6444
2006, 110, 6444-6446 Published on Web 03/15/2006
Quantitative Classification of Covalent and Noncovalent H-Bonds Sławomir J. Grabowski,*,†,‡ W. Andrzej Sokalski,§ Edyta Dyguda,§ and Jerzy Leszczyn´ ski‡ Department of Physics and Chemistry, UniVersity of Ło´ dz´, Pomorska 149/153, 90-136 Ło´ dz´, Poland, Computational Center for Molecular Structure and Interactions, Jackson State UniVersity, Jackson, Mississippi 39217, and Department of Chemistry, Wrocław UniVersity of Technology, Wyb. Wyspian´ skiego 27, 50-370 Wrocław, Poland ReceiVed: January 5, 2006; In Final Form: March 1, 2006
The covalent nature of interactions within various hydrogen bonded molecular aggregates has been characterized by the two entirely different computational methods: Bader analysis of the electron density and variationperturbation partitioning of the intermolecular interaction energy. Analysis of 34 complexes representing different types of hydrogen bonds indicates that the proton-acceptor distance ∼1.8 Å and the ratio of delocalization and electrostatic terms ∼0.45 constitutes approximately a borderline between covalent and noncovalent hydrogen bonds. The latter ratio could be used to characterize quantitatively the degree of the covalent nature of transition state interactions with active site residues, a quantity essential for an enzyme catalytic activity.
The physical nature of interactions involved in enzyme catalysis still remains a matter of controversy. The widely accepted explanation originally presented by Pauling concerning the enormous catalytic activity of enzymes by their active site noncovalent interactions with the corresponding transition states1 has been recently challenged by the hypothesis that nearly all enzymes covalently speed reactions.2 In most enzyme systems transition state interactions involve breaking and forming of various classes of hydrogen bonding. Therefore, a quantitative classification of covalent and noncovalent hydrogen bonding is now a very timely issue to be addressed. Due to the complex enzyme structure and lack of sufficiently precise experimental data, quantum chemical characteristics remain perhaps the major method of choice. The problem of covalency of H-bonds is well known in biochemical processes and is studied from time to time.3 There are numerous examples of the short, strong H bonds (SSHBs) playing a key role in such enzymes as hydrolase enzymes, lyases and several isomerases, serine proteases, aspartate amino transferase, ketosteroid isomerase, triosephosphate isomerase, and many others.4 What does it mean that an H-bond is covalent in nature? There is no distinct quantitative or even semiquantitative definition, but in a few studies some examples are reported and/or the characteristics of such systems are analyzed. For example, Gilli and co-workers have introduced the electrostatic-covalent Hbond model.5 According to that model the covalent nature of an H-bond increases with increasing strength and decreasing proton-acceptor distance (H‚‚‚Y). Resonance assisted H-bonds (RAHB) and charge assisted H-bonds (CAHB) may be char* Corresponding author. E-mail:
[email protected]. † University of Ło ´ dz´. ‡ Jackson State University. § Wrocław University of Technology.
10.1021/jp0600817 CCC: $33.50
acterized by very short H‚‚‚Y distances (RH‚‚‚Y) and may be very strong and, in such cases, are covalent in nature. The Bader theory6 is very useful for studying various interactions since it provides more precise quantitative measures to describe them. For example, for any pair of interacting atoms the characteristics of the corresponding bond critical point (BCP), such as the electron density at the BCP (FC) and its Laplacian (∇2FC) allows the covalent character to be recognized. For covalent bonds, the electron density at the BCP is of the order of ∼0.1 au, while for typical noncovalent interactions such as weak H-bonds and van der Waals complexes, it is at least one order lower (∼0.01 au or even less). The negative value of the ∇2F reveals a concentration of electron charge between the pair of interacting atoms. This indicates the shared interaction - the covalent bond. For positive values of ∇2FC, there is a depletion of electron charge for ionic and van der Waals interactions, which include weak H-bonds. However, for extremely strong H-bonds (for example, the RAHB in the crystal structure of benzylacetone7), the ∇2FC value was found to be negative for both H‚‚‚O interactions within the intramolecular O-H‚‚‚O bridge, since the proton is near the middle of the O‚ ‚‚O distance, shared between oxygen atoms. This is powerful evidence for the covalent nature of the H-bond since the experimental electron density was used to apply the Bader theory. ∇2FC is related to the other properties of BCP (according to virial theorem)
(1/4)∇2FC ) 2GC + VC, (HC ) GC + VC)
(1)
GC is the kinetic electron energy density which is always positive, VC is the potential electron energy density which is negative, and HC is the total electron energy density, considering all values at the BCP. Some authors claim that if ∇2FC is positive and HC is negative for any H-bonds, then the interaction is partly covalent in nature.8 The latter parameters are compared here © 2006 American Chemical Society
Letters
J. Phys. Chem. B, Vol. 110, No. 13, 2006 6445 TABLE 1: Properties of Selected Complexes: H‚‚‚Y Distances (Å) Binding Energies (kcal/mol); EDEL(R)/ EEL(1) Ratio and Topological Parameters (au) Are Given
Figure 1. Classification of H-bond interactions. The dependence between the H‚‚‚Y distance [Å] and the ratio of delocalization and electrostatic interaction energy terms. Different types of H-bonds are analyzed (see legend). Full figures designate systems where HC < 0. The other systems are indicated by open figures.
with the geometrical and energetic properties of various Hbonds. CAHBs, intermolecular RAHBs (for example, homonuclear O-H‚‚‚O in formic and acetic acid centrosymmetric dimers, heteronuclear RAHBs in formamide dimer), X-H‚‚‚π (where X-H is the proton donating bond), and the other as a translinear water dimer are considered. Another quantitative measure of the covalent nature of H-bonds versus purely electrostatic bonding could be derived from the theory of intermolecular interactions capable of characterizing strong hydrogen bonds. This is possible within the hybrid variation-perturbation approach free of nonphysical basis set superposition error (BSSE) where the following interaction energy components are defined:9
∆E ) EEL(1) + EEX(1) +EDEL(R) + ECORR(2)
(2)
where EEL(1) is the first-order electrostatic interaction energy term, EEX(1) is the exchange repulsion term, and EDEL(R) and ECORR(2) correspond to delocalization and correlation terms. The higher order delocalization term is the only term which could be associated with covalent interactions since it involves intermolecular charge transfer excitations directed toward the intermolecular region. This term is usually heavily contaminated by BSSE, which is eliminated here by the counterpoise approach.10 It was found very recently that for strong charge assisted dihydrogen bonds where the H‚‚‚H intermolecular contacts are close to 1 Å, EDEL(R) is the most important attractive term of the interaction energy, while for other conventional H-bonds this is the EEL(1) term.11 Hence the aim of this study was to investigate if there are any intercorrelations between ∇2FC and HC on one hand and RH‚‚‚Y and the interaction energy terms on the other hand. Figure 1 presents the characteristics of several classes of H-bonds mentioned above. MP2/6-311++G(d,p) full optimizations have been performed for 34 complexes connected through: resonance assisted H-bonds (RAHBs), 13 complexes, positive and negative charge assisted H-bonds (CAHB(+) and CAHB(-)), 12 species, as well as the other H-bonds. One can observe that for H-bonds which are at least partially covalent (HC < 0), the ratio of EDEL(R) and EEL(1) is approximately greater than ∼0.45. Data collected in Figure 1 indicate clearly that if the delocalization term becomes more
complex
RH‚‚‚Y
∆E
ratio
HC
∇2FC
(F‚‚‚H‚‚‚F)(HCOOH)2 F-H‚‚‚H-Li formamide dimer water dimer F-H‚‚‚C2H2- T-shaped HCCH‚‚‚OH2
1.138 1.726 1.399 1.903 1.950 2.186 2.443
-61.1 -13.6 -13.4 -12.1 -4.5 -3.2 -2.5
0.82 0.48 0.55 0.36 0.25 0.45 0.22
-0.207 -0.003 -0.009 0.001 0.002 0.003 0.002
-0.349 0.129 0.057 0.096 0.091 0.053 0.052
dominant, the degree of covalent interactions increases. It is possible to observe three regions of H-bond interactions: covalent (RH‚‚‚Y < 1.2 Å), partially covalent (RH‚‚‚Y between 1.2 and 1.8 Å), and noncovalent (RH‚‚‚Y > 1.8 Å). This is justified since the following characteristics of the topological parameters may be indicated for these regions, respectively: ∇2FC < 0 and HC < 0, ∇2FC > 0 and HC < 0, and ∇2FC > 0 and HC > 0. Most important is that the EDEL(R)/EEL(1) ratio may be treated as an approximate criterion to indicate the degree of covalent nature of hydrogen bonding. There is only one case for which EDEL(R)/EEL(1) < 0.45 and HC < 0: the unique H2O‚‚‚HF complex. However, in this case HC is equal to -0.0001 au. For the other covalent interactions, the HC values are much greater (if one takes absolute values): -0.207 au for the (FHF)- ion (covalent region) or -0.0026 au for H‚‚‚O of the formic acid dimer (partially covalent region). It is worth mentioning that this “sharp division” of H-bond interactions does not provide the strict criteria of covalency but shows that the topological parameters are in line with the ratio of the delocalization/ electrostatic components of the intermolecular interaction energy. In addition, Figure 1 allows the regions of the specific interactions to be defined approximately. One can observe that all CAHBs are covalent or at least partially covalent. The intermolecular homonuclear O-H‚‚‚O RAHBs are partially covalent (formic acid or acetic acid dimer). The formamide dimer represents the heteronuclear N-H‚‚‚O RAHB. In this case the delocalization is not as important as the other attractive term, the electrostatic energy. Positive value of HC indicates the noncovalent nature of interaction. The translinear water dimer also belongs to the latter region. Further, the X-H‚‚‚π systems are included (Figure 1, triangles), and one of them is at the border line (the EDEL(R)/ EEL(1) ratio equals 0.45). This is the FH‚‚‚C2H2 complex. However, in this case RH‚‚‚Y is far from 1.8 Å (∼2.2 Å). Additionally, it should be mentioned that for complexes with π-electrons as proton acceptors, the binding energies are small and the attractive energy terms are comparable in magnitude. Table 1 shows the characteristics of the selected complexes presented previously in Figure 1 (see Supporting Information for details of all systems considered). One can see that Table 1 includes the three cases mentioned above: (FHF)- as an example of the CAHB(-) system is characterized by both negative values of HC and ∇2FC. The dimer of formic acid as a homonuclear RAHB belongs to the region of partial covalency, with ∇2FC >0 and HC < 0. The formamide dimer as a heteronuclear RAHB represents the third group where both ∇2FC and HC are positive. Hence, one can see that the application of the variationperturbation decomposition of interaction energy as well as of the Bader theory and the geometrical parameters analysis allow to characterize in more detail the degree of covalent nature of H-bonds and can be further applied to more complex enzyme systems.
6446 J. Phys. Chem. B, Vol. 110, No. 13, 2006 Acknowledgment. This work was supported by the State Committee for Scientific Research (KBN No. 3T09A 138 26), Wrocław University of Technology, and NIH grant S06M008047. Calculations were performed at the Wrocław Centre for Networking and Supercomputing (WCSS), Poland. Supporting Information Available: The full list of complexes analyzed with the binding energies and other data is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Pauling, L. Nature 1948, 161, 707. (2) Zhang, X.; Houk, K. N. Acc. Chem. Res. 2005, 38, 379.
Letters (3) Frey, P. A. Magn. Reson. Chem. 2001, 39, 190. (4) Harris, T. K.; Mildvan, A. S. Proteins 1999, 35, 275. (5) Gilli, G.; Gilli, P. J. Mol. Struct. 2000, 552, 1. (6) Bader, R. F. W. Atoms in Molecules, A Quantum Theory; Oxford University Press: Oxford, 1990. (7) Madsen, G. K. H.; Iversen, B. B.; Larsen, F. K.; Kapon, M.; Reisner, G. M.; Herbstein, F. H. J. Am. Chem. Soc. 1998, 120, 10040. (8) Cremer, D.; Kraka, E. Angew. Chem. Int. Ed. Engl. 1984, 23, 627. (9) Sokalski, W. A.; Roszak, S.; Pecul, K. Chem. Phys. Lett. 1988, 153, 153. (b) Sokalski, W. A.; Roszak, S. J. Mol. Struct. (THEOCHEM) 1991, 234, 387. (10) Boys, R. F.; Bernardi, F. Mol. Phys. 1970, 19, 553. (11) Grabowski, S. J.; Sokalski, W. A.; Leszczynski, J. J. Phys. Chem. A 2005, 109, 4331.
