think of propane vs. propene vs. propyne vs. propanol vs. propanal vs. propenal, etc.) and all this needs to be carefully recognized and translated.

My interest here is that chemical names including IUPAC names are really not the lingua franca of chemistry. Yes, chemists do use names but we really rely most on chemical structure drawings – that’s the surest way of transmitting our meaning to one another. But images are not a very good way for computers to communicate meaning. And that’s where the InChI label steps in. InChIs provide a standard means for two chemists (or two computers) to exchange chemical information without introducing errors and without the need for an intervening third-party to guarantee the meaning.

Here is a simple example of the benefit of the InChI using the first example from Sayle’s article. Figure 1 in his paper has the two similarly names compounds phenylacetate 1 and phenyl acetate 2. Note the critical importance of the blank space (actually this blank space is omitted in Figure 1 of the paper indicating just how easy it is for errors to sneak in!). Sayle points out that many languages beside English do not make use of whitespace in the way that English does, so that this translation must be done with special care.

Now the InChIs of 1 and 2 are unambiguous and will be the same in all (human) languages, eliminating the need of translation concerns. And if you’re unhappy with the length of the InChI, the InChIKey provides a fixed length string that captures almost all of the information of the InChI itself.

All compounds mentioned in my blog are listed at the end with their InChIs to promote the exchange of information and to encourage search-and-retrieval through the web. The leader in this sort of technology has been the Chemspider site, and I urge you to explore it and the use of InChIs.

As an aside, for all you Star Trek nerds, the paper includes this quote

and includes a reference to the Klingon Language Institute! This just might be the first time Klingon has appeared in a chemistry journal!

References

(1) Sayle, R., "Foreign Language Translation of Chemical Nomenclature by Computer," J. Chem. Inf. Model. 2009, DOI: 10.1021/ci800243w.

What is the rate determining step in the Hajos-Parrish-Eder-Sauer-Wiechert reaction (reaction 1)? This basic question of the mechanism for the first example of the use of proline as a catalyst remains unanswered, though a recent paper by Meyer and Houk¹ does moves us forward.

Their ¹³C kinetic isotope effect study revealed that only the nucleophilic ketone (the carboyl of the butyl chain) experiences any significant effect, with a value of about 1.03. B3LYP/6-31G(d,p) computations of the three transition states shown below were performed for both the gas phase and solution using IEF-PCM. Calculations of the transition state for the formation of the C-C bond (TS3) predicts no kinetic isotope effect, indicating that it is not the rate limiting step, in conflict with previous² suggestions. The transition states for the formation of the carbinolamine (TS1) and formation of the iminium (TS2) both predict an isotope effect comparable with experiment. TS1 is about 3 kcal mol^-1 higher in energy than TS2. The authors conclude that a step prior to formation of the C-C is the rate limiting step of the Hajos-Parrish-Eder-Sauer-Wiechert reaction, but cannot discern between the two possibilities examined.

References

(1) Zhu, H.; Clemente, F. R.; Houk, K. N.; Meyer, M. P., "Rate Limiting Step Precedes C-C Bond Formation in the Archetypical Proline-Catalyzed Intramolecular Aldol Reaction," J. Am. Chem. Soc., 2009, 131, 1632-1633, DOI: 10.1021/ja806672y.

(2) Clemente, F. R.; Houk, K. N., "Computational Evidence for the Enamine
Mechanism of Intramolecular Aldol Reactions Catalyzed by Proline," Angew. Chem. Int. Ed., 2004, 43, 5766-5768, DOI: 10.1002/anie.200460916.

InChIs

2-methyl-2-(3-oxobutyl)cyclopentane-1,3-dione:
InChI=1/C10H14O3/c1-7(11)5-6-10(2)8(12)3-4-9(10)13/h3-6H2,1-2H3
InChIKey=OZBYSCPBJGAYMQ-UHFFFAOYAW

(3aS,7aS)-3a-hydroxy-7a-methyl-3,4,6,7-tetrahydro-2H-indene-1,5-dione:
InChI=1/C10H14O3/c1-9-4-2-7(11)6-10(9,13)5-3-8(9)12/h13H,2-6H2,1H3/t9-,10+/m1/s1
InChIKey=PUHCDQVSBDIJTM-ZJUUUORDBA

Following on their prediction that the thiol of cysteine¹ is more acidic than the carboxylic acid group (see this post), Kass has examined the acidity of tyrosine 1.² Which is more acidic: the hydroxyl (leading to the phenoxide 2) or the carboxyl (leading to the carboxylate 3) proton?

Kass optimized the structures of tyrosine and its two possible conjugate bases at B3LYP/aug-cc-pVDZ, shown in Figure 1, and also computed their energies at G3B3. 2 is predicted to be 0.2 kcal mol^-1 lower in energy than 3 at B3LYP and slightly more stable at G3B3 (0.5 kcal mol^-1). However, both computational methods underestimate the acidity of acetic acid more than that of phenol. When the deprotonation energies are corrected for this error, the phenolic proton is predicted to be 0.4 kcal mol^-1 more acidic than the carboxylate proton at B3LYP and 0.9 kcal mol^-1 more acidic at G3B3.

1
2	3

Figure 1. B3LYP/aug-cc-pVDZ optimized structures of tyrosine 1 and its two conjugate bases 2 and 3.²

Gas phase experiments indicate that deprotonation of tyrosine leads to a 70:30 mixture of the phenoxide to carboxylate anions. The computations are in nice agreement with this experiment. (A Boltzmann weighting of the computed lowest energy conformers makes only a small difference to the distribution relative to using simply the single lowest energy conformer.) This demonstrates once again the important role of solvent, since only the carboxylate anion is seen in aqueous solution.

References

(1) Tian, Z.; Pawlow, A.; Poutsma, J. C.; Kass, S. R., "Are Carboxyl Groups the Most Acidic Sites in Amino Acids? Gas-Phase Acidity, H/D Exchange Experiments, and Computations on Cysteine and Its Conjugate Base," J. Am. Chem. Soc., 2007, 129, 5403-5407, DOI: 10.1021/ja0666194.

(2) Tian, Z.; Wang, X.-B.; Wang, L.-S.; Kass, S. R., "Are Carboxyl Groups the Most Acidic Sites in Amino Acids? Gas-Phase Acidities, Photoelectron Spectra, and Computations on Tyrosine, p-Hydroxybenzoic Acid, and Their Conjugate Bases," J. Am. Chem. Soc., 2009, 131, 1174-1181, DOI: 10.1021/ja807982k.

InChIs

1: InChI=1/C9H11NO3/c10-8(9(12)13)5-6-1-3-7(11)4-2-6/h1-4,8,11H,5,10H2,(H,12,13)/t8-/m0/s1/f/h12H
InChIKey=OUYCCCASQSFEME-QAXLLPJCDY

2: InChI=1/C9H11NO3/c10-8(9(12)13)5-6-1-3-7(11)4-2-6/h1-4,8,11H,5,10H2,(H,12,13)/p-1/t8-/m0/s1/fC9H10NO3/q-1
InChIKey=OUYCCCASQSFEME-HVHKCMLZDU

3: InChI=1/C9H11NO3/c10-8(9(12)13)5-6-1-3-7(11)4-2-6/h1-4,8,11H,5,10H2,(H,12,13)/p-1/t8-/m0/s1/fC9H10NO3/h11h,12H/q-1
InChIKey=OUYCCCASQSFEME-XGYCJDCADS

I missed this when it came out, but Quast, Sander and Borden have made the very interesting non-Kekule diradical 1.¹

³1

The EPR spectra shows the characteristic six-line signal, with zero-field splitting parameters consistent with related triplet diradicals. The Curie-Weiss plot is linear from 4.6 to 22.9 K. These data suggest a triplet ground state. CASSCF(14,14)/6-31G* computations indicate that the triplet lies 8.5 kcal mol^-1 below the singlet. The optimized triplet geometry is shown in Figure 1. The triplet ground state is consistent with the Borden-Davidson rules for radicals.²

31

Figure 1. CASSCF(14,14)/6-31G* optimized structure of triplet 1.

References

(1) Quast, H.; Nudling, W.; Klemm, G.; Kirschfeld, A.; Neuhaus, P.; Sander, W.; Hrovat, D. A.; Borden, W. T., "A Perimidine-Derived Non-Kekule Triplet Diradical," J. Org. Chem. 2008, 73, 4956-4961, DOI: 10.1021/jo800589y.

(2) Borden, W. T.; Davidson, E. R., "Effects of electron repulsion in conjugated hydrocarbon diradicals," J. Am. Chem. Soc. 1977, 99, 4587-4594, DOI: 10.1021/ja00456a010.

InChIs

1: InChI=1/C20H27N3/c1-19(2,3)13-8-12-9-14(20(4,5)6)11-16-17(12)15(10-13)22-18(21-7)23-16/h8-11H,1-7H3,(H2,21,22,23)/f/h22-23H
InChIKey=XAKUHDACNAUAAB-PDJAEHLQCL