Solvation Difference Maps as Probes of Intramolecular Hydrogen Bonding: An Application of Hyperactive Molecules

Henry S. Rzepa^*, Christopher Leach and Omer Casher

Department of Chemistry, Imperial College, London, SW7 2AY.

Summary

Experimental data for the equilibrium between the di-axial (1, X = OH) and di-equatorial (2, X = OH) conformations of cis 3-X-cyclohexanol in a variety of solvents is compared with quantitative SCF-MO level AM1 and PM3 COSMO solvation calculations. An analysis using 2D solvation energy contour maps, in which the effect of changing solvent dielectric is represented as a time-dependent animation of the 2D map, reveals geometrical regions associated with intramolecular hydrogen bonds which show up as prominent ridges. Geometries associated with features in these maps are presented to the user as "hyperactive molecules" via the World-Wide-Web mechanism. These are invoked by defining clickable regions within the 2D maps and hyperlinking these to molecular coordinates in MOPAC format using chemical MIME types. Results for cis 3-X-cyclohexanol (X= ethyne, Ph) are analysed for evidence of pi-facial hydrogen bonding interactions.

Introduction

Abraham et al [1] have recently provided accurate Gibb's free energy changes for the equilibrium between di-axial (1, X= OH) and di-equatorial (2, X = OH) conformations of cyclohexan-1-X, 3-ol in fourteen solvents using NMR techniques. In non-polar solvents, the two conformations are approximately equally populated, but as the solvent polarity increases, 2 becomes increasingly favoured. This was interpreted as indicating that the stabilisation of 1 via intramolecular hydrogen bonding is removed in the more polar solvents.

This is supported by a theoretical study[2] of intramolecular hydrogen bonding in systems such as glucose and 1,2-ethanediol, from which Cramer and Truhlar concluded that intramolecularly hydrogen bonded conformers remain as the global minima upon aqueous solvation, albeit by less energy than prior to solvation. The recent introduction by Klamt[3] of the COSMO solvation algorithm into semi-empirical SCF-MO hamiltonians such as PM3 allows calculation of the dielectric screening energy component via an atom centred distributed multipole analysis in a cavity defined by a realistic solvent accessible surface. This method allows molecular conformational analyses to be performed in which all molecular geometries are fully optimised over a range of values of the dielectric constant of the surrounding medium. Hitherto, approximations involving cavities of assumed spherical or ellipsoidal dimensions have inhibited meaningful comparisons between molecules where substantial changes in geometry occur, and it has not been possible to vary the permittivity of the medium continuously. We have previously shown[4] that the combined AM1 or PM3/COSMO approach successfully models the energetics of isomeric systems which differ only in the presence of a single covalent bond. We considered cyclohexane-1,3-diol as an ideal system to evaluate the performance of the COSMO method specifically, for systems differing only in a weaker hydrogen bond.

This system also forces consideration of how the computational data might be presented. Two problems have to be addressed. Firstly, whilst the conformational energies can be visualised as 2D energy maps, we felt that the most important aspect was how to illustrate these change with solvent polarity. Secondly, we felt it important to annotate the 2D maps with representations of the molecular geometries in various regions of interest without losing the clarity of the presentation. We show in this paper how both these aspects have been solved by employing a combination of animating the 2D map into the form of an MPEG movie, and associating regions of the 2D maps with molecular coordinates using chemical MIME types[5] and presentation using the World-Wide-Web.[6]

Computational Details

Theoretical calculations were carried out using the AM1 and PM3 semi-empirical self-consistent field molecular orbital methods, as implemented in the program MOPAC 93. The solvation model that was used was the COSMO Hamiltonian[3], with energies calculated as enthalpies. No attempt was made to convert these to free energies because the many low frequency modes associated with these molecules render inappropriate the rigid-rotor-harmonic-oscillator approximation used to convert normal frequencies to entropies. Other corrections related to the free energy of cavitation and dispersion terms [2] are not available in the current version of COSMO. The extensive subtraction of similar quantities in the solvation difference maps could be expected to minimise the effects of these approximations. The keywords PRECISE, EF, RMIN=-100, GNORM=0.5 and GEO-OK were used for maximum accuracy. To produce the two dimensional grids, the dihedral angles of the hydroxyl O-H bonds relative to the cyclohexane ring were changed in steps of 18° to give a square grid of dimension 20. The COSMO algorithm was invoked using the keyword EPS=solvent dielectric. The 2D grids were produced and normalised to unity by subtraction of each cell from the corresponding values for EPS=1 (gas phase), thus leaving only features associated with changing solvent polarity visible. These solvent-difference grids were visualised in Microsoft Excel v5.0 and converted to a series of bitmapped images, one for each value of the solvent polarity. A sequence of these images were converted to animation format using QuickTime compression and to MPEG format for presentation using the World-Wide-Web as a delivery mechanism. Minimum energy conformations were obtained from the 2D grids, and re-optimised fully.

Results and Discussion.

The calculated enthalpies of formation for 1 and 2 for various substituents X are shown in the Table. For the diol (X=OH), the AM1 calculations indicate that the di-axial systems is 5.5 kJ mol^-1 less stable than the di-equatorial form. This accords with the well known observation that the strength of OH...O interactions can be underestimated by this method. This difference is increased to 12 kJ mol^-1when the solvent dielectric is increased to 80, which accords well with the experimental observation that the di-equatorial form predominates in more polar solvents. Put simply, the di-equatorial form benefits from the full solvation of both hydroxyl groups, whereas the di-axial form loses the equivalent of one hydrogen bond to stabilisation by the solvent.

That this effect is directly due to the loss of the intramolecular hydrogen bond can be illustrated as follows. Figure 1 shows a full conformational energy map calculated at the AM1 level for 1 (X=OH) as a function of the rotational dihedral angle of the two OH groups. The circled regions indicate available molecular co-ordinates when viewed with a suitable viewing package.

In order to simplify the diagram, we have calculated a difference map in which the energy at each point in the grid for a dielectric constant of 1 is subtracted from that calculated at a value of the dielectric of 80. Thus the map reveals the solvation energy as a result of the conformational orientation of the two OH groups. The low energy regions corresponding to greatest solvation energy are those where no intramolecular hydrogen bond is present, whilst the ridges seen in the isometric projection are precisely those associated with such a hydrogen bond. The ridge like features are obviously absent for the gas phase, and only become prominent as the calculated dielectric is increased from 1.

Further information about this phenomenon can be delivered by two "multimedia" techniques. Firstly, an animation of the solvation map as a function of varying solvent dielectric can be made to reveal the growth of the "hydrogen bond ridge". Using the metaphor of the World-Wide Web, the animation files in Quicktime (diequatorial, diaxial) or MPEG (diequatorial, diaxial) format can be delivered to the user via "hot-spots" or hyperlinks built into the actual isometric map and shown as buttons in the top right of the diagram. Secondly, molecular coordinates can be associated with chemical MIME types[5]such that when a particular region of the solvation map is activated, the coordinates are transferred to the user's computer and visualised using a suitable visualisation program. Thus the reader can themselves verify that the ridges actually correspond to geometries containing an intramolecular hydrogen bond. Furthermore, since the optimised molecular coordinates are now available to them, they can also verify the energies we report in the Table as being accurate and reproducible.

In Figure 2, the same series of calculations are presented for the di-equatorial system 2. Because no intramolecular hydrogen bond can be disrupted in this system, the entire map is virtually featureless, and no discernible ridges can be seen.

Table. Calculated AM1 (PM3) enthalpies (kJ mol^-1) for 3-substituted di-axial and di-equatorial Cyclohexanols

System                     Dielectric=1              Dielectric=80           
2, X = OH                 -540.1(-480.2)            -589.6(-522.9)              
1, X = OH                 -534.6(-475.7)            -577.6(-514.6)                    
2, X = ethyne             -110.3( -77.6)            -144.8(-106.4)
1, X = ethyne             -102.2( -73.6)            -131.1( -98.0)                    
2, X = Ph                 -230.4(-186.8)            -268.5(-216.9)                   
1, X = Ph                 -214.2(-179.1)            -249.4(-206.8)                    
2, X = p-NO2-Ph           -217.3(-224.8)            -296.1(-334.9)                    
1, X = p-NO2-Ph           -200.3(-216.2)            -277.0(-324.0)                    
2, X = p-MeO-Ph           -388.9(-345.8)            -440.1(-385.3)                    
1, X = p-MeO-Ph           -372.6(-337.9)            -420.9(-375.0)

We have recently discussed[7] crystallographic evidence that alkyne and aromatic groups can participate in significantly short hydrogen bond interactions. Unfortunately, crystal structures give no indication of the energetics of such interactions. Following the approach of Abraham et al[1] a system such as (1, X=ethyne) may provide one means of estimating the strength of such interactions experimentally. Whilst experimental studies are under way, we set the scene by modelling these systems (Table). At the AM1 level, the di-axial system was calculated to be 8.1 kJ mol^-1 less stable than the di-equatorial in the gas phase, a value quite similar to the diol, and which increased to 13.7 kJ mol^-1 at a dielectric of 80. These values are very similar to the basic diol system, which suggests that experimental studies should yield similar results for the alkyne system. Hydrogen bonding to phenyl groups is similarly well established[7] and in this system we also have the opportunity for structure-activity studies by varying the ring substitution.[8] A solvation energy map (1, X=Ph, Figure 3) constructed along similar lines to the diol, in which the rotation angle of both the OH and the phenyl ring are varied, resulted in similar but less promiment ridges to those observed for the diol.

The orientation involving direct OH...pi bonding is hyperlinked to coordinates so that readers can inspect the geometry for themselves. The AM1 energetics (Table) show that the di-axial conformation is intrinsically less stable than the di-equatorial form, compared to the diol system (16.2 kJ mol^-1). Solvation again increases this energy difference, but by less than the diol. The effect of substituents was negligible, suggesting they should have no perceptible effect on the axial/equatorial ratios. Experimental results relating to these predictions will be reported elsewhere.

We conclude that the COSMO solvation algorithm allows energy maps to be constructed with inclusion of complete geometry optimisation, and represents a significant advance in the ability to model the conformational properties of molecules in solution. The use of animations, hyperlinked 2D diagrams and the delivery of molecular coordinates in the form of hyperactive molecules serves to simplify diagrams, whilst adding value for the reader by providing them with working models. We believe that such forms of scientific publication can only serve to enhance the quality of reported scientific data.

References

[1]R. J. Abraham, E. J. Chambers and W. A. Thomas, J. Chem. Soc, Perkin Trans. 2, 1993, 1061.

[2]C. J. Cramer and D. Truhlar, J. Am. Chem. Soc., 1993, 115, 5745, ibid, 1994, 116, 3892.

[3] A. Klamt and G. Schürmann, J. Chem. Soc., Perkin Trans. 2, 1993, 799.

[4] H. S. Rzepa and G. Suner, J. Chem. Soc., Perkin Trans 2, 1994, 1397. See http://www.ch.ic.ac.uk/rzepa/RSC/P2/4_02709D.html

[5] O. Casher, G. Chandramohan, M. Hargreaves, C. Leach, P. Murray-Rust, R. Sayle, H. S. Rzepa, B. J. Whitaker, J. Chem. Soc., Perkin Trans. 2, 1995, 7. See http://www.ch.ic.ac.uk/rzepa/RSC/P2/4_05970K.html

[6] H. S. Rzepa, B. J. Whitaker and M. J. Winter, J. Chem. Soc., Chem. Commun, 1994, 1907. See http://www.ch.ic.ac.uk/rzepa/RSC/CC/4_02963A.html

[7] H. S. Rzepa, M. H. Smith and M. L. Webb, J. Chem. Soc., Perkin Trans 2, 1994, 703. See http://www.ch.ic.ac.uk/rzepa/RSC/P2/3_05613l.html

[8] Further details will be reported in C. Leach and H. S. Rzepa, J. Chem. Soc., Perkin Trans. 2, to be submitted.