J. Phys. Chem. 1988, 92, 5635-5639
5635
AM1 Molecular Orbital Study of Hydrogen Bonding. Gas-Phase Hydration of Protonated Diamines J. J. Dannenberg* and Laura K. Vinson Department of Chemistry, City University of New York, Hunter College and the Graduate School, 695 Park Avenue, New York, New York 10021 (Received: December 2, 1987)
Fully optimized AM1 molecular orbital calculation are reported for protonated 1,2-diaminoethane, 1,3-diaminopropane, values are in good agreement and 1,4-diaminobutane, each hydrated by up to four water molecules. The calculated MJ,fl with gas-phase experimental results. The waters interact almost exclusively with the protonated ammonium rather than the unprotonated amine. The hydrogen bonds are bifurcated in all cases. Variations in the structures of the hydration complexes are correlated with the differences in the M h y d for the individual water molecules.
Molecular orbital (MO) theory has been very successful in modeling the structures of most ground-state molecules containing the atoms H through 0. Even fairly unsophisticated approaches give reasonably reliable ground-state geometries. One major exception to this has been hydrogen bonds. Despite their obvious importance in innumerable chemical and biological phenomena, they have been only poorly rendered by using anything less than extremely complex molecular orbital theory.' Unfortunately, the level of calculation necessary to properly describe the hydrogen bond makes any thorough geometric search too costly except for a few very small systems. There have been many reports of ab initio calculations on hydrogen bonding. Optimistic interpretations of small basis set calculations have generally not been substantiated. In our own laboratory, we observed significant geometrical changes in the fully optimized NH4+.H20 geometry2 as the basis set was increased from STO-3G to 4-31G, 6-31G, 6-31G*, and 6-31G**.' Semiempirical calculations also met with very limited success. Some apparently reasonable results have been reported by using C N D 0 / 2 and M I N D 0 / 3 technique^.^ These results are suspect, however, as the same methods are quite poor at calculating the water dimerss6 as well as other kinds of intermolecular interactions involving hydrogen non- (or partial) bonding interactions, for example, in transition states for hydrogen abstractions.' MNDO, which has been the most successful of the widely used semiempirical methods, is totally incapable of describing hydrogen bonds.2v8 This is presumably due to an imbalance in repulsion and attraction terms between hydrogens and other atoms. The same problem is manifest in the overestimation of activation energies for hydrogen abstraction and for other situations where H atoms have proximate nonbonding interactions with other atoms. The AM1 molecular orbital methodg is closely related to the MNDO'O method. Among the significant changes is the correction (1) (a) Scheiner, S.; Szczesniak, M. S.; Bigham, L. D. Int. J. Quantum Chem. 1983, 23, 739. (b) Alagona, G.; Ghio, C.; Kollman, P. J. Am. Chem. Soc. 1983, 105, 5226. (c) Frisch, M. J.; Pople, J. A.; Del Bene, J. E. J. Chem. Phys. 1983,78,4063. (d) Yeo, G. A.; Ford, T. A. J. Mol. Struct. 1986,141, 331. (2) Dannenberg, J. J.; Pierce, J., unpublished results. (3) With the GAUSSIAN 80 program: Binkley, J. S.; Whiteside, R. A.; Krishnan, R.; Seeger, R.; DeFrees, D. J.; Schlegel, H. B.; Topiol, S.;Kahn, L. R.; Pople, J. A,, available from the Quantum Chemistry Program Exchange. (4) Paul, S. 0.;Ford, T. A. Spectrochim. Acta, Parr A 1986, 42, 681. ( 5 ) (a) Klopman, G.; Andreozzi, P.; Hopffinger; A. J.; Kibuchi, 0.; Dewar, M. J. S.J. Am. Chem. SOC.1978,100,6268. (b) Zielenski, T. J.; Breen, D. L.; Rein, R. J. Am. Chem. SOC.1978,100, 6266. (6) Thiel, W. Theor. Chim. Acta 1978, 48, 357. (7) Rayez-Meaume, M.-T., Dannenberg, J. J.; Whitten, J. L. J . Am. Chem. Soc. 1978, 100, 747. (8) Salk, S.H. S.;Chen, T. S.; Hagen, D. E.; Lutrus, C. K. Theor. Chim. Acta 1986, 70, 3. (9) Dewar, M. J. S.; Zoebisch, E. G.; Healy, E. F.; Stewart, J. J. P. J. Am. Chem. Soc. 1985, 107, 3902. (10) Dewar, M. J. S.; .Thiel, W. J. Am. Chem. SOC.1977, 99, 4899.
TABLE I: Enthalpy of Solvation
species
waters
-AH.kcal/mol calcd exptl
2 3 4
13.4 11.7 10.6 9.9
14.7 12.0
NH2(CH2)3NH3+
1
12.6 10.8 11.1 9.8 11.9 9.7 9.6 9.4
11.4 9.9 10.4
"2(CH2)4"3+
2 3 4 1 2 3 4
NH2(CH2)2NH3
1
11.0
9.4 11.0
of the imbalance of hydrogen-atom nonbonded interactions. AM 1 does predict a reasonable energy for the water dimer." It was hoped that this method could provide a reasonably accessible means for describing hydrogen bonds in larger systems than was previously possible. A recent study has shown AM1 to be reasonably accurate in predicting the solvation of ammonium ions by ammonia and water.I2 Molecular orbital calculations should be compared with gasphase experimental data whenever possible. Mautner has measured the gas-phase AH values for the hydration of individual water molecules with protonated 1,2-diaminoethane, I, 1,3-diaminopropane, 11, and 1,Cdiaminobutane, III.I3 The measurements were made by equilibrating the protonated diamines with differing concentrations of water and measuring the masses of the species. In this manner, the energetics of the association of the protonated diamines with water can be measured. N o direct structural information, however, is obtained in this manner. H e also measured the enthalpies of cyclization of the protonated diamines. His values are significantly lower than those reported earlier by Kebarle.I4 We have undertaken to calculate the energies and optimized geometries of 1-111, each hydrated with from one to four waters. (1 1) The stabilization energy of 3.3 kcal/mol for the water dimer reported in ref 9 is in error. The correct value is 5.5 kcal/mol. The structure of the optimized dimer maximizes the interactions of the hydrogens and oxygen lone pairs. Three hydrogens interact with three oxygen lone pairs. This structure differs from the generally accepted linear hydrogen bond predicted by many ab initio calculations and several experiments. It should be noted that the AMI structure is highly ordered. It remains possible that the minimum on the free energy surface at the experimental temperatures may differ from that on the potential energy surface. We thank E. Evleth for bringing this to our attention. Since that time the same observation has been made in several other laboratories. (12) Galera, S.; Lluch, J. M.; Oliva, A,; Bertran, J. THEOCHEM 1988, 163, 101. (13) Meot-Ner (Mautner), M.; Hamlet, P.; Hunter, E. P.; Field, F. H . J . Am. Chem. SOC.1980,102,6393. Meot-Ner (Mautner), M.Acc. Chem. Res. 1984, 27, 186. (14) Yamdagni, R.; Kebarle, P. J. Am. Chem. SOC.1973, 95, 3504.
0022-3654/88/2092-5635$01.50/0Q 1988 American Chemical Societv
5636 The Journal of Physical Chemistry, Vol. 92, No. 20, 1988
Dannenberg and Vinson r-
TABLE II: Enthalpy of Cvclization for Protonated Diamines -AHcvc, kcal/mol species NH2(CH2)2NH3t NH2(CH2)jNHSt NH2(CH2)4NH3t
method 4.4
8.2 10.4
i
calcd exptl A method B method C method D 7.3 6.7 9.0 14.2 15.0 10.6 119 18.5 8.7
4
I
In this manner, we provide a fairly rigorous test for the AM1 methodology. If the calculated energies are in reasonable agreement with the measured values, we may place reasonable confidence in the calculated geometries. Thus, we hope to increase our understanding of the intimate interactions between the protonated diamines and water molecules.
Methods As mentioned previously, the AM1 approximation to molecular orbital theory was used throughout. For each structure considered, all of the internal coordinates (up to 11 1, for the case of 111plus four waters) were optimized by using the Fletcher-Powell-Davidon algorithm as implemented in the AMPAC M O ~ r 0 g r a m . l As ~ might be expected, the surfaces can be quite complex, containing multiple minima. Care was taken to find as many of the minima as possible. Multiple optimizations of each complex were performed until we were confident that we had sufficiently explored the surface. In particular, for each complex all of the following interactions were explored through optimization of the appropriate geometries: (a) interaction of a water 0 with each of the hydrogens on both the protonated and unprotonated amines; (b) interaction of a water 0 with two hydrogens of the protonated amine or one hydrogen from each of the amines; (c) bridging an OH of a water between the N of the unprotonated amine and a proton on the protonated amine; (d) hydrogen bonding between water molecules. In the course of this work we performed numerous optimizations and found over 50 local minima. There is, of course, no foolproof way of knowing that we have explored all significant minima.
.A-
\
Results and Discussion Energetics. The calculated enthalpies for the interaction of 1-111 with individual water molecules is presented in Table I. The agreement between the experimental and calculated values is immediately obvious. The geometries of the lowest energy complexes are displayed in Figures 1-3. As there are generally several other minima available for the complexes, some only a kcal/mol or so above the global minima, the measured enthalpies at 298 K should be slightly higher than that of the global minimum, due to the partial population of other minima. Interestingly, all of the calculated AH values of complexation for I1 and 111 are too large (negative), as might be expected. The opposite observation for I is discussed below. All of the protonated diamines are predicted to have internal hydrogen bonds between the protonated and unprotonated amines. Mautner reported “cyclization” enthalpies, AHcyc,for 1-111. To determine these values, he compared the proton affinities of each diamine with that of the simple amine formed by replacing one of the amino groups with a methyl group. We have attempted to calculate these values using two different procedures. In the first, we calculate the respective heats of formation of the protonated and unprotonated diamines and amines involved in Mautner’s procedure (method A). In the second (method B), we compare the enthalpies of each protonated diamine in its bridged conformation with that of the same species in its best extended conformation. The results are presented in Table I1 and compared with the experimental AHqc values taken from Mautner’s original publication (method C) and by utilizing the experimental in place of the calculated heats of formation, as in method B, (method D). L
(15) This program was kindly provided by Prof,
M. J. s. Dewar and
developed by his research group. It is available from the Quantum Chemistry Program Exchange (QCPE).
Figure 1. Structures for the global minima calculated for protonated lNiaminoethane, I, hydrated by zero to four water molecules (A-E,
respectively).
The Journal of Physical Chemistry, Vol. 92, No. 20, 1988 5637
Gas-Phase Hydration of Protonated Diamines L
A
,I
i l
-
3
'i -
'?c3
;I
t
C Y
ClcH
d'
3
"
c L
Figure 3. Structures for the global minima calculated for protonated 1,2-diarninobutane,111, hydrated by zero to four water molecules (A-E,
respectively).
n L L
Figure 2. Structures for the global minima calculated for protonated 1,2-diaminopropane, 11, hydrated by zero to four water molecules (A-E,
respectively).
The agreement between the calculated and the reported values is not as good as one might hope, although they are in excellent agreement with a recent ab initio calculation at the MP2/D95V** levelI6 (-7.2 versus -7.3 kcal/mol by using method B). The reasons for this are not completely clear. One should note, however, that the calculated values each involve the accumulation of errors from four different M O calculations. The errors seem to be in the heats of formation for the unprotonated diamines. (16) Ikuta, S.; Nomura, 0. THEOCHEM 1987, 152, 3 1 5 .
5638
Dannenberg and Vinson
The Journal of Physical Chemistry, Vol. 92, No. 20, 1988 TABLE IV
TABLE 111
species "2(CH2)2"3'
"z(CHz)3"3'
NH2(CH2)4NH3'
waters 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4
H'-N
dist, A 2.6 2.6 2.6 2.7 2.7 1.9 2.0 2.4 2.3 2.4 1.7 1.7 1.8 1.8 1.8
N-H' ...N angle, deg 97.7 96.9 96.3 94.1 92.9 139.4 137.0 110.8 115.1 109.5 166.4 162.8 157.8 155.7 155.8
It is worthy of note that only one of the reported" values, that for 1,2-diaminoethane,'* was actually measured; the other two were estimated. The calculated heats of formation of the protonated species, 1-111 (136.2, 125.3, and 115.9 kcal/mol, respectively) are in good agreement with the values reported (135.1, 124.0, and 115.0 kcal/mol, respectively).13 The calculations are nevertheless in error, as the differences in the respective heats of formation of the protonated and unprotonated diamines (proton affinities) for the calculated and reported values do not agree as well as expected. Geometries. As can be seen from Table 111and Figures 1A-3A, and H bond is longest in I, becoming progressively shorter in I1 and 111 (2.56, 1.90, and 1.68 A, respectively). The N-H+--N angle opens (97.7, 139.4, and 166.4', respectively), and the atomic charge on the bridging proton increases (0.27, 0.29, and 0.30, respectively) for the same progression. Clearly, the H bond, weak in I, due to its inability to assume a favorable conformation for H bonding without introducing more strain energy than the H bond is worth, is becoming stronger, and more "normal" as the ring increases in size. As waters are added to all three protonated diamines, there is a tendency for the H bond to become longer and the N-H'--H angle to become more acute (see Table 111). The effects are rather different in each of the three cases, however. Since the internal H bond is quite long, and the N-H+--H angle quite acute in I; neither changes much as water molecules are added. For 11, however, the internal H bond lengthens significantly upon addition of each of the first two waters and then remains reasonably constant upon addition of the other two waters. The N-H'-N angle decreases from the 137-140' range to the 109-1 16O range upon addition of the third water. This phenomenon is likely due to a conformational preference for the longer internal H bond coupled with a conformational flexibility that allows for a short internal H bond in the absence of external stabilization. For 111, the internal H bond is initially short and does not change significantly with the addition of water molecules. The N-H+-.H angle decreases slightly upon addition of the first two waters and then remains roughly constant. The conformation of cyclized 111 allows a nearly linear intramolecular H bond with little strain. The relative stabilization energies of Table I (both calculated and experimental) seem consistent with this interpretation. The stabilization for the complexation of the first water molecule is greatest for I, where the internal hydrogen bond is the weakest, and decreases as the diamine becomes larger. One should note, however, that this trend may also be partly due to fact that larger ions are generally less stabilized by solvent as they can more easily delocalize their charges internally. Inspection of Table I indicates that each additional water molecule has less of a stabilizing effect than the previous one, except for the third water attached to 11. It is notable that the (17) Lias, S. G.; Liebman, J. L.; Levin, R. D. J . Phys. Chern. Ref. Data 1984, 13, 695. (18) Good, W. D.;Moore, R. T. J . Chem. Eng. Data 1970, 15, 150.
charge on the NH3+group species
OH70
NH2(CH2)2NH3+ 0.721 1 NH2(CH2),NH3' 0.6922 0.6521 NH2(CH,),NH,'
1 H,O
2H,O
3 H,O
4 H,O
0.7340 0.7151 0.6799
0.7457 0.7425 0.7045
0.7524 0.7475 0.7151
0.7490 0.7457 0.7234
TABLE V ~~
species
total charge on the water molecules 1 H2O 2 H2O 3 HzO 4H20
NH2(CH2)2NH3+0.0060 NH2(CH2),NH3+ 0.0053 NH*(CH,),NH,' 0.0047
0.0102 0.0087 0.0093
0.0162 0.0138 0.0120
0.0207 0.0226 0.0120
calculations reproduce this observation. This phenomenon might be due to the fact that the conformational relaxation (noticed particularly in the case of 11) has ended after the first two waters have been added. The effective AHhydfor each water should be the actual L i f & corrected for the conformational energy change. Neither the intramolecular H bond, nor the N-H+-H angle changes significantly after the second water is added, so there is no longer a conformational energy correction for the addition of the third and fourth waters. This factor is only significant for 11, as this is the only protonated diamine that is predicted to undergo large conformational changes as waters are added. In the case of all three protonated diamines, the first water molecule added has a bifurcated interaction with the protonated amine (see Figures 1-3). The interactions are between the oxygen and the two protons not involved in the internal H bond. The second water molecule again interacts in a bifurcated fashion with its oxygen interacting with both the proton involved in the internal H bond and one of the other two H atoms. The third water has another bifurcated interaction, so that each of the oxygens of the protonated amine. Conversely, each of the hydrogens on the protonated amine interacts with two different water molecules. The structures are more complex, as each water molecule hydrogen bonds to another one. When a fourth water molecule is added, the complexes become different for each of the three protonated diamines. In each case, however, the H bonding of each proton on the protonated amine to two different waters is maintained. In the case of I, the fourth water is interspersed between a proton of the protonated amine and a water oxygen. In the case of 11, the fourth water bridges between a proton on each nitrogen (forming a third H bond to one of the ammonium protons). In 111, it interacts with two other waters, forming two H bonds with one, and one with the other; in addition there is an H bond formed to one of the hydrogens on the unprotonated amine, which is slightly longer than the others. It is worthy of note that the geometries that correspond to the global minimum for each of the protonated diamines hydrated with four waters were explicitly explored on the potential surfaces for the other two cases. The net charge on the ammonium group for each complex is presented in Table IV. For each protonated diamine, the charge on the ammonium group increases with increasing water complexation. This behavior is almost certainly due to the reduced demand upon the cation for internal charge delocalization as the number of attached waters increases. This is also useful in rationalizing the observation that (with the exception of I1 with four waters) none of the water molecules interact with the unprotonated -NH, group. Mautner has suggested that the first two water molecules might bind each to a proton on a different nitrogen atom in I and 11. His reasoning was based upon the observation that the entropy of hydration, A s h y & was significantly more negative for addition of the third water. If the first two waters bind to hydrogens attached to different nitrogens, they should be out of each other's way. Inspection of Figures 1-3 indicates that the first two waters do not interact appreciably in the bifurcated structures indicated. However, with the addition of the third water molecule, there is significant interaction between the waters. Thus, the calculated structures appear to be in agreement with the observed A s h y , +
J. Phys. Chem. 1988, 92, 5639-5642 Bifurcated H-bonding structures are often predicted by extended basis set a b initio calculation^,'^ even in cases where small basis sets calculations predict linear H bonds.lb Experimental studies of the rotation of ammonium ion in aqueous solution are in accord with bifurcated H bonds between water and ammonium iomZ0 Table V displays the total charge densities on the water molecules in each hydration cluster. The accumulation of positive charge on the water molecules increases less with the addition of each new water molecule, as would be expected. The prediction of some charge transfer seems in accord with a recent orbital analysis of t4e water dimerz1 and earlier suggestions by Klemperer?2 It is also invoked as an explanation of the failure of small basis set a b initio calculations to predict bifurcated structures.lb (1 9) See, for example: (a) Kistenmacher, H.; Popkie, H.; Clementi, E. J. Chem. Phys. 1973,58,5627. (b) Kollman, P. J . Am. Chem. SOC.1977,99,
4875. (20) Perrin, C. L.; Gipe, R. K. J . Am. Chem. Soc. 1986,108,1088; Science (Washington, D.C.) 1987, 238, 1393. (21) Reed. A. E.: Weinhold. F. J. Chem. Phvs. 1983. 78. 4066. (22j Harris, S.J:; Janda, K.'C.; Novick, S.6.;Klembrer, W. J . Chem. Phys. 1975, 63, 5285.
5639
Conclusion The results of the present AM1 calculations seem in good agreement with the experimental results of Mautner. They are also consistent with the results of large basis set calculations on smaller systems. From the present study, it would seem that the AM1 molecular orbital method might be an extremely effective and economical means of modeling systems containing hydrogen bonds. The present calculations also suggest that hydration of protonated diamines occurs primarily at the protonated nitrogen (at least when no more than four waters are considered). The initial interactions involve bifurcated H bonds between each water and two protons. After the third water is added, some solvent structuring begins to take place. The ammonium hydrogens eventually each have hydrogen bonds to two different waters, as well.
Acknowledgment. This work was supported, in part, by a PSC-BHE grant from the Research Foundation of the City University of New York. We thank Dr. Michael Mautner for several fruitful conversations. Registry No. I, 1 15960-32-2; 11, 115942-66-0; 111, 1 15942-67- 1.
Intramolecular Hydrogen Bonding In a Monoglyceride Lipid Studied by Fourier Transform Infrared Spectroscopy A. Holmgren,* G. Lindblom, and L. B.-A Johansson Department of Physical Chemistry, University of Umei. S-901 87 Umei, Sweden (Received: December 3, 1987; In Final Form: April 5, 1988)
The infrared spectra of the carbonyl and hydroxyl stretching modes of 1-monooctanoinwere examined. The C=O stretching mode of 1-monooctanoin shows two absorption bands in solvents and in a lamellar liquid crystalline phase formed with water. It is concluded that this splitting is due to intramolecular interactions. The IR spectra of the C=O and 0-H stretching modes of 1-monooctanoinin chloroform and acetonitrile and at various temperatures have been examined. Taken together, these data strongly suggest that the intramolecular interaction is a hydrogen bonding between the sn-3 hydroxyl and the carbonyl group of 1-monmtanoin. The similarities in the IR spectra of 1-monmtanoin and I-monoolein in the 1750-1700-cm-' range support the same explanation for the behavior of the C=O stretch in the latter lipid molecule.
Introduction In recent years FT-IR spectroscopy has been shown to be a useful technique for studies of physicochemical properties of surfactants in solution,14 model membranes,%* and the lipids in biological membra ne^.^^'^ In particular we are interested in using FT-IR for studies of linear dichroism of macroscopically aligned (1) Umemura, J.; Cameron, D. G.; Mantsch, H. H. J. Chem. Phys. 1980, 84, 2212. (2) Umemura, J.; Mantsch, H. H.; Cameron, D. G. J. Colloid Interface Sci. 1981, 83, 558. (3) Kawai, T.; Umemura, J.; Takenaka, T. Colloid Polym. Sci. 1984,262,
61. (4) Holmgren, A.; Fontell, K.; Lindblom, G. Acta Chem. Scand. 1986,40, 299. (5) Holmgren, A,; Johanuon, L. B.-A.; Lindblom, G. J. Phys. Chem. 1987, 91, 5298. (6) Mantsch, H. H.; Cameron, D. G.; Umemura, J.; Casal, H. L. J. Mol. Struct. 1980, 60, 263. (7) Mantsch, H. H.; Martin, A.; Cameron, D. G. Biochemistry 1981,20, 3138. (8) Mendelsohn, R.; Dluhy, R. A.; Crawford, T.; Mantsch, H. H. Biochemistry 1984, 23, 1498. (9) Mendelsohn, R.; Anderle, G.; Jaworsky, M.; Mantsch, H. H.; Dluhy, R. A. Biochim. Biophys. Acta 1984, 775,215. (IO) C a d , H. L.; Cameron, D. G.; Jarell, H. C.; Smith, I. C. P.; Mantsch,, H. H. Chem. Phys. Lipids 1982, 30, 17.
0022-3654/88/2092-5639$01 .50/0
lamellar liquid crystalline phases, in order to get information about the system (e.g., hydrogen bonding in membrane surfaces) that is not easily obtained by other spectroscopical methods. During the development of the FT-IR linear dichroism spectroscopy,s we found that lamellar phases of monoglycerides (monooctanoin and monoolein) gave rise to two absorption bands in the region of the carbonyl stretching vibrations. Previously it has been that the carbonyl stretching region (1700-1750 cm-') for dipalmitoylphosphatidylcholine (DPPC) is similarly comprised of at least two absorption bands having their maxima at 1721 and 1739 cm-I. These two bands were assigned to the carbonyl groups of the two different acyl chains of the lecithin molecule. It was suggested that the carbonyl group of the acyl chain sn-2 is located more closely to the polar head group region while the carbonyl group of the sn-1 acyl chain has a more hydrophobic environment. Lysophosphatidylcholine, having only one acyl chain, on the other hand, showed only one band in this spectral region. Therefore, the phosphatidylcholine investigations strongly indicate that the lamellar phase structure is not causing the two bands observed (11) Mushayakarara, E.; Levin, I. W. J . Phys. Chem. 1982, 86, 2324. (12) Levin, I. W.; Mushayakarara, E.; Biffman, R. J . Raman Spectrosc. 1982, 13, 23. (13) OLeary, T. J.; Levin, I. W. J. Phys. Chem. 1984, 88, 1790.
0 1988 American Chemical Society
