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Could geometry considerations help take into account solute–solvent hydrogen bonding in continuum solvation models?
Chemical Physics Letters 473 (2009) 354–357
Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Could geometry considerations help take into account solute–solvent hydrogen bonding in continuum solvation models? Liliana Mammino * Department of Chemistry, University of Venda, P/bag X5050, Thohoyandou 0950, South Africa
a r t i c l e
i n f o
Article history: Received 17 February 2009 In final form 6 April 2009 Available online 8 April 2009
a b s t r a c t One of the problems in modelling solute–solvent interactions is the difficulty of incorporating the consideration of solute–solvent hydrogen bonding into continuum-type models. The Letter proposes an option utilizing geometry-character considerations to modify the cavity representing the solute, when solute– solvent hydrogen bonding is possible. The computed geometrical characteristics of adducts with explicit water molecules H-bonded to donor–acceptor sites of selected solute molecules suggest the possibility of utilizing these characteristics to design modifications of the solute-cavity contour in correspondence to H-bond donor–acceptor sites, so as to enable the inclusion of at least part of the hydrogen-bonding effects into the overall continuum-type description. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction The importance of studying the situation and behaviour of molecules in a medium stems from the fact that, in real situations, most molecules are in an environment; e.g., biologically active molecules exert their activity in solution, because they are dissolved in some fluid within living organisms. The interactions between the solute molecule and the surrounding solvent molecules may cause modifications of various properties of the solute molecule, with respect to its in vacuo situation: geometry; bond-lengths and related properties [1]; relative energies of different isomers or of different conformers [1]; electron population on an atom [1]; relative separations of the molecule’s energy levels and, consequently, electronic [2] and vibrational transitions [3]; relative acidity of two species [4]; reaction rates [4,5]; molecular recognition [6,7]. Continuum models, viewing the solute molecule as embedded in a cavity within the continuum solvent, are the most extensively utilized to estimate the bulk effects of the solvent on the solute molecule. In particular, the polarisable continuum model (PCM) [8–35] has developed to levels of flexibility and description-abilities enabling it to treat a continuously expanding range of aspects [36,37]. The cavity is built on the basis of geometry-character considerations – by ideally considering a solute-sphere ‘rolling’ on the surface identified by van-der-Waals-radii spheres representing the atoms of the solute molecule, so that sharp spheres-intersections are smoothed to define a solvent-accessible surface [38–40]. However, continuum models do not take into specific account solute–solvent hydrogen bonding [41] – a stronger, more local* Fax: +27 15 9624749. E-mail address: [email protected] 0009-2614/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2009.04.008
ised and inherently directional type of interaction. The current communication presents some reflections on the possibility of utilizing information from the geometries of adducts with explicit water molecules to derive geometry-character considerations that may enable the incorporation of at least part of the effects of solute–solvent H-bonding into the construction of the cavity, by conveniently adapting its shape. The case of water as a solvent is considered as reference in the discussion, as the most important/typical solvent capable of making H-bonds. 2. Geometry features of solute–solvent hydrogen bonding, viewed in terms of the approach of a solvent molecule to the solute molecule Solvent molecules can H-bond only with specific sites of the solute molecule, and with specific directionality, largely determined by the orientation of the lone pairs in the H-bond acceptor atom. H-bonding brings the concerned solvent molecule considerably closer to the solute molecule than other (weaker) types of interactions. The geometry features of such solvent-to-solute approaching appear to follow rather regular patterns for the same type of donor/ acceptor sites in the solute molecule, as highlighted by the study of adducts with explicit water molecules. Fig. 1 shows some of these patterns and Table 1 reports the geometry parameters of the relevant intermolecular H-bonds, since these parameters characterize and describe the way the solvent molecule approaches the solute molecule in the vicinity of the donor/acceptor site; the values highlight fairly regular patterns for the same type of donor/acceptor sites; Fig. 2 shows the uninterrupted patterns around the entire phloroglucinol molecule [42]. Table 1 shows both the MP2/631++G(d,p) and the HF/6-31G(d,p) results: the former option is optimal for the description of hydrogen bonding [43], because of
L. Mammino / Chemical Physics Letters 473 (2009) 354–357
355
Fig. 1. Representative adducts with common arrangements of water molecules around the H-bond donor/acceptor sites of the central molecule. MP2/6-31++G(d,p) results.
including correlation [44] and dispersion [45] effects and the presence of diffuse functions in the basis set [43,46–49]), while HF/631G(d,p) can be utilized also for larger molecular systems, for which more sophisticated options become unaffordable. All the calculations were performed using the GAUSSIAN 03 package, revision D.01 [50]. The models in Fig. 1 clearly show that the water molecule/s H-bonding to the solute molecule approach it more closely than all the others water molecules. The latter may be considered as responding to the water-molecules distribution corresponding to the cavity generated in continuum models (i.e., as approaching the solute molecule at the distance identified by the cavity surface). This suggests that the way in which a water molecule forming an H-bond approaches the solute molecule can be viewed/ approximated as a ‘pocket’ in the cavity, or an ‘indent’ on the cavity surface-contour; in other words, the cavity surface would ‘cave inwards’ in the region corresponding to the H-bond. The size of the pocket is determined by the size of a water molecule, that can still be viewed as a solvent-sphere (as when defining the solvent-accessible surface). The inner part of the pocket (the part towards the solute molecule) would follow the contour of the
solvent-sphere closely (practically coinciding with the contour of a solvent-hemisphere), while the outer part would broaden so that the rim of the pocket smoothes into the rest of the cavity surface. The smoothing would take into account the way the other water molecules (the ones not forming H-bonds with the solute) approach the solute molecule and the way they approach the water molecule H-bonded to the solute. The depth of the pocket should respond to the solute–solvent approach, that is described by the H-bond parameters; however, some scaling of the depth identified on this basis might be convenient, to better match the way the PCM model would evaluate the interaction corresponding to the pocket-region with the known ranges of the energy of the given H-bond (that can be – at least roughly – estimated, e.g., from calculations of adducts with one water molecule H-bonded to the given solute-molecule site, like the adducts with one water molecule reported in Table 1 for alcohols and phenols). For solvents whose molecular shape is less apt to be approximated by a sphere than the water molecules, additional geometry considerations may be needed to ensure that the depth of the pocket, and the way its outer part smoothes into the rest of the cavity surface, better respond to the way in which the solvent mol-
356
L. Mammino / Chemical Physics Letters 473 (2009) 354–357
Table 1 Parameters (H-bond length, donor–acceptor distance (e.g., O O distance) and H-bond angle) of intermolecular hydrogen bonds between main donor/acceptor sites in the solute molecule and water molecules, evaluated from adducts of the given solutes. MP2/6-31++G(d,p) and HF/6-31G(d,p) results. Adduct
Site (atom) in the central molecule engaged in the H-bond
MP2/6-31++G(d,p) H-bond length (Å)
Donor–acceptor distance (Å)
H-bond angle
H-bond length (Å)
Donor–acceptor distance (Å)
H-bond angle
H of OH H of OH O of OH H of OH H of OH O of OH H of OH H of OH O of OH
1.940 1.794 1.774 1.941 1.797 1.775 1.881 1.741 1.821
2.910 2.759 2.740 2.911 2.762 2.742 2.855 2.716 2.777
179.12 166.97 166.29 179.67 167.23 166.23 178.10 168.44 164.33
2.028 1.888 1.915 2.029 1.892 1.920 1.959 1.838 1.980
2.975 2.829 2.848 2.972 2.834 2.856 2.906 2.784 2.899
180.00 168.60 165.33 174.35 169.14 165.20 175.06 169.32 162.02
Carboxylic acids, Z form of COOH Formic acid, 4aq H of COOH sp2 O of COOH sp3 O of COOH Acetic acid, 4aq H of COOH sp2 O of COOH sp3 O of COOH Benzoic acid, 4aq H of COOH sp2 O of COOH sp3 O of COOH
1.501 1.919 1.942 1.531 1.895 1.902 1.512 1.878 1.914
2.536 2.854 2.871 2.555 2.839 2.842 2.541 2.825 2.851
173.38 160.03 159.12 171.98 161.97 161.51 172.50 162.89 160.73
1.650 2.020 2.110 1.676 1.999 2.076 1.673 1.992 2.119
2.629 2.939 3.016 2.649 2.924 2.992 2.646 2.916 3.032
173.79 162.42 159.49 172.34 163.88 162.01 172.90 163.51 161.43
Carboxylic acids, E form of COOH Formic acid, 6aq H of COOH sp2 O of COOH sp3 O of COOH Acetic acid, 6aq H of COOH sp2 O of COOH sp3 O of COOH Benzoic acid, 6aq H of COOH sp2 O of COOH sp3 O of COOH
1.588 1.873 2.009 1.627 1.847 1.979 1.621 1.837 2.038
2.591 2.842 2.957 2.627 2.817 2.930 2.622 2.807 2.924
173.35 171.57 165.45 175.40 171.63 166.53 172.39 171.10 150.98
1.711 1.965 3.091 1.744 1.945 2.156 1.794 1.963 2.169
2.670 2.903 2.175 2.706 2.885 3.081 2.677 2.913 2.976
171.16 168.40 162.92 175.33 168.89 165.59 151.44 175.76 142.31
Amines Methylamine, 1aq Ethylamine, 1aq Aniline, 1aq
N of NH2 N of NH2 N of NH2
1.920 1.920 2.006
2.880 2.880 2.978
165.71 166.03 174.88
2.076 2.078 2.173
3.019 3.020 3.120
170.61 170.27 175.72
sp2 sp2 sp2 sp2 sp2 sp2
2.040 2.040 1.986 1.998 1.973 1.983
2.873 2.873 2.905 2.864 2.916 2.866
142.88 142.94 157.12 147.44 163.32 150.27
2.142 2.146 2.105 2.117 2.086 2.197
2.957 2.958 3.010 2.953 3.006 2.952
143.54 143.18 159.31 146.56 163.36 147.79
Alcohols and phenols Methanol, 1aq Methanol, 3aq Ethanol, 1aq Ethanol, 3aq Phenol, 1aq Phenol, 3aq
Aldehydes Formaldehyde, 2aq Acetaldehyde, 2aq Benzaldehyde, 2aq
O O O O O O
Fig. 2. The symmetry of the phloroglucinol molecule enables a particularly clear illustration of the geometry arrangements of H-bonded and non-H-bonded water molecules around the central molecule.
HF/6-31G(d,p)
ecule H-bonds to the solute molecule and to the neighbouring solvent molecules. Some additional considerations may contribute to support the suggested approach. Solute molecules more often H-bond one solvent molecule per donor/acceptor site, and this is always true when the water molecule is H-bond acceptor (e.g., to a free OH), as bifurcations on such H atoms appear to be rare. This may justify the approximation of considering one solvent-sphere for each donor/acceptor site of the solute molecule. Only for cases in which two water molecules regularly H-bond to the same donor/acceptor site (e.g., the two water molecules symmetrically bonding to the sp2 O of aldehydes, approaching it from the directions of its two lone pairs), the possibility of considering two solvent-spheres may become interesting. The actual situation in a liquid is dynamic and, therefore, statictype descriptions can only consider time-averaged situations. Given the directionality of H-bonds, the consideration of a pocket in the cavity would be consistent with the time-average criterion, as the individual solvent molecule H-bonded to a given site of the
L. Mammino / Chemical Physics Letters 473 (2009) 354–357
solute molecule is likely to change with time, but the way the solvent molecule H-bonded at a given time approaches the solute molecule (the characteristics of the H-bond) can be expected to remain the same. 3. Discussion and conclusions Geometry-based considerations suggest that geometrical modifications of the shape of the cavity describing the approach of solvent molecules to a given solute molecule, in correspondence to H-bond donor/acceptor sites of the solute molecule, may enable the incorporation of a significant proportion of the effects of solute–solvent hydrogen bonding, through apt consideration of the extent to which the H-bonded solvent molecule comes close to the solute molecule. The geometry modification would correspond to a pocket or indent in the cavity surface, whose shape and size are determined by the size of the solvent molecules, by the characteristics of the given H-bond, and by the appropriate smoothing of the way the outer region of the pocket continues into the rest of the cavity surface. Because of its structure and description flexibility, the PCM model is the most apt to incorporate the suggested type of geometry modification. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
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Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Could geometry considerations help take into account solute–solvent hydrogen bonding in continuum solvation models? Liliana Mammino * Department of Chemistry, University of Venda, P/bag X5050, Thohoyandou 0950, South Africa
a r t i c l e
i n f o
Article history: Received 17 February 2009 In final form 6 April 2009 Available online 8 April 2009
a b s t r a c t One of the problems in modelling solute–solvent interactions is the difficulty of incorporating the consideration of solute–solvent hydrogen bonding into continuum-type models. The Letter proposes an option utilizing geometry-character considerations to modify the cavity representing the solute, when solute– solvent hydrogen bonding is possible. The computed geometrical characteristics of adducts with explicit water molecules H-bonded to donor–acceptor sites of selected solute molecules suggest the possibility of utilizing these characteristics to design modifications of the solute-cavity contour in correspondence to H-bond donor–acceptor sites, so as to enable the inclusion of at least part of the hydrogen-bonding effects into the overall continuum-type description. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction The importance of studying the situation and behaviour of molecules in a medium stems from the fact that, in real situations, most molecules are in an environment; e.g., biologically active molecules exert their activity in solution, because they are dissolved in some fluid within living organisms. The interactions between the solute molecule and the surrounding solvent molecules may cause modifications of various properties of the solute molecule, with respect to its in vacuo situation: geometry; bond-lengths and related properties [1]; relative energies of different isomers or of different conformers [1]; electron population on an atom [1]; relative separations of the molecule’s energy levels and, consequently, electronic [2] and vibrational transitions [3]; relative acidity of two species [4]; reaction rates [4,5]; molecular recognition [6,7]. Continuum models, viewing the solute molecule as embedded in a cavity within the continuum solvent, are the most extensively utilized to estimate the bulk effects of the solvent on the solute molecule. In particular, the polarisable continuum model (PCM) [8–35] has developed to levels of flexibility and description-abilities enabling it to treat a continuously expanding range of aspects [36,37]. The cavity is built on the basis of geometry-character considerations – by ideally considering a solute-sphere ‘rolling’ on the surface identified by van-der-Waals-radii spheres representing the atoms of the solute molecule, so that sharp spheres-intersections are smoothed to define a solvent-accessible surface [38–40]. However, continuum models do not take into specific account solute–solvent hydrogen bonding [41] – a stronger, more local* Fax: +27 15 9624749. E-mail address: [email protected] 0009-2614/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2009.04.008
ised and inherently directional type of interaction. The current communication presents some reflections on the possibility of utilizing information from the geometries of adducts with explicit water molecules to derive geometry-character considerations that may enable the incorporation of at least part of the effects of solute–solvent H-bonding into the construction of the cavity, by conveniently adapting its shape. The case of water as a solvent is considered as reference in the discussion, as the most important/typical solvent capable of making H-bonds. 2. Geometry features of solute–solvent hydrogen bonding, viewed in terms of the approach of a solvent molecule to the solute molecule Solvent molecules can H-bond only with specific sites of the solute molecule, and with specific directionality, largely determined by the orientation of the lone pairs in the H-bond acceptor atom. H-bonding brings the concerned solvent molecule considerably closer to the solute molecule than other (weaker) types of interactions. The geometry features of such solvent-to-solute approaching appear to follow rather regular patterns for the same type of donor/ acceptor sites in the solute molecule, as highlighted by the study of adducts with explicit water molecules. Fig. 1 shows some of these patterns and Table 1 reports the geometry parameters of the relevant intermolecular H-bonds, since these parameters characterize and describe the way the solvent molecule approaches the solute molecule in the vicinity of the donor/acceptor site; the values highlight fairly regular patterns for the same type of donor/acceptor sites; Fig. 2 shows the uninterrupted patterns around the entire phloroglucinol molecule [42]. Table 1 shows both the MP2/631++G(d,p) and the HF/6-31G(d,p) results: the former option is optimal for the description of hydrogen bonding [43], because of
L. Mammino / Chemical Physics Letters 473 (2009) 354–357
355
Fig. 1. Representative adducts with common arrangements of water molecules around the H-bond donor/acceptor sites of the central molecule. MP2/6-31++G(d,p) results.
including correlation [44] and dispersion [45] effects and the presence of diffuse functions in the basis set [43,46–49]), while HF/631G(d,p) can be utilized also for larger molecular systems, for which more sophisticated options become unaffordable. All the calculations were performed using the GAUSSIAN 03 package, revision D.01 [50]. The models in Fig. 1 clearly show that the water molecule/s H-bonding to the solute molecule approach it more closely than all the others water molecules. The latter may be considered as responding to the water-molecules distribution corresponding to the cavity generated in continuum models (i.e., as approaching the solute molecule at the distance identified by the cavity surface). This suggests that the way in which a water molecule forming an H-bond approaches the solute molecule can be viewed/ approximated as a ‘pocket’ in the cavity, or an ‘indent’ on the cavity surface-contour; in other words, the cavity surface would ‘cave inwards’ in the region corresponding to the H-bond. The size of the pocket is determined by the size of a water molecule, that can still be viewed as a solvent-sphere (as when defining the solvent-accessible surface). The inner part of the pocket (the part towards the solute molecule) would follow the contour of the
solvent-sphere closely (practically coinciding with the contour of a solvent-hemisphere), while the outer part would broaden so that the rim of the pocket smoothes into the rest of the cavity surface. The smoothing would take into account the way the other water molecules (the ones not forming H-bonds with the solute) approach the solute molecule and the way they approach the water molecule H-bonded to the solute. The depth of the pocket should respond to the solute–solvent approach, that is described by the H-bond parameters; however, some scaling of the depth identified on this basis might be convenient, to better match the way the PCM model would evaluate the interaction corresponding to the pocket-region with the known ranges of the energy of the given H-bond (that can be – at least roughly – estimated, e.g., from calculations of adducts with one water molecule H-bonded to the given solute-molecule site, like the adducts with one water molecule reported in Table 1 for alcohols and phenols). For solvents whose molecular shape is less apt to be approximated by a sphere than the water molecules, additional geometry considerations may be needed to ensure that the depth of the pocket, and the way its outer part smoothes into the rest of the cavity surface, better respond to the way in which the solvent mol-
356
L. Mammino / Chemical Physics Letters 473 (2009) 354–357
Table 1 Parameters (H-bond length, donor–acceptor distance (e.g., O O distance) and H-bond angle) of intermolecular hydrogen bonds between main donor/acceptor sites in the solute molecule and water molecules, evaluated from adducts of the given solutes. MP2/6-31++G(d,p) and HF/6-31G(d,p) results. Adduct
Site (atom) in the central molecule engaged in the H-bond
MP2/6-31++G(d,p) H-bond length (Å)
Donor–acceptor distance (Å)
H-bond angle
H-bond length (Å)
Donor–acceptor distance (Å)
H-bond angle
H of OH H of OH O of OH H of OH H of OH O of OH H of OH H of OH O of OH
1.940 1.794 1.774 1.941 1.797 1.775 1.881 1.741 1.821
2.910 2.759 2.740 2.911 2.762 2.742 2.855 2.716 2.777
179.12 166.97 166.29 179.67 167.23 166.23 178.10 168.44 164.33
2.028 1.888 1.915 2.029 1.892 1.920 1.959 1.838 1.980
2.975 2.829 2.848 2.972 2.834 2.856 2.906 2.784 2.899
180.00 168.60 165.33 174.35 169.14 165.20 175.06 169.32 162.02
Carboxylic acids, Z form of COOH Formic acid, 4aq H of COOH sp2 O of COOH sp3 O of COOH Acetic acid, 4aq H of COOH sp2 O of COOH sp3 O of COOH Benzoic acid, 4aq H of COOH sp2 O of COOH sp3 O of COOH
1.501 1.919 1.942 1.531 1.895 1.902 1.512 1.878 1.914
2.536 2.854 2.871 2.555 2.839 2.842 2.541 2.825 2.851
173.38 160.03 159.12 171.98 161.97 161.51 172.50 162.89 160.73
1.650 2.020 2.110 1.676 1.999 2.076 1.673 1.992 2.119
2.629 2.939 3.016 2.649 2.924 2.992 2.646 2.916 3.032
173.79 162.42 159.49 172.34 163.88 162.01 172.90 163.51 161.43
Carboxylic acids, E form of COOH Formic acid, 6aq H of COOH sp2 O of COOH sp3 O of COOH Acetic acid, 6aq H of COOH sp2 O of COOH sp3 O of COOH Benzoic acid, 6aq H of COOH sp2 O of COOH sp3 O of COOH
1.588 1.873 2.009 1.627 1.847 1.979 1.621 1.837 2.038
2.591 2.842 2.957 2.627 2.817 2.930 2.622 2.807 2.924
173.35 171.57 165.45 175.40 171.63 166.53 172.39 171.10 150.98
1.711 1.965 3.091 1.744 1.945 2.156 1.794 1.963 2.169
2.670 2.903 2.175 2.706 2.885 3.081 2.677 2.913 2.976
171.16 168.40 162.92 175.33 168.89 165.59 151.44 175.76 142.31
Amines Methylamine, 1aq Ethylamine, 1aq Aniline, 1aq
N of NH2 N of NH2 N of NH2
1.920 1.920 2.006
2.880 2.880 2.978
165.71 166.03 174.88
2.076 2.078 2.173
3.019 3.020 3.120
170.61 170.27 175.72
sp2 sp2 sp2 sp2 sp2 sp2
2.040 2.040 1.986 1.998 1.973 1.983
2.873 2.873 2.905 2.864 2.916 2.866
142.88 142.94 157.12 147.44 163.32 150.27
2.142 2.146 2.105 2.117 2.086 2.197
2.957 2.958 3.010 2.953 3.006 2.952
143.54 143.18 159.31 146.56 163.36 147.79
Alcohols and phenols Methanol, 1aq Methanol, 3aq Ethanol, 1aq Ethanol, 3aq Phenol, 1aq Phenol, 3aq
Aldehydes Formaldehyde, 2aq Acetaldehyde, 2aq Benzaldehyde, 2aq
O O O O O O
Fig. 2. The symmetry of the phloroglucinol molecule enables a particularly clear illustration of the geometry arrangements of H-bonded and non-H-bonded water molecules around the central molecule.
HF/6-31G(d,p)
ecule H-bonds to the solute molecule and to the neighbouring solvent molecules. Some additional considerations may contribute to support the suggested approach. Solute molecules more often H-bond one solvent molecule per donor/acceptor site, and this is always true when the water molecule is H-bond acceptor (e.g., to a free OH), as bifurcations on such H atoms appear to be rare. This may justify the approximation of considering one solvent-sphere for each donor/acceptor site of the solute molecule. Only for cases in which two water molecules regularly H-bond to the same donor/acceptor site (e.g., the two water molecules symmetrically bonding to the sp2 O of aldehydes, approaching it from the directions of its two lone pairs), the possibility of considering two solvent-spheres may become interesting. The actual situation in a liquid is dynamic and, therefore, statictype descriptions can only consider time-averaged situations. Given the directionality of H-bonds, the consideration of a pocket in the cavity would be consistent with the time-average criterion, as the individual solvent molecule H-bonded to a given site of the
L. Mammino / Chemical Physics Letters 473 (2009) 354–357
solute molecule is likely to change with time, but the way the solvent molecule H-bonded at a given time approaches the solute molecule (the characteristics of the H-bond) can be expected to remain the same. 3. Discussion and conclusions Geometry-based considerations suggest that geometrical modifications of the shape of the cavity describing the approach of solvent molecules to a given solute molecule, in correspondence to H-bond donor/acceptor sites of the solute molecule, may enable the incorporation of a significant proportion of the effects of solute–solvent hydrogen bonding, through apt consideration of the extent to which the H-bonded solvent molecule comes close to the solute molecule. The geometry modification would correspond to a pocket or indent in the cavity surface, whose shape and size are determined by the size of the solvent molecules, by the characteristics of the given H-bond, and by the appropriate smoothing of the way the outer region of the pocket continues into the rest of the cavity surface. Because of its structure and description flexibility, the PCM model is the most apt to incorporate the suggested type of geometry modification. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
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