Are Bond Critical Points Really Critical for Hydrogen Bonding?

Lane, J. R.; Contreras-García, J.; Piquemal, J.-P.; Miller, B. J.; Kjaergaard, H. G. J. Chem. Theor. Comput. 2013, 9, 3263
Contributed by Steven Bachrach.
Reposted from Computational Organic Chemistry with permission

One of the more controversial components of Bader’s Atoms-In-Molecules (AIM) theory is the contention that there is a one-to-one correspondence between the existence of a bond critical point and the existence of a chemical bond. I discuss this matter in my book and also in these posts (1 and 2). Lane and co-workers now examine this relationship with regard to hydrogen bonds.¹

They examine the topological structure of the electron density of the series 1,2-ethanediol 1, 1,3-propanediol 2, and 1,3-butanediol 3. They find a bond critical point (bcp) between the hydrogen of one hydroxyl group and the oxygen of the second hydroxyl group for the two large compounds 2 and 3. This forms a ring, and a ring critical point is located as well. However, for 1 they find no bond critical point associated with what might be the intramolecular hydrogen bond in 1. For all three diols, the OH stretching frequencies are diminished relative to monoalcohols. So geometrically and spectroscopically there appears to be a hydrogen bond, but rigorous application of Bader’s notion of bonding says that there is no “bond” in 1.

Lane and coworkers go on to show that the electron density in the three diols is really topologically identical, just differing in a matter of degree. They conclude that the existence of a bond critical point should not be the sole arbiter of bonding, but one of the criteria that can be utilized to assess bonding.

While I am not at all in conflict with this conclusion, the paper contains some issues that need be addressed. First off, “bonding” is not a concept of either-or, rather there is a continuum of bonding. Hydrogen bonding should not at all be confused with covalent or ionic bonding – it is dramatically weaker and so one might consider whether the bcp criteria is applicable at all. The authors really fall into this trap stating “… the absence of a BCP should not necessarily be considered evidence as to the absence of a chemical bond (emphasis mine).” Do we want to consider a hydrogen bond as a chemical bond?

I think the key element overlooked in this study is the strength of the “hydrogen bond”. While not determined in the study, undoubtedly the hydrogen bond strength increases in the order 1 < 2 < 3. What is really to be gained by arguing there is or is not a “hydrogen bond” in all or some of these three molecules? The ring-like conformation is the lowest energy conformation for all three. This is driven by some electrostatic attraction between the OH dipole of one hydroxyl group for the dipole of the second hydroxyl group. When do we want to call this attraction a hydrogen bond? What do we gain by not doing so for all three? If we understand that there is an energy continuum of hydrogen bonding, from weak to weaker, doesn’t that provide enough of a model to interpret and predict chemical structure and behavior?

References

(1) Lane, J. R.; Contreras-García, J.; Piquemal, J.-P.; Miller, B. J.; Kjaergaard, H. G. J. Chem. Theor. Comput. 2013, 9, 3263-3266, DOI: DOI: 10.1021/ct400420r.

InChIs

1: InChI=1S/C2H6O2/c3-1-2-4/h3-4H,1-2H2
InChIKey=>LYCAIKOWRPUZTN-UHFFFAOYSA-N

2: InChI=1S/C3H8O2/c4-2-1-3-5/h4-5H,1-3H2
InChIKey=YPFDHNVEDLHUCE-UHFFFAOYSA-N

3: InChI=1S/C4H10O2/c5-3-1-2-4-6/h5-6H,1-4H2
InChIKey=WERYXYBDKMZEQL-UHFFFAOYSA-N

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Crystal Structure Determination of the Nonclassical 2-Norbornyl Cation

Scholz, F.; Himmel, D.; Heinemann, F. W.; Schleyer, P. v. R.; Meyer, K.; Krossing, I. Science 2013, 341, 62
Contributed by Steven Bachrach.
Reposted from Computational Organic Chemistry with permission

A long sought-after data point critical to the non-classical cation story has finally been obtained. The elusive x-ray crystal structure of a norbornyl cation was finally solved.¹ The [C₇H₁₁]⁺[Al₂Br₇]^- salt was crystallized in CH₂Br₂ at low temperature (40 K). This low temperature was needed to prohibit rotation of the norbornyl cation within the crystal (the cation is near spherical and so subject to relatively easy rotation within the crystal matrix) and hydride scrambling among the three carbons (C₁, C₂, and C₆) involved in the non-classical cation structure.

The authors report a number of different structures, all very similar, depending on slight differences in the crystals used. However, the important features are consistent with all of the structures. The cation is definitely of the non-classical type (see Figure 1) with the basal C₁-C₂ bond length of 1.39 Å similar that in benzene and long non-classical C₁-C₆ and C₂-C₆ distances of 1.80 Å. These distances match very well with the MP2(FC)/def2-QZVPP optimized distances of 1.393 and 1.825 Å, respectively.

Figure 1. X-ray structure of norbornyl cation.

References

(1) Scholz, F.; Himmel, D.; Heinemann, F. W.; Schleyer, P. v. R.; Meyer, K.; Krossing, I. "Crystal Structure Determination of the Nonclassical 2-Norbornyl Cation," Science 2013, 341, 62-64, DOI:10.1126/science.1238849.

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Synthesis, Structural Analysis, and Properties of [8]Circulenes

Feng, C.-N.; Kuo, M.-Y.; Wu, Y.-T. Angew. Chem. Int. Ed. 2013, 52, 7791
Contributed by Steven Bachrach.
Reposted from Computational Organic Chemistry with permission

Circulenes are molecules where a central ring is composed of fused benzenoids. Corranulene can also be named [5]circulene and coronene is [6]circulene. In a previous post I discussed the topology of the circulenes. This earlier work suggested that [8]annulene 1 would have a saddle-shape. This hypothesis has now been confirmed with the synthesis of the substituted [8]circulene 2 by Wu and co-workers.¹

1

2

The x-ray structure does show a saddle geometry for 2. The central 8-member ring is tub-shaped, even more puckered that cyclooctatetraene (COT) itself, though the bonds in 2 are nearly of equal length. The bond lengths involving the central carbon atoms appear consistent with an [8]radialene-type structure.

The ωB97X-D/6-31G** optimized geometries of the parent compound 1 and the synthesized compound2 are shown in Figure 1. These computed structures are very similar to each other, along with being very similar to the x-ray structure of 2.

1

2

Figure 1. ωB97X-D/6-31G** optimized geometries of 1 and 2.
(Don’t forget that you can click on these structures – and any other structure on my blog – to interactively manipulate and visualize them, something worth doing here!)

The computed NICS(0) (at HF/6-31+G* – I would really rather have seen these computed with some density functional, preferably at ωB97X-D/6-31G**) values for the six-member rings of both 1 and 2 are negative, ranging from -8.9 ppm to -4.0 ppm, indicating aromatic character. The NICS(0) value at the center of the 8-member ring is +9.8 ppm in 1 and +12.2 ppm in 2. The authors argue that this value cannot discriminate the 8-member ring from that in COT (NICS(0) = 1.98 ppm, the expected value for a non-aromatic ring) and [8]radialene (NICS(0) = -1.2 ppm, also an expected value for a non-aromatic ring). However, they are silent on whether this might actually imply some antiaromatic character to the 8-member ring, which would be consistent with the equivalent bond lengths around the ring.

The authors note that there should be a second isomer of 2 resulting from a flip of the tub. Variable temperature NMR does not show any change in the spectrum, though with a different substituted [8]circulene they do see some coalescence, suggesting a large flipping barrier of at least 20 kcal mol^-1. A computational search for this flipping/inversion might be interesting as the transition state is likely to not be planar.

References

(1) Feng, C.-N.; Kuo, M.-Y.; Wu, Y.-T. "Synthesis, Structural Analysis, and Properties of [8]Circulenes,"Angew. Chem. Int. Ed. 2013, 52, 7791-7794, DOI: 10.1002/anie.201303875.

InChIs

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

2: InChI=1S/C96H80/c1-49-17-33-65(34-18-49)81-73-57(9)58(10)75-83(67-37-21-51(3)22-38-67)85(69-41-25-53(5)26-42-69)77-61(13)62(14)79-87(71-45-29-55(7)30-46-71)88(72-47-31-56(8)32-48-72)80-64(16)63(15)78-86(70-43-27-54(6)28-44-70)84(68-39-23-52(4)24-40-68)76-60(12)59(11)74(82(81)66-35-19-50(2)20-36-66)90-89(73)91(75)93(77)95(79)96(80)94(78)92(76)90/h17-48H,1-16H3
InChIKey=DEKWLSGHBADDAQ-UHFFFAOYSA-N

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A grossly warped nanographene and the consequences of multiple odd-membered-ring defects

Kawasumi, K.; Zhang, Q.; Segawa, Y.; Scott, L. T.; Itami, K. Nat Chem 2013, advance online publication
Contributed by Steven Bachrach.
Reposted from Computational Organic Chemistry with permission

Scott and Itami report on a graphene fragment that is highly warped.¹ They have prepared 1 by three separate procedures, one of which starts with corranulene and in two steps makes the product!

1

The five 7-member rings warp the structure so that it is non-planar. In fact the molecule has negative curvature, reminiscent of a riding saddle. They report the x-ray structure, outside of the fullerenes, the largest hydrocarbon reported by x-ray crystallography. Because of its non-planar geometry, 1 does not pack well and so it is soluble in a variety of solvents.

The authors have obtained the structure of 1 at B3LYP/6-31G(d), shown in Figure 1. The central corranulene component is a shallow bowl, much less shallow than in corranulene itself. This suggests that the compound might flip with a relatively low barrier. The computed barrier is only 1.7 kcal mol^-1. Due to the negative curvatures associated with the seven-member rings, 1 is chiral and the ring flipping process leaves the chirality unchanged. A second transition was located that leads to racemization through a transition state of C_s symmetry. The barrier for this racemization is computed to be 18.9 kcal mol^-1. Variable temperature ¹H NMR analysis does show that at room temperature 1 (substituted with one t-butyl ring on each of the ten exterior phenyl rings) undergoes rapid motion that equilibrates all of the protons. However, at lower temperature the signals for ring protons do separate. This leads to the barrier or the racemization process of 13.6 kcal mol^-1. The ring flip is not frozen out at the temperatures explored.

1

1-TSflip

1-TSrac

Figure 1. B3LYP/6-31G(d) optimized structures of 1 and the transition states for flipping and racemization. (Remember that all structures in my blog are active – click on them to run Jmol and manipulate the 3-D structure.)

Compound 1 is an example of a very interesting negative curvature hydrocarbon, especially unusual for what might be considered an aromatic compound.

References

(1) Kawasumi, K.; Zhang, Q.; Segawa, Y.; Scott, L. T.; Itami, K. "A grossly warped nanographene and the consequences of multiple odd-membered-ring defects," Nat Chem 2013, advance online publication, DOI: 10.1038/nchem.1704.

InChIs

1: InChI=1S/C80H30/c1-11-31-32-12-2-23-43-44-24-5-15-35-36-16-6-27-47-48-28-9-19-39-40-20-10-30-50-49-29-8-18-38-37-17-7-26-46-45-25-4-14-34-33-13-3-22-42-41(21-1)51(31)61-62(52(32)43)72-65(55(35)44)66(56(36)47)74-69(59(39)48)70(60(40)50)75-68(58(38)49)67(57(37)46)73-64(54(34)45)63(53(33)42)71(61)76-77(72)79(74)80(75)78(73)76/h1-30H
InChIKey=KMAOOAQTQHCOHV-UHFFFAOYSA-N

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The Binding of Benzoarylsulfonamide Ligands to Human Carbonic Anhydrase is Insensitive to Formal Fluorination of the Ligand

Matthew R. Lockett, Heiko Lange, Benjamin Breiten, Annie Heroux, Woody Sherman, Dmitrij Rappoport, Patricia O. Yau, Philip W. Snyder, and George M. Whitesides Angew. Chem. Int. Ed. 2013, 52, 7714
Contributed by +Jan Jensen

Accurate modeling the hydrophobic effect (or effects) is probably the biggest challenge to computational drug design (see for example this CC Highlight).  The hydrophobic effect on protein-ligand binding is generally thought to come from the release of structured and entropically unfavorable water molecules from the hydrophobic surfaces of the ligand and binding pocket. However, is also possible that the release of strongly bound water molecules to the protein/or ligand contributes to this effect.

I find this article important for two reasons:

1) The thorough characterization, including x-ray structures, of the binding of homologous ligands provides a valuable benchmark for computational studies.  The authors show that fluorination, commonly thought to increase the hydrophobic contribution to the binding free energy indeed increases the entropy of binding, but does so without decreasing the binding free energy.

The fluorinated ligand is indeed more hydrophobic as measured by buffer/octanol partitioning so what's going on?  One answer may be the difference in strongly bound water molecules observed in the protein-ligand x-ray structures: six and ten for the un- and fluorinated ligand, respectively. However, a simple correction based on the number of strongly bound water molecules is unlikely: a homologous un- and fluorinated ligand pair showed large differences in the binding enthalpy and entropy but smaller difference in number of strongly bound water molecules (four and seven, respectibely).

2) The supplementary material provides a fantastic list of important papers in this area.  I have reproduced the list below and added links, where available, to the articles.

From supplementary materials

Water-centric view of protein-ligand binding (relevant references in chronological order).

1. Solvation. A Molecular Dynamics Study of a Dipeptide in Water. 

2. A Direct Measure of the Contribution of Solvent Reorganization to the Enthalpy of Binding.

3. How Water Provides the Impetus for Molecular Recognition in Aqueous Solution. 

4. Thermodynamic Solvent Isotope Effects and Molecular Hydrophobicity, Adv. Biophys. Chem. 1997, 6, 1 (not available on-line)

5. Hydrophobicity at Small and Large Length Scales. 

6. Computational Prediction of Native Protein Ligand-Binding and Enzyme Active Site Sequences.

7. Role of the Active-Site Solvent in the Thermodynamics of Factor Xa Ligand Binding. 

8. Hydrophobicity of Protein Surfaces: Separating Geometry from Chemistry.

9. The Thermodynamics of Protein-Ligand Interaction and Solvation: Insights for Ligand Design.

10. Dewetting and Hydrophobic Interactions in Physical and Biological Systems.

11. Extent of Enthalpy-Entropy Compensation in Protein-Ligand Binding.

12. Contribution of Explicit Solvent Effects to the Binding Affinity of Small-Molecule Inhibitors in Blood Coagulation Factor Serine Proteases.

13. Dissecting the Hydrophobic Effect on the Molecular Level: the Role of Water, Enthalpy, and Entropy in Ligand Binding to Thermolysin.

14. Ligand Binding Stepwise Disrupts Water Network in Thrombin: Enthalpic and Entropic Changes Reveal Classical Hydrophobic Effect.

15. Development of New Cyclic Plasmin Inhibitors with Excellent Potency and Selectivity.

Enthalpy-entropy compensation in protein-ligand binding (relevant references in chronological order).

1. Enthalpy-Entropy Compensation Phenomena in Water Solutions of Proteins and Small Molecules: A Ubiquitous Propery of Water.

2. Win Some, Lose Some—Enthalpy-Entropy Compensation in Weak Intermolecular Forces. (pdf)

3. Application of a Generalized Enthalpy-Entropy Relationship to Binding Cooperativity and Weak Associations in Solution.

4. Enthalpy-Entropy Compensation is not a General Feature of Weak Association. 

5. Extent of Enthalpy-Entropy Compensation in Protein-Ligand Binding.

6. Thermodynamics of Ligand Binding and Efficiency.

7. A Multidisciplinary Approach to Probing Enthalpy-Entropy Compensation and the Interfacial Mobility Model.

8. Enthalpy-Entropy Transduction Caused by Conformational Shifts can Obscure the Forces Driving Protein-Ligand Binding.

9. Extreme Entropy-Enthalpy Compensation in a Drug-Resistant Variant of HIV-1 Protease.

10. Dissecting the Hydrophobic Effect on the Molecular Level: the Role of Water, Enthalpy, and Entropy in Ligand Binding to Thermolysin.

I thank Derek Lowe for bringing this paper to my attention

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Nonamethylcyclopentyl Cation Rearrangement Mysteries Solved

Tantillo, D. J.; Schleyer, P. v. R. Org. Lett. 2013, 15, 1725
Contributed by Steven Bachrach.
Reposted from Computational Organic Chemistry with permission

The nine methyl groups of nonamethylcyclopentyl cation 1 all interconvert with a barrier of 7 kcal mol^-1. However, at low temperature only partial scrambling occurs: there are two sets of methyl groups, one containing five groups and the other containing four methyl groups. The barrier for this scrambling is only 2.5 kcal mol^-1. While this behavior was found more than 20 years ago, Tantillo and Schleyer¹ only now have offered a complete explanation.

1

The ground state structure of 1 is shown in Figure 1 and has C₁ symmetry. The two pseudo-axial methyl groups adjacent to the cationic center show evidence of hyperconjugation: long C-C bonds and Me-C-C⁺ angles of 100°.

The transition state TS1¸also in Figure 1, is of C_s symmetry. This transition state leads to interchange of the pseudo-axial methyls, and interchange of the pseudo-equatorial methyls, but no exchange between the members of these two groups. The M06-2x/6-31+G(d,p) and mPW1PW91/6-31+G(d,p) estimate of this barrier is 1.5 and 2.5 kcal mol^-1, respectively. This agrees well with the experiment.

1
TS1	TS2

Figure 1. B3LYP/6-3+G(d,p) optimized geometries.

A second transition state TS2 was found and it corresponds with a twisting motion that interconverts an axial methyl with an equatorial methyl. This TS has C_s symmetry (shown in Figure 1) and the eclipsing interaction give rise to a larger barrier: 7.3 (M06-2x/6-31+G(d,p)) and 6.7 kcal mol^-1 (mPW1PW91/6-31+G(d,p)). So twisting through TS2 and scrambling through TS1 allows for complete exchange of all 9 methyl groups.

An interesting point also made by these authors is that these three structures represent the continuum of cationic structure: a classical (localized) cation in TS2, a bridged structure in TS1 and hyperconjugated cation in 1.

References

(1) Tantillo, D. J.; Schleyer, P. v. R. “Nonamethylcyclopentyl Cation Rearrangement Mysteries Solved,” Org. Lett. 2013, 15, 1725-1727, DOI: 10.1021/ol4005189.

InChIs

1: InChI=1S/C14H27/c1-10-11(2,3)13(6,7)14(8,9)12(10,4)5/h1-9H3/q+1
InChIKey=WUGVCUSQGLXERW-UHFFFAOYSA-N

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Towards First Principles Calculation of Electron Impact Mass Spectra of Molecules

Stefan Grimme Angew. Chem. Int. Ed. 2013, 52, 6306
Contributed by +Jan Jensen

Quantum chemistry has contributed significantly to nearly all spectroscopic methods used in chemistry, but comparatively less so for mass spectrometry.  This might be about to change thanks to this very interesting study by Stefan Grimme.

Grimme presents a new program called QCEIMS, which together with the quantum programs ORCA, DFTB+, and MNDO, is used to predict electron impact mass spectra of molecules in a black box fashion.

The method starts with a ca 50 ps equilibrated ground state NVE Born-Oppenheimer MD simulation of the neutral molecule (M) using, for example, OM2 or DFTB3 (typically at 500 K).

The ionization from electron impact is simulated by randomly choosing a number of snapshots as starting points for new 5-10 ps NVE MD simulations with excess thermal energy.  Unrestricted, fractional occupation number wavefunctions are used and excess thermal energy is applied at the first step of each MD.  OM2 or DFTB3 can usually be used but KS-DFT/DZ may be necessary for cases where the fragmentations involve complex reaction mechanisms.

The charged fragments in the resulting "hot ion" ensemble are then identified and counted to yield the mass spectrum. Roughly 1-100 million energy and gradient evaluations are needed for good agreement with experimental spectra.


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