Search Results for "stacking"

Oblong molecule stacking

π-π-stacking has been a major theme of my blog, and is discussed in Chapter 3.5.4 in the Second Edition of my book. Most examples involved molecules that are nearly circular (like benzene or triphenylene). Hartley and co-workers discuss the π-π-stacking of the oblong molecule 1, comparing its experimental features with computed features of the model compound 2.1

The key spectroscopic feature associated with assembly of 1 are the changes in the 1H chemical shifts with increasing concentration. For example, the chemical shift of the three protons on the triphenylene unit shift upfield by 0.30 to 0.66 ppm as the concentration increases from 10-5 to 10-2 M.

To see if these NMR shift changes are due to association of 1, they employed a computational approach. First they optimized the structure of model compound 2 at B3LYP/6-31G(d) (Shown in Figure 1a). Then using this fixed geometry, they computed the 1H chemical shifts of the dimer of 2. They explored the stacking distance (ranging from 3.2 to 4.0 Å along with varying the displacement of the two molecules along the major axis from 0.0 to 6.0 Å, finding the best fit to the chemical shifts with a separation of 3.6 Å and a displacement along the major axis of 3.5 Å. Using these two fixed values, they explored displacement of the molecules along the minor axis, along with rotation of the two molecules. The best fit to the experimental chemical shifts was with a displacement of 0.5 Å along the short axis and no rotation. This structure is shown in Figure 1b, with a RMS error of only 0.09 ppm from experiment. Models of the trimer show poorer fit to the experimental data.





Figure 1. B3LYP/6-31G(d) (a) optimized structure of 2 and the (b) structure of the best fit of the dimer of 2. (As always, clicking on these images will allow you to manipulate the 3-D structure using JMol – highly recommended for the dimer.)

Using some smaller models and the B97-D functional, they argue that the displacement, which is substantially larger than the displacement found in stacked triphenylene, results from the need to minimize the steric interactions between the alkoxyl chains.


(1) Chu, M.; Scioneaux, A. N.; Hartley, C. S. "Solution-Phase Dimerization of an Oblong Shape-Persistent Macrocycle," J. Org. Chem. 2014, 79, 9009–9017; DOI: 10.1021/jo501260c.


1: InChI=1S/C116H148O10/c1-11-21-31-41-59-117-95-71-87-51-55-91-75-97-99(103-81-111(121-63-45-35-25-15-5)115(125-67-49-39-29-19-9)85-107(103)105-83-113(123-65-47-37-27-17-7)109(79-101(97)105)119-61-43-33-23-13-3)77-93(91)57-53-89-70-90(74-96(73-89)118-60-42-32-22-12-2)54-58-94-78-100-98(76-92(94)56-52-88(69-87)72-95)102-80-110(120-62-44-34-24-14-4)114(124-66-48-38-28-18-8)84-106(102)108-86-116(126-68-50-40-30-20-10)112(82-104(100)108)122-64-46-36-26-16-6/h69-86H,11-50,59-68H2,1-10H3

2: InChI=1S/C76H68O10/c1-11-77-55-31-47-21-25-51-35-57-59(63-41-71(81-15-5)75(85-19-9)45-67(63)65-43-73(83-17-7)69(79-13-3)39-61(57)65)37-53(51)27-23-49-30-50(34-56(33-49)78-12-2)24-28-54-38-60-58(36-52(54)26-22-48(29-47)32-55)62-40-70(80-14-4)74(84-18-8)44-66(62)68-46-76(86-20-10)72(82-16-6)42-64(60)68/h29-46H,11-20H2,1-10H3

Aromaticity Steven Bachrach 13 Nov 2014 No Comments

π-π stacking (part 2)

An alternative take on the nature of the interaction in π-stacking is offered by Wheeler and Houk.1 They start by examining the binding between benzene and a series of 24 substituted benzenes. Two representative dimmers are shown in Figure 1, where the substituent is NO2 or CH2OH. As was noted in a number of previous studies,2-6 the binding with any substituted benzene is stronger than the parent benzene dimer. Nonetheless, Wheeler and Houk point out that the binding energy has a reasonable correlation with σm. It appears that the benzene dimer itself is the outlier; the binding energy when the substituent is CH2OH, whose σm value is zero, is bound more tightly than the benzene dimer. They conclude that there is a dispersive interaction between any substituent and the other benzene ring.





Figure 1. MO5-2X/6-31+G(d) optimized geometries of (a) C6H6-C6H5NO2, (b) C6H6-C6H5CH2OH, (c) C6H6-HNO2, and (d) C6H6-HCH2OH.1

They next constructed an admittedly very crude model system whereby the substituted benzene C6H5X is replaced by HX; the corresponding models are also shown in Figure 1. The binding energies of these model dimmers correlates very well with the real dimmers, with r = 0.91. Rather than involving the interaction of the π-electrons, the origin of the enhanced binding in aromatic dimers involves electrostatic interactions of the substituent with the other aromatic ring – effectively the quadrupole of the unsubstituted ring interacts with the dipoles of the substituent and its ring system. In addition, the inherent dispersive interaction increase the binding.


(1) Wheeler, S. E.; Houk, K. N., "Substituent Effects in the Benzene Dimer are Due to Direct Interactions of the Substituents with the Unsubstituted Benzene," J. Am. Chem. Soc., 2008, 130, 10854-10855, DOI: 10.1021/ja802849j.

(2) Sinnokrot, M. O.; Sherrill, C. D., "Unexpected Substituent Effects in Face-to-Face π-Stacking Interactions," J. Phys. Chem. A, 2003, 107, 8377-8379, DOI: 10.1021/jp030880e.

(3) Sinnokrot, M. O.; Sherrill, C. D., "Substituent Effects in π-&pi Interactions: Sandwich and T-Shaped Configurations," J. Am. Chem. Soc., 2004, 126, 7690-7697, DOI: 10.1021/ja049434a.

(4) Sinnokrot, M. O.; Sherrill, C. D., "Highly Accurate Coupled Cluster Potential Energy Curves for the Benzene Dimer: Sandwich, T-Shaped, and Parallel-Displaced Configurations," J. Phys. Chem. A, 2004, 108, 10200-10207, DOI: 10.1021/jp0469517

(5) Lee, E. C.; Kim, D.; Jurecka, P.; Tarakeshwar, P.; Hobza, P.; Kim, K. S., "Understanding of Assembly Phenomena by Aromatic-Aromatic Interactions: Benzene Dimer and the Substituted Systems," J. Phys. Chem. A 2007, 111, 3446-3457, DOI: 10.1021/jp068635t.

(6) Grimme, S.; Antony, J.; Schwabe, T.; Mück-Lichtenfeld, C., "Density functional theory with dispersion corrections for supramolecular structures, aggregates, and complexes of
(bio)organic molecules," Org. Biomol. Chem. 2007, 741-758, DOI: 10.1039/b615319b

Aromaticity &Houk Steven Bachrach 09 Sep 2008 3 Comments

π-π stacking

The importance of the interactions between neighboring aromatic molecules cannot be overemphasized – π-π-stacking is invoked to explain the structure of DNA, the hydrophobic effect, molecular recognition, etc. Nonetheless, the nature of this interaction is not clear. In fact the commonly held notion of π-π orbital overlap is not seen in computations.

Grimme1 has now carefully examined the nature of aromatic stacking by comparison with aliphatic analogues. He has examined dimers formed of benzene 1, naphthalene 2, anthracene 3, and teracene 4 and compared these with the dimers of their saturated analogues (cyclohexane 1s, decalin 2s, tetradecahydroanthracene 3s, and octadecahydrotetracene 4s. The aromatic dimmers were optimized in the T-shaped and stacked arrangements, and these are shown for 3 along with the dimer of 3s in Figure 1. These structures are optimized at B97-D/TZV(2d,2p) – a functional designed for van der Waals compounds. Energies were then computed at B2LYP-D/QZV3P, double-hybrid functional that works very well for large systems.

Figure 1. Optimized structures of 3s, 3t, and 3a.

The energies for formation of the complexes are listed in Table 1. The first interesting result here is that the benzene and naphthalene dimmers (whether stacked or T-shaped) are bound by about the same amount as their saturated analogues. Grimme thus warns that “caution is required to not overestimate the effect of the π system”.

Table 1. Complexation energy (kcal mol-1)






T-shape (t)





Stacked saturated (s)





Stacked aromatics (a)





The two larger aromatics here do show a significantly enhanced complexation energy than their saturated analogues, and Grimme refers to this extra stabilization as the π-π stacking effect (PSE). Energy decomposition analysis suggests that electrostatic interactions actually favor the complexation of the saturated analogues over the aromatics. However, Pauli exchange repulsion essentially cancels the electrostatic attraction for all the systems, and it is dispersion that accounts for the dimerization energy. Dispersion increases with size of the molecule, and “classical” dispersion forces (the R-6 relationship) accounts for more than half of the dispersion energy in the saturated dimmers, while it is the non-classical, or orbital-based, dispersion that dominates in the stacked aromatic dimmers. Grimme attributes this to “special nonlocal electron correlations between the π electrons in the two fragments at small interplane distances”.


(1) Grimme, S., "Do Special Noncovalent π-π Stacking Interactions Really Exist?," Angew. Chem. Int. Ed., 2008, 47, 3430-3434, DOI: 10.1002/anie.200705157.


1: InChI=1/C6H6/c1-2-4-6-5-3-1/h1-6H

1s: InChI=1/C6H12/c1-2-4-6-5-3-1/h1-6H2

2: InChI=1/C10H8/c1-2-6-10-8-4-3-7-9(10)5-1/h1-8H

2s: InChI=1/C10H18/c1-2-6-10-8-4-3-7-9(10)5-1/h9-10H,1-8H2

3: InChI=1/C14H10/c1-2-6-12-10-14-8-4-3-7-13(14)9-11(12)5-1/h1-10H

3s: InChI=1/C14H24/c1-2-6-12-10-14-8-4-3-7-13(14)9-11(12)5-1/h11-14H,1-10H2

4: InChI=1/C18H12/c1-2-6-14-10-18-12-16-8-4-3-7-15(16)11-17(18)9-13(14)5-1/h1-12H

4s: InChI=1/C18H30/c1-2-6-14-10-18-12-16-8-4-3-7-15(16)11-17(18)9-13(14)5-1/h13-18H,1-12H2

Aromaticity &DFT &Grimme Steven Bachrach 19 May 2008 3 Comments

π-π Stacking

I did not present π-π stacking in the book, but I think if I ever do a second edition, I will include a discussion of it. I’m not sure quite where it would fit in given the current structure of the book (I discuss DNA bases and base pairs in the context of solvation in Chapter 6), but the paper I will discuss next gives me some idea – π-π stacking is a sensitive test of the quality of computational methods and this could be part of Chapter 1 as a discussion of the failings of methods, especially DFT.

Swart and Bickelhaupt have examined a series of π-π stacked pairs, evaluating them regarding how DFT performs.1 Their first example is the benzene dimer (Table 1). At CCSD(T) the dimer binding energy is 1.7 kcal mol-1 and the rings are 3.9 Å apart. LDA, KT1 (yet another newly minted functional2,3), and BHandH get the separation and binding energy reasonably well. PW91 gets the distance too big and underestimates the binding energy. But most important is that the other (more traditional) functionals indicate that the PES is entirely repulsive! This is a manifestation of many functionals’ inability to properly account for dispersion.

Table 1. Optimized separation distance (rmin, Å) and binding energy (kcal mol-1)
of the benzene dimer using the TZ2P basis set.1



























Next, they compare 14 different orientations of stacked dimmers of cytosine. The energies of these dimmers were computed using again a variety of functionals and compared to MP2/CBS energies with a correction for CCSD(T). The mean absolute deviations (MAD) for the energies using the various functionals are listed in Table 2. Again, LDA and KT1 perform quite well, but most functionals do quite poorly.

Table 2. Mean absolute deviations of the energies of 14 cytosine
stacked dimer structures compared to their MP2 energies.



















Similar results are also demonstrated for stacked DNA bases and also stacked base pairs. These authors conclude that the KT1 functional appears suitable for treating π-π stacking. One should also consider some of the new functionals from the Truhlar group,4-6 which unfortunately are not included in this study.


(1) Swart, M.; van der Wijst, T.; Fonseca, C.; Bickelhaput, F. M., "π-π Stacking Tackled with Density Functional Theory," J. Mol. Model. 2007, 13, 1245-1257, DOI: 10.1007/s00894-007-0239-y.

(2) Keal, T. W.; Tozer, D. J., "The Exchange-Correlation Potential in Kohn–Sham Nuclear Magnetic Resonance Shielding Calculations," J. Chem. Phys. 2003, 119, 3015-3024, DOI: 10.1063/1.1590634

(3) Keal, T. W.; Tozer, D. J., "A Semiempirical Generalized Gradient Approximation Exchange-Correlation Functional," J. Chem. Phys. 2004, 121, 5654-5660, DOI: 10.1063/1.1784777.

(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) 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.

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

DFT Steven Bachrach 26 Nov 2007 No Comments

Reaction selectivity in the synthesis of paeoveitol

Xu, Liu, Xu, Gao, and Zhao report a very efficient synthesis of paeoveitol 1 by the [4+2]-cycloaddition of paeveitol D 2 with the o-quinone methide 3.1 What is interesting here is the selectivity of this reaction. In principle the cyloadditon can give four products (2 different regioisomeric additions along with endo/exo selectivity) and it could also proceed via a Michael addition.

They performed PCM(CH2Cl2)/M06-2x/6-311+G(d,p) computations on the reaction of 2 with 3 and located two different transition states for the Michael addition and the four cycloaddition transition states. The lowest energy Michael and cycloaddition transition states are shown in Figure 1. The barrier for the cycloaddition is 17.6 kcal mol-1, 2.5 kcal mol-1 below that of the Michael addition. The barriers for the other cycloaddition paths are at more than 10 kcal mol-1 above the one shown. This cycloaddition TS is favored by a strong intermolecular hydrogen bond and by π-π-stacking. In agreement with experiment, it is the transition state that leads to the observed product.

Michael TS

[4+2] TS

Figure 1. Optimized geometries of the lowest energy TSs for the Michael and [4+2]cycloaddtion routes. Barrier heights (kcal mol-1) are listed in parenthesis.


(1) Xu, L.; Liu, F.; Xu, L.-W.; Gao, Z.; Zhao, Y.-M. "A Total Synthesis of Paeoveitol," Org. Lett. 2016, ASAP, DOI: 10.1021/acs.orglett.6b01736.

paeoveitol 1: InChI=1S/C21H24O3/c1-5-21-10-14-6-11(2)17(22)8-15(14)13(4)20(21)24-19-7-12(3)18(23)9-16(19)21/h6-9,13,20,22-23H,5,10H2,1-4H3/t13-,20-,21-/m1/s1

paeveitol D 2: InChI=1S/C9H10O2/c1-3-7-5-8(10)6(2)4-9(7)11/h3-5,10H,1-2H3/b7-3+

3: InChI=1S/C9H10O2/c1-3-7-5-8(10)6(2)4-9(7)11/h3-5,10H,1-2H3/b7-3+

Diels-Alder Steven Bachrach 02 Aug 2016 No Comments

Highly efficient Buckycatchers

Capturing buckyballs involves molecular design based on non-covalent interactions. This poses interesting challenges for both the designer and the computational chemist. The curved surface of the buckyball demands a sequestering agent with a complementary curved surface, likely an aromatic curved surface to facilitate π-π stacking interactions. For the computational chemist, weak interactions, like dispersion and π-π stacking demand special attention, particularly density functionals designed to account for these interactions.

Two very intriguing new buckycatchers were recently prepared in the Sygula lab, and also examined by DFT.1 Compounds 1 and 2 make use of the scaffold developed by Klärner.2 In these two buckycatchers, the tongs are corranulenes, providing a curved aromatic surface to match the C60 and C70 surface. They differ in the length of the connector unit.

B97-D/TZVP computations of the complex of 1 and 2 with C60 were carried out. The optimized structures are shown in Figure 1. The binding energies (computed at B97-D/QZVP*//B97-D/TZVP) of these two complexes are really quite large. The binding energy for 1:C60 is 33.6 kcal mol-1, comparable to some previous Buckycatchers, but the binding energy of 2:C60 is 50.0 kcal mol-1, larger than any predicted before.



Figure 1. B97-D/TZVP optimized geometries of 1:C60and 2:C60.

Measurement of the binding energy using NMR was complicated by a competition for one or two molecules of 2 binding to buckyballs. Nonetheless, the experimental data show 2 binds to C60 and C70 more effectively than any previous host. They were also able to obtain a crystal structure of 2:C60.


(1) Abeyratne Kuragama, P. L.; Fronczek, F. R.; Sygula, A. "Bis-corannulene Receptors for Fullerenes Based on Klärner’s Tethers: Reaching the Affinity Limits," Org. Lett. 2015, ASAP, DOI: 10.1021/acs.orglett.5b02666.

(2) Klärner, F.-G.; Schrader, T. "Aromatic Interactions by Molecular Tweezers and Clips in Chemical and Biological Systems," Acc. Chem. Res. 2013, 46, 967-978, DOI: 10.1021/ar300061c.


1: InChI=1S/C62H34O2/c1-63-61-57-43-23-45(41-21-37-33-17-13-29-9-5-25-3-7-27-11-15-31(35(37)19-39(41)43)53-49(27)47(25)51(29)55(33)53)59(57)62(64-2)60-46-24-44(58(60)61)40-20-36-32-16-12-28-8-4-26-6-10-30-14-18-34(38(36)22-42(40)46)56-52(30)48(26)50(28)54(32)56/h3-22,43-46H,23-24H2,1-2H3/t43-,44+,45+,46-

2: InChI=1S/C66H36O2/c1-67-65-51-24-45-43-23-44(42-20-38-34-16-12-30-8-4-27-3-7-29-11-15-33(37(38)19-41(42)43)59-55(29)53(27)56(30)60(34)59)46(45)25-52(51)66(68-2)64-50-26-49(63(64)65)47-21-39-35-17-13-31-9-5-28-6-10-32-14-18-36(40(39)22-48(47)50)62-58(32)54(28)57(31)61(35)62/h3-22,24-25,43-44,49-50H,23,26H2,1-2H3/t43-,44+,49+,50-

Aromaticity &fullerene &host-guest Steven Bachrach 30 Nov 2015 No Comments

o-Phenylene conformations

In solution ortho-phenylenes preferentially coil into a helix with the phenyl rings stacked. However, 25-50% of these chains will typically misfold. Hartley and coworkers have reported the use of substituents to increase the percentage of perfectly folded chains.1

They synthesized two isomeric o-phenylenes, differing in the substitution pattern (1 and 2), with chain length of 6 to 10 phenyl rings. Substituents included methoxy, acetoxy, nitrile, and triflate. They principally employed 1H NMR to assess the conformational distribution, and used computations to confirm the conformation.

Ideally folded conformations of 1 and 2 with eight phenyl rings are shown in Figure 1. The dihedral angle formed by two adjacent phenyl rings are typically about ±55° or ±130°.



Figure 1. Idealized folding of 1 and 2 with X=OH.
Hydrogens omitted in these images, but full structures available, through Jmol, by clicking on the image.)

Given the size of these systems, and the conformation flexibility not just of the chain but with each substituent, a full search to identify the global minimum was not undertaken. Rather, a library of conformations was generated with MM, the lowest 200 conformations were then reoptimized at PM7 and then the energies were determined at PCM/B97-D/TZV(2d,2p). The lowest energy conformer was then reoptimized at this DFT level. Three conformations of 3 and 4 are shown in Figure 2 with triflate as the substituent with six phenyl rings. The first conformer has optimal stacking (perfect folding), the second conformer as one misfold at the end, and the third conformer has no stacking at all.

– ideal fold

– one misfold

3 – all misfold

4 – ideal fold

– one misfold

– all misfold

Figure 2. Optimized geometries of conformers of 3 and 4.
(Remember that clicking on one of these images will bring up the JMol applet allowing you to rotate and visualize the molecule in 3-D – a very useful feature here!)

NMR chemical shifts were then computed using these geometries at PCM/WP04/6-31G(d). In all cases examined, the chemical shifts of the major conformation was confirmed to be the perfect folding one by comparison with the computed chemical shifts. The examined substituents enhanced the proportion of properly folded chains in all cases, often to the extent where no minor conformer was observed at all.


(1) Mathew, S.; Crandall, L. A.; Ziegler, C. J.; Hartley, C. S. "Enhanced Helical Folding of ortho-Phenylenes through the Control of Aromatic Stacking Interactions," J. Am. Chem. Soc. 2014, 136, 16666-16675, DOI:10.1021/ja509902m.


3: InChI=1S/C42H26F18O18S6/c43-37(44,45)79(61,62,63)23-5-1-21(2-6-23)29-13-9-25(81(67,68,69)39(49,50)51)17-33(29)35-19-27(83(73,74,75)41(55,56)57)11-15-31(35)32-16-12-28(84(76,77,78)42(58,59)60)20-36(32)34-18-26(82(70,71,72)40(52,53)54)10-14-30(34)22-3-7-24(8-4-22)80(64,65,66)38(46,47)48/h1-20H,(H,61,62,63)(H,64,65,66)(H,67,68,69)(H,70,71,72)(H,73,74,75)(H,76,77,78)

4: InChI=1S/C42H26F18O18S6/c43-37(44,45)79(61,62,63)23-6-4-21(5-7-23)33-17-25(81(67,68,69)39(49,50)51)9-13-30(33)35-19-27(83(73,74,75)41(55,56)57)11-15-32(35)36-20-28(84(76,77,78)42(58,59)60)10-14-31(36)34-18-26(82(70,71,72)40(52,53)54)8-12-29(34)22-2-1-3-24(16-22)80(64,65,66)38(46,47)48/h1-20H,(H,61,62,63)(H,64,65,66)(H,67,68,69)(H,70,71,72)(H,73,74,75)(H,76,77,78)

Aromaticity Steven Bachrach 21 Jan 2015 No Comments

Computational Organic Chemistry, Second Edition – what’s new in Chapters 1-4

In this and the next post I discuss some of the new materials in the Second Edition of my book Computational Organic Chemistry. 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. What I present in this and the next post are those sections or chapters that are entirely new. This post covers chapters 1-4 and the next post covers chapters 5-9.

Chapter 1: Quantum Mechanics for Organic Chemistry

The section on Density Functional Theory has been expanded and updated to include

  • a presentation of Jacob’s ladder, Perdew’s organizational model of the hierarchy of density
  • a discussion of dispersion corrections, principally Grimme’s “-D” and “-D3” corrections
  • a discussion of Grimme’s double hybrid functions and Martin’s DSD-DFT method (dispersion corrected, spin-component scaled double hybrid)
  • and a brief discussion of functional selection

The discussion of basis set superposition error (BSSE) is expanded and includes intramolecular BSSE. A new section has been added to discuss QM/MM methods including ONIOM. The discussion of potential energy surfaces is expanded, including presentation of more complicated surfaces that including valley-ridge inflection (VRI) points. Lastly, the chapter concludes with an interview of Prof. Stefan Grimme.

Chapter 2. Computed Spectral Properties and Structure Identification

This is essentially a brand new chapter dealing with how computed spectral properties have been used in structural identification. The chapter begins with a presentation of computed structural features (bond lengths and angles) and how they compare with experiment. Next, I present some studies of computer IR spectra and their use in structure identification. The bulk of this chapter deals with NMR. I present methods for computing NMR with scaling techniques. The statistical methods of Goodman (CP1 and DP4) are described in the context of discriminating stereoisomers. The section ends with five case studies where computed NMR spectra were used to identify chemical structure. Next, computed optical activity including ORD and ECD and VCD used for structure determination are described through 6 case studies. This chapter ends with an interview of Prof. Jonathan Goodman.

Chapter 3. Fundamentals of Organic Chemistry

The main addition to this chapter is an extensive discussion of alkane isomerism, and the surprising failure of many standard density functionals (including B3LYP) to properly account for isomer energies. The work in this area led to the recognition of the importance of dispersion and medium-range correlation, and the development of new functionals and dispersion corrections. Other new sections include a case study of the acidity of amino acids (especially cysteine and tyrosine where the most acidic proton in the gas phase is not the carboxylic acid proton), and two added studies of aromaticity: (a) the competition between aromaticity and strain and (b) π-π stacking.

Chapter 4. Pericyclic Reactions

The chapter is updated from the first addition with two major additions. First, a section on bispericyclic reactions is added. This type of reaction is important in the context of a number of reactions that display dynamic effects (see Chapter 8). Second, the notion of transition state distortion energy as guiding reaction selectivity is described.

The highlights of the new materials in Chapters 5-9 will appear in the next blog post.

Second Edition Steven Bachrach 15 Apr 2014 No Comments

Is CCSD(T)/CBS really the gold standard?

The gold standard in quantum chemistry is the method that is considered to be the best, the one that gives accurate reproduction of experimental results. The CCSD(T) method is often referred to as the gold standard, especially when a complete basis set (CBS) extrapolation is utilized. But is this method truly accurate, or simply the highest level method that is within our reach today?

Řezáč and Hobza1 address the question of the accuracy of CCSD(T)/CBS by examining 24 small systems that exhibit weak interactions, including hydrogen bonding (e.g. in the water dimer and the waterammonia complex), dispersion (e.g. in the methane dimer and the methaneethane complex) and π-stacking (e.g. as in the stacked ethene and ethyne dimers). Since weak interactions result from quantum mechanical effects, these are a sensitive probe of computational rigor.

A CCSD(T)/CBS computation, a gold standard computation, still entails a number of approximations. These approximations include (a) an incomplete basis set dealt with by an arbitrary extrapolation procedure; (b) neglect of higher order correlations, such as complete inclusion of triples and omission of quadruples, quintuples, etc.; (c) usually the core electrons are frozen and not correlated with each other nor with the valence electrons; and (d) omission of relativistic effects. Do these omissions/approximations matter?

Comparisons with calculations that go beyond CCSD(T)/CBS to test these assumptions were made for the test set. Inclusion of the core electrons within the correlation computation increases the non-covalent bond, but the average omission is about 0.6% of the binding energy. The relativistic effect is even smaller, leaving it off for these systems involving only first and second row elements gives an average error of 0.1%. Comparison of the binding energy at CCSD(T)/CBS with those computed at CCSDT(Q)/6-311G** shows an average error of 0.9% for not including higher order configuration corrections. The largest error is for the formaldehyde dimer (the complex with the largest biding energy of 4.56 kcal mol-1) is only 0.08 kcal mol-1. If all three of these corrections are combined, the average error is 1.5%. It is safe to say that the current gold standard appears to be quite acceptable for predicting binding energy in small non-covalent complexes. This certainly gives much support to our notion of CCSD(T)/CBS as the universal gold standard.

An unfortunate note: the authors state that the data associated with these 24 compounds (the so-called A24 dataset) is available on their web site (, but I could not find it there. Any help?


(1) Řezáč, J.; Hobza, P. "Describing Noncovalent Interactions beyond the Common Approximations: How Accurate Is the “Gold Standard,” CCSD(T) at the Complete Basis Set Limit?," J. Chem. Theor. Comput., 2013, 9, 2151–2155, DOI: 10.1021/ct400057w.

QM Method Steven Bachrach 28 May 2013 3 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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