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The rotational barrier of formamide in various solvents
Journal of Molecular Structure, 91 (1983) 289-294 THEOCHEM Elsevier Scientific Publishing Company, Amsterdam
THE ROTATIONAL SOLVENTS
HANS-JGRG
HOFMANN
Sektion Biowissenschaften (G.D. R.) (Received
16 March
-
Printed
BARRIER OF FORMAMIDE
and GUSTAV and Sektion
in The Netherlands
IN VARIOUS
PEINEL Physik
of the Karl Marx
University,
Leipzig
1982)
ABSTRACT The solvent influence on the rotational barrier of formamide has been studied by means of PCILO supermolecule calculations. The results indicate an increase in the barrier caused by the medium in the order acetone, pure liquid formamide and water. Thus, a more rigid structure of the peptide bond is expected with higher solvent polarity. INTRODUCTION
The formation of hydrogen bonds between amide molecules in a pure liquid or between amide and solvent molecules in mixed solvent systems may be responsible for specific bonding and structural properties of such solutions. Formamide is the simplest representative of this class of compounds. It can be regarded as a model system for the peptide linkage. Theoretical and experimental studies of formamide-solvent systems could therefore provide information about the hydrogen bonding in such solutions and contribute to a better understanding of more complex biological systems. In this paper, we present the results of a theoretical examination of the solvent influence on the rotational barrier of formamide. Experimental investigations indicate a strong solvent dependence of the barrier. Thus, barrier heights of 70.7 f 7.9 (75.3 [l]), 79.1 f 4.2 and 89.1 + 5.4 kJ mol-’ were determined in acetone, in the pure liquid and in water, respectively [ 21 (cf. also refs 3-7). Values of the barrier height of the isolated formamide molecule were calculated by means of various quantum chemical methods [ 7-161. These values are often in close agreement with experimental data for polar solvents. The starting point for our study is the hypothesis visualized in Fig. 1, according to which, an increase in the rotational barrier will result from interactions of the amino group of the formamide molecule with electrondonating groups and of the carbonyl group with electron-accepting groups. Thus, solvent molecules which are capable of fulfilling both these conditions should cause the greatest barrier enhancement. This hypothesis is confirmed by the trend observed in the experimental values. Hence, the barrier of the 0166-1280/83/0000-0000/$03.00
0 1983
Elsevier
Scientific
Publishing
Company
290
donor
acceptor
\ acceptor
donor
Fig. 1. Interaction model of the solvent influence on the rotational barrier of formamide.
isolated molecule should not surpass the value estimated in acetone. This is also supported by experimental findings, which indicate a decrease in the rotation barrier if liquid formamide is diluted in apolar solvents [ 171. In order to prove the correctness of this hypothesis, supermolecule calculations were performed on aggregates consisting of several formamide molecules as a model for the pure liquid, formamide and acetone molecules and formamide and water molecules, respectively, as models for the corresponding mixed solvent systems. Obviously, supermolecule calculations limited to a few solvent molecules can only be regarded as a first step in the description of formamide solutions. Greater insight would presumably be achieved by the consideration of a greater number of solvent molecules in connection with a statistical thermodynamic treatment [ 181. However, for the solvation of the polar regions of molecules, monosolvation models or models which consider a small number of solvent molecules step-bystep often provide reliable information [ 19-211 . DETAILS OF THE CALCULATIONS
The semiempirical PCILO method was employed for all the calculations [ 221. Previous studies have demonstrated that this method is well suited to the study of intermolecular phenomena [ 23,241. The geometries of the
corresponding planar and rotated aggregates were determined by means of an automatic optimization technique [ 251. The optimization process was confined to the intermolecular geometry parameters. The internal coordinates of the molecules were kept fixed at the experimentally measured values. For the formamide-water complexes, three situations were examined in detail: the hydration of the amino and carbonyl groups, respectively, by two water molecules and the hydration of the formamide molecule by five water molecules. In the last case, the ab initio data of Alagona et al. were selected as the starting point of the PCILO optimization [26]. Comparing the waterformamide interaction energies at the various water positions (cf. Fig. 2) with the water dimer interaction energy, Pullman et al. [ 271 concluded that only four water molecules form the first hydration shell in the molecular plane. Our calculations confirm this result [28]. However, the consideration of a fifth water molecule along the CH bond of formamide does not significantly influence the barrier problem.
291
97.9
Fig. 2. Optimized formamide-water barriers (in kJ mol-I).
supermolecule structures and values of the rotational
The pure liquid was characterized by various dimers, trimers, tetramers and pentamers of formamide. The selection of these models was prompted by the results of ab initio studies of Hinton and Harpool [29] and Pullman et al. [ 271. Typical hydrogen-bonding effects can be expected between the carbonyl oxygen atom of acetone and the amino group of formamide. Corresponding to this situation, three different arrangements of formamideacetone complexes were investigated. RESULTS
AND DISCUSSION
Figures 2-4 depict the calculated optimum arrangements of all the aggregates, the energy values of the barrier heights for various rotational possibilities are also given. The PCILO barrier of the isolated formamide molecule amounts to 68.6 kJ mol-‘. It is evident that the barrier increases in the order acetone, pure liquid and water. The strongest effect exists in the formamide pentahydrate (97.9 kJ mol-‘, experimental value 89.1 kJ mol-‘). The theoretical value is expected to be greater because of the optimum structure of the pentahydrate complex, whereas the aqueous solution should represent a mixture of more or less hydrated formamide species. It is impossible to obtain the increase in the barrier height of the pentahydrate by addition of the calculated values for the two dihydrates. Comparing the positions of the water molecules in the various hydrated forms, there are considerable differences with respect to the orientation of the water molecules 2 and 3 (cf. Fig. 2), which form a hydrogen bond in the pentahydrate. The breaking of this bond is responsible for an additional increase in the barrier.
292
Fig. 3. Optimized (in kJ mol-I).
formamide
aggregate
structures
and values of the rotational
barriers
A detailed analysis presented previously [28,30] shows that the enhancement of the formamide barrier in aqueous solution is caused by differences in the electrostatic interactions between solute and solvent molecules and differences in cavity formation in the planar and perpendicular conformations. This analysis also provides a good explanation for the surprising fact that solvation models which are unable to consider specific interactions predict the same solvent influence on the barrier as indicated by our former calculations using a classical continuum model [ 311 or those of Duben and Miertus [ 321 using a solvaton model. Thus, the changes in the electron distribution in the planar and perpendicular conformations of formamide are reflected in the different strengths of the hydrogen bonds considered by the super-molecule approximation and the large decrease in the dipole moment, which is responsible for the qualitatively correct result of the continuum approach. However, the limitations of predictions based on continuum methods are evident in the case of specific interactions. Only the same tendency of the change in electrostatic solute-solvent interactions on the one hand and the reorientation of the solvation shell around the forma-
293
75.8
bHH
HYC\
c/c
VH
J, i\\~
\NP!O
‘w
/
\
724
Fig. 4. Optimized formamide-acetone barriers (in kJ mol-I).
complex structures and values of the rotational
mide conformations, which is not considered in the classical cavity treatment, on the other, assures agreement in principle. Apart from the hypothetical formamide pentamer, nearly identical values for the rotational barrier were obtained for the pure liquid and the formamide-acetone system based on the models given in Figs. 3 and 4, respectively, The higher barrier calculated for the pentamer illustrates the somewhat greater tendency for barrier enhancement in liquid formamide than in acetone, as experimentally measured. For a description of the situation in the pure liquid, consideration of the linear formamide trimer and, above all, the so called lcis tetramer, which contains linear and cyclic structural elements, should be included. According to Pullman et al. [27], the l-cis tetramer is compatible with all the experimental data (dielectric and spectroscopic properties). Thus, this species should predominate in liquid formamide followed by linear chain structures. As regards the barrier problem, there are no major differences between the linear trimer and the l-cis tetramer. Confirming the hypothesis, central CN bond barrier of the linear trimer is slightly greater than those of the terminal CN bonds. Based on his experimental data, Kamei [2] postulated a stronger interaction between formamide and water molecules than between neighbouring formamide molecules. According to our calculations, the average energy value per hydrogen bond for the formamide pentahydrate and the formamide pentamer are 26.0 and 19.4 kJ mol-‘, respectively.
294
CONCLUSIONS
The results of our calculations confirm the original hypothesis regarding the influence of the solvent on the rotational barrier of formamide. The same model is also valid to explain the influence of electrolytes on the barrier [ 331. The barrier increases in the order acetone, pure liquid and water. Thus, a more rigid structure for the peptide bond is expected in more polar solvents and when influenced by electrolytes. Extending our conclusions to substituted amides, e.g. dimethylformamide, the same general solvent effect is expected but to a lesser extent. Comparison of the barriers in the formamide trimer and the corresponding formamide dihydrate (when both complexes are solvated only at the carbonyl group) shows only small differences between the influences of the two solvents. REFERENCES 1 2 3 4 5 6
B. Sunners, L. H. Piette and W. G. Schneider, Can. J. Chem., 38 (1960) 681. H. Kamei, Bull. Chem. Sot. Jpn., 41 (1969) 2269. H. Kessler, Angew. Chem. Int. Ed. Engl., 9 (1970) 219. W. E. Stewart and T. H. Siddall, Chem. Rev., 70 (1970) 517. T. Drakenberg and S. Forsen, J. Phys. Chem., 74 (1970) 1. L. M. Jackman, in L. M. Jackman and F. A. Cotton (Eds.), Dynamic Nuclear Magnetic Resonance Spectroscopy, Academic Press, New York, 1975, p. 209. 7 T. Drakenberg, K. I. Dahlquist and S. Forsen, J. Phys. Chem., 76 (1972) 2178. 8 D. Peters and J. Peters, J. Mol. Struct., 50 (1978) 133. 9 L. B. Harding and W. A. Goddard, J. Am. Chem. Sot., 97 (1975) 6300. 10 M. Perricaudet and A. Pullman, Int. J. Pept. Protein Res., 5 (1973) 99. 11 L. Radom and N. V. Riggs, Aust. J. Chem., 33 (1980) 249. 12 L. Radom, W.A. Lathan, W. J. Hehre and J.A.Pople, Aust. J. Chem., 25 (1972) 1601. 13 L. L. Shipman and R. E. Christoffersen, J. Am. Chem. Sot., 95 (1973) 1408. 14 D. H. Christensen, R. N. Kortzeborn, B. Bak and J. J. Led, J. Chem. Phys., 53 (1970) 3912. 15 R. F. Nalewajski, J. Am. Chem. Sot., 100 (1978) 41. 16 R. Ditchfield, W. J. Hehre and J. A. Pople, J. Chem. Phys., 54 (1971) 724. 17 J. C. Woodbrey and M. T. Rogers, J. Am. Chem. Sot., 84 (1962) 13. 18 A. Warshel, J. Phys. Chem., 83 (1979) 1640. 19 S. Roman0 and E. Clementi, Gazz. Chim. Ital., 108 (1978) 319. 20 S. Roman0 and E. Clementi, Int. J. Quantum Chem., 14 (1978) 839. 21 S. Roman0 and E. Clementi, Int. J. Quantum Chem., 17 (1980) 1007. 22 J. P. Malrieu,Mod. Theor. Chem., 7 (1977) 69. 23 R. Lochmann and T. Weller, Int. J. Quantum Chem., 10 (1976) 905. 24 R. Lochmann and H.J. Hofmann, Int. J. Quantum Chem., 11(1977) 427. 25 J. W. McIver and A. Komornicki, Chem. Phys. Lett., 10 (1971) 303. 26 G. Alagona, A. Pullman, E. Scrocco and J. Tomasi, Int. J. Pept. Protein Res., 5 (1973) 251. 27 A. Pullman, H. Berthod, C. GiessnerPrettre, J. F. Hinton and D. Harpool, J. Am. Chem. Sot., 100 (1978) 3991. 28 H.J. Hofmann, G. Peinel and T. Weller, Int. J. Quantum Chem., 16 (1979) 379. 29 J. F. Hinton and R. D. Harpool, J. Am. Chem. SOC., 99 (1977) 349. 30 G. Peinel and H. J. Hofmann, Wiss. Z. Univ. Leipzig, 28 (1979) 611. 31 F. Birnstock, H.J. Hofmann and H.-J. Kohler, Theor. Chim. Acta, 42 (1976) 311. 32 A. J. Duben and S. Miertus, Theor. Chim. Acta, 60 (1981) 327. 33 A. J. Lees, B. P. Straughan and D. J. Gardiner, J. Mol. Struct., 71 (1981) 61.
THE ROTATIONAL SOLVENTS
HANS-JGRG
HOFMANN
Sektion Biowissenschaften (G.D. R.) (Received
16 March
-
Printed
BARRIER OF FORMAMIDE
and GUSTAV and Sektion
in The Netherlands
IN VARIOUS
PEINEL Physik
of the Karl Marx
University,
Leipzig
1982)
ABSTRACT The solvent influence on the rotational barrier of formamide has been studied by means of PCILO supermolecule calculations. The results indicate an increase in the barrier caused by the medium in the order acetone, pure liquid formamide and water. Thus, a more rigid structure of the peptide bond is expected with higher solvent polarity. INTRODUCTION
The formation of hydrogen bonds between amide molecules in a pure liquid or between amide and solvent molecules in mixed solvent systems may be responsible for specific bonding and structural properties of such solutions. Formamide is the simplest representative of this class of compounds. It can be regarded as a model system for the peptide linkage. Theoretical and experimental studies of formamide-solvent systems could therefore provide information about the hydrogen bonding in such solutions and contribute to a better understanding of more complex biological systems. In this paper, we present the results of a theoretical examination of the solvent influence on the rotational barrier of formamide. Experimental investigations indicate a strong solvent dependence of the barrier. Thus, barrier heights of 70.7 f 7.9 (75.3 [l]), 79.1 f 4.2 and 89.1 + 5.4 kJ mol-’ were determined in acetone, in the pure liquid and in water, respectively [ 21 (cf. also refs 3-7). Values of the barrier height of the isolated formamide molecule were calculated by means of various quantum chemical methods [ 7-161. These values are often in close agreement with experimental data for polar solvents. The starting point for our study is the hypothesis visualized in Fig. 1, according to which, an increase in the rotational barrier will result from interactions of the amino group of the formamide molecule with electrondonating groups and of the carbonyl group with electron-accepting groups. Thus, solvent molecules which are capable of fulfilling both these conditions should cause the greatest barrier enhancement. This hypothesis is confirmed by the trend observed in the experimental values. Hence, the barrier of the 0166-1280/83/0000-0000/$03.00
0 1983
Elsevier
Scientific
Publishing
Company
290
donor
acceptor
\ acceptor
donor
Fig. 1. Interaction model of the solvent influence on the rotational barrier of formamide.
isolated molecule should not surpass the value estimated in acetone. This is also supported by experimental findings, which indicate a decrease in the rotation barrier if liquid formamide is diluted in apolar solvents [ 171. In order to prove the correctness of this hypothesis, supermolecule calculations were performed on aggregates consisting of several formamide molecules as a model for the pure liquid, formamide and acetone molecules and formamide and water molecules, respectively, as models for the corresponding mixed solvent systems. Obviously, supermolecule calculations limited to a few solvent molecules can only be regarded as a first step in the description of formamide solutions. Greater insight would presumably be achieved by the consideration of a greater number of solvent molecules in connection with a statistical thermodynamic treatment [ 181. However, for the solvation of the polar regions of molecules, monosolvation models or models which consider a small number of solvent molecules step-bystep often provide reliable information [ 19-211 . DETAILS OF THE CALCULATIONS
The semiempirical PCILO method was employed for all the calculations [ 221. Previous studies have demonstrated that this method is well suited to the study of intermolecular phenomena [ 23,241. The geometries of the
corresponding planar and rotated aggregates were determined by means of an automatic optimization technique [ 251. The optimization process was confined to the intermolecular geometry parameters. The internal coordinates of the molecules were kept fixed at the experimentally measured values. For the formamide-water complexes, three situations were examined in detail: the hydration of the amino and carbonyl groups, respectively, by two water molecules and the hydration of the formamide molecule by five water molecules. In the last case, the ab initio data of Alagona et al. were selected as the starting point of the PCILO optimization [26]. Comparing the waterformamide interaction energies at the various water positions (cf. Fig. 2) with the water dimer interaction energy, Pullman et al. [ 271 concluded that only four water molecules form the first hydration shell in the molecular plane. Our calculations confirm this result [28]. However, the consideration of a fifth water molecule along the CH bond of formamide does not significantly influence the barrier problem.
291
97.9
Fig. 2. Optimized formamide-water barriers (in kJ mol-I).
supermolecule structures and values of the rotational
The pure liquid was characterized by various dimers, trimers, tetramers and pentamers of formamide. The selection of these models was prompted by the results of ab initio studies of Hinton and Harpool [29] and Pullman et al. [ 271. Typical hydrogen-bonding effects can be expected between the carbonyl oxygen atom of acetone and the amino group of formamide. Corresponding to this situation, three different arrangements of formamideacetone complexes were investigated. RESULTS
AND DISCUSSION
Figures 2-4 depict the calculated optimum arrangements of all the aggregates, the energy values of the barrier heights for various rotational possibilities are also given. The PCILO barrier of the isolated formamide molecule amounts to 68.6 kJ mol-‘. It is evident that the barrier increases in the order acetone, pure liquid and water. The strongest effect exists in the formamide pentahydrate (97.9 kJ mol-‘, experimental value 89.1 kJ mol-‘). The theoretical value is expected to be greater because of the optimum structure of the pentahydrate complex, whereas the aqueous solution should represent a mixture of more or less hydrated formamide species. It is impossible to obtain the increase in the barrier height of the pentahydrate by addition of the calculated values for the two dihydrates. Comparing the positions of the water molecules in the various hydrated forms, there are considerable differences with respect to the orientation of the water molecules 2 and 3 (cf. Fig. 2), which form a hydrogen bond in the pentahydrate. The breaking of this bond is responsible for an additional increase in the barrier.
292
Fig. 3. Optimized (in kJ mol-I).
formamide
aggregate
structures
and values of the rotational
barriers
A detailed analysis presented previously [28,30] shows that the enhancement of the formamide barrier in aqueous solution is caused by differences in the electrostatic interactions between solute and solvent molecules and differences in cavity formation in the planar and perpendicular conformations. This analysis also provides a good explanation for the surprising fact that solvation models which are unable to consider specific interactions predict the same solvent influence on the barrier as indicated by our former calculations using a classical continuum model [ 311 or those of Duben and Miertus [ 321 using a solvaton model. Thus, the changes in the electron distribution in the planar and perpendicular conformations of formamide are reflected in the different strengths of the hydrogen bonds considered by the super-molecule approximation and the large decrease in the dipole moment, which is responsible for the qualitatively correct result of the continuum approach. However, the limitations of predictions based on continuum methods are evident in the case of specific interactions. Only the same tendency of the change in electrostatic solute-solvent interactions on the one hand and the reorientation of the solvation shell around the forma-
293
75.8
bHH
HYC\
c/c
VH
J, i\\~
\NP!O
‘w
/
\
724
Fig. 4. Optimized formamide-acetone barriers (in kJ mol-I).
complex structures and values of the rotational
mide conformations, which is not considered in the classical cavity treatment, on the other, assures agreement in principle. Apart from the hypothetical formamide pentamer, nearly identical values for the rotational barrier were obtained for the pure liquid and the formamide-acetone system based on the models given in Figs. 3 and 4, respectively, The higher barrier calculated for the pentamer illustrates the somewhat greater tendency for barrier enhancement in liquid formamide than in acetone, as experimentally measured. For a description of the situation in the pure liquid, consideration of the linear formamide trimer and, above all, the so called lcis tetramer, which contains linear and cyclic structural elements, should be included. According to Pullman et al. [27], the l-cis tetramer is compatible with all the experimental data (dielectric and spectroscopic properties). Thus, this species should predominate in liquid formamide followed by linear chain structures. As regards the barrier problem, there are no major differences between the linear trimer and the l-cis tetramer. Confirming the hypothesis, central CN bond barrier of the linear trimer is slightly greater than those of the terminal CN bonds. Based on his experimental data, Kamei [2] postulated a stronger interaction between formamide and water molecules than between neighbouring formamide molecules. According to our calculations, the average energy value per hydrogen bond for the formamide pentahydrate and the formamide pentamer are 26.0 and 19.4 kJ mol-‘, respectively.
294
CONCLUSIONS
The results of our calculations confirm the original hypothesis regarding the influence of the solvent on the rotational barrier of formamide. The same model is also valid to explain the influence of electrolytes on the barrier [ 331. The barrier increases in the order acetone, pure liquid and water. Thus, a more rigid structure for the peptide bond is expected in more polar solvents and when influenced by electrolytes. Extending our conclusions to substituted amides, e.g. dimethylformamide, the same general solvent effect is expected but to a lesser extent. Comparison of the barriers in the formamide trimer and the corresponding formamide dihydrate (when both complexes are solvated only at the carbonyl group) shows only small differences between the influences of the two solvents. REFERENCES 1 2 3 4 5 6
B. Sunners, L. H. Piette and W. G. Schneider, Can. J. Chem., 38 (1960) 681. H. Kamei, Bull. Chem. Sot. Jpn., 41 (1969) 2269. H. Kessler, Angew. Chem. Int. Ed. Engl., 9 (1970) 219. W. E. Stewart and T. H. Siddall, Chem. Rev., 70 (1970) 517. T. Drakenberg and S. Forsen, J. Phys. Chem., 74 (1970) 1. L. M. Jackman, in L. M. Jackman and F. A. Cotton (Eds.), Dynamic Nuclear Magnetic Resonance Spectroscopy, Academic Press, New York, 1975, p. 209. 7 T. Drakenberg, K. I. Dahlquist and S. Forsen, J. Phys. Chem., 76 (1972) 2178. 8 D. Peters and J. Peters, J. Mol. Struct., 50 (1978) 133. 9 L. B. Harding and W. A. Goddard, J. Am. Chem. Sot., 97 (1975) 6300. 10 M. Perricaudet and A. Pullman, Int. J. Pept. Protein Res., 5 (1973) 99. 11 L. Radom and N. V. Riggs, Aust. J. Chem., 33 (1980) 249. 12 L. Radom, W.A. Lathan, W. J. Hehre and J.A.Pople, Aust. J. Chem., 25 (1972) 1601. 13 L. L. Shipman and R. E. Christoffersen, J. Am. Chem. Sot., 95 (1973) 1408. 14 D. H. Christensen, R. N. Kortzeborn, B. Bak and J. J. Led, J. Chem. Phys., 53 (1970) 3912. 15 R. F. Nalewajski, J. Am. Chem. Sot., 100 (1978) 41. 16 R. Ditchfield, W. J. Hehre and J. A. Pople, J. Chem. Phys., 54 (1971) 724. 17 J. C. Woodbrey and M. T. Rogers, J. Am. Chem. Sot., 84 (1962) 13. 18 A. Warshel, J. Phys. Chem., 83 (1979) 1640. 19 S. Roman0 and E. Clementi, Gazz. Chim. Ital., 108 (1978) 319. 20 S. Roman0 and E. Clementi, Int. J. Quantum Chem., 14 (1978) 839. 21 S. Roman0 and E. Clementi, Int. J. Quantum Chem., 17 (1980) 1007. 22 J. P. Malrieu,Mod. Theor. Chem., 7 (1977) 69. 23 R. Lochmann and T. Weller, Int. J. Quantum Chem., 10 (1976) 905. 24 R. Lochmann and H.J. Hofmann, Int. J. Quantum Chem., 11(1977) 427. 25 J. W. McIver and A. Komornicki, Chem. Phys. Lett., 10 (1971) 303. 26 G. Alagona, A. Pullman, E. Scrocco and J. Tomasi, Int. J. Pept. Protein Res., 5 (1973) 251. 27 A. Pullman, H. Berthod, C. GiessnerPrettre, J. F. Hinton and D. Harpool, J. Am. Chem. Sot., 100 (1978) 3991. 28 H.J. Hofmann, G. Peinel and T. Weller, Int. J. Quantum Chem., 16 (1979) 379. 29 J. F. Hinton and R. D. Harpool, J. Am. Chem. SOC., 99 (1977) 349. 30 G. Peinel and H. J. Hofmann, Wiss. Z. Univ. Leipzig, 28 (1979) 611. 31 F. Birnstock, H.J. Hofmann and H.-J. Kohler, Theor. Chim. Acta, 42 (1976) 311. 32 A. J. Duben and S. Miertus, Theor. Chim. Acta, 60 (1981) 327. 33 A. J. Lees, B. P. Straughan and D. J. Gardiner, J. Mol. Struct., 71 (1981) 61.