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Influence of proton transfer on the geometry of the donor and acceptor in NHN+ hydrogen bonds
Journal of Molecular Structure 976 (2010) 11–18
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Journal of Molecular Structure journal homepage: www.elsevier.com/locate/molstruc
Influence of proton transfer on the geometry of the donor and acceptor in NHN+ hydrogen bonds Irena Majerz a,*, Ivar Olovsson b a b
Faculty of Chemistry, University of Wroclaw, Joliot-Curie 14, 50-383 Wroclaw, Poland Department of Materials Chemistry, Ångström Laboratory, Box 538, SE-751 21 Uppsala, Sweden
a r t i c l e
i n f o
Article history: Received 13 July 2009 Received in revised form 9 October 2009 Accepted 9 October 2009 Available online 13 November 2009 Keywords: NHN+ hydrogen bonds Proton transfer Influence on geometry Theoretical calculations
a b s t r a c t The correlation between distances X–H and H–Y in hydrogen bonds has been studied extensively but it is difficult to determine experimentally individual changes in the internal structure of the molecules involved in the hydrogen bonds. In the present study the influence of proton transfer on the geometry of donors and acceptors in NHN+ hydrogen bonds has been investigated by theoretical calculations at the B3LYP/6-31++G** level of theory using the Gaussian03 system. The selected compounds provide examples of both inter- and intramolecular hydrogen bonds. Typically, the largest changes are in the bonds involving the closest neighbors to the NHN bridge atoms, but in certain cases the geometrical features of parts that are more remote from the bridge atoms are also affected, and can result in significant changes of the conformation of the molecules. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction Proton transfer in hydrogen bonds plays a fundamental role in many simple inorganic and organic compounds. Also many biological processes at some stage involve the formation and breaking of H bonds and proton transfer from the donor to the acceptor atom is often an important step in these processes. Although the H bond is relatively weak, the structure of both the donor and acceptor may be modified in the proton transfer process. This is reflected not only in the hydrogen bridge itself but also in changes of the geometry of the donor (X) and acceptor (Y) groups participating in the H bond. The correlation between the distances X–H and H–Y has been studied extensively [1–4] but it is more difficult to investigate systematic changes in the internal structure of the donor and acceptor. The intrinsic influence of proton transfer on the geometry of the proton donors and acceptors may be masked by other effects, such as crystal packing and influence of the anions and cations. An additional problem is to find a sufficiently numerous series of similar complexes with different degrees of proton transfer. Such systematic investigations have been possible, for example, for complexes of phenols with pyridines [5]. These compounds cover a very broad range of acid–base properties with similar proton donors and acceptors and it was possible to study a series of structures with different degrees of proton transfer. In most other cases it is not easy to obtain a similar series of compounds. It could also be shown that the exper* Corresponding author. Tel.: +48 071 315 28 16; fax: +48 071 328 23 48. E-mail addresses: [email protected] (I. Majerz), Ivar.Olovsson@m kem.uu.se (I. Olovsson). 0022-2860/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.molstruc.2009.10.012
imental structures can be correctly reproduced by ab initio calculations [6]. This has demonstrated that theoretical calculations can be used as an additional tool when a systematic investigation of experimental structures with different degrees of proton transfer is not possible. Theoretical calculations also allow investigations of individual effects and predict trends that are especially important when the changes are very small and at the limit of the precision of the experimental measurements. 2. Systems investigated The present project involves theoretical investigations of the influence of proton transfer on the structure of the molecules participating in NHN+ hydrogen bonds. The investigated compounds include both inter- and intramolecular hydrogen bonds and the project is a continuation of our earlier studies of compounds with NHN+ bonds [7]. In the previous work, the proton transfer path in the hydrogen bonds has been determined from theoretical potential-energy surfaces and the purpose now is to investigate also the effect of the proton transfer on the geometrical parameters of the donor and acceptor moieties. In particular it is important to determine which parts of the donors and acceptors are most sensitive to the proton transfer reaction. The chemical names and hydrogen bond geometries of the investigated complexes are given in Table 1. The cations of the complexes are shown in Scheme 1. In ROHTIR [8] and LEQHIY [9] the hydrogen bonds are intermolecular. In JACSAH [10], GERZUY [11] and HIDSAO [12] the intramolecular hydrogen bonds are shielded in a cavity formed by the aliphatic chains. WERZAU [13], SAKKEU [14], KAHRIU [14] and
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Table 1 Geometry and chemical names of the complexes. Geometry of the hydrogen bonds (Å, °). X-ray data. REFCODE
ROHTIR LEQHIY JACSAH GERZUY HIDSAO WERZAU SAKKEU KAHRIU YULTOO FEGQOX
Compound name
Methylammoniummethylamine tetraphenylborate Bis(imidazole) 2-hydroxy-5,5-dimethyl-1,3,2-dioxaphosphorinane-2-sulfide 1,6-Dimethyl-1,6-diazacyclododecane iodide dichloromethane solvate 1,7-Diazabicyclo(5.4.3)tetradecane trifluoromethanesulfonate 1,4,7,10-Tetra-azabicyclo(5.5.3)pentadecane dibromideperchlorate 1,8-Bis(dimethylamino)naphthalene thiocyanate 1-Dimethylamino-9-dimethylammonio dibenzothiophenetetrafluoroborate 2,20 -Bis(dimethylamino)biphenyl hydrobromide monohydrate 1,12-Bis(dimethylamino) benzo(c)phenanthrene hydroiodide 1,2-Cyclopentadienyldibenzylimine
Scheme 1. The cations of the investigated compounds together with CSD refcodes.
Crystal N. . .N
NHN
2.620 2.674 2.602 2.555 2.566 2.573 2.587 2.650 2.700 2.614
180.00 179.99 169.23 159.97 157.42 155.77 173.06 175.33 177.04 127.94
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YULTOO [15] are examples of proton sponges. WERZAU and SAKKEU are rigid and the NHN bridge has only a limited possibility to be modified in the proton transfer process. In KAHRIU and YULTOO the conformation can be adapted to the changes of the NHN bond. FEGQOX [16] is an example of an intramolecular hydrogen bond with a very bent NHN bond. The correlations resulting from the analysis demonstrate which parts of the structure are most sensitive to proton transfer. Plotting of the separate curves for all the compounds is only meant to demonstrate their spread. 3. Theoretical calculations Two different methods may be applied to determine the transfer path of the proton from the donor to the acceptor. The first is searching for the transition state and in the next step performing an IRC (Intrinsic Reaction Path) calculation. In the IRC method the proton is moved in a limited range of distances around the transition state. The IRC calculations were performed for 12 points around the transition state with a step size of 0.2 Bohr. In the second method the N–H distance is kept constant and all other geometrical parameters are optimized. This method allows moving the proton in very broad range, shifting it from very close to the donor to close to the acceptor. For each of the investigated compound the NH bond was changed from 0.7 to 2.1 Å in steps of 0.1 Å with other geometric parameters optimized. The crystallographically determined structure was used as a starting point in the optimization procedure. The criterion of correct optimization of geometry was that all values of vibrational frequencies except those connected to the proton in the hydrogen bridge were real. It should be noted that in these calculations the proton transfer path has in all cases been assumed to occur along the N–H direction defined by the original nitrogen and hydrogen positions in the experimental structure. This approach will be correct for the systems with linear hydrogen bonds, ROHTIR and LEQHIY. However, in the other systems with bent hydrogen bonds the proton will successively deviate from this direction in the transfer process. The calculations were performed out to d-values ± 1.5 Å. However, such large d-values are in practice completely unrealistic, as illustrated by the following example. The shortest internuclear N–H distance observed experimentally is about 1.2 Å (from neutron diffraction studies). Assume that the H bond is considerably bent and that N1–H + H–N2 is 3.00 Å. The maximum asymmetry, d = N1– H H–N2, will be then 1.20 1.80 = 0.60 Å. The diagrams have therefore been truncated at d = ±0.60 Å. For all compounds investigated in this paper except ROHTIR both calculation methods were applied. The geometry of the NHN+ hydrogen bonds was taken from the CSD data base [17]. As the formulae of the compounds selected are sometimes very complicated the refcodes are used in the text. Ab initio calculations were carried out at the B3LYP/6-31++G** level of theory using the Gaussian03 system [18]. The most sensitive to the calculation method is the N. . .N distance and to investigate the influence of the calculation method, the results from optimization with constant N–H distance and the results from the IRC method are compared in Fig. 1a for LEQHIY as an example of an intermolecular and in Fig. 1b for WERZAU as a typical intramolecular hydrogen bond. Independent of the calculation method the proton motion results in analogous changes in the molecular geometry. Both methods identically reproduce the shape and location of the minima in the curves and the only difference is that optimization of the geometry with constant N–H distances results in a dependency of N. . .N as function of NH–NH which is not symmetrical, although this asymmetry is not very significant and may be considered as a methodological artifact. The agreement between the two calculation methods was checked for all the correlations presented in
Fig. 1. Comparison of the N. . .N/d correlation from the IRC method and the optimization method for (a) LEQHIY, (b) Werzau. Filled circles (black): optimization; unfilled circles (red): IRC. (For interpretation of color mentioned in this figure legend the reader is referred to the web version of the article.)
the following and in the d range limited to the real N–H distances the geometrical parameters are identical. 4. Results 4.1. Geometrical parameters of the hydrogen bridge 4.1.1. Correlation between the NH and HN distances The parameters of the hydrogen bridge are, as expected, the most sensitive to proton transfer. Although the molecules analyzed in this paper are significantly different, some general features of the NHN hydrogen bridge are common to all of them. The interdependence of the NH and HN distances is shown in Fig. 2a. On the horizontal axis the HN2 distance has been successively changed in steps of 0.1 Å, while on the vertical axis the N1H distance is the result of geometry optimization. For the intermolecular OHN hydrogen bonds in the amine–phenol complexes analysed by Majerz et al. [5] and Majerz and Koll [6], the correlation was independent of the proton donor and acceptor. The correlations in Fig. 2a are also relatively similar, ex-
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with an intramolecular hydrogen bonds and with different proton transfer degree depending on the anion. In Fig. 2b experimental X-ray and neutron diffraction data for all complexes of this cation with different anions (CSD data) are plotted together with the theoretical correlation curve of N1H versus HN2 for WERZAU. Although most of the experimental points have been determined by X-ray diffraction (which cannot determine the proton position very accurately) the data fit the theoretical curve quite well. However, for compounds with very short N–H distances, corrections must be applied to reflect the correct internuclear distances and the points will then be close to the theoretical curve [19]. 4.1.2. Correlation between the N. . .N distance and the degree of proton transfer Fig. 3 shows the correlation between the N. . .N distance and proton transfer degree expressed as the difference (d) between the N1H and HN2 distances. In comparison with the NH/HN correlation curves in Fig. 2, the N. . .N/d correlation curves are more dissimilar. As expected, when the proton is located at the midpoint of the N. . .N distance, the H bond is also the shortest. The minimum value of the N. . .N distance is different for the investigated compounds and varies from 2.50 to 2.62 Å. Also the location of the minima is slightly different for the different compounds. It is difficult to relate the minimum value of the N. . .N distance to the strength of the H bond and the structure of the particular compound. This result is very important as the length of the hydrogen bond (N. . .N) is commonly used as a measure of the strength of the hydrogen bond. In the literature, NHN bonds are sometimes compared with the shortest OHO hydrogen bonds. A minimum value of about 2.40 Å is rather typical for the O...O distance but this is quite different from the shortest experimental N. . .N distance of about 2.50 Å. As pointed out above, an H bond is shortest when the proton is located at the midpoint of the N. . .N distance. The correlations of NHN angle with d parameter (Figure in Supplementary materials) illustrate that intermolecular H bonds are always linear, independent of the proton transfer degree. Intramolecular H bonds will become closest to linear when the proton is located at the midpoint. When proton transfer is connected with overcoming of steric hindrances, as in YULTOO, the NHN angle is particularly dependent of the degree of proton transfer.
Fig. 2. (a) NH/HN correlation. The separate curves illustrate the different behavior of the investigated compounds. Note. For the curves on the left-hand side of the vertical dashed line the distances HN2 < 1.2 Å are too short to represent true internuclear distances. (b) Theoretical correlation curve for the cation of WERZAU and experimental data points for complexes of this cation with different anions (from CSD). Filled circles: X-ray structures, empty circles (red): neutron structures. (For interpretation of color mentioned in this figure legend the reader is referred to the web version of the article.)
cept for the left part where the proton is located close to one of the nitrogen atoms (N2), where there is a large spread in the N1H distances. However, it should be noted that the HN2 distance in this part is too short – the true shortest internuclear N–H distance is around 1.2 Å (cf. above). The correlation curves for the two complexes with intermolecular hydrogen bonds (ROHTIR and LEQHIY) are located in the upper part of the diagram and the uppermost curves correspond to KAHRIU and YULTOO. Fig. 2a demonstrates that the correlation of the proton distances is similar for all the complexes and is not very sensitive to the character of the donor and acceptor. The cation of WERZAU is representative of a very big group of complexes (1,8-bis(dimethylamino)naphthalene or ‘proton sponges’)
Fig. 3. Correlation between the N. . .N distance and the difference d = N1H HN2. This difference is used as a measure of the degree of proton transfer.
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4.2. Other structural parameters 4.2.1. Intermolecular NHN hydrogen bonds Among the investigated compounds ROHTIR and LEQHIY form intermolecular hydrogen bonds and ROHTIR is one of the simplest possible examples of this type. The discussion of the influence of proton transfer on the structural parameters involving atoms which are not part of the H bond is limited to the changes of N– C distances, as illustrated for ROHTIR. The N–C distance of the donor cation becomes shorter during the proton transfer and at the same time the N–C bond of the acceptor becomes longer (Figure in Supplementary materials). When the proton is located in the middle between the donor and acceptor groups, the two N–C bonds are equal. The general dependence on proton transfer of the N–C single bonds (with N being part of the H bond) in LEQHIY is the same as in ROHTIR. In the imidazole ring these bonds change from 1.375 to 1.395 Å as the proton moves from the donor to the acceptor. Although the C–C bond is not in immediate neighborhood of the hydrogen bridge, proton transfer also influences this bond, and it changes from 1.355 to 1.380 Å. In the proton transfer process the electron clouds of the proton donor and acceptor are reorganized and the C–C bond changes its character from a double bond to a single bond, as reflected in the above bond lengths. The N@C double bond is less sensitive to proton transfer, the change being within 0.007 Å. Changes of other bond lengths in the imidazole ring are around 0.015 Å. It is expected that the above changes in the bond distances are accompanied by changes in the bond angles in the imidazole rings. The changes in the angles involving the N atoms (with N being part of the H bond) are less than 1°. Unexpectedly, the biggest changes (about 4°) are seen in the angles involving the other N atom (Figure in Supplementary materials). LEQHIY is an example of a cation where proton transfer results in a general rearrangement of the electron clouds in the proton donor and acceptor moieties, and in consequence leads to bond character changes within the imidazole rings. Changes of the geometrical parameters are even larger in the bonds and angles involving atoms which do not participate in the hydrogen bond. 4.2.2. Intramolecular hydrogen bond in JACSAH, GERZUY and HIDSAO In these compounds the N atoms that are involved in the intramolecular hydrogen bond, are additionally linked by aliphatic chains. In JACSAH there are two chains with four methylene groups. In GERZUY three chains are linked to the N atoms, with three, four and five methylene groups, respectively. In HIDSAU two five-membered chains and one three-membered chain are linked to the N atoms; the methylene group in the middle of the five-membered chains is replaced by a N atom. The presence of all these aliphatic chains restricts the maximum N. . .N distance. The major changes in these complexes on proton transfer are limited to the N–C distances and NCC angles (with N being part of the H bond): the N–C distance in the four- and five-membered chains changes from 1.47 to 1.52 Å. In GERZUY the N–C distance involving the three-membered chain changes from 1.49 to 1.55 Å. But in HIDSAO the change in the corresponding N–C distance is the same as in the longer chains. The changes in the NCC angles are dependent on the particular molecule. The NCC angles in JACSAH are almost constant in the whole range of proton transfer degree. In GERZUY and HIDSAO the NCC angles in the four- and five-membered chains have a maximum when the proton is located at the center of the hydrogen bridge, as shown in Fig. 4a for HIDSAU. The CCC angle in the three-membered chain is minimum when the proton is located at the hydrogen bridge center (Fig. 4b, upper curve). The minimum for the NCC angles is shifted from the central location as shown in Fig. 4b (lower curve); these angles become
Fig. 4. HIDSAO: dependence of the angles on the proton transfer degree. (a) Angles involving the carbon atoms next to the N atoms. Solid curves: the NCC angles, shaded on the left side of the diagram; dotted curves: the NCC angles on the right side. (b) Upper curve CCC angles, lower solid and dotted curves NCC angles in the three-membered chain.
equal when the proton is centrally located. The situation is the same in GERZUY. 4.2.3. Intramolecular hydrogen bond in WERZAU, SAKKEU, KAHRIU and YULTOO The next group of compounds with intramolecular hydrogen bonds includes 1,8-bis(dimethylamino)naphthalene (WERZAU), an example of the so-called proton sponges. Here, two methyl substituents at each nitrogen atom form a closed cavity. In the CSD data base there are many complexes of 1,8-bis(dimethylamino)naphthalene cations with different anions but no clear influence of proton transfer on the bond lengths and angles involving atoms close to the NHN hydrogen bond can be seen in the crystal data. The hydrogen bond is probably too weak in comparison with the influence of the anion and packing effects and theoretical modelling is the only method capable of providing information about the small effects of proton transfer. Comparison of the theoretical and experimental NH bond lengths discussed by Majerz and Koll [6] demonstrates that theoretical calculations of the hydrogen
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bonds are actually able to reveal the structural changes caused by proton transfer. SAKKEU, KAHRIU and YULTOO with two methyl groups at each N atom can also be classified as proton sponges. In SAKKEU the N. . .N distance is elongated due to the additional aromatic ring between the six-membered rings. In KAHRIU the six-membered rings are linked by a single bond which makes conformational changes possible. YULTOO is more complicated with four rings, and the N. . .N distance is somewhat elongated. It may be expected that the most sensitive to proton transfer are the N–C bonds, both to the aromatic ring and to the methyl groups. The correlations of N–Cmethyl in all present compounds are similar to the correlations in ROHTIR. The bond lengths change from 1.46 to 1.52 Å. The details of the correlations depend on the particular compound. The correlations of N–Car (the bonds linking the N atoms with the aromatic rings) are similar and the bonds change from 1.42 to 1.50 Å. The spread of the correlation curves for the N–Car bonds is smaller than for N–Cmethyl. Proton transfer has a similar influence also on the C–C bonds in the aromatic ring close to the N atoms. These changes are systematic in the theoretical calculations, but are limited to 0.25 Å for KAHRIU and YULTOO and 0.15 Å for WERZAU and SAKKEU. As mentioned earlier, the N...N distance is strongly dependent on the location of the proton and is the shortest when the proton is centrally located (Fig. 3). For the 1,8-bis(dimethylamino)naphthalene cations the changes in the N...N distance connected with proton shifts can only be realized by changes in the NCC and CCC angles. For WERZAU, these changes are shown in Fig. 5. The curves are of two types. The CCC angle with the central C atom common to both aromatic rings (upper curve) has a minimum for a central location of the proton. The CCC angles in the aromatic rings (with the central C linked to N; middle curve) show slightly bent curves, crossing at d = 0 Å. The NCC angles (lower curve) have a minimum at d = 0 Å. All the correlations shown for WERZAU have a similar shape for SAKKEU, with comparable changes in the bond distances and angles (the angle changes are limited to around 3°). The theoretical calculations suggest that the results are of universal character, common to all proton sponges. In KAHRIU the aromatic rings are linked by a single bond and shortening of the N. . .N distance is not necessarily realized by
Fig. 5. WERZAU: dependence of the angles on the proton transfer degree. The angles in question are marked (for details see Fig. 7 caption).
decreasing of the NCC angle. Shortening of the N. . .N distance is realized by significant reorientation of the aromatic rings: the dihedral CCCC angle changes from 47° to 52° (Figure in Supplementary materials). At the same time all the methyl groups undergo libration. Proton shift is accompanied by changes in the angles close to the hydrogen bridge but all the angles change along curves without a minimum. Changes of the NCC angles in YULTOO are similar to those for KAHRIU. Shortening of the N. . .N distance by decreasing the NCC angle is most significant for WERZAU. In SAKKEU the N. . .N distance is longer and for this reason the changes in the NCC angles on proton transfer are less pronounced. In KAHRIU and YULTOO the changes in the N. . .N distance are realized by changes in the conformation of the whole molecule and are, therefore, less strongly connected with the decrease of the NCC angles. In all the cations of WERZAU, SAKKEU, KAHRIU and YULTOO the changes of the NCC angles involving the carbon atoms in the aromatic ring next to the N atoms are in a range of 4° and the correlation curves consist of a set of straight lines. From the above we notice that in intramolecular hydrogen bonds proton transfer in
Fig. 6. YULTOO: dependence of the angles on the proton transfer degree. (a) Torsion angles involving the methyl groups, (b) torsion angles involving the carbon atoms of the fused aromatic rings.
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general only slightly influences the structural parameters near the N atoms. However, in special cases the changes can be more significant, as seen in the KAHRIU case. The most significant change in conformation on proton transfer occurs in YULTOO (Fig. 6), and is expressed by mutual reorientation of the aromatic rings. Changes in the bond lengths and angles are similar to those in WERZAU, SAKKEU and KAHRIU. KAHRIU and YULTOO are examples of complexes in which proton transfer results in significant conformational changes.
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complexes. The changes in the double bond N@C are smaller than in the C–C bonds more remote from the hydrogen bridge, which are changed about 0.06 Å on proton transfer. As in WERZAU, shortening of the N. . .N distance is connected with changes of the NCC angles. The N. . .N distance becomes the shortest when the proton moves towards the center (Fig. 3) and Fig. 1b shows that the NCC and CCC angles will then also decrease as expected. Unexpectedly, however, the change is the largest for the NCC angle involving the C atom in the six-membered ring. 5. Conclusions
4.2.4. FEGQOX, a molecule with very bent intramolecular hydrogen bond The intramolecular hydrogen bond in FEGQOX is different from those in the other complexes as the NHN bond in the crystal structure is very far from linear (NHN = 128°). The NHN bond in the fully optimized structure is also not linear (139°) and proton transfer is connected with shifting of the proton out of the N. . .N line. It might be suggested that in such a hydrogen bond the molecular geometry should not change significantly on proton transfer but the correlations in Fig. 7a show that the effect is stronger than in the other
In general, a weak interaction such as hydrogen bonding does not significantly change the geometry of the donor and acceptor. Changes due to hydrogen bonding may also be masked by other effects. Typically, the largest changes are limited to bonds involving the closest neighbors of the bridge atoms. KAHRIU and YULTOO illustrate a situation where proton transfer is connected not only with changes of the bond lengths and angles involving the bridge N atoms but also with significant changes of the conformation. In LEQHIY the bond character of both the proton donor and acceptor moieties is changed in the proton transfer process. In FEGQOX changes of the geometry on proton transfer are larger in the parts of the molecule not directly connected with the bridge atoms. All examples discussed in this paper show that the typical correlation curves for bond length/proton transfer degree cross when the proton is centrally located. All these correlation curves have a slightly sigmoidal shape. The angle correlation curves have either a similar shape or have a minimum. The influence of proton transfer on the geometry of other parts of the complex depends on the particular molecule and can be significant for some of the complexes. Acknowledgments This work has been supported by a grant from the Trygger Foundation for Scientific Research. The Wroclaw Center for Networking and Supercomputing is acknowledged for generous computer time. We thank Prof. Mariusz Jaskolski for valuable comments. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.molstruc.2009.10.012. References
Fig. 7. FEGQOX: dependence of different structural parameters on the proton transfer degree. (a) Bond distances, (b) angles, as marked in the diagrams.
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Journal of Molecular Structure journal homepage: www.elsevier.com/locate/molstruc
Influence of proton transfer on the geometry of the donor and acceptor in NHN+ hydrogen bonds Irena Majerz a,*, Ivar Olovsson b a b
Faculty of Chemistry, University of Wroclaw, Joliot-Curie 14, 50-383 Wroclaw, Poland Department of Materials Chemistry, Ångström Laboratory, Box 538, SE-751 21 Uppsala, Sweden
a r t i c l e
i n f o
Article history: Received 13 July 2009 Received in revised form 9 October 2009 Accepted 9 October 2009 Available online 13 November 2009 Keywords: NHN+ hydrogen bonds Proton transfer Influence on geometry Theoretical calculations
a b s t r a c t The correlation between distances X–H and H–Y in hydrogen bonds has been studied extensively but it is difficult to determine experimentally individual changes in the internal structure of the molecules involved in the hydrogen bonds. In the present study the influence of proton transfer on the geometry of donors and acceptors in NHN+ hydrogen bonds has been investigated by theoretical calculations at the B3LYP/6-31++G** level of theory using the Gaussian03 system. The selected compounds provide examples of both inter- and intramolecular hydrogen bonds. Typically, the largest changes are in the bonds involving the closest neighbors to the NHN bridge atoms, but in certain cases the geometrical features of parts that are more remote from the bridge atoms are also affected, and can result in significant changes of the conformation of the molecules. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction Proton transfer in hydrogen bonds plays a fundamental role in many simple inorganic and organic compounds. Also many biological processes at some stage involve the formation and breaking of H bonds and proton transfer from the donor to the acceptor atom is often an important step in these processes. Although the H bond is relatively weak, the structure of both the donor and acceptor may be modified in the proton transfer process. This is reflected not only in the hydrogen bridge itself but also in changes of the geometry of the donor (X) and acceptor (Y) groups participating in the H bond. The correlation between the distances X–H and H–Y has been studied extensively [1–4] but it is more difficult to investigate systematic changes in the internal structure of the donor and acceptor. The intrinsic influence of proton transfer on the geometry of the proton donors and acceptors may be masked by other effects, such as crystal packing and influence of the anions and cations. An additional problem is to find a sufficiently numerous series of similar complexes with different degrees of proton transfer. Such systematic investigations have been possible, for example, for complexes of phenols with pyridines [5]. These compounds cover a very broad range of acid–base properties with similar proton donors and acceptors and it was possible to study a series of structures with different degrees of proton transfer. In most other cases it is not easy to obtain a similar series of compounds. It could also be shown that the exper* Corresponding author. Tel.: +48 071 315 28 16; fax: +48 071 328 23 48. E-mail addresses: [email protected] (I. Majerz), Ivar.Olovsson@m kem.uu.se (I. Olovsson). 0022-2860/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.molstruc.2009.10.012
imental structures can be correctly reproduced by ab initio calculations [6]. This has demonstrated that theoretical calculations can be used as an additional tool when a systematic investigation of experimental structures with different degrees of proton transfer is not possible. Theoretical calculations also allow investigations of individual effects and predict trends that are especially important when the changes are very small and at the limit of the precision of the experimental measurements. 2. Systems investigated The present project involves theoretical investigations of the influence of proton transfer on the structure of the molecules participating in NHN+ hydrogen bonds. The investigated compounds include both inter- and intramolecular hydrogen bonds and the project is a continuation of our earlier studies of compounds with NHN+ bonds [7]. In the previous work, the proton transfer path in the hydrogen bonds has been determined from theoretical potential-energy surfaces and the purpose now is to investigate also the effect of the proton transfer on the geometrical parameters of the donor and acceptor moieties. In particular it is important to determine which parts of the donors and acceptors are most sensitive to the proton transfer reaction. The chemical names and hydrogen bond geometries of the investigated complexes are given in Table 1. The cations of the complexes are shown in Scheme 1. In ROHTIR [8] and LEQHIY [9] the hydrogen bonds are intermolecular. In JACSAH [10], GERZUY [11] and HIDSAO [12] the intramolecular hydrogen bonds are shielded in a cavity formed by the aliphatic chains. WERZAU [13], SAKKEU [14], KAHRIU [14] and
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Table 1 Geometry and chemical names of the complexes. Geometry of the hydrogen bonds (Å, °). X-ray data. REFCODE
ROHTIR LEQHIY JACSAH GERZUY HIDSAO WERZAU SAKKEU KAHRIU YULTOO FEGQOX
Compound name
Methylammoniummethylamine tetraphenylborate Bis(imidazole) 2-hydroxy-5,5-dimethyl-1,3,2-dioxaphosphorinane-2-sulfide 1,6-Dimethyl-1,6-diazacyclododecane iodide dichloromethane solvate 1,7-Diazabicyclo(5.4.3)tetradecane trifluoromethanesulfonate 1,4,7,10-Tetra-azabicyclo(5.5.3)pentadecane dibromideperchlorate 1,8-Bis(dimethylamino)naphthalene thiocyanate 1-Dimethylamino-9-dimethylammonio dibenzothiophenetetrafluoroborate 2,20 -Bis(dimethylamino)biphenyl hydrobromide monohydrate 1,12-Bis(dimethylamino) benzo(c)phenanthrene hydroiodide 1,2-Cyclopentadienyldibenzylimine
Scheme 1. The cations of the investigated compounds together with CSD refcodes.
Crystal N. . .N
NHN
2.620 2.674 2.602 2.555 2.566 2.573 2.587 2.650 2.700 2.614
180.00 179.99 169.23 159.97 157.42 155.77 173.06 175.33 177.04 127.94
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YULTOO [15] are examples of proton sponges. WERZAU and SAKKEU are rigid and the NHN bridge has only a limited possibility to be modified in the proton transfer process. In KAHRIU and YULTOO the conformation can be adapted to the changes of the NHN bond. FEGQOX [16] is an example of an intramolecular hydrogen bond with a very bent NHN bond. The correlations resulting from the analysis demonstrate which parts of the structure are most sensitive to proton transfer. Plotting of the separate curves for all the compounds is only meant to demonstrate their spread. 3. Theoretical calculations Two different methods may be applied to determine the transfer path of the proton from the donor to the acceptor. The first is searching for the transition state and in the next step performing an IRC (Intrinsic Reaction Path) calculation. In the IRC method the proton is moved in a limited range of distances around the transition state. The IRC calculations were performed for 12 points around the transition state with a step size of 0.2 Bohr. In the second method the N–H distance is kept constant and all other geometrical parameters are optimized. This method allows moving the proton in very broad range, shifting it from very close to the donor to close to the acceptor. For each of the investigated compound the NH bond was changed from 0.7 to 2.1 Å in steps of 0.1 Å with other geometric parameters optimized. The crystallographically determined structure was used as a starting point in the optimization procedure. The criterion of correct optimization of geometry was that all values of vibrational frequencies except those connected to the proton in the hydrogen bridge were real. It should be noted that in these calculations the proton transfer path has in all cases been assumed to occur along the N–H direction defined by the original nitrogen and hydrogen positions in the experimental structure. This approach will be correct for the systems with linear hydrogen bonds, ROHTIR and LEQHIY. However, in the other systems with bent hydrogen bonds the proton will successively deviate from this direction in the transfer process. The calculations were performed out to d-values ± 1.5 Å. However, such large d-values are in practice completely unrealistic, as illustrated by the following example. The shortest internuclear N–H distance observed experimentally is about 1.2 Å (from neutron diffraction studies). Assume that the H bond is considerably bent and that N1–H + H–N2 is 3.00 Å. The maximum asymmetry, d = N1– H H–N2, will be then 1.20 1.80 = 0.60 Å. The diagrams have therefore been truncated at d = ±0.60 Å. For all compounds investigated in this paper except ROHTIR both calculation methods were applied. The geometry of the NHN+ hydrogen bonds was taken from the CSD data base [17]. As the formulae of the compounds selected are sometimes very complicated the refcodes are used in the text. Ab initio calculations were carried out at the B3LYP/6-31++G** level of theory using the Gaussian03 system [18]. The most sensitive to the calculation method is the N. . .N distance and to investigate the influence of the calculation method, the results from optimization with constant N–H distance and the results from the IRC method are compared in Fig. 1a for LEQHIY as an example of an intermolecular and in Fig. 1b for WERZAU as a typical intramolecular hydrogen bond. Independent of the calculation method the proton motion results in analogous changes in the molecular geometry. Both methods identically reproduce the shape and location of the minima in the curves and the only difference is that optimization of the geometry with constant N–H distances results in a dependency of N. . .N as function of NH–NH which is not symmetrical, although this asymmetry is not very significant and may be considered as a methodological artifact. The agreement between the two calculation methods was checked for all the correlations presented in
Fig. 1. Comparison of the N. . .N/d correlation from the IRC method and the optimization method for (a) LEQHIY, (b) Werzau. Filled circles (black): optimization; unfilled circles (red): IRC. (For interpretation of color mentioned in this figure legend the reader is referred to the web version of the article.)
the following and in the d range limited to the real N–H distances the geometrical parameters are identical. 4. Results 4.1. Geometrical parameters of the hydrogen bridge 4.1.1. Correlation between the NH and HN distances The parameters of the hydrogen bridge are, as expected, the most sensitive to proton transfer. Although the molecules analyzed in this paper are significantly different, some general features of the NHN hydrogen bridge are common to all of them. The interdependence of the NH and HN distances is shown in Fig. 2a. On the horizontal axis the HN2 distance has been successively changed in steps of 0.1 Å, while on the vertical axis the N1H distance is the result of geometry optimization. For the intermolecular OHN hydrogen bonds in the amine–phenol complexes analysed by Majerz et al. [5] and Majerz and Koll [6], the correlation was independent of the proton donor and acceptor. The correlations in Fig. 2a are also relatively similar, ex-
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with an intramolecular hydrogen bonds and with different proton transfer degree depending on the anion. In Fig. 2b experimental X-ray and neutron diffraction data for all complexes of this cation with different anions (CSD data) are plotted together with the theoretical correlation curve of N1H versus HN2 for WERZAU. Although most of the experimental points have been determined by X-ray diffraction (which cannot determine the proton position very accurately) the data fit the theoretical curve quite well. However, for compounds with very short N–H distances, corrections must be applied to reflect the correct internuclear distances and the points will then be close to the theoretical curve [19]. 4.1.2. Correlation between the N. . .N distance and the degree of proton transfer Fig. 3 shows the correlation between the N. . .N distance and proton transfer degree expressed as the difference (d) between the N1H and HN2 distances. In comparison with the NH/HN correlation curves in Fig. 2, the N. . .N/d correlation curves are more dissimilar. As expected, when the proton is located at the midpoint of the N. . .N distance, the H bond is also the shortest. The minimum value of the N. . .N distance is different for the investigated compounds and varies from 2.50 to 2.62 Å. Also the location of the minima is slightly different for the different compounds. It is difficult to relate the minimum value of the N. . .N distance to the strength of the H bond and the structure of the particular compound. This result is very important as the length of the hydrogen bond (N. . .N) is commonly used as a measure of the strength of the hydrogen bond. In the literature, NHN bonds are sometimes compared with the shortest OHO hydrogen bonds. A minimum value of about 2.40 Å is rather typical for the O...O distance but this is quite different from the shortest experimental N. . .N distance of about 2.50 Å. As pointed out above, an H bond is shortest when the proton is located at the midpoint of the N. . .N distance. The correlations of NHN angle with d parameter (Figure in Supplementary materials) illustrate that intermolecular H bonds are always linear, independent of the proton transfer degree. Intramolecular H bonds will become closest to linear when the proton is located at the midpoint. When proton transfer is connected with overcoming of steric hindrances, as in YULTOO, the NHN angle is particularly dependent of the degree of proton transfer.
Fig. 2. (a) NH/HN correlation. The separate curves illustrate the different behavior of the investigated compounds. Note. For the curves on the left-hand side of the vertical dashed line the distances HN2 < 1.2 Å are too short to represent true internuclear distances. (b) Theoretical correlation curve for the cation of WERZAU and experimental data points for complexes of this cation with different anions (from CSD). Filled circles: X-ray structures, empty circles (red): neutron structures. (For interpretation of color mentioned in this figure legend the reader is referred to the web version of the article.)
cept for the left part where the proton is located close to one of the nitrogen atoms (N2), where there is a large spread in the N1H distances. However, it should be noted that the HN2 distance in this part is too short – the true shortest internuclear N–H distance is around 1.2 Å (cf. above). The correlation curves for the two complexes with intermolecular hydrogen bonds (ROHTIR and LEQHIY) are located in the upper part of the diagram and the uppermost curves correspond to KAHRIU and YULTOO. Fig. 2a demonstrates that the correlation of the proton distances is similar for all the complexes and is not very sensitive to the character of the donor and acceptor. The cation of WERZAU is representative of a very big group of complexes (1,8-bis(dimethylamino)naphthalene or ‘proton sponges’)
Fig. 3. Correlation between the N. . .N distance and the difference d = N1H HN2. This difference is used as a measure of the degree of proton transfer.
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4.2. Other structural parameters 4.2.1. Intermolecular NHN hydrogen bonds Among the investigated compounds ROHTIR and LEQHIY form intermolecular hydrogen bonds and ROHTIR is one of the simplest possible examples of this type. The discussion of the influence of proton transfer on the structural parameters involving atoms which are not part of the H bond is limited to the changes of N– C distances, as illustrated for ROHTIR. The N–C distance of the donor cation becomes shorter during the proton transfer and at the same time the N–C bond of the acceptor becomes longer (Figure in Supplementary materials). When the proton is located in the middle between the donor and acceptor groups, the two N–C bonds are equal. The general dependence on proton transfer of the N–C single bonds (with N being part of the H bond) in LEQHIY is the same as in ROHTIR. In the imidazole ring these bonds change from 1.375 to 1.395 Å as the proton moves from the donor to the acceptor. Although the C–C bond is not in immediate neighborhood of the hydrogen bridge, proton transfer also influences this bond, and it changes from 1.355 to 1.380 Å. In the proton transfer process the electron clouds of the proton donor and acceptor are reorganized and the C–C bond changes its character from a double bond to a single bond, as reflected in the above bond lengths. The N@C double bond is less sensitive to proton transfer, the change being within 0.007 Å. Changes of other bond lengths in the imidazole ring are around 0.015 Å. It is expected that the above changes in the bond distances are accompanied by changes in the bond angles in the imidazole rings. The changes in the angles involving the N atoms (with N being part of the H bond) are less than 1°. Unexpectedly, the biggest changes (about 4°) are seen in the angles involving the other N atom (Figure in Supplementary materials). LEQHIY is an example of a cation where proton transfer results in a general rearrangement of the electron clouds in the proton donor and acceptor moieties, and in consequence leads to bond character changes within the imidazole rings. Changes of the geometrical parameters are even larger in the bonds and angles involving atoms which do not participate in the hydrogen bond. 4.2.2. Intramolecular hydrogen bond in JACSAH, GERZUY and HIDSAO In these compounds the N atoms that are involved in the intramolecular hydrogen bond, are additionally linked by aliphatic chains. In JACSAH there are two chains with four methylene groups. In GERZUY three chains are linked to the N atoms, with three, four and five methylene groups, respectively. In HIDSAU two five-membered chains and one three-membered chain are linked to the N atoms; the methylene group in the middle of the five-membered chains is replaced by a N atom. The presence of all these aliphatic chains restricts the maximum N. . .N distance. The major changes in these complexes on proton transfer are limited to the N–C distances and NCC angles (with N being part of the H bond): the N–C distance in the four- and five-membered chains changes from 1.47 to 1.52 Å. In GERZUY the N–C distance involving the three-membered chain changes from 1.49 to 1.55 Å. But in HIDSAO the change in the corresponding N–C distance is the same as in the longer chains. The changes in the NCC angles are dependent on the particular molecule. The NCC angles in JACSAH are almost constant in the whole range of proton transfer degree. In GERZUY and HIDSAO the NCC angles in the four- and five-membered chains have a maximum when the proton is located at the center of the hydrogen bridge, as shown in Fig. 4a for HIDSAU. The CCC angle in the three-membered chain is minimum when the proton is located at the hydrogen bridge center (Fig. 4b, upper curve). The minimum for the NCC angles is shifted from the central location as shown in Fig. 4b (lower curve); these angles become
Fig. 4. HIDSAO: dependence of the angles on the proton transfer degree. (a) Angles involving the carbon atoms next to the N atoms. Solid curves: the NCC angles, shaded on the left side of the diagram; dotted curves: the NCC angles on the right side. (b) Upper curve CCC angles, lower solid and dotted curves NCC angles in the three-membered chain.
equal when the proton is centrally located. The situation is the same in GERZUY. 4.2.3. Intramolecular hydrogen bond in WERZAU, SAKKEU, KAHRIU and YULTOO The next group of compounds with intramolecular hydrogen bonds includes 1,8-bis(dimethylamino)naphthalene (WERZAU), an example of the so-called proton sponges. Here, two methyl substituents at each nitrogen atom form a closed cavity. In the CSD data base there are many complexes of 1,8-bis(dimethylamino)naphthalene cations with different anions but no clear influence of proton transfer on the bond lengths and angles involving atoms close to the NHN hydrogen bond can be seen in the crystal data. The hydrogen bond is probably too weak in comparison with the influence of the anion and packing effects and theoretical modelling is the only method capable of providing information about the small effects of proton transfer. Comparison of the theoretical and experimental NH bond lengths discussed by Majerz and Koll [6] demonstrates that theoretical calculations of the hydrogen
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bonds are actually able to reveal the structural changes caused by proton transfer. SAKKEU, KAHRIU and YULTOO with two methyl groups at each N atom can also be classified as proton sponges. In SAKKEU the N. . .N distance is elongated due to the additional aromatic ring between the six-membered rings. In KAHRIU the six-membered rings are linked by a single bond which makes conformational changes possible. YULTOO is more complicated with four rings, and the N. . .N distance is somewhat elongated. It may be expected that the most sensitive to proton transfer are the N–C bonds, both to the aromatic ring and to the methyl groups. The correlations of N–Cmethyl in all present compounds are similar to the correlations in ROHTIR. The bond lengths change from 1.46 to 1.52 Å. The details of the correlations depend on the particular compound. The correlations of N–Car (the bonds linking the N atoms with the aromatic rings) are similar and the bonds change from 1.42 to 1.50 Å. The spread of the correlation curves for the N–Car bonds is smaller than for N–Cmethyl. Proton transfer has a similar influence also on the C–C bonds in the aromatic ring close to the N atoms. These changes are systematic in the theoretical calculations, but are limited to 0.25 Å for KAHRIU and YULTOO and 0.15 Å for WERZAU and SAKKEU. As mentioned earlier, the N...N distance is strongly dependent on the location of the proton and is the shortest when the proton is centrally located (Fig. 3). For the 1,8-bis(dimethylamino)naphthalene cations the changes in the N...N distance connected with proton shifts can only be realized by changes in the NCC and CCC angles. For WERZAU, these changes are shown in Fig. 5. The curves are of two types. The CCC angle with the central C atom common to both aromatic rings (upper curve) has a minimum for a central location of the proton. The CCC angles in the aromatic rings (with the central C linked to N; middle curve) show slightly bent curves, crossing at d = 0 Å. The NCC angles (lower curve) have a minimum at d = 0 Å. All the correlations shown for WERZAU have a similar shape for SAKKEU, with comparable changes in the bond distances and angles (the angle changes are limited to around 3°). The theoretical calculations suggest that the results are of universal character, common to all proton sponges. In KAHRIU the aromatic rings are linked by a single bond and shortening of the N. . .N distance is not necessarily realized by
Fig. 5. WERZAU: dependence of the angles on the proton transfer degree. The angles in question are marked (for details see Fig. 7 caption).
decreasing of the NCC angle. Shortening of the N. . .N distance is realized by significant reorientation of the aromatic rings: the dihedral CCCC angle changes from 47° to 52° (Figure in Supplementary materials). At the same time all the methyl groups undergo libration. Proton shift is accompanied by changes in the angles close to the hydrogen bridge but all the angles change along curves without a minimum. Changes of the NCC angles in YULTOO are similar to those for KAHRIU. Shortening of the N. . .N distance by decreasing the NCC angle is most significant for WERZAU. In SAKKEU the N. . .N distance is longer and for this reason the changes in the NCC angles on proton transfer are less pronounced. In KAHRIU and YULTOO the changes in the N. . .N distance are realized by changes in the conformation of the whole molecule and are, therefore, less strongly connected with the decrease of the NCC angles. In all the cations of WERZAU, SAKKEU, KAHRIU and YULTOO the changes of the NCC angles involving the carbon atoms in the aromatic ring next to the N atoms are in a range of 4° and the correlation curves consist of a set of straight lines. From the above we notice that in intramolecular hydrogen bonds proton transfer in
Fig. 6. YULTOO: dependence of the angles on the proton transfer degree. (a) Torsion angles involving the methyl groups, (b) torsion angles involving the carbon atoms of the fused aromatic rings.
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general only slightly influences the structural parameters near the N atoms. However, in special cases the changes can be more significant, as seen in the KAHRIU case. The most significant change in conformation on proton transfer occurs in YULTOO (Fig. 6), and is expressed by mutual reorientation of the aromatic rings. Changes in the bond lengths and angles are similar to those in WERZAU, SAKKEU and KAHRIU. KAHRIU and YULTOO are examples of complexes in which proton transfer results in significant conformational changes.
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complexes. The changes in the double bond N@C are smaller than in the C–C bonds more remote from the hydrogen bridge, which are changed about 0.06 Å on proton transfer. As in WERZAU, shortening of the N. . .N distance is connected with changes of the NCC angles. The N. . .N distance becomes the shortest when the proton moves towards the center (Fig. 3) and Fig. 1b shows that the NCC and CCC angles will then also decrease as expected. Unexpectedly, however, the change is the largest for the NCC angle involving the C atom in the six-membered ring. 5. Conclusions
4.2.4. FEGQOX, a molecule with very bent intramolecular hydrogen bond The intramolecular hydrogen bond in FEGQOX is different from those in the other complexes as the NHN bond in the crystal structure is very far from linear (NHN = 128°). The NHN bond in the fully optimized structure is also not linear (139°) and proton transfer is connected with shifting of the proton out of the N. . .N line. It might be suggested that in such a hydrogen bond the molecular geometry should not change significantly on proton transfer but the correlations in Fig. 7a show that the effect is stronger than in the other
In general, a weak interaction such as hydrogen bonding does not significantly change the geometry of the donor and acceptor. Changes due to hydrogen bonding may also be masked by other effects. Typically, the largest changes are limited to bonds involving the closest neighbors of the bridge atoms. KAHRIU and YULTOO illustrate a situation where proton transfer is connected not only with changes of the bond lengths and angles involving the bridge N atoms but also with significant changes of the conformation. In LEQHIY the bond character of both the proton donor and acceptor moieties is changed in the proton transfer process. In FEGQOX changes of the geometry on proton transfer are larger in the parts of the molecule not directly connected with the bridge atoms. All examples discussed in this paper show that the typical correlation curves for bond length/proton transfer degree cross when the proton is centrally located. All these correlation curves have a slightly sigmoidal shape. The angle correlation curves have either a similar shape or have a minimum. The influence of proton transfer on the geometry of other parts of the complex depends on the particular molecule and can be significant for some of the complexes. Acknowledgments This work has been supported by a grant from the Trygger Foundation for Scientific Research. The Wroclaw Center for Networking and Supercomputing is acknowledged for generous computer time. We thank Prof. Mariusz Jaskolski for valuable comments. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.molstruc.2009.10.012. References
Fig. 7. FEGQOX: dependence of different structural parameters on the proton transfer degree. (a) Bond distances, (b) angles, as marked in the diagrams.
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