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An ab initio study of intramolecular hydrogen bonding in malonic acid and its monoanion
Journal of Molecular Structure (Theochem), 109 (1984) 51-60 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
AN AB INITIO STUDY OF INTRAMOLECULAR HYDROGEN BONDING IN MALONIC ACID AND ITS MONOANION
M. MERCHAN, F. TOMAS* and I. NEBOT-GIL Departamento de Q&mica-Fisica, Cktedra de Quimica General, Facultad Quimicas, Universidad de Valencia, Bw$sot, Valencia, (Spain)
de Ciencias
(Received 8 November 1983)
ABSTRACT Ab initio calculations have been performed on malonic and hydrogen malonate acids. The studied conformations were optimized at the STO-3G level and the STO-3G optimal geometries used for single point 4-31G calculations. For malonic acid the most stable conformation occurs in the absence of hydrogen bonding. In hydrogen malonate acid a symmetrical C,, hydrogen-bonded structure is found to be the most stable and a barrier height of 4.0 kcal mol-’ is obtained with the 4-31G basis set for the single-minimum hydrogen potential energy curve. INTRODUCTION
Intramolecular hydrogen bonded structures are believed to influence significantly physical and chemical properties of a great number of substances [ 11. Thus, for instance, ionization of dibasic acids is affected by hydrogen bonds within the molecules. In 1953 Hunter [2] pointed out that internal hydrogen bonding will increase the ratio of the first to the second ionization constants of maleic and of some other dicarboxylic acids. Following Hunter’s qualitative treatment, McDaniel and Brown [3] studied a large number of other dibasic acids and found experimental evidence in certain substituted malonic acids that intramolecular hydrogen bonding was responsible for the unusually high dissociation constant ratio k1/k2. Generally, the first ionization constant is larger and the second smaller than expected, the latter effect being more pronounced. This would imply greater stability of the monoanion, in relation to diacid, by formation of an intramolecular hydrogen bond. To explain the high constant ratio k1/k2 there may be other factors besides hydrogen bonding, as have been suggested by other authors [4] who established that, for most dibasic acids, the effect of hydrogen bonding on kl/kz is negligible relative to the electrostatic effect. However, Tanford [5] has made calculations on malonic acids using a modified form of the *To whom correspondence
should be addressed.
0166-1280/84/$03.00
o 1984 Elsevier Science Publishers B.V.
52
Kirkwood-Westheimer theory which indicate that interactions such as hydrogen bonding play a large role in determining the dissociation constants. Since those early works appeared [2,3] experimental evidence in support of the intramolecular hydrogen bonding hypothesis has continued to accumulate. Study of the thermodynamics of the dissociation of malonic acid in aqueous solution [6] suggested that hydrogen malonate ion has an internally hydrogen-bonded structure which seems likely to involve a symmetrical hydrogen bond. However, using IR spectroscopy, Chapman et al. [ 71 reached the conclusion that a strong symmetrical hydrogen bond is not present in aqueous solutions of potassium hydrogen malonate. The apparent discord between thermodynamic and IR results concerning the symmetry of the hydrogen bond in the ion has been explained by these same authors in regard to time scales associated with both techniques. Additional IR studies [8-lo] of malonic acids are also in agreement with the above conclusions. On the other hand the studies of Miles et al. [ll] using the temperature jump method indicate that a strong intramolecular hydrogen bond is formed in aqueous solutions of dialkyl substituted malonic acids. The NMR spectra of aqueous solutions of some malonic acids [ 121 also give evidence for an internally hydrogen-bonded structure in the single ionized acid. In the homologous series of oxalic acids, dissociation constants have been determined in acetonitrile [13]. The intramolecular hydrogen bond in the monoanion molecule was found to be quite stable but the strength of this bond decreases with increasing distance between the carboxyl groups; thus the most favorable situation would be found in hydrogen malonate ion. Despite the experimental support, as far as we are aware no theoretical studies have been carried out on the intramolecular hydrogen bonding ability of malonic acid and its monoanion. In fact, only a theoretical conformational analysis is available for malonic acid [ 141 using experimental geometry [ 151. Recently, the interactions of malonate dianion with metals have been the subject of theoretical studies [16] as a model for understanding the physiological behaviour of 7-carboxyglutamic acid, an amino acid found in several important proteins. No theoretical studies are available for hydrogen malonate acid. In view of the importance of malonic acid in organic and inorganic chemistry and also the differences which have arisen among experimentalists, we consider an ab initio study to be of great value in obtaining more conclusive results. The aim of this paper is to study different conformations of malonic and hydrogen malonate acids and evaluate, if present, the stabilization energy of intramolecular hydrogen bonding. The results are presented in two parts corresponding to malonic and hydrogen malonate acid, respectively.
53 CALCULATIONS
The ab initio MO-LCAO-SCF calculations were performed by the GAUSSIAN 70 series of programs 1171 on a UNIVAC 1100/80 computer. The conformations studied are shown schematically in Fig. 1. For each species considered we have carried out a complete optimization with simple parabolic fits to each parameter at the RHF/STO-3G minimal basis set [ 181. The STO-3G optimum geometries of structures I-VII, obtained in this way, were then used for single point split valence RHF/4-31G calculations [ 191. In the present work standard valence shell scale factors have been used. In order to find the conformation which corresponds to the absolute minimum a conformational energy map for hydrogen malonate acid was constructed at the STO-3G level. Finally, the hydrogen potential energy curve was built for the internally hydrogen-bonded monoanion. RESULTS AND DISCUSSION
Malonic acid The conformations studied for malonic acid (I-III) are shown in Fig. 1. In I the two carboxyl groups are orthogonal to each other, one of them coplanar with the carbon skeleton, the dihedral angles 0(7)C(3)C(l)C(2) and 0(4)C(2)C(l)C(3) being 0” and 90”, respectively. Structures II and III have the carboxyl groups coplanar with the C( 3)C( l)C(2) plane and differ mainly in the placement of H(6).
II
H&--C; O-. 8
'05-H,
/
c3 '0
7
IV
V
VI
Fig. 1. Malonic acid and hydrogen malonate ion conformations.
54
The initial geometrical parameters were taken from the crystal data of malonic acid [ 151 and no symmetry restrictions were imposed during optimization. The STO-3G optimum geometries of conformations I-III are summarized in Table 1, according to the numbering in Fig. 1. The trends of the optimal bond lengths are similar for the three conformations. As regards bond angles we quote the opening of the C( 3)C( l)C( 2) angle for the planar structures, II and III, in relation to the perpendicular one, I, due to steric hindrance. In Table 2 total and relative energies are listed. Relative energies indicate TABLE 1 Calculated (RHF/STO-3G) Parameter
geometries of malonic acid conformations Conformation I
II
III
Bond lengths (A) C(2)C(l) C(3FAl) G(4)C(2) 0(5)C(2) H(6)0(5) G(7)C(3) 0(8)C(3) Ht9)0(8) H(lO)C(l) Wll)C(l)
1.542 1.546 1.225 1.375 0.985 1.225 1.376 0.986 1.089 1.089
1.553 1.549 1.220 1.376 0.989 1.225 1.375 0.989 1.090 1.090
1.573 1.548 1.217 1.368 0.993 1.234 1.364 0.989 1.089 1.089
Bond angles e) c(3w)c(2) 0(4)C(2)Cu) 0(5)C(2)C(l) H(6)0(5)C(2) 0(7)C(3)C(l) 0(8)C(3)CU) H(9)0(8)C(3) H(lO)C(l)C(3) H(ll)C(l)C(3)
108.9 120.4 114.0 105.1 120.5 114.1 104.8 109.8 109.8
114.7 121.9 117.2 105.4 121.8 113.4 105.0 109.7 109.7
113.9 119.8 118.9 107.5 121.3 114.8 105.8 109.2 109.2
TABLE 2 Total and relative energies of malonic acid conformations geometries Structure
Total energies (a.u.) STO-3G
I (perpendicular) II (reference) III (H-bonded)
-409.88682 -409.88155 -409.88643
4-31G -414.77862 -414.76742 -414.77330
at the RHF/STO-3G
optimal
Relative energies (kcal mold ) STO-3G
4-31G
0.0 3.3 0.2
0.0 7.0 3.3
55
that the stabilizations of the planar conformations, II and III, are overestimated at the STO-3G level. We could evaluate the stability of the hydrogenbonded structure, III, by taking as reference the non-bonded conformation, II. The stabilization energies of III with respect to II are 3.1 and 3.7 kcal mol-’ at the STO-3G and 4-31G basis sets, respectively. This stabilization can be related to the formation of the intramolecular hydrogen bond in III, although there are more different factors between these two conformations intrinsic to the nature of that special bond. However, even if III is energetically favorable in relation to II, the intramolecular hydrogen bond is not strong enough to counteract the repulsions since the carboxyl groups are too close and therefore the minimum energy conformation is not planar, as can be seen in Table 2. This result agrees with previous work [14] where conformational analysis shows an absolute minimum appears when the two carboxyl groups are nearly perpendicular, although a large portion of the conformational space is accessible through low energy barriers. Table 3 shows the Mulliken population analysis [20] for the main atoms involved in the hydrogen bonding. It can be seen that the total overlap population between O(7) and H(6), having an interatomic distance of 1.559 A, is small in conformation III, even at the 4-31G level. The dipole moment is also given for each conformation in Table 3. The value for the perpendicular structure, I, at the 4-31G level is in good agreement with the experimental one (2.56 D in dioxane solution [21]). However, the STO-3G result reflects the general tendency of minimal basis sets to underestimate electric moments and charge transfer [ 221. Hydrogen malona te acid The conformations studied for hydrogen malonate acid (IV-VII) are shown in Fig. 1. In IV the carboxylate group is coplanar with the C(3)C( l)C( 2) TABLE
3
Mulliken population analysis for malonic acid conformations I STO-3G Net atomic charges G(5) -0.288 G(7) -0.265 B(6) 0.216 Total overlap populations G(5)W6) 0.257 G(7)W6) Dipole moment(D) 1.173
II 4-31G
STO-3G
III 4-31G
STO-3G
4-31G
-0.712 -0.564 0.443
-0.280 -0.249 0.210
-0.683 -0.536 0.434
-0.338 -0.283 0.256
-0.749 -0.648 0.501
0.249
0.256
0.246 0.001
0.254 0.031
0.233 0.037
2.427
0.979
1.768
4.554
6.443
56
plane and the carboxyl group is perpendicular to it. The non-bonded planar structure is represented in V. Conformations VI and VII are also planar but intramolecularly hydrogen-bonded, belonging to C, and C,, symmetry, respectively. The optimal geometrical parameters of malonic acid were used as initial parameters for hydrogen malonate conformations. The STO-3G optimum geometries of IV-VII are summarized in Table 4. The more important features observed from Table 4 are an increase of the C-C and O-H bond lengths in the planar C,, conformation, VII, in relation to the other conformations, to obtain a symmetrical interaction of H(6) with O(5) and O(7), and opening of the C(3)C(l)C(2) angle in the case of the planar non-bonded form, V, due to steric hindrance of coplanar carboxyl and carboxylate groups. In Table 5 total and relative energies of conformations IV-VII are listed. It is readily seen that the greater stability of the planar bonded forms, VI and VII, with respect to the reference planar structure, V, is exaggerated at the STO-3G level. This stabilization depends on basis-set size much more for hydrogen malonate than for malonic acid, as it usually occurs in hydrogen bonded anionic systems [ 231. Moreover, structures VI and VII are energetically lower than the perpendicular form, IV, which is presumed to have
TABLE 4 Calculated (RHF/STO-3G) Parameter
geometries of hydrogen malonate conformations
Conformation Iv
V
VI
VII
Bond lengths (A) C(W(l) C(3KxU o(4)w o(5w) W6W5) 0(7)C(3) o(3W3) M-W(1) H(lW(l)
1.536 1.619 1.230 1.383 0.987 1.271 1.269 1.087 1.087
1.569 1.624 1.232 1.374 0.991 1.268 1.272 1.087 1.087
1.557 1.591 1.232 1.344 1.042 1.310 1.249 1.087 1.087
1.593 1.593 1.238 1.325 1.155 1.325 1.238 1.087 1.087
Bond angles (“) c(3)ww) o(4wm1) o(5mww W6)0(5)C(2) O(7YA3M1) 0(3)C(3)C(l) H(9Ml)C(3) WWX1)C(3)
111.9 123.0 115.1 103.8 111.7 115.3 110.5 110.5
116.4 122.1 117.8 102.7 113.6 114.0 111.1 111.1
108.6 119.5 117.0 106.1 119.9 116.1 110.3 110.3
110.3 117.9 117.8 104.3 117.8 117.9 110.0 110.0
57 TABLE 5 Total and relative energies of hydrogen malonate ion conformations optimal geometries Structure
Total energies (a.u.) STO-3G
4-3 1G
at the RHF/STO-3G
Relative energies (kcal mol-’ ) STO-3G
IV (perpendicular) V (reference) VI (H-bonded (Cs)) VII (H-bonded (C,,))
-409.14738 -409.13396 -409.19205 -409.19977
-414.22573 -414.20184 -414.23646 -414.24285
0.0 8.4 -28.0 -32.9
4-31G 0.0 15.0 -6.7 -10.7
the least steric hindrance. If this were the case, only the stabilization by hydrogen bonding could explain the results obtained. To prove that the perpendicular structure, IV, is a minimum of the nonbonded forms, a conformational energy map was built taking as geometrical parameters the optimal ones for IV (see Table 4). The STO-3G con-
Fig. 2. Hydrogen malonate ion. STO-3G conformationai energy map: e1 = 0(7)C(3)C(l)C(2) and 6, = 0(4)C(2)C( l)C(3). Contour lines are drawn in kcal rnol-’ units from the lowest minimum.
58 TABLE 6 Mulliken population analysis for hydrogen malonate ion conformations IV STO-3G Net atbmic charges G(5) -0.302 G(7) -0.486 H(6) 0.175
V 4-31G
STO-3G
VI 4-3 1G
STO-3G
VII 4-31G
STO-3G
4-31G
-0.731 -0.773 0.405
-0.264 -0.474 0.165
-0.654 -0.747 0.383
-0.439 -0.462 0.279
-0.809 -0.829 0.517
-0.444 -0.444 0.266
-0.833 -0.833 0.535
Total overlap populations 0(5)H(6) 0.250 0.239 0(7)H(6)
0.244
0.230 0.002
0.185 0.129
0.163 0.123
0.154 0.154
0.136 0.136
formational energy map was calculated at 30” steps of dihedral angles el, 0(7)C(3)C(l)C(2), and 13~,0(4)C(2)C(l)C(3), where (0”, 90”) corresponds to the perpendicular structure, IV. The conformational energy map (see Fig. 2) is only represented on the conformational space O”180” due to molecular symmetry. The perpendicular structure, IV, is only 0.2 kcal molml higher than the (MO”, 93”) one, where the lowest minimum is placed. Effectively, for hydrogen malonate acid the planar bonded structures VI and VII are preferred to any non-bonded conformations. This conclusion is in accord with crystal data, e.g. potassium hydrogen malonate [24]. Unlike the free acid, the anion in solid KC304H3 is nearly coplanar and has twofold symmetry. It can be seen in Table 5 that the C, conformation, VI, is energetically higher than the Czv one (structure VII). The energy differences are 4.9 and 4.0 kcal mol-’ with STO-3G and 4-31G basis sets, respectively. It can be observed in Table 6 that the total overlap population between O( 7) and H(6), at an interatomic distance of 1.199 A, is appreciable for the C, hydrogen bonded structure, VI. Nevertheless, for the Czv conformation, VII, a more effective overlap between H(6) and O(5), O(7) has happened, this being the reason for its lower energy. To study the potential energy curve for the proton transfer reaction, H(6), we have to choose an appropriate reaction coordinate. We assume that the geometry changes, going from Czv to C, conformations, can be obtained by means of a linear interpolation on all geometry parameters and so we can simulate this reaction by the reaction coordinate “Y”. The values of r = 1 correspond to the STO-3G optimal Czv structure, r = 0 to the STO-3G optimal C, one, and r = 0.5 to the midpoint between those two obtained by linear interpolation. This type of reaction coordinate has been employed previously in a very similar problem [25]. Figure 3 shows the calculated hydrogen bond potential energy curve with the 4-31G basis set. In view of the potential energy curve the hydrogen bond is strong enough to result in a single minimum potential for the proton transfer reaction.
59
Fig. 3. Hydrogen maionate ion. Calculated hydrogen bond potential energy curve with 4-31G basis set. At r = 0.5 total energy is -414.24038 au. CONCLUSIONS
For malonic acid strong enough intramolecular hydrogen bonding to compensate the steric hindrance when the two carboxyl groups are coplanar does not exist. However, a symmetrical C2, hydrogen-bonded conformation was found to be the most stable in the case of the monoanion. From the above results we can conclude that intramolecular hydrogen bonded structures play an important role in explaining the constant ratio kl/kz of malonic acids. ACKNOWLEDGMENT
One of us, M. MerchAn, thanks the Ministerio de Education y Ciencia of Spain for a research grant. REFERENCES 1 G. C. Pimentel and A. L. McClellan, The Hydrogen Bond, W. H. Freeman, San Francisco, 1960. 2 L. Hunter, Chem. Ind., (1953) 155; cf. I. Jones and F. G. Soper, J. Chem. Sot., (1936) 133. 3 (a) D. H. McDaniel and H. C. Brown, Science, 118 (1953) 370. (b) H. C. Brown, D. H. McDaniel and 0. Hiifliger, in E. A. Braude and F. C. Nachod (Eds.), Determination of Organic Structures by Physical Methods, Academic Press, New York, 1955. 4 F. H. Westheimer and 0. T. Benfey, J. Am. Chem. Sot., 78 (1956) 5309. 5 C. Tanford, J. Am. Chem. Sot., 79 (1957) 5348. 6 S. N. Das and D. J. G. Ives, Proc. Chem. Sot., (1961) 373. 7 D. Chapman, D. R. Lloyd and R. H. Prince, J. Chem. Sot., (1964) 550. 8 P. K. Glasoe and J. R. Hutchison, J. Phys. Chem., 68 (1964) 1562. 9 E. S. Hanrahan, Spectrochim. Acta, 22 (1966) 1243.
60 10 W. J. De Klein, Spectrochim. Acta, Part A, 27 (1971) 93. 11 M. H. Miles, E. M. Eyring, W. W. Epstein and R. E. Ostlund, J. Phys. Chem., 69 (1965) 467. 12 H. B. Evans and J. H. Goldstein, Spectrochim. Acta, Part A, 24 (1968) 73. 13 I. M. Kolthoff and M. K. Chantooni, Jr., J. Am. Chem. Sot., 97 (1975) 1376. 14 D. Ajb, I. Fragall, G. Granozzi and E. Tondello, J. Mol. Struct., 38 (1977) 245. 15 J. A. Goedkoop and C. H. MacGillavry, Acta Crystallogr., 10 (1957) 125. 16 K. E. Gottschalk, R. G. Hiskey, L. G. Pedersen and K. A. Koehler, J. Mol. Struct., Theochem, 76 (1981) 197; 85 (1981) 337; 87 (1982) 155. 17 W. J. Hehre, W. A. Lathan, R. Ditchfield, M. D. Newton and J. A. Pople, GAUSSIAN 70, QCPE Program No. 236, Quantum Chemistry Program Exchange, Indiana University, Bloomington, IN, U.S.A. 18 W. J. Hehre, R. F. Stewart and J. A. Pople, J. Chem. Phys., 51(1969) 2657. 19 R. Ditchfield, W. J. Hehre and J. A. Pople, J. Chem. Phys., 54 (1971) 724. 20 R. S. Mulliken, J. Chem. Phys., 23 (1955) 1833. 21 A. L. McClellan, Tables of Experimental Dipole Moments, W. H. Freeman, San Francisco, 22 ;A&19y* ars y and M. Urban, Lecture Notes in Chemistry: Ab Initio Calculations, Methods and Applications in Chemistry, Springer-Verlag, Berlin, 1980. 23 P. A. Kollman, in H. F. Shaefer III (Ed.), Modern Theoretical Chemistry, Vol. 4, Applications of Electronic Structure Theory : Hydrogen Bonding and Donor-Acceptor Interactions, Plenum Press, New York, 1977, p. 109. 24 (a) J. G. Shne, J. C. Speakman and R. Parthasarathy, J. Chem. Sot. A, (1970) 1919. (b) M. Currie and J. C. Speakman, J. Chem. Sot. A, (1970) 1923. 25 G. Karlstriim, B. JSnsson, B. Roos and H. Wennerstrom, J. Am. Chem. Sot., 98 (1976) 6851.
AN AB INITIO STUDY OF INTRAMOLECULAR HYDROGEN BONDING IN MALONIC ACID AND ITS MONOANION
M. MERCHAN, F. TOMAS* and I. NEBOT-GIL Departamento de Q&mica-Fisica, Cktedra de Quimica General, Facultad Quimicas, Universidad de Valencia, Bw$sot, Valencia, (Spain)
de Ciencias
(Received 8 November 1983)
ABSTRACT Ab initio calculations have been performed on malonic and hydrogen malonate acids. The studied conformations were optimized at the STO-3G level and the STO-3G optimal geometries used for single point 4-31G calculations. For malonic acid the most stable conformation occurs in the absence of hydrogen bonding. In hydrogen malonate acid a symmetrical C,, hydrogen-bonded structure is found to be the most stable and a barrier height of 4.0 kcal mol-’ is obtained with the 4-31G basis set for the single-minimum hydrogen potential energy curve. INTRODUCTION
Intramolecular hydrogen bonded structures are believed to influence significantly physical and chemical properties of a great number of substances [ 11. Thus, for instance, ionization of dibasic acids is affected by hydrogen bonds within the molecules. In 1953 Hunter [2] pointed out that internal hydrogen bonding will increase the ratio of the first to the second ionization constants of maleic and of some other dicarboxylic acids. Following Hunter’s qualitative treatment, McDaniel and Brown [3] studied a large number of other dibasic acids and found experimental evidence in certain substituted malonic acids that intramolecular hydrogen bonding was responsible for the unusually high dissociation constant ratio k1/k2. Generally, the first ionization constant is larger and the second smaller than expected, the latter effect being more pronounced. This would imply greater stability of the monoanion, in relation to diacid, by formation of an intramolecular hydrogen bond. To explain the high constant ratio k1/k2 there may be other factors besides hydrogen bonding, as have been suggested by other authors [4] who established that, for most dibasic acids, the effect of hydrogen bonding on kl/kz is negligible relative to the electrostatic effect. However, Tanford [5] has made calculations on malonic acids using a modified form of the *To whom correspondence
should be addressed.
0166-1280/84/$03.00
o 1984 Elsevier Science Publishers B.V.
52
Kirkwood-Westheimer theory which indicate that interactions such as hydrogen bonding play a large role in determining the dissociation constants. Since those early works appeared [2,3] experimental evidence in support of the intramolecular hydrogen bonding hypothesis has continued to accumulate. Study of the thermodynamics of the dissociation of malonic acid in aqueous solution [6] suggested that hydrogen malonate ion has an internally hydrogen-bonded structure which seems likely to involve a symmetrical hydrogen bond. However, using IR spectroscopy, Chapman et al. [ 71 reached the conclusion that a strong symmetrical hydrogen bond is not present in aqueous solutions of potassium hydrogen malonate. The apparent discord between thermodynamic and IR results concerning the symmetry of the hydrogen bond in the ion has been explained by these same authors in regard to time scales associated with both techniques. Additional IR studies [8-lo] of malonic acids are also in agreement with the above conclusions. On the other hand the studies of Miles et al. [ll] using the temperature jump method indicate that a strong intramolecular hydrogen bond is formed in aqueous solutions of dialkyl substituted malonic acids. The NMR spectra of aqueous solutions of some malonic acids [ 121 also give evidence for an internally hydrogen-bonded structure in the single ionized acid. In the homologous series of oxalic acids, dissociation constants have been determined in acetonitrile [13]. The intramolecular hydrogen bond in the monoanion molecule was found to be quite stable but the strength of this bond decreases with increasing distance between the carboxyl groups; thus the most favorable situation would be found in hydrogen malonate ion. Despite the experimental support, as far as we are aware no theoretical studies have been carried out on the intramolecular hydrogen bonding ability of malonic acid and its monoanion. In fact, only a theoretical conformational analysis is available for malonic acid [ 141 using experimental geometry [ 151. Recently, the interactions of malonate dianion with metals have been the subject of theoretical studies [16] as a model for understanding the physiological behaviour of 7-carboxyglutamic acid, an amino acid found in several important proteins. No theoretical studies are available for hydrogen malonate acid. In view of the importance of malonic acid in organic and inorganic chemistry and also the differences which have arisen among experimentalists, we consider an ab initio study to be of great value in obtaining more conclusive results. The aim of this paper is to study different conformations of malonic and hydrogen malonate acids and evaluate, if present, the stabilization energy of intramolecular hydrogen bonding. The results are presented in two parts corresponding to malonic and hydrogen malonate acid, respectively.
53 CALCULATIONS
The ab initio MO-LCAO-SCF calculations were performed by the GAUSSIAN 70 series of programs 1171 on a UNIVAC 1100/80 computer. The conformations studied are shown schematically in Fig. 1. For each species considered we have carried out a complete optimization with simple parabolic fits to each parameter at the RHF/STO-3G minimal basis set [ 181. The STO-3G optimum geometries of structures I-VII, obtained in this way, were then used for single point split valence RHF/4-31G calculations [ 191. In the present work standard valence shell scale factors have been used. In order to find the conformation which corresponds to the absolute minimum a conformational energy map for hydrogen malonate acid was constructed at the STO-3G level. Finally, the hydrogen potential energy curve was built for the internally hydrogen-bonded monoanion. RESULTS AND DISCUSSION
Malonic acid The conformations studied for malonic acid (I-III) are shown in Fig. 1. In I the two carboxyl groups are orthogonal to each other, one of them coplanar with the carbon skeleton, the dihedral angles 0(7)C(3)C(l)C(2) and 0(4)C(2)C(l)C(3) being 0” and 90”, respectively. Structures II and III have the carboxyl groups coplanar with the C( 3)C( l)C(2) plane and differ mainly in the placement of H(6).
II
H&--C; O-. 8
'05-H,
/
c3 '0
7
IV
V
VI
Fig. 1. Malonic acid and hydrogen malonate ion conformations.
54
The initial geometrical parameters were taken from the crystal data of malonic acid [ 151 and no symmetry restrictions were imposed during optimization. The STO-3G optimum geometries of conformations I-III are summarized in Table 1, according to the numbering in Fig. 1. The trends of the optimal bond lengths are similar for the three conformations. As regards bond angles we quote the opening of the C( 3)C( l)C( 2) angle for the planar structures, II and III, in relation to the perpendicular one, I, due to steric hindrance. In Table 2 total and relative energies are listed. Relative energies indicate TABLE 1 Calculated (RHF/STO-3G) Parameter
geometries of malonic acid conformations Conformation I
II
III
Bond lengths (A) C(2)C(l) C(3FAl) G(4)C(2) 0(5)C(2) H(6)0(5) G(7)C(3) 0(8)C(3) Ht9)0(8) H(lO)C(l) Wll)C(l)
1.542 1.546 1.225 1.375 0.985 1.225 1.376 0.986 1.089 1.089
1.553 1.549 1.220 1.376 0.989 1.225 1.375 0.989 1.090 1.090
1.573 1.548 1.217 1.368 0.993 1.234 1.364 0.989 1.089 1.089
Bond angles e) c(3w)c(2) 0(4)C(2)Cu) 0(5)C(2)C(l) H(6)0(5)C(2) 0(7)C(3)C(l) 0(8)C(3)CU) H(9)0(8)C(3) H(lO)C(l)C(3) H(ll)C(l)C(3)
108.9 120.4 114.0 105.1 120.5 114.1 104.8 109.8 109.8
114.7 121.9 117.2 105.4 121.8 113.4 105.0 109.7 109.7
113.9 119.8 118.9 107.5 121.3 114.8 105.8 109.2 109.2
TABLE 2 Total and relative energies of malonic acid conformations geometries Structure
Total energies (a.u.) STO-3G
I (perpendicular) II (reference) III (H-bonded)
-409.88682 -409.88155 -409.88643
4-31G -414.77862 -414.76742 -414.77330
at the RHF/STO-3G
optimal
Relative energies (kcal mold ) STO-3G
4-31G
0.0 3.3 0.2
0.0 7.0 3.3
55
that the stabilizations of the planar conformations, II and III, are overestimated at the STO-3G level. We could evaluate the stability of the hydrogenbonded structure, III, by taking as reference the non-bonded conformation, II. The stabilization energies of III with respect to II are 3.1 and 3.7 kcal mol-’ at the STO-3G and 4-31G basis sets, respectively. This stabilization can be related to the formation of the intramolecular hydrogen bond in III, although there are more different factors between these two conformations intrinsic to the nature of that special bond. However, even if III is energetically favorable in relation to II, the intramolecular hydrogen bond is not strong enough to counteract the repulsions since the carboxyl groups are too close and therefore the minimum energy conformation is not planar, as can be seen in Table 2. This result agrees with previous work [14] where conformational analysis shows an absolute minimum appears when the two carboxyl groups are nearly perpendicular, although a large portion of the conformational space is accessible through low energy barriers. Table 3 shows the Mulliken population analysis [20] for the main atoms involved in the hydrogen bonding. It can be seen that the total overlap population between O(7) and H(6), having an interatomic distance of 1.559 A, is small in conformation III, even at the 4-31G level. The dipole moment is also given for each conformation in Table 3. The value for the perpendicular structure, I, at the 4-31G level is in good agreement with the experimental one (2.56 D in dioxane solution [21]). However, the STO-3G result reflects the general tendency of minimal basis sets to underestimate electric moments and charge transfer [ 221. Hydrogen malona te acid The conformations studied for hydrogen malonate acid (IV-VII) are shown in Fig. 1. In IV the carboxylate group is coplanar with the C(3)C( l)C( 2) TABLE
3
Mulliken population analysis for malonic acid conformations I STO-3G Net atomic charges G(5) -0.288 G(7) -0.265 B(6) 0.216 Total overlap populations G(5)W6) 0.257 G(7)W6) Dipole moment(D) 1.173
II 4-31G
STO-3G
III 4-31G
STO-3G
4-31G
-0.712 -0.564 0.443
-0.280 -0.249 0.210
-0.683 -0.536 0.434
-0.338 -0.283 0.256
-0.749 -0.648 0.501
0.249
0.256
0.246 0.001
0.254 0.031
0.233 0.037
2.427
0.979
1.768
4.554
6.443
56
plane and the carboxyl group is perpendicular to it. The non-bonded planar structure is represented in V. Conformations VI and VII are also planar but intramolecularly hydrogen-bonded, belonging to C, and C,, symmetry, respectively. The optimal geometrical parameters of malonic acid were used as initial parameters for hydrogen malonate conformations. The STO-3G optimum geometries of IV-VII are summarized in Table 4. The more important features observed from Table 4 are an increase of the C-C and O-H bond lengths in the planar C,, conformation, VII, in relation to the other conformations, to obtain a symmetrical interaction of H(6) with O(5) and O(7), and opening of the C(3)C(l)C(2) angle in the case of the planar non-bonded form, V, due to steric hindrance of coplanar carboxyl and carboxylate groups. In Table 5 total and relative energies of conformations IV-VII are listed. It is readily seen that the greater stability of the planar bonded forms, VI and VII, with respect to the reference planar structure, V, is exaggerated at the STO-3G level. This stabilization depends on basis-set size much more for hydrogen malonate than for malonic acid, as it usually occurs in hydrogen bonded anionic systems [ 231. Moreover, structures VI and VII are energetically lower than the perpendicular form, IV, which is presumed to have
TABLE 4 Calculated (RHF/STO-3G) Parameter
geometries of hydrogen malonate conformations
Conformation Iv
V
VI
VII
Bond lengths (A) C(W(l) C(3KxU o(4)w o(5w) W6W5) 0(7)C(3) o(3W3) M-W(1) H(lW(l)
1.536 1.619 1.230 1.383 0.987 1.271 1.269 1.087 1.087
1.569 1.624 1.232 1.374 0.991 1.268 1.272 1.087 1.087
1.557 1.591 1.232 1.344 1.042 1.310 1.249 1.087 1.087
1.593 1.593 1.238 1.325 1.155 1.325 1.238 1.087 1.087
Bond angles (“) c(3)ww) o(4wm1) o(5mww W6)0(5)C(2) O(7YA3M1) 0(3)C(3)C(l) H(9Ml)C(3) WWX1)C(3)
111.9 123.0 115.1 103.8 111.7 115.3 110.5 110.5
116.4 122.1 117.8 102.7 113.6 114.0 111.1 111.1
108.6 119.5 117.0 106.1 119.9 116.1 110.3 110.3
110.3 117.9 117.8 104.3 117.8 117.9 110.0 110.0
57 TABLE 5 Total and relative energies of hydrogen malonate ion conformations optimal geometries Structure
Total energies (a.u.) STO-3G
4-3 1G
at the RHF/STO-3G
Relative energies (kcal mol-’ ) STO-3G
IV (perpendicular) V (reference) VI (H-bonded (Cs)) VII (H-bonded (C,,))
-409.14738 -409.13396 -409.19205 -409.19977
-414.22573 -414.20184 -414.23646 -414.24285
0.0 8.4 -28.0 -32.9
4-31G 0.0 15.0 -6.7 -10.7
the least steric hindrance. If this were the case, only the stabilization by hydrogen bonding could explain the results obtained. To prove that the perpendicular structure, IV, is a minimum of the nonbonded forms, a conformational energy map was built taking as geometrical parameters the optimal ones for IV (see Table 4). The STO-3G con-
Fig. 2. Hydrogen malonate ion. STO-3G conformationai energy map: e1 = 0(7)C(3)C(l)C(2) and 6, = 0(4)C(2)C( l)C(3). Contour lines are drawn in kcal rnol-’ units from the lowest minimum.
58 TABLE 6 Mulliken population analysis for hydrogen malonate ion conformations IV STO-3G Net atbmic charges G(5) -0.302 G(7) -0.486 H(6) 0.175
V 4-31G
STO-3G
VI 4-3 1G
STO-3G
VII 4-31G
STO-3G
4-31G
-0.731 -0.773 0.405
-0.264 -0.474 0.165
-0.654 -0.747 0.383
-0.439 -0.462 0.279
-0.809 -0.829 0.517
-0.444 -0.444 0.266
-0.833 -0.833 0.535
Total overlap populations 0(5)H(6) 0.250 0.239 0(7)H(6)
0.244
0.230 0.002
0.185 0.129
0.163 0.123
0.154 0.154
0.136 0.136
formational energy map was calculated at 30” steps of dihedral angles el, 0(7)C(3)C(l)C(2), and 13~,0(4)C(2)C(l)C(3), where (0”, 90”) corresponds to the perpendicular structure, IV. The conformational energy map (see Fig. 2) is only represented on the conformational space O”180” due to molecular symmetry. The perpendicular structure, IV, is only 0.2 kcal molml higher than the (MO”, 93”) one, where the lowest minimum is placed. Effectively, for hydrogen malonate acid the planar bonded structures VI and VII are preferred to any non-bonded conformations. This conclusion is in accord with crystal data, e.g. potassium hydrogen malonate [24]. Unlike the free acid, the anion in solid KC304H3 is nearly coplanar and has twofold symmetry. It can be seen in Table 5 that the C, conformation, VI, is energetically higher than the Czv one (structure VII). The energy differences are 4.9 and 4.0 kcal mol-’ with STO-3G and 4-31G basis sets, respectively. It can be observed in Table 6 that the total overlap population between O( 7) and H(6), at an interatomic distance of 1.199 A, is appreciable for the C, hydrogen bonded structure, VI. Nevertheless, for the Czv conformation, VII, a more effective overlap between H(6) and O(5), O(7) has happened, this being the reason for its lower energy. To study the potential energy curve for the proton transfer reaction, H(6), we have to choose an appropriate reaction coordinate. We assume that the geometry changes, going from Czv to C, conformations, can be obtained by means of a linear interpolation on all geometry parameters and so we can simulate this reaction by the reaction coordinate “Y”. The values of r = 1 correspond to the STO-3G optimal Czv structure, r = 0 to the STO-3G optimal C, one, and r = 0.5 to the midpoint between those two obtained by linear interpolation. This type of reaction coordinate has been employed previously in a very similar problem [25]. Figure 3 shows the calculated hydrogen bond potential energy curve with the 4-31G basis set. In view of the potential energy curve the hydrogen bond is strong enough to result in a single minimum potential for the proton transfer reaction.
59
Fig. 3. Hydrogen maionate ion. Calculated hydrogen bond potential energy curve with 4-31G basis set. At r = 0.5 total energy is -414.24038 au. CONCLUSIONS
For malonic acid strong enough intramolecular hydrogen bonding to compensate the steric hindrance when the two carboxyl groups are coplanar does not exist. However, a symmetrical C2, hydrogen-bonded conformation was found to be the most stable in the case of the monoanion. From the above results we can conclude that intramolecular hydrogen bonded structures play an important role in explaining the constant ratio kl/kz of malonic acids. ACKNOWLEDGMENT
One of us, M. MerchAn, thanks the Ministerio de Education y Ciencia of Spain for a research grant. REFERENCES 1 G. C. Pimentel and A. L. McClellan, The Hydrogen Bond, W. H. Freeman, San Francisco, 1960. 2 L. Hunter, Chem. Ind., (1953) 155; cf. I. Jones and F. G. Soper, J. Chem. Sot., (1936) 133. 3 (a) D. H. McDaniel and H. C. Brown, Science, 118 (1953) 370. (b) H. C. Brown, D. H. McDaniel and 0. Hiifliger, in E. A. Braude and F. C. Nachod (Eds.), Determination of Organic Structures by Physical Methods, Academic Press, New York, 1955. 4 F. H. Westheimer and 0. T. Benfey, J. Am. Chem. Sot., 78 (1956) 5309. 5 C. Tanford, J. Am. Chem. Sot., 79 (1957) 5348. 6 S. N. Das and D. J. G. Ives, Proc. Chem. Sot., (1961) 373. 7 D. Chapman, D. R. Lloyd and R. H. Prince, J. Chem. Sot., (1964) 550. 8 P. K. Glasoe and J. R. Hutchison, J. Phys. Chem., 68 (1964) 1562. 9 E. S. Hanrahan, Spectrochim. Acta, 22 (1966) 1243.
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