The Journal of
Physical Chemistry
0 Copyright 1994 by the American Chemical Society
VOLUME 98, NUMBER 51, DECEMBER 22, 1994
LETTERS Amide- Water and Amide- Amide Hydrogen Bond Strengths? David A. Dixon and Kerwin D. Dobbs* DuPont Central Research and Development, Experimental Station, P . 0. Box 80328, Wilmington, Delaware 19880-0328
James J. Valentini Department of Chemistry, Columbia University, New York, New York I0027 Received: September 23, 1994; In Final Form: November 1, 1994@
The hydrogen bond strengths between a water molecule and a model amide, N-meth).dcetamide (NMA), and between two N M A molecules have been calculated by using ab initio molecular orbital theory. The most extensive calculations were performed at the MP2 level with correlation consistent basis sets. For trunsNMAoH20, the most stable configurations (AZP98= -6.1 kcaYmo1) have the water acting as a proton donor to the carbonyl oxygen. For cis-NMA-HzO, the most stable configuration (AZP9*= -8.1 kcal/mol) has two hydrogen bonds, a water proton donor bond to the carbonyl oxygen and an amide NH proton donor bond to the water oxygen. The trans-NMA dimer has a single hydrogen bond ( A P 9 8= -6.9 kcaymol), whereas the cis-NMA dimer is cyclic with two hydrogen bonds (AZPg8= -14.1 kcdmol). The calculations show that hydrogen bonding can significantly stabilize the higher energy cis isomer of the amide functional group relative to the truns isomer.
Introduction The nature of the amide functional group has long been of fundamental interest because of its presence as a repeat unit in biological macromolecules and industrial polymers such as nylon and Kevlar. In polyamides, both amide-water and amideamide hydrogen bonding interactions influence the overall bonding, structure, and dynamics of these materials. However, the actual strengths of these hydrogen-bonding interactions are not well-known. Spectroscopic studies of self-association of amides in solution yield equilibrium constants for amide-amide hydrogen bond From these equilibrium constants, hydrogen bond
* To whom correspondence should be addressed. f @
DuPont contribution No. 6955. Abstract published in Advance ACS Abstracts, December 1, 1994.
0022-365419412098-13435$04.50/0
strengths can be estimated. Recent NMR measurements'O have yielded relative strengths for amide-amide and amide-water hydrogen bonds but not absolute values. Recent resonance Raman studies by Triggs and Valentini11J2suggest that there are significant differences among ostensibly similar amideamide hydrogen bonds. These experiments do not, however, yield values for the hydrogen bond strengths. Previous ab initio molecular orbital calculations have not been performed at a high enough level to produce reliable amidewater and amide-amide hydrogen bond strengths.13-*l To provide a better understanding of these important bond strengths, we describe high-level ab initio molecular orbital calculations on model systems which contain either amide-water or amideamide hydrogen bonds. The calculations presented here should be of sufficient quality to provide accurate hydrogen bond strengths for these systems.
0 1994 American Chemical Society
Letters
13436 J. Phys. Chem., Vol. 98, No. 51, 1994 Calculations All calculations were done with the program system Gaussian 92.22 A polarized double-c valence basis set (DZP)23was used to optimize the geometries and to calculate the vibrational frequencies at the Hartree-Fock level for the structures described below. In the geometry optimizations, all metric parameters for the monomers and the associated complexes were fully optimized. In order to predict reliable associationenergies, single-pointenergy calculations with the much larger augmented correlation consistent polarized valence double-c basis set (augcc-pVDZ)% were done for the optimum Hartree-Fock structures at the second-order Moller-Plesset correlated level with only the valence electrons correlated (MP2(FC)).25 Association energies are reported in terms of both A e (electronic energy difference at 0 K) and AH298 (enthalpic energy difference at 298 K which includes zero-point energy differences, thermal corrections, and the work term). The counterpoise methodz6 was used to estimate the basis set superposition error (BSSE) in the association energies.
Results and Discussion N-Methylacetamide (NMA) is the smallest amide which can represent the amide function in polyamides. The amide-water systems examined consisted of trans- and cis-NMA interacting with a single water molecule. Dimers of trans- and cis-NMA were studied in order to model the amide-amide interaction. The amide-water and amide-amide hydrogen bond strengths are defined as the electronic (A@) and enthalpic association energies for reactions 1 and 2.
NMA
+ H,O -NMA.H,O
2NMA- NMA-NMA In order to assess whether the level of the calculations reported here for reactions 1 and 2 are adequate, we used our methods to calculate the association energy of the HzO dimer, reaction 3, for which there are a number of high-quality
2H20
- H,OH,O
(3)
calculation^.^^-^^ The results are shown in Table 1 and are compared to the best available calculations. Energy values with and without basis set superposition error (BSSE) correction are shown. For the electronic association energy, A@, Szalewicz et al.27 reported a Hartree-Fock (HF) limit of -3.7 f 0.05 kcal/mol and a correlation energy limit of -4.7 f 0.35 kcal/ mol. The HF association energy reported by Xantheas and Dunningz8 agrees with the HF limit of Szalewicz et al.,27but they reported a slightly lower correlated association energy of -4.4 kcaYmol if BSSE is included. Feller reported a slightly lower value of -3.6 kcal/mol and a slightly higher value of -4.8 kcaYmol for the HF and correlated association energies, r e s p e c t i ~ e l y .Feller ~ ~ noted in the limit of a complete basis set that the correlated association energy should be -5.0 kcal/m01.~~ Feller also noted,z9 as does Del Bene,31 that the association energies for the water dimer obtained at the MP2 level with augmented correlation consistent basis sets and no BSSE correction are in much better agreement with the complete basis set limit value. From Table 1, our HF/DZP value (with the BSSE correction) is -1 kcal/mol lower than the HF limit, whereas the HF/aug-cc-pVDZ value is the same as the HF limit. Our MP2/aug-cc-pVDZ value (without BSSE) of -5.2 kcaY mol is within 0.2 kcal/mol of the predicted correlated value at the complete basis set limit. The inclusion of the BSSE
TABLE 1: Electronic and Enthalpic Association Energiee (kcaymol) for the Water Dimer A e
methodb
HFIDZF
w/o BSSE
wlBSSE
AH298
WIO BSSE
wlBSSE
-5.0 -4.6
HF/aug-cc-pVDZC -3.8 MP2/a~g-cc-pVDZ'.~ -5.2 H F l [ 9 ~ 6 ~ 3 d 2 f / 6 ~ 3 ~ 2 d y-g3.8 MP4/[5~4p3dlf/4~3pld]~f;s -4.9 HFlaug-cc-pVDZi -3.9 MP2/a~g-cc-pVDZ+~ -5.3 MP4/aug-cc-pVDUjk -5.4 HFlaug-cc-pVQZ' -3.6 MP2/aug-cc-pVQZd,' -5.1 MP4/aug'-cc-pVTZd," -5.0 experiment"
-3.3 -2.9 -3.7 -2.1 -2.0 -4.4 (-5.0)e -3.5 -2.7 (-3.3)' -3.7 -4.4h -3.7 -4.4 -4.4 -3.6 -4.8 -3.2 -3.6 i 0.5
For reaction 3, A,!$ is the electronic energy difference at 0 K and AnRT, where APg8 takes the value of AI$ and incorporates zero-point energy and thermal corrections; An = - 1 for this reaction. Nomenclature refers to "energy levelhasis set" singlepoint calculations. The geometries were optimized at the HFIDZP level (current work). Single-point correlation calculations on valence electrons only. e BSSE correction has been scaled by 25% (see text). f Reference geometries were used in the calculations (ref 27). 8 See ref 27 for further details on the descriptions of the basis sets. This is the initial value before incorporating estimated corrections for dispersion energy and basis set defects. These corrections yield the final value of 4.7 i 0.35. See ref 27 for details. I The geometries were optimized at the HFIaug-cc-pVDZ level (ref 28). j Single-point correlation calculations on all electrons. The geometries were optimized at the MP2/ aug-cc-pVDZ level (ref 28). Reference geometries were used in the calculations (ref 29). The geometries were optimized at the MP21 6-31+G(d,p) level with all electrons correlated (ref 31). From ref 32. This value determined at 373 K.
H98 = APg8
+
'
correction at the MP2 level gives a value of -4.4 kcaymol, in agreement with the values of other workers for this type of basis set. This corresponds to a BSSE correction of 0.8, which overestimates the complete basis set limit by 0.6 kcal/mol. This suggests that it would be appropriate to scale the BSSE correction and only use 25% of this value for the water dimer interaction. This scaling factor of 25% may be too small for the amide-water interactions because the BSSE is somewhat larger due to the presence of more basis functions on the amide. However, it does provide a lower limit for the BSSE correction. On the basis of these comparisons, we should be able to predict reliable amide-water and amide-amide enthalpies of association (hydrogen bond strengths), that is, the energetics of reactions 1 and 2. The best theoretical values for the water dimer electronic association energy favor the lower range of the experimentally predicted value of -5.4 f 0.7 kcal/m01.~~ The best calculated number for the enthalpy of association at 298 K is -3.3 kcal/ mol based on our frequencies and the scaled BSSE (complete basis set limit) value. The experimental enthalpy of association of -3.6 f 0.5 kcaYm01~~ was determined at 373 K, and our computed value at this temperature, -3.1 kcal/mol, falls within the error limits of the experimental value. It is possible that one may need to consider how changes in the zero-point energy and thermal corrections, especially with the inclusion of anharmonic effects, will affect the calculated value for AH(7). The fully optimized structures (global minima) for the amide-water complexes are shown in Figures 1 and 2, and for the amide-amide complexes, the fully optimized structures are shown in Figure 3. The electronic (A@) and enthalpic (AH298) association energies for the amide-water and amideamide complexes are given in Tables 2 and 3, respectively. The correlated association energies in Tables 2 and 3 are reported
Letters
J. Phys. Chem., Vol. 98, No. 51, 1994 13437
T2
T3 Figure 1. HFDZP fully optimized structures for truns-NMA.Hz0 (Tl, T2, T3). Hydrogen bond lengths are given in angstroms.
I
2.222
; 1
2.003
'4 \
c2 c1 Figure 2. HFDZP fully optimized structures for cis-NMA.Hz0 (Cl, C2, C3). Hydrogen bond lengths are given in angstroms. with the full BSSE and the scaled (by 25%) BSSE applied to the uncorrected values. Only the scaled BSSE enthalpic association energies (M98) will be quoted in the remaining discussion when refemng to hydrogen bond strengths. For trans-NMkH20, a water molecule can act as an acceptor and bind to the amide proton (T-l), or it can be a donor and bind to the carbonyl oxygen in two different positions (T-2 and T-3). For cis-NMkH20, structure C-1 is similar to T-2, but structure C-2 is unique in that the water molecule simultaneously acts as an acceptor and donor, thereby forming two hydrogen bonds to the amide group. The trans-NMA dimer (T-D) has a near linear CO*.H(N) angle (168.3') with the planes of the amide groups nearly perpendicularto one another. The cyclic structure for the cis-NMA dimer (C-D) has the amide functionalities lying in a plane. The hydrogen bond strength (@98) between water as a proton acceptor and the amide hydrogen in trans-NMA as the proton donor (T-1) is -4.0 kcdmol. Water binding as a proton donor to either of the two possible positions about the carbonyl oxygen in trans-NMA (structures T-2 and T-3) is much stronger, resulting in a hydrogen bond strength of -6.1 kcal/mol for either structure. For the same type of hydrogen bond in cis-NMA
(structure C-1), the association energy has essentially the same value, -6.0 kcdmol. Due to the presence of two hydrogenbonding interactions, the largest association energy for the amide-water complexes is for structure C-2 (-8.1 kcaumol). Previous calculations by Guo and Karplus on the transNMhH20 structures showed the same trends in relative hydrogen bond strengths that we predict, namely, AI$ values (as compared to our M g 8 values) of -7.3 kcal for the T-2 and T-3 structures and -5.4 kcdmol for the T-1 structure.20 However, the calculations of Guo and Karplus were carried out at a much lower level of theory. Their AI$ values are at the HF/6-31G* level with no inclusion of electron correlation, and no attempt was made to provide an estimate of BSSE corrections, although at the HF level these corrections should be quite small. The HF/6-3 1G*-optimized geometries were obtained with the constraint of C, symmetry, which does not result in minima structures. Furthermore, the 6-31G* basis set is inadequate for hydrogen-bonding studies since it lacks both the necessary polarization functions for hydrogen when doing geometry optimizations and the additional polarization and diffuse functions needed to properly and reliably describe the relative energetics.
Letters
13438 J. Phys. Chem., Vol. 98, No. 51, 1994
‘,
2.003
‘,
CD
TD
Figure 3. HF/DZP fully optimized structures for trans-NMA (TD) and cis-NMA (CD) dimers. Hydrogen bond lengths are given in angstroms. TABLE 2: Electronic Association Energiev (kcaymol) for Amide- Water and Amide-Amide Systems A g
structured T-1 T-2 T-3 c-1 c-2 T-D C-D
HFDZPb w/o BSSE wlBSSE -4.9 -4.5 -6.1 -6.1 -6.8 -6.1 -6.7 -6.1 -1.6 -8.4 -6.5 -5.8 -11.8 -11.0
HFlaug-cc-pVDZb w/o BSSE wlBSSE -3.8 -3.5 -6.0 -5.1 -6.0 -5.1 -5.9 -5.6 -1.2 -6.8 -5.9 -5.4 -11.0 -10.5
MP2/aug-c~-pVDZ*~~ w/o BSSE wlBSSE wlscBSSE‘ -5.7 -4.8 -5.5 -8.1 -7.0 -7.8 -8.2 -7.0 -7.9 -8.0 -7.0 -7.7 -10.2 -8.9 -9.9 -8.9 -7.2 -8.5 - 16.4 -14.0 -15.8
a A g is the electronic energy difference at 0 K for either reaction 1 or 2. Nomenclature refers to “energy levellbasis set” single-point calculations on the HF/DzP optimized geometries. MP2 single-pointcalculations on valence electrons only. See Figures 1,2, and 3 for structures. Numbers correspond to a BSSE correction which has been scaled by 25% (see text).
TABLE 3: Enthalpic Association Energiet? (kcaYmol) for Amide-Water and Amide-Amide Systems AH298
”ZPb w/o BSSE -3.4 -5.0 -5.0 -5.0 -6.5 -5.0
HF/aug-cc-pVDZb w/o BSSE wlBSSE -2.3 -2.0 -4.3 -4.0 -4.3 -3.9 -4.2 -3.9 -5.3 -4.9 -4.3 -3.8 -9.3 -8.8
MP2/aug-cc-pVDZbsc structured wlBSSE w/o BSSE wlBSSE w/scBSSE‘ T-1 -3.0 -4.2 -3.3 -4.0 T-2 -4.4 -6.4 -5.3 -6.1 -4.4 T-3 -5.3 -6.1 -6.4 c-1 -4.4 -6.3 -5.2 -6.0 c-2 -5.7 -8.4 -7.0 -8.1 T-D -4.2 -7.3 -5.6 -6.9 C-D -10.1 -9.2 -14.7 -12.3 -14.1 a AH298= A,?P9*+ AnRT, where At?98 takes the electronic energy difference at 0 K for either reaction 1 or 2 and incorporates zero-point energy and thermal corrections; An = -1 for reactions 1 and 2. Nomenclature refers to “energy levellbasis set” single-point calculations on the HFlDZP optimized geometries. MP2 single-point calculations on valence electrons only. See Figures 1,2, and 3 for structures. Numbers correspond to a BSSE correction which has been scaled by 25% (see text). Both molecules in the NMA dimer are larger than water, leading to the BSSE correction for the amide-amide interaction being larger due to the presence of more basis functions on the “ghost” structure when doing the counterpoise calculations. Although the 25% scaling factor may again be too small, it provides a lower limit for the BSSE correction whereas the full BSSE correction represents an upper limit. Our calculations predict the single amide-amide (NH.* O=C)hydrogen-bonding interaction in the trans-NMA dimer (T-D) to have an energy ( A P g 8 )of -6.9 kcaYmol. For the cis-NMA dimer (C-D), the association energy of - 14.1 kcdmol is slightly more than twice that of the trans dimer because of the presence of two NH. * O = C hydrogen-bonding interactions. A very recent communication by Guo and Karplus21reported a A€$value (as
compared to our M g 8 value) of -6.8 kcaYmol at the HF/631G* level for a trans-NMA dimer. Again, the level of calculation is too low to give a reliable prediction for the energetics of this dimer. The results in Table 3 show that a single amide-amide hydrogen bond strength is comparable to a single amide-water hydrogen bond strength. The data also show that a single amide molecule can form two hydrogen bonds to another molecule, resulting in an association energy which is significantly larger than a single hydrogen bond strength. This latter interaction requires a proton on the amide N and a cis-amide conformation. The hydrogen bond strength for the C-2 structure, where the water molecule is interacting with both the carbonyl oxygen and the amide hydrogen, is 2.0 kcaVmol less than the sum of
J. Phys. Chem., Vol. 98, No. 51, 1994 13439
Letters the hydrogen bond strengths for T-1 and T-3, whereas the double hydrogen bonding interaction in C-D results in an association energy which is more than twice as large as the hydrogen bond strength in T-D. Our structural results for C-2 and C-D are not unique since structures of two molecules participating in multiple hydrogen bonds to each other have been previously calculated.1 4 3 The double hydrogen bonding between H20 and cis-NMA stabilizes this isomer relative to trans-NMA. The cis isomer of uncomplexed NMA is predicted to be less stable than the = 2.3 corresponding trans isomer, Al$ (cis - trans) = Mg8 kcaUmol at our highest level of calculation. However, the energy difference between the most stable complexes of NMA with water shows that the cis-NMA-HZO complex is only 0.5 kcaUmol less stable than the trans-NMA-H20 complex. The hydrogen bond stabilization of the cis isomer is even more pronounced for the NMA dimer. The cis-NMA dimer is actually more stable than the trans-NMA dimer by 6.7 kcaY mol. The presence of the two hydrogen bonds leads to a pair of higher energy cis structures being lower in energy than a pair of lower energy trans structures. The present and previous studies on simple model hydrogenbonded systems show that hydrogen bonding in real-world systems will be complex and may not easily be reduced to a simple conceptual model. For example, ab initio studies of cyclic water clusters, (H20), where n = 2-6, showed that the total association energies varied linearly with n but that the incremental association energies for reaction 4 do not vary in a
(4) regular fashion; the hydrogen bond energies are not additive in this system.28b This latter point was considered in a previous amide-water study20 and is also evident in our work as discussed above. Our calculations model the interaction between two isolated molecules, either a water molecule and an NMA molecule or two NMA molecules. The amide is predicted to form just as strong a hydrogen bond with another amide as it does with a water molecule. However, in order to better represent what occurs in solution, additional solvent and/or clustering effects need to be considered. We define solvent effects as the changes made to the molecular properties of an isolated solute by the solvent. These effects can be modeled, for example, by a reaction field approach.33 Clustering occurs when several molecules interact strongly enough so that they form an identifiable molecular cluster in which the molecular properties of the individual cluster-bound molecules are different from those of isolated molecules. This could be represented either by a solute molecule in a solvent shell for dilute solutions or by a solute cluster embedded in the solvent for high concentrations at which the solute molecules are interacting with each other. For example, a dilute aqueous solution of NMA could have several water molecules hydrogen bonded to an NMA molecule, but it is not yet clear what the local structure about the NMA will be or how the properties of the cluster molecules will change.
To our knowledge, there have been no reported computational investigations of the complete solvent effects for hydrogenbonded amide species. Guo and Karplus have begun to explore clustering effects by looking at a single trans-NMA molecule interacting with two and three water molecule^^^^^^ and by examining a trans-NMA dimer interacting with one to three donor (water, ethyl alcohol, ethylene glycol, trifluoroethanol, and formamide) and/or acceptor (water, formamide, and transNMA) molecules.21 We are currently investigatingboth solvent and clustering effects in amide-water systems. Preliminary results indicate that these effects are significant and necessary to provide a complete understanding of the hydrogen-bonding interactions in these systems.
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