Search Results for "protobranching"

Protobranching and the origin of the stability of branched alkanes

Once again, into the breach…

Ess, Liu, and De Proft offer another analysis of the protobranching effect.1 As a reminder, Schleyer, Mo and Houk and coworkers argue that the reason why branched alkanes are more stable than linear ones is a stabilizing 1,3-interaction that they call protobranching.2 This proposal has been met with both supporters and vigorous attacks – see these posts.

What is new here is a partitioning of the total DFT energy into three terms. The critical term is one based on the Weizäcker kinetic energy, which is defined as the integral of the gradient of the density squared divided by the density. They call this a “steric energy term”. The second term is the standard electrostatic term, and the last term, which really just picks up the slack, is a “fermionic quantum term”.

Using this partition, they examine a series of bond separation reactions involving alkanes with differing degrees of “protobranches”. The upshot is that the steric energy, which is destabilizing, is less in branched alkanes that linear ones. However, the fermionic quantum term essentially cancels this out, as branched alkanes, being more compact, are more destabilized by this fermionic effect than are linear alkanes. So, the only remaining term, electrostatics is responsible for the branched alkanes being more stable than linear alkanes.

This does not ultimately resolve the issue of whether the protobranching effect, as defined by Schleyer, Mo and Houk, is real, but these authors purposely chose to avoid that question.


(1) Ess, D. H.; Liu, S.; De Proft, F., "Density Functional Steric Analysis of Linear and Branched Alkanes," J. Phys. Chem. A, 2010, ASAP, DOI: 10.1021/jp108577g

(2) Wodrich, M. D.; Wannere, C. S.; Mo, Y.; Jarowski, P. D.; Houk, K. N.; Schleyer, P. v. R., "The Concept of Protobranching and Its Many Paradigm Shifting Implications for Energy Evaluations," Chem. Eur. J. 2007, 13, 7731-7744, DOI: 10.1002/chem.200700602

Uncategorized Steven Bachrach 15 Feb 2011 No Comments

A Protobranching model?

Kemnitz and co-workers have added to the protobranching debate (see these earlier posts i, ii, iii) with a proposal for how branching can be stabilizing.1 A normal chemical bond can be described within the valence bond prescription as an interplay of three different contributors: a covalent term (a) and two ionic terms (b and c). For a typical covalent bond, term a dominates, and for the recently proposed “charge-shift” bond (see this post), the ionic VB terms dominate.

Kemnitz now examines propane using a valence bond method and finds the following. The dominant VB term is the standard, two-covalent bond structure I. Next in importance are the single bond ionic VB structures II. Lastly, the 1,3-ionic structures III contribute about 9% to the total VB wavefunction. These contributions are only possible with branching and provide a net stabilization of about 1.6 kcal mol-1. This energy is nearly identical to the stabilization energy associated with the protobranching concept proposed by Schleyer, Houk and Mo. This type of ionic structure just might be the mechanism for protobranching stabilization.


(1) Kemnitz, C. R.; Mackey, J. L.; Loewen, M. J.; Hargrove, J. L.; Lewis, J. L.; Hawkins, W.
E.; Nielsen, A. F., "Origin of Stability in Branched Alkanes," Chem. Eur. J. 2010, 16,6942-6949, DOI: 10.1002/chem.200902550

Uncategorized Steven Bachrach 15 Jun 2010 No Comments

Protobranching once again!

An interesting little discussion on the meaning of “protobranching” appears in a comment1 and reply2 in J. Phys. Chem. A. Fishtik1 calls out the concept of protobranching on three counts:

  1. It is inconsistent to count a single protobranch for propane, but then not have three protobranches in cyclopropane
  2. It is inappropriate to utilize methane as a reference species.
  3. Group additivities work well.

I tend to side more with Schleyer2 in his rebuttal of these charges, and so will present from this perspective. First off, Schleyer argues that he can define protobranch anyway he wants! (He in fact cites a quote of Humpty Dumpty from Lewis Carroll to support this stance!) Schleyer is of course correct. Fishtik should really have argued “Does Schleyer’s definition of protobranch add to our understanding of strain?” So Fishtik claims that there is an internal inconsistency in Schleyer’s definition – taking the view point that the C-(C)2(H)2 group is identical to the protobranch. Schleyer counters that no, the protobranch is this group along with the caveat that the two terminal carbons are not connected, like they are in cyclopropane. I really prefer Gronert’s approach here – where he argues for just what are the implications of Schleyer’s definition (see this post).

Fishtik refuses to use methane as a reference since it is a unique molecule. Again, if one takes the group-centric view, then methane possesses a group that no other compound has. But Schleyer counters that one is free to choose whatever reference one thinks is appropriate, just be sure to understand what properties are conserved or not conserved when using that reference selection. To me, this is really the key for the entire discussion: choose one’s references in such a way as to minimize differences between your reference compound(s) and the molecule(s) you are trying to explore to just the property of interest. So, if one is interested in quantifying ring strain, the reference compounds should be not only be strain-free but they should differ in no other way from the cyclic molecule other than the presence of the ring! Unfortunately, there is no unique or non-arbitrary way to do this! Schleyer’s approach and Fishtik’s approach differ in just what properties they believe are important to conserve and which properties they are going to lump into the concept “ring strain”.

Fishtik shows a whole slew of reactions that demonstrate the consistency of group additivity methods. Schleyer correctly points out that these examples are really intimately related and represent only one type of definition. Again, there is really no unique set of references, and many, many different models have been developed, all of which can match experimental data quite well – like for example heats of formation. The key is what these models say in terms of interpreting, say, these heats of formation. Can one rationalize trends and make predictions with the model? If so, then it has utility. If not, then the model should be discarded. Ultimately, Fishtik’s argument is that the protobranching model does not assist us in understanding strain – Schleyer would obviously beg to differ!


(1) Fishtik, I., "Comment on "The Concept of Protobranching and Its Many Paradigm Shifting Implications for Energy Evaluations"," J. Phys. Chem. A, 2010, ASAP, DOI: 10.1021/jp908894q

(2) Schleyer, P. v. R.; McKee, W. C., "Reply to the "Comment on ‘The Concept of Protobranching and Its Many Paradigm Shifting Implications for Energy Evaluations’"," J. Phys. Chem. A, 2010, ASAP, DOI: 10.1021/jp909910f

Uncategorized Steven Bachrach 13 Apr 2010 3 Comments

Protobranching rebutted

Gronert1 has published a scathing criticism of the concept of “protobranching” (see my previous blog post) put forth by Schleyer, Houk and Ma2 – SHM for short. As a review, protobranching is the term coined by SHM for attractive 1,3-interactions in alkanes. They argue that these attractive 1,3-interactions are the reason for the energetic stability of the branched alkanes over the straight-chain alkanes. Their argument largely rests on the fact that Reaction 1 is exothermic by 2.8 kcal mol-1.

2 CH2CH3 → CH4 + CH3CH2CH3           Reaction 1

Gronert’s arguments are many and I will discuss only some of them. First, he notes that choosing ethane and methane as the reference molecules leads to all alkanes being stabilized. The stabilization energy of n-heptane is 5.7 kcal mol-1 and that of n-heptane is 14.1 kcal mol-1; is this a difference that is meaningful? Under the protobranching method, the stabilization energies of norbornane and n-heptane are quite similar (13.8 and 14.1 kcal mol-1, respectively) – does that mean they are equally strained? Similarly, protobranching leads to an extraordinary prediction for the resonance energy of benzene: 69 kcal mol-1. (I find these arguments quite compelling – the use of protobranching extenuates to magnitude of many chemical effects like ring strain, π-conjugation and resonance energy to the point that they become unusable.)

Gronert notes that the C-C-C angle in propane is larger than 109.5°, suggestive of a repulsive force, and one that is in fact much larger than suggested by SHM. The “attractive interaction” is not reproduced in intermolecular models. He points out the SHM attribute the attractive 1,3-interaction in alkenes to hyperconjugation and not to protobranching, and further notes that SHM correct for the strength of the C-H bond in ethyne but not for the Csp-C bond in propyne, nor do they make any such corrections for the alkenes.

But Gronert’s main complaint rests on the fact that there is simply no evidence for an attractive 1,3-interaction. All previous suggestions for this have been refuted by many others over the past 30 years. SHM’s main support rests on the ability to fit the thermodynamic trends, but Gronert points out that many other possibilities exist for doing so, including a repulsive model. There is ample evidence to support a repulsive interaction. It seems to me that Schleyer, Houk and Ma have their work cut out for them to carefully rebut Gronert’s arguments.


(1) Gronert, S., "The Folly of Protobranching: Turning Repulsive Interactions into Attractive Ones and Rewriting the Strain/Stabilization Energies of Organic Chemistry," Chem. Eur. J. 2009, DOI: 10.1002/chem.200800282

(2) Wodrich, M. D.; Wannere, C. S.; Mo, Y.; Jarowski, P. D.; Houk, K. N.; Schleyer, P. v. R., "The Concept of Protobranching and Its Many Paradigm Shifting Implications for Energy Evaluations," Chem. Eur. J. 2007, 13, 7731-7744, DOI: 10.1002/chem.200700602

Uncategorized Steven Bachrach 01 May 2009 6 Comments


Schleyer and Houk1 offer a provocative paper examining the reference compounds that one chooses when trying to evaluate such concepts as ring strain energy and aromaticity. I discuss this at length in Chapter 2 of the book, focusing on the isodesmic, homodesmotic, and group equivalent reactions.

Their work starts with the isodesmic reaction

CH3CH2CH3 + CH4 → 2 CH3CH3

and note that this reaction is endothermic by 2.83 kcal mol-1. They argue that 1,3-dialkyl interactions are stabilizing, and call this effect “protobranching”.

Gronert2,3 has recently described the counterargument – that 1,3-dialkyl groups are repulsive – but whether the interaction is attractive or repulsive is not my concern here. Let’s proceed assuming that protobranching is in fact stabilizing.

Schleyer and Houk demonstrate that the stabilization of protobranching is nicely additive. In Table 1 are simple bond separation (isodesmic) reactions of straight-chain alkanes and cycloalkanes. This can then be extended to argue for why branched alkanes are more stable than their straight-chain analogues – namely, branched chains have more 1,3-dialkyl interactions and these are stabilizing. They note that the group separation reaction of iso-butane is more endothermic than that of pentane, yet the difference is neatly ascribed to protobranching.

Table 1. Energy of reactions and energy per protobranch (PB) using experimental heats of formation.



# PB

E per PB

CH3CH2CH3 + CH4 → 2 CH3CH3




CH3(CH2)2CH3 + 2 CH4 → 3 CH3CH3




CH3(CH2)3CH3 + 4 CH4 → 6 CH3CH3




(CH2)6 + 6 CH4 → 6 CH3CH3




CH(CH3)3 + 2 CH4 → 3 CH3CH3




Now the interesting aspect is when this concept of protobranching is applied to ring systems. The conventional (homodesmotic) reaction for cyclopropane is

(CH2)3 + 3 C2H6 → 3 CH3CH2CH3 ΔH = -27.7 kcal mol-1

Schleyer and Houk argue that protobranching is not balanced in this reaction, and the consequence is that since propane is stabilized by about 2.8 kcal mol-1, the reaction energy should be reduced by 8.4 kcal mol-1. Thus the ring strain energy (RSE) of cyclopropane is 19.3 kcal mol-1. This is essentially the value obtained when one employs the isodesmic reaction to evaluate the RSE of cyclopropane, namely

(CH2)3 + 3 CH4 → 3 C2H6 ΔH = -19.2 kcal mol-1

And this isodesmic reaction has balanced protobrancing (none!) on both sides. The reaction that balances protobranching (two on each side) for obtaining the RSE of cyclobutane is

(CH2)4 + 2 CH4 → 2 CH3CH2CH3 ΔH = -21.0 kcal mol-1

Protobranching corrections need also be made to the question of aromatic stabilization energy or resonance energy of benzene. For example, since cyclohexane is invoked as one of the reference compounds in the following reaction, the resulting energy must be corrected for six protobranching interactions.

2 C2H4 + (CH2)6 → (CH)6 + 3 C2H6

The question now becomes “Is protobranching real and do we need to correct for it?” Further studies should be performed.


(1) Wodrich, M. D.; Wannere, C. S.; Mo, Y.; Jarowski, P. D.; Houk, K. N.; Schleyer, P. v. R., "The Concept of Protobranching and Its Many Paradigm Shifting Implications for Energy Evaluations," Chem. Eur. J. 2007, 13, 7731-7744, DOI: 10.1002/chem.200700602

(2) Gronert, S., "Evidence that Alkyl Substitution Provides Little Stabilization to Radicals: The C-C Bond Test and the Nonbonded Interaction Contradiction," J. Org. Chem., 2006, 71, 7045-7048, DOI: 10.1021/jo060797y.

(3) Gronert, S., "An Alternative Interpretation of the C-H Bond Strengths of Alkanes," J. Org. Chem., 2006, 71, 1209-1219, DOI: 10.1021/jo052363t.

Houk &Schleyer Steven Bachrach 15 Oct 2007 1 Comment

Origin of DFT failures – part II

Here’s one more attempt to discern the failure of DFT to handle simple alkanes (see this earlier post for a previous attempt to answer this question). Tsuneda and co-workers1 have employed long-range corrected (LC) DFT to the problem of the energy associated with “protobranching”, i.e., from the reaction

CH3(CH2nCH3 + n CH4 → (n+1) CH3CH3

They computed the energy of this reaction for the normal alkanes propane through decane using a variety of functionals, and compared these computed values with experimentally-derived energies. Table 1 gives the mean unsigned error for a few of the functionals. The prefix “LC” indicated inclusion of long-range corrections, “LCgau” indicates the LC scheme with a gaussian attenuation, and “LRD” indicates inclusion of long-range dispersion.

Table 1. Mean unsigned errors of the “protobranching”
reaction energy of various functional compared to experiment.


(kcal mol-1)



















A number of important conclusions can be drawn. First, with both LC and LRD very nice agreement with experiment can be had. If only LC is included, the error increases on average by over 1 kcal mol-1. The MO6-2x functional, touted as a fix of the problem, does not provide complete correction, though it is vastly superior to B3LYP and other hybrid functionals. The authors conclude that the need for LC incorporation points out that the exchange functional lacks the ability to account for this effect. Medium-range correlation is not the main source of the problem as large discrepancies in the reaction energy error occur when different functionals are used that are corrected for LC and LRD. Choice of functional still matters, but LC correction appears to be a main culprit and further studies of its addition to standard functionals would be most helpful.


(1) Song, J.-W.; Tsuneda, T.; Sato, T.; Hirao, K., "Calculations of Alkane Energies Using Long-Range Corrected DFT Combined with Intramolecular van der Waals Correlation," Org. Lett. 2010, 12, 1440–1443, DOI: 10.1021/ol100082z

DFT Steven Bachrach 25 May 2010 6 Comments

Problems with DFT

We noted in Chapter 2.1 some serious errors in the prediction of bond dissociation energies using B3LYP. For example, Gilbert examined the C-C bond dissociation energy of some simple branched alkanes.1 The mean absolute deviation (MAD) for the bond dissociation energy predicted by G3MP2 is 1.7 kcal mol-1 and 2.8 kcal mol-1 using MP2. In contrast, the MAD for the B3LYP predicted values is 13.7 kcal mol-1, with some predictions in error by more than 20 kcal mol-1. Furthermore, the size of the error increases with the size of the molecule. Consistent with this trend, Curtiss and co-workers noted a systematic underestimation of the heat of formation of linear alkanes of nearly 0.7 kcal mol-1 per bond using B3LYP.2

Further evidence disparaging the general performance of DFT methods (and B3LYP in particular) was presented in a paper by Grimme and in two back-to-back Organic Letters articles, one by Schreiner and one by Schleyer. Grimme3 noted that the relative Energy of two C8H18 isomers, octane and 2,2,3,3-tetramethylbutane are incorrectly predicted by DFT methods (Table 1). While MP2 and CSC-MP2 (spin-component-scaled MP2) correctly predict that the more branched isomer is more stable, the DFT methods predict the inverse! Grimme attributes this error to a failure of these DFT methods to adequately describe medium-range electron correlation.

Table 1. Energy (kcal mol-1) of 2,2,3,3-tetramethylbutane relative to octane.

Method ΔE
Expta 1.9 ± 0.5
MP2b,c 4.6
SCS-MP2b,c 1.4
PBEb,c -5.5
TPSShb,c -6.3
B3LYPb,c -8.4
BLYPb,c -9.9
M05-2Xd,e 2.0
M05-2Xc,d 1.4

aNIST Webbook ( bRef. 3. cUsing the cQZV3P basis set and MP2/TZV(d,p) optimized geometries. dRef. 4. eCalculated at M05-2X/6-311+G(2df,2p).

Schreiner5 also compared the energies of hydrocarbon isomers. For example, the three lowest energy isomers of C12H12 are 1-3, whose B3LYP/6-31G(d) structures are shown in Figure 1. What is disturbing is that the relative energies of these three isomers depends strongly upon the computational method (Table 2), especially since these three compounds appear to be quite ordinary hydrocarbons. CCSD(T) predicts that 2 is about 15 kcal mol-1 less stable than 1 and that 3 lies another 10 kcal mol-1 higher in energy. MP2 exaggerates the separation by a few kcal mol-1. HF predicts that 1 and 2 are degenerate. The large HF component within B3LYP leads to this DFT method’s poor performance. B3PW91 does reasonably well in reproducing the CCSD(T) results.

Table 2. Energies (kcal mol-1) of 2 and 3 relative to 1.

Method 2 3
CCSD(T)/cc-pVDZ//MP2(fc)/aug-cc-pVDZa 14.3 25.0
CCSD(T)/cc-pVDZ//B3LYP/6-31+G(d)a 14.9 25.0
MP2(fc)/aug-cc-pVDZa 21.6 29.1
MP2(fc)/6-31G(d)a 23.0 30.0
HF/6-311+(d) a 0.1 6.1
B3LYP/6-31G(d)a 4.5 7.2
B3LYP/aug-cc-pvDZa 0.4 3.1
B3PW91/6-31+G(d) a 17.3 23.7
B3PW91/aug-cc-pVDZa 16.8 23.5
KMLYP/6-311+G(d,p)a 28.4 41.7
M05-2X/6-311+G(d,p)b 16.9 25.4
M05-2X/6-311+G(2df,2p)b 14.0 21.4

aRef. 5. bRef. 4.



xyz file



xyz file



xyz file

Figure 1. Structures of 1-3 at B3LYP/6-31G(d).

Another of Schreiner’s examples is the relative energies of the C1010 isomers; Table 3 compares their relative experimental heats of formation with their computed energies. MP2 adequately reproduces the isomeric energy differences. B3LYP fairs quite poorly in this task. The errors seem to be most egregious for compounds with many single bonds. Schreiner recommends that while DFT-optimized geometries are reasonable, their energies are unreliable and some non-DFT method should be utilized instead.

Table 3. Relative C10H10 isomer energies (kcal mol-1)5



Rel. E(B3LYP)

Rel. E(MP2)




























aCorrelation coefficient between Rel. ΔHf and Rel. E(B3LYP). bCorrelation coefficient between Rel. ΔHf and Rel. E(MP2).

Schleyer’s example of poor DFT performance is in the isodesmic energy of Reaction 1 evaluated for the n-alkanes.6 The energy of this reaction becomes more positive with increasing chain length, which Schleyer attributes to stabilizing 1,3-interactions between methyl or methylene groups. (Schleyer ascribes the term “protobranching” to this phenomenon.) The stabilization energy of protobranching using experimental heats of formation increases essentially linearly with the length of the chain, as seen in Figure 2.

n-CH3(CH2)mCH3 + mCH4 → (m + 1)C2H6         Reaction 1

Schleyer evaluated the protobranching energy using a variety of methods, and these energies are also plotted in Figure 2. As expected, the G3 predictions match the experimental values quite closely. However, all of the DFT methods underestimate the stabilization energy. Most concerning is the poor performance of B3LYP. All three of these papers clearly raise concerns over the continued widespread use of B3LYP as the de facto DFT method. Even the new hybrid meta-GGA functionals fail to adequately predict the protobranching phenomenon, leading Schleyer to conclude: “We hope that Check and Gilbert’s pessimistic admonition that ‘a computational chemist cannot trust a one-type DFT calculation’1 can be overcome eventually”. These papers provide a clear challenge to developers of new functionals.

Figure 2. Comparison of computed and experimental protobranching stabilization energy (as defined in Reaction 1) vs. m, the number of methylene groups of the n-alkane chain.6

Truhlar believes that one of his newly developed functionals answers the call for a reliable method. In a recent article,4 Truhlar demonstrates that the M05-2X7 functional performs very well in all three of the cases discussed here. In the case of the C8H18 isomers (Table 1), M05-2X properly predicts that 2,2,3,3-tetramethylbutane is more stable than octane, and estimates their energy difference within the error limit of the experiment. Second, M05-2X predicts the relative energies of the C12H12 isomers 1-3 within a couple of kcal mol-1 of the CCSD(T) results (see Table 2). Last, in evaluating the isodesmic energy of Reaction 1 for hexane and octane, M05-2X/6-311+G(2df,2p) predicts energies of 11.5 and 17.2 kcal mol-1 respectively. These are in excellent agreement with the experimental values of 13.1 kcal mol-1 for butane and 19.8 kcal mol-1 for octane.

Truhlar has also touted the M05-2X functional’s performance in handling noncovalent interactions.8 For example, the mean unsigned error (MUE) in the prediction of the binding energies of six hydrogen-bonded dimers is 0.20 kcal mol-1. This error is comparable to that from G3 and much better than CCSD(T). With the M05-2X functional already implemented within NWChem and soon to be released within Gaussian and Jaguar, it is likely that M05-2X may supplant B3LYP as the new de facto functional in standard computational chemical practice.

Schleyer has now examined the bond separation energies of 72 simple organic molecules computed using a variety of functionals,9 including the workhorse B3LYP and Truhlar’s new M05-2X. Bond separation energies are defined by reactions of each compound, such as three shown below:

The new M05-2X functional performed the best, with a mean absolute deviation (MAD) from the experimental energy of only 2.13 kcal mol-1. B3LYP performed much worse, with a MAD of 3.96 kcal mol-1. As noted before, B3LYP energies become worse with increasing size of the molecules, but this problem is not observed for the other functionals examined (including PW91, PBE, and mPW1PW91, among others). So while M05-2X overall appears to solve many of the problems noted with common functionals, it too has some notable failures. In particular, the error is the bond separation energies of 4, 5, and 6 is -8.8, -6.8, and -6.0 kcal mol-1, respectively.


(1) Check, C. E.; Gilbert, T. M., “Progressive Systematic Underestimation of Reaction Energies by the B3LYP Model as the Number of C-C Bonds Increases: Why Organic Chemists Should Use Multiple DFT Models for Calculations Involving Polycarbon Hydrocarbons,” J. Org. Chem. 2005, 70, 9828-9834, DOI: 10.1021/jo051545k.

(2) Redfern, P. C.; Zapol, P.; Curtiss, L. A.; Raghavachari, K., “Assessment of Gaussian-3 and Density Functional Theories for Enthalpies of Formation of C1-C16 Alkanes,” J. Phys. Chem. A 2000, 104, 5850-5854, DOI: 10.1021/jp994429s.

(3) Grimme, S., “Seemingly Simple Stereoelectronic Effects in Alkane Isomers and the Implications for Kohn-Sham Density Functional Theory,” Angew. Chem. Int. Ed. 2006, 45, 4460-4464, DOI: 10.1002/anie.200600448

(4) Zhao, Y.; Truhlar, D. G., “A Density Functional That Accounts for Medium-Range Correlation Energies in Organic Chemistry,” Org. Lett. 2006, 8, 5753-5755, DOI: 10.1021/ol062318n

(5) Schreiner, P. R.; Fokin, A. A.; Pascal, R. A.; deMeijere, A., “Many Density Functional Theory Approaches Fail To Give Reliable Large Hydrocarbon Isomer Energy Differences,” Org. Lett. 2006, 8, 3635-3638, DOI: 10.1021/ol0610486

(6) Wodrich, M. D.; Corminboeuf, C.; Schleyer, P. v. R., “Systematic Errors in Computed Alkane Energies Using B3LYP and Other Popular DFT Functionals,” Org. Lett. 2006, 8, 3631-3634, DOI: 10.1021/ol061016i

(7) Zhao, Y.; Schultz, N. E.; Truhlar, D. G., “Design of Density Functionals by Combining the Method of Constraint Satisfaction with Parametrization for Thermochemistry, Thermochemical Kinetics, and Noncovalent Interactions,” J. Chem. Theory Comput. 2006, 2, 364-382, DOI: 10.1021/ct0502763.

(8) Zhao, Y.; Truhlar, D. G., “Assessment of Model Chemistries for Noncovalent Interactions,” J. Chem. Theory Comput. 2006, 2, 1009-1018, DOI: 10.1021/ct060044j.

(9) Wodrich, M. D.; Corminboeuf, C.; Schreiner, P. R.; Fokin, A. A.; Schleyer, P. v. R., “How Accurate Are DFT Treatments of Organic Energies?,” Org. Lett., 2007, 9, 1851-1854, DOI: 10.1021/ol070354w.


1: InChI=1/C11H10/c1-2-5-7-3(1)4(1)8-6(2)10-9(5)11(7,8)10/h1-10H

2: InChI=1/C12H12/c1-2-4-10-6-8-11-7-5-9(3-1)12(10)11/h1-12H

3: InChI=1/C12H12/c1-2-4-8-11(7-3-1)12-9-5-6-10-12/h1-12H

4: InChI=1/C6H6/c1-4-5(2)6(4)3/h1-3H2

5: InChI=1/C8H10/c1-3-7-5-6-8(7)4-2/h3-4H,1-2,5-6H2

6: InChI=1/C10H10/c1-2-8-5-6-9-4-3-7(1)10(8)9/h1-10H

DFT &Schleyer &Schreiner &Truhlar Steven Bachrach 13 Jul 2007 5 Comments