Search Results for "bifurcat"

Bifurcation on a terpene synthesis pathway

Unusual potential energy surfaces are a theme of this blog and my book (see chapter 7). Examples might include bifurcations and valley inflection points and often lead to unusual dynamics. Tantillo has now reported a bifurcation on the PES for terpene synthesis, specifically the pathway for synthesis of abietadiene.1

Tantillo discusses two possible cation rearrangement pathways. The first is pretty ordinary, but in the second, the precursor cation 1 can rearrange through either of two transition states 2a or 2b (Scheme 1). The IRC computation from 2a connects back to 1, but in the forward direction it connects to another transition state 3. This TS (3) connects products 4 and 5. These structures are drawn in Figure 1.

Thus, the potential energy surface displays a bifurcation, and one might expect unusual dynamic effects to operate.

Scheme 1




Figure 1. B3LYP/6-31+G(d,p) optimized transition structures of 2-3.1


(1) Hong, Y. J.; Tantillo, D. J., "A potential energy surface bifurcation in terpene biosynthesis," Nature Chem. 2009, 1, 384-389 DOI: 10.1038/nchem.287.

Dynamics Steven Bachrach 21 Sep 2009 5 Comments

Bifurcating organic reactions

Ken Houk has produced a very nice minireview on bifurcations in organic reactions.1 This article is a great introduction to a topic that has broad implication for mechanistic concepts. Bifurcations result when a valley-ridge inflection point occurs on or near the intrinsic reaction coordinate. This inflection point allows trajectories to split into neighboring basins (to proceed to different products) without crossing a second transition state. In the examples discussed, the reactant crosses a single transition state and then leads to two different products. This is the so-called “two-step no intermediate” process.

I discuss the implications of these kinds of potential energy surfaces, and other ones of a pathological nature, in the last chapter of my book. Very interesting reaction dynamics often are the result, leading to a mechanistic understanding far from the ordinary!


(1) Ess, D. H.; Wheeler, S. E.; Iafe, R. G.; Xu, L.; Çelebi-Ölçüm, N.; Houk, K. N., "Bifurcations on Potential Energy Surfaces of Organic Reactions," Angew. Chem. Int. Ed. 2008, DOI: 10.1002/anie.200800918

Dynamics &Houk Steven Bachrach 11 Sep 2008 No Comments

Dynamics in a [3,3]-rearrangement

Bispericyclic reactions occur when two different pericyclic reactions merge to have a single transition state. An example of this is the joining of two [3,3]-sigmatopic rearrangements of 1 that merge to have a single transition state. Lopez, Faza, and Lopez have examined the dynamics of this reaction.1

Because of the symmetry of the species along this reaction pathway, the products of the two different rearrangements are identical, and will be formed in equal amounts, though they are produced from a single transition state with the reaction pathway bifurcating due to a valley-ridge inflection post TS.

The interesting twist that is explored here is when 1 is substituted in order to break the symmetry. The authors have examined 3x with either fluorine, chlorine, or bromine. The critical points on the reactions surface were optimized at M06-2X/Def2TZVPP. In all three cases a single bispericyclic transition state 3TS1x is found, which leads to products 4a and 4b. A second transition state 4TSx corresponds to the [3,3]-rearrangement that interconverts the two products. The structures of 1TS, 3TS1F, and 3TS1Cl are shown in Figure 1.




Figure 1. M06-2X/Def2TZVPP optimized geometries of 1TS, 3TS1F, and 3TS1Cl.

The halogen substitution breaks the symmetry of the reaction path. This leads to a number of important changes. First, the C4-C5 and C7-C8 distances, which are identical in 1TS, are different in the halogen cases. Interestingly, the distortions are dependent on the halogen: in 3TS1F C4-C5 is 0.2 Å longer than C7-C8, but in 3TS1Cl C7-C8 is much longer (by 0.65 Å) than C4-C5. Second, the products are no longer equivalent with the halogen substitution. Again, this is halogen dependent: 4bF is 4.0 kcal mol-1 lower in energy than 4aF, while 4aCl is 8.2 kcal mol-1 lower than 4bCl.

These difference manifest in very different reaction dynamics. With trajectories initiated at the first (bispericyclic) transiting state, 89% end at 4bF and 9% end at 4aF, a ratio far from unity that might be expected from both products resulting from passage through the same TS. The situation is even more extreme for the chlorine case, where all 200 trajectories end in 4aCl. This is yet another example of the role that dynamics play in reaction outcomes (see these many previous posts).


1) Villar López, R.; Faza, O. N.; Silva López, C., "Dynamic Effects Responsible for High Selectivity in a [3,3] Sigmatropic Rearrangement Featuring a Bispericyclic Transition State." J. Org. Chem. 2017, 82 (9), 4758-4765, DOI: 10.1021/acs.joc.7b00425.


1: InChI=1S/C9H12/c1-3-9-6-4-8(2)5-7-9/h1-2,4-7H2

2: InChI<=1S/C9H12/c1-7-4-5-8(2)9(3)6-7/h1-6H2

3F: InChI=1S/C9H8F4/c1-3-7-5-4-6(2)8(10,11)9(7,12)13/h1-2,4-5H2

3Cl: InChI=1S/C9H8Cl4/c1-3-7-5-4-6(2)8(10,11)9(7,12)13/h1-2,4-5H2

4aF: InChI=1S/C9H8F4/c1-5-4-6(8(10)11)2-3-7(5)9(12)13/h1-4H2

4aCl: InChI=1S/C9H8Cl4/c1-5-4-6(8(10)11)2-3-7(5)9(12)13/h1-4H2

4bF: InChI=1S/C9H8F4/c1-5-4-6(2)8(10,11)9(12,13)7(5)3/h1-4H2

4bCl: InChI=1S/C9H8Cl4/c1-5-4-6(2)8(10,11)9(12,13)7(5)3/h1-4H2

Cope Rearrangement &Dynamics Steven Bachrach 05 Jun 2017 No Comments

SpnF revisited

Medvedev, et al. have examined the cyclization step in the formation of Spinosyn A, which is catalyzed by the putative Diels-Alderase enzyme SpnF.1 This work follows on the computational study done by Houk, Singleton and co-workers,2 which I have discussed in this post (Dynamics in a reaction where a [6+4] and [4+2] cycloadditons compete). In fact, I recommend that you read the previous post before continuing on with this one. In summary, Houk, et al. found that a single transition state connects reactant 1 to both 2 and 3. The experimental product with the enzyme SpnF is 3. In the absence of enzyme, Houk, et al. suggest that reactions will cross the bispericyclic transition state TS-BPC (TS1 in the previous post) leading primarily to 2, which then undergoes a Cope rearrangement to get to product 3. Some molecules will follow pathways that go directly to 3.

The PCM(water)/M06-2x/6-31+G(d) study by Medvedev, et al. first identifies 560 conformations of 3. Next, they identified 384 TSs lying within 30 kcal mol-1 from the lowest TS. These can be classified as either TS-DA (leading directly to 3) or TS-BPC (which may lead to 2 by steepest descent, but can bifurcate towards 3). They opt to utilize the Atoms-in-Molecules theory to identify bond critical points to categorize these TS, and find that 144 are TS-BPC and 240 are TS-DA. (The transition state found by Houk, et al. is the second lowest energy TS found in this study, 0.29 kcal mol-1 higher in energy that the lowest TS and also of TS-BPC type.)

They also examined two alternative routes. First, they propose a path that first takes 1 to 4 via an alternative Diels-Alder reaction, and a second Cope rearrangement (TS-Cope2) takes this to 2, which can then convert to 3 via TS-Cope1. The other route involves a biradical pathway to either A or B. These alternatives prove to be non-competitive, with transition state energies significantly higher than either TS-DA or TS-BPC.

Returning to the set of TS-DA and TS-BPC transition states, while the former are more numerous, the latter are lower in energy. In summary, this study further complicates the complex situation presented by Houk, et. al. In the absence of catalyst, 1 can undergo either a Diels-Alder reaction to 3, or pass through a bispericyclic transition state that can lead to 3, but principally to 2 and then undergo a Cope rearrangement to get to 3. The question that ends my previous post on this subject — “ just what role does the enzyme SpnF play?” — remains to be answered.


1) Medvedev, M. G.; Zeifman, A. A.; Novikov, F. N.; Bushmarinov, I. S.; Stroganov, O. V.; Titov, I. Y.; Chilov, G. G.; Svitanko, I. V., "Quantifying Possible Routes for SpnF-Catalyzed Formal Diels–Alder Cycloaddition." J. Am. Chem. Soc. 2017, 139, 3942-3945, DOI: 10.1021/jacs.6b13243.

2) Patel, A.; Chen, Z.; Yang, Z.; Gutiérrez, O.; Liu, H.-w.; Houk, K. N.; Singleton, D. A., "Dynamically Complex [6+4] and [4+2] Cycloadditions in the Biosynthesis of Spinosyn A." J. Am. Chem. Soc. 2016, 138, 3631-3634, DOI: 10.1021/jacs.6b00017.


1: InChI=1S/C24H34O5/c1-3-21-15-12-17-23(27)19(2)22(26)16-10-7-9-14-20(25)13-8-5-4-6-11-18-24(28)29-21/h4-11,16,18-21,23,25,27H,3,12-15,17H2,1-2H3/b6-4+,8-5+,9-7+,16-10+,18-11+/t19-,20+,21-,23-/m0/s1

2: InChI=1S/C24H34O5/c1-3-19-8-6-10-22(26)15(2)23(27)20-12-11-17-14-18(25)13-16(17)7-4-5-9-21(20)24(28)29-19/h4-5,7,9,11-12,15-22,25-26H,3,6,8,10,13-14H2,1-2H3/b7-4-,9-5+,12-11+/t15-,16-,17-,18-,19+,20+,21-,22+/m1/s1

3: InChI=1S/C24H34O5/c1-3-19-5-4-6-22(26)15(2)23(27)11-10-20-16(9-12-24(28)29-19)7-8-17-13-18(25)14-21(17)20/h7-12,15-22,25-26H,3-6,13-14H2,1-2H3/b11-10+,12-9+/t15-,16+,17-,18-,19+,20-,21-,22+/m1/s1

Uncategorized Steven Bachrach 11 Apr 2017 1 Comment

Dynamics in a reaction where a [6+4] and [4+2] cycloadditons compete

Enzyme SpnF is implicated in catalyzing the putative [4+2] cycloaddition taking 1 into 3. Houk, Singleton and co-workers have now examined the mechanism of this transformation in aqueous solution but without the enzyme.1 As might be expected, this mechanism is not straightforward.

Reactant 1, transition states, and products 2 and 3 were optimized at SMD(H2O)/M06-2X/def2-TZVPP//B3LYP-D3(BJ)//6-31+G(d,p). Geometries and relative energies are shown in Figure 1. The reaction 12 is a formal [6+4] cycloaddition, and the reaction 13 is a formal [4+2] cycloaddition. Interestingly, only a single transition state could be located TS1. It is a bispericyclic TS (see Chapter 4 of my book), where these two pericyclic reaction sort of merge together. After TS1 is traversed the potential energy surface bifurcates, leading to 2 or 3. This is yet again an example of a single TS leading to two different products. (See the many posts I have written on this topic.) The barrier height is 27.6 kcal mol-1, with 2 lying 13.1 kcal mol-1 above 3. However, the steepest descent pathway from TS1 leads to 2. There is a second transition state TScope that describes a Cope rearrangement between 2 and 3. Using the more traditional TS theory description, 1 undergoes a [6+4] cycloaddition to form 2 which then crosses a lower barrier (TScope) to form the thermodynamically favored 3, which is the product observed in the enzymatically catalyzed reaction.

1 (0.0)

TS1 (27.6)

2 (4.0)

3 (-9.1)


Figure 1. B3LYP-D3(BJ)//6-31+G(d,p) optimized geometries and relative energies in kcal mol-1.

Molecular dynamics computations were performed on this system by tracking trajectories starting in the neighborhood of TS1 on a B3LYP-D2/6-31G(d) PES. The results are that 63% of the trajectories end at 2, 25% end at 3, and 12% recross back to reactant 1, suggesting an initial formation ratio for 2:3 of 2.5:1. The reactions are very slow to cross through the “transition zone”, typically 2-3 times longer than for a usual Diels-Alder reaction (see this post).

Once again, we see an example of dynamic effects dictating a reaction mechanism. The authors pose a tantalizing question: Can an enzyme control the outcome of an ambimodal reaction by altering the energy surface such that the steepest downhill path from the transition state leads to the “desired” product(s)? The answer to this question awaits further study.


(1) Patel, A; Chen, Z. Yang, Z; Gutierrez, O.; Liu, H.-W.; Houk, K. N.; Singleton, D. A. “Dynamically
Complex [6+4] and [4+2] Cycloadditions in the Biosynthesis of Spinosyn A,” J. Amer. Chem. Soc. 2016, 138, 3631-3634, DOI: 10.1021/jacs.6b00017.


1: InChI=1S/C24H34O5/c1-3-21-15-12-17-23(27)19(2)22(26)16-10-7-9-14-20(25)13-8-5-4-6-11-18-24(28)29-21/h4-11,16,18-21,23,25,27H,3,12-15,17H2,1-2H3/b6-4+,8-5+,9-7+,16-10+,18-11+/t19-,20+,21-,23-/m0/s1

2: InChI=1S/C24H34O5/c1-3-19-8-6-10-22(26)15(2)23(27)20-12-11-17-14-18(25)13-16(17)7-4-5-9-21(20)24(28)29-19/h4-5,7,9,11-12,15-22,25-26H,3,6,8,10,13-14H2,1-2H3/b7-4-,9-5+,12-11+/t15-,16-,17-,18-,19+,20+,21-,22+/m1/s1

3: InChI=1S/C24H34O5/c1-3-19-5-4-6-22(26)15(2)23(27)11-10-20-16(9-12-24(28)29-19)7-8-17-13-18(25)14-21(17)20/h7-12,15-22,25-26H,3-6,13-14H2,1-2H3/b11-10+,12-9+/t15-,16+,17-,18-,19+,20-,21-,22+/m1/s1

cycloadditions &Diels-Alder &Dynamics &Houk &Singleton Steven Bachrach 30 Aug 2016 1 Comment

Structure of the 2-fluoroethanol trimer

Here is another fine example of the power of combining experiment and computation. Xu and co-worker has applied the FT microwave technique, which has been used in conjunction with computation by the Alonso group (especially) as described in these posts, to the trimer of 2-fluoroethanol.1 They computed a number of trimer structures at MP2/6-311++G(2d,p) in an attempt to match up the computed spectroscopic constants with the experimental constants. The two lowest energy structures are shown in Figure 1. The second lowest energy structure has nice symmetry, but it does not match up well with the experimental spectra. However, the lowest energy structure is in very good agreement with the experiments.



Table 1. MP2/6-311++G(2d,p) optimized structures and relative energies (kJ mol-1) of the two lowest energy structures of the trimer of 2-fluoroethanol. The added orange lines in the lowest energy structure denote the bifurcated hydrogen bonds identified by QTAIM.

Of particular note is that topological electron density analysis (also known as quantum theoretical atoms in a molecule, QTAIM) of the wavefunction of the lowest energy structure of the trimer identifies two hydrogen bond bifurcations. The authors suggest that these additional interactions are responsible, in part, for the stability of this lowest energy structure.


(1) Thomas, J.; Liu, X.; Jäger, W.; Xu, Y. "Unusual H-Bond Topology and Bifurcated H-bonds in the 2-Fluoroethanol Trimer," Angew. Chem. Int. Ed. 2015, 54, 11711-11715, DOI: 10.1002/anie.201505934.


2-fluoroethanol: InChI=1S/C2H5FO/c3-1-2-4/h4H,1-2H2, InChIKey=GGDYAKVUZMZKRV-UHFFFAOYSA-N

Hydrogen bond &MP Steven Bachrach 20 Oct 2015 1 Comment

Computational Organic Chemistry, Second Edition – what’s new in Chapters 5-9

This post continues my presentation of what’s new in the second edition of my book Computational Organic Chemistry. I present here a brief summary of the new materials in chapters 5-9. (See this previous post for what’s new in chapters 1-4.)

Every chapter has been updated, meaning that the topics from the First Edition that remain in this Second Edition (and that’s most of them) have been updated with any new relevant work that have appeared since 2007, when the First Edition was published. In addition, the following new subjects have been included.

Chapter 5. Diradicals and Carbenes

One of the major additions to the entire book appears in Chapter 5: the discovery of tunneling in a variety of carbenes. This work, pioneered by Schreiner and Allen, led to the discovery of tunneling control, a third means, in conjunction with thermodynamic control and kinetic control, for controlling product formation. This work is an exemplar of the synergy provided by experiments done in partnership with computations. The chapter also includes an interview with Prof. Peter Schreiner.

Chapter 6. Organic Reactions of Anions

The discussion on proline-catalyzed aldols includes many new computations, especially dealing with the possible intermediacy of oxazolidinones. A section on thiurea-catalyzed Claisen rearrangements, from the Jacobsen group, concludes the chapter, showing how the computational approaches to organocatalyzed reactions can be extended beyond the aldol and aldol-like reactions.

Chapter 7. Solution-Phase Organic Chemistry

A discussion of solvent effects on amino acid structure has been added. This work focusses on the use of microsolvation to model local solvent effects, particularly in cases where proper accounting of strong hydrogen bonds can be critical in assessing behaviors.

Chapter 8. Organic Reaction Dynamics

A great deal of new materials appears in this chapter. Since the publication of the first edition of the book, many new studies have been published that greatly expand the types of organic reactions that are subject to dynamic effects. Of particular note are the many new examples of reactions on bifurcating surfaces. Some studies, principally by Singleton, now provide some guidance and hints towards predicting what types of reactions might exhibit non-statistical dynamics. Two new non-statistical dynamic types are presented: the roaming reactions and the roundabout mechanism in the SN2 reaction. The chapter ends with a detailed case study of the Wolff rearrangement.

Chapter 9. Computational Approaches to Understanding Enzymes

The last chapter is entirely new, and features how the techniques of computational organic chemistry, as discussed in the previous eight chapters, can be employed toward explicating enzymatic reactions. The chapter is not an in-depth survey of all of the activities in computational enzyme action – that would require its own full-length book – but rather it’s an overview to inspire you. The chapter begins with a brief discussion of enzymatic models, including the Pauling paradigm and Goodman’s model. Then computational strategies for addressing the large molecules involved in enzymatic studies are presented including QM/MM, adiabatic mapping, and the use of some very large-scale computations as benchmarks. Next, I present two case studies: of chorismate mutase and of catechol-O-methyltransferase (COMT). The chapter ends with a presentation of the progress in de novo design of enzymes capable of catalyzing specific reactions as developed by Baker and Houk.

Second Edition Steven Bachrach 16 Apr 2014 1 Comment

More strange dynamics from the Singleton Group

Once again the Singleton group reports experiments and computations that require serious reconsideration of our notions of reaction mechanisms.1 In this paper they examine the reaction of dichloroketene with labeled cis-2-butene. With 13C at the 2 position of 2-butene, two products are observed, 1 and 1’, in a ratio of 1’:1 = 0.993 ± 0.001. This is the opposite what one might have imagined based on the carbonyl carbon acting as an electrophile.

The first interesting item is that B3LYP/6-31+G** fails to predict the proper structure of the transition state. It predicts an asymmetric structure 2, shown in Figure 1, while MPW1k/6-31+G**, M06, and MP2 predict a Cs transition structure 3. The Cs TS is confirmed by a grid search of M06-2x geometries with CCSD(T)/6-311++G88/PCM(CH2Cl2) energies.



Figure 1. Optimized TSs 2 (B3LYP/6-31+G**) and 3 (MPW1K/6-31+G**).

The PES using proper computational methods is bifurcating past TS 3, falling downhill to product 1 or 1’. Lying on the Cs plane is a second transition state that interconverts 1 and 1’. On such a surface, conventional transition state theory would predict equal amounts of 1 and 1’, i.e. no isotope effect! So they must resort to a trajectory study – which would be impossibly long if not for the trick of making the labeled carbon super-heavy – like 28C,44C, 76C and 140C and then extrapolating back to just ordinary 13C. These trajectories indicate a ratio of 1’:1 of 0.990 in excellent agreement with the experimental value of 0.993.

Interestingly, most trajectories recross the TS, usually by reaching into the region near the second TS. However, the recrossing decreases with increasing isotopic mass, and this leads to the isotope effect. It turns out the vibrational mode 3 breaks the Cs symmetry; movement in one direction along mode 3 has no mass dependence but in the opposite direction, increased mass leads to decreased recrossing – or put in another way, in this direction, increased mass leads more often to product.

But one can understand this reaction from a statistical point of view as well. If one looks at the free energy surface, there is a variational TS near 3, but then there is a second set of variational transition states (one leading to 1 and one to 1’) which are associated with the formation of the second C-C bond. In a sense there is an intermediate past 3 that leads to two entropic barriers, one on a path to 1 and one on the path to 1’. RRKM using this model gives a ratio of 0.992 – again in agreement with experiment! It is as Singleton notes “perplexing”; how do you reconcile the statistical view with the dynamical (trajectory) view? Singleton has no full explanation.

Lastly, they point out that a similar situation occurs in the organocatalyzed Diels-Alder reaction of MacMillan shown below.2 (This reaction is also discussed in a previous post.) Now Singleton finds that the “substituent effects, selectivity, solvent effects, isotope effects and activation parameters” are all dictated by a second variational TS far removed from the conventional electronic TS.


(1) Gonzalez-James, O. M.; Kwan, E. E.; Singleton, D. A., "Entropic Intermediates and Hidden Rate-Limiting Steps in Seemingly Concerted Cycloadditions. Observation, Prediction, and Origin of an Isotope Effect on Recrossing," J. Am. Chem. Soc. 2012, 134, 1914-1917, DOI: 10.1021/ja208779k

(2) Ahrendt, K. A.; Borths, C. J.; MacMillan, D. W. C., "New Strategies for Organic Catalysis: The First Highly Enantioselective Organocatalytic Diels-Alder Reaction," J. Am. Chem. Soc. 2000, 122, 4243-4244, DOI: 10.1021/ja000092s.


2-butene: InChI=1/C4H8/c1-3-4-2/h3-4H,1-2H3/b4-3-

Dichloroketene: InChI=1/C2Cl2O/c3-2(4)1-5

1 (no isotope): InChI=1/C6H8Cl2O/c1-3-4(2)6(7,8)5(3)9/h3-4H,1-2H3/t3-,4+/m0/s1

cycloadditions &Dynamics &Isotope Effects &Singleton Steven Bachrach 06 Mar 2012 2 Comments

Substitution vs. addition: dynamic effects

Reactions whose outcomes depend on dynamic processes is a major theme of my book and this blog. The recent study of the reaction of a nucleophile (hydroxide) with bromoacetophenones adds yet another case for post-transition state product determination.

Itoh and Yamataka have examined the reaction of hydroxide with substitutes α-bromoacetophenones 1.1 The nucleophile can attack at the carbonyl carbon or the α-carbon, though both lead ultimately to the same product, as shown in Scheme 1.

Scheme 1

B3LYP/6-31+G* computations of the reaction surface with a variety of different substituents on the phenyl ring of 1 located in all cases a single transition state for the two different reactions (addition and substitution). This TS is shown in Figure 1 for the parent case (X=H).

Figure 1. The single transition state for the addition and substitution reaction of 1 and hydroxide.

Tracing the IRC forward leads to either the carbonyl addition product or the substitution product, and which path is traced depends to some extent on the nature of the substituent. Most intriguing is that trajectories initiated at the transition state lead to both products. So once again, we see a case where a single transition state leads to two products, and product selectivity is determine by the dynamics – the initial conditions at the TS dictate which of the two products is eventually obtained.


(1) Itoh, S.; Yoshimura, N.; Sato, M.; Yamataka, H., "Computational Study on the Reaction Pathway of α-Bromoacetophenones with Hydroxide Ion: Possible Path Bifurcation in the Addition/Substitution Mechanism," J. Org. Chem., 2011, 70, 8294–8299, DOI: 10.1021/jo201485y

Dynamics &Substitution Steven Bachrach 24 Oct 2011 13 Comments

Topics for a new edition of Computational Organic Chemistry

I am very much contemplating a second edition of my book Computational Organic Chemistry, which is the basis of this blog. I have been in touch with Wiley and they are enthusiastic about a second edition.

Here is a list of some of the things I am contemplating as new topics for the second edition

  1. Discussion of the failures of many of the standard functionals (like B3LYP) to treat simple organics
  2. Predicting NMR, IR and ORD spectra
  3. Möbius compounds, especially aromatics
  4. π-π-stacking
  5. tunneling in carbenes (Schreiner and Allen’s great work)
  6. acidity of amino acids and remote protons
  7. bifurcating potential energy surfaces and the resultant need for dynamic considerations
  8. even more examples of dynamics – especially the roundabout SN2

So, I would like to ask my readers for suggestions of other ideas for new topics to add to the book. These can be extensions of the topics already covered, or brand new areas!

Additionally, I am planning on interviewing a few more people for the book, similar in spirit to the 6 interviews in the first addition. Again, I welcome any suggestions for computational chemists to interview!

Uncategorized Steven Bachrach 09 Aug 2011 6 Comments

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