Planar or Nonplanar: What Is the Structure of Urea in Aqueous

J. Phys. Chem. B 2007, 111, 11511-11515

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Planar or Nonplanar: What Is the Structure of Urea in Aqueous Solution? Jose Manuel Hermida-Ramo´ n,*,‡ Anders O 2 hrn,† and Gunnar Karlstro1 m† Department of Theoretical Chemistry, Chemical Center, UniVersity of Lund, P.O.B. 124, S-221 00 Lund, Sweden, Departamento de Quı´mica Fı´sica, Facultade de Quı´mica, UniVersidade de Vigo, Campus Lagoas Marcosende s/n, 36200 Vigo, Spain ReceiVed: May 10, 2007; In Final Form: July 31, 2007

A combined quantum chemical statistical mechanical method has been used to study the solvation of urea in water, with emphasis on the structure of urea. The model system consists of three parts: a Hartree-Fock quantum chemical core, 99 water molecules described with a polarizable force-field, and a dielectric continuum. A free-energy profile along the transition of urea from planar to a nonplanar structure is calculated. This mode in aqueous solution is found to be floppy. That is, the structure of urea in water is not welldefined because the planar to nonplanar transition requires an energy of the order of the thermal energy at room temperature. We discuss the implications of this finding for simulation studies of urea in polar environments like water and proteins.

1. Introduction Urea, CO(NH2)2, is structurally very simple, but it still has remarkable properties, historical as well as chemical ones. When it first was synthesized from an inorganic salt almost 180 years ago,1 it threw the vitalism theory into doubt. A few decades later, the belief that inorganic and organic material were fundamentally different was no longer tenable. From our modern perspective of chemistry nowadays, there still remain unresolved questions about the chemical properties of urea. For example, there are still discussions about the vibrational assignment of urea in aqueous solution.2 Further, the effect urea has on the water structure has attracted a great deal of interest.2-9 The reason is that urea has been shown to possess a denaturing ability on proteins. Some researchers have explained this ability with a “structure breaking effect” of urea on water, which subsequently modifies the important hydrophobic interactions between the different parts of the protein. However, alternative hypotheses exist as well.10,11 Several simulation studies of urea, water, and occasionally some organic material (protein or some simpler hydrophobic model compound) have thus been published.7,12-25 We note also that urea plays a role in the production of different resins26 and barbituric acid.27 There is also a more fundamental question about urea that has not been definitely resolved, which still can be of importance for the studies outlined above. Namely, the structure of urea in an environment, such as water or a protein surface or interior, is not exactly known. Several studies of X-ray28 and neutron diffraction29,30 indicate that there is a planar structure for crystalline urea with a sp2 hybridization of the nitrogen atoms (thus the hydrogen atoms are coplanar with the rest of the molecule). Some early studies31,32 of the infrared and Raman spectra of urea in the solid state and in polar solvents also predict planar structure of urea. On the other hand, a study of the infrared spectra by King33 of urea in an argon matrix suggests that the amino groups have a pyramidal disposition, that is, the hydrogen atoms are not in the same plane as the carbon and * Corresponding author. E-mail: [email protected]. † University of Lund. ‡ Universidade de Vigo.

nitrogen atoms. The same conclusion was reached by the authors of the first structural analysis34 of urea in gas phase using a microwave technique. Finally, theoretical ab initio studies35,36 also find a nonplanar structure for urea in gas phase. Nowadays, it seems generally accepted that urea in gas phase is nonplanar and in a solid state has a planar conformation, with a total of eight hydrogen bonds with six neighbors. However, the conformation of this molecule is not clear when it is solvated in a polar solvent, like water. What structure (or lack of structure) urea has in solution will determine its hydration number and thus possibly also determine its action on proteins through its influence on the hydrophobic interaction. In the present work, we use a combined quantum chemical statistical mechanical method, called QMSTAT,37,38 on a system composed of a quantum chemically described urea molecule surrounded by 99 classically described water molecules. The purpose of this work is to analyze the solvation of urea and through free-energy perturbation calculations gain further insight into the structure of urea in an aqueous medium. To the best of our knowledge, there is only one previous QM/MM study of this system with a similar goal in mind by Ishida et al.22 They represent the water molecules with a simple point charge (SPC)39-like model plus some Lennard-Jones parameters and no polarization; the statistical mechanical problem is solved with the reference interaction site model,40 which is an integral equation approach. Our model includes polarization of the water molecules, uses an exact Monte Carlo simulation to solve the statistical mechanical problem, and further includes a pseudopotential-like operator to model the Pauli repulsion between urea and solvent; this operator (or any equivalent) is not present in the study of Ishida et al. We hence believe that our study can shed further light on the issue of the structure of urea in aqueous solution and also provide some assessment of the previous findings of Ishida et al. 2. Method and Computational Details In the present study, we use a QM/MM method, called QMSTAT. It has been used before in several studies of different systems in ground37,38,41-43 and excited44-47 states. A detailed

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explanation of this model is provided in these papers (see especially refs 37,44), therefore this section will be only a summary of the model. In the model, a quantum chemical part is surrounded by a number of classical solvent (water) molecules, and both these regions are in turn surrounded by a dielectric continuum. The interaction between the classical molecules is described by a NEMO approach,48 and the interaction with the dielectric continuum is given by the image charge approximation.49,50 An effective Hamiltonian operator is constructed for urea Heff ) H0 + Velec + Vind + Vnon-elec

TABLE 1: Parameters for the Urea-Water Systema interaction repulsion field damping dispersion

(1)

where H0 is the Hamiltonian for urea in gas phase, and Velec is the perturbation from the permanent charge distribution of water, represented as a set of point charges. To facilitate the evaluation of the electrostatic interaction between the charge density of urea and the solvent point charges, the urea charge density is multicenter multipole expanded in a set of multipoles (up to quadrupolar order) in several centers in urea. The same expansion is used to evaluate the perturbation from the induced dipoles on water, Vind. Because Vind depends on the charge density of urea, a nonlinear problem is obtained, which is solved with the usual generalized self-consistent reaction field method, that is, through iteration.51,52 In addition to the electrostatic contributions, we also include a nonelectrostatic perturbation, Vnon-elec. It models the effect on urea from the antisymmetry requirements between solvent and solute. This effect can be of importance when the quantum chemical part is allowed to relax. If there is nothing that prevents the charge density of the solute to “escape” into the solvent due to the unshielded charges out there, the calculation runs the risk of excessive polarization, or in the words of Surja´n and A Ä ngya´n, variational distortion.53 For further discussion of this operator, see previous publications. Two additional terms in the solute-solvent interaction are added to the total energy. A dispersion energy that depends on a set of distributed 1/r-6 terms and an extra repulsion term needed to model the very short-range repulsion, where Vnon-elec is not adequate. The latter term depends on the solute-solvent wave function overlap raised to the power of 6. To avoid the occurrence of the polarization catastrophe, the electric field is multiplied by a damping function: (1 - e-(ar))4, where a is a fitted parameter and r is the distance between the quantum and classical sites. The Schro¨dinger equation for the effective Hamiltonian is approximately solved with the Hartree-Fock method using a compact basis of natural orbitals.54 The procedure to build this basis set is described elsewhere.37,38 We only note that the number of natural orbitals in the basis is 32. To construct the basis of orbitals and to obtain the fitted parameters included in the above operators, quantum chemical calculations with an ANO basis set55 have been performed using the MOLCAS package.56 A 10s6p3d basis set contracted to 4s3p2d was used to the description of the oxygen, carbon, and nitrogen atoms, and a 7s3p/3s2p contraction was used for the hydrogen atoms. To obtain the fitted parameters, a total of 61 single-point counterpoise-corrected calculations have been done on the supermolecular surface of the urea-water dimer at the MP2 level of theory. A least-square method is used to get the fitted parameters. They are given in Table 1. The relevant equations for these parameters are available in previous publications. Finally, the statistical mechanical problem is solved with Monte Carlo simulations. One urea molecule is embedded by 99 classically described water molecules, and the whole system is kept inside a spherical dielectric cavity of variable radius. A

parameter

value

d b a DO-H DO-O DC-H DC-O DN-H DN-O DH-H DH-O

-0.61 1.9 0.55 5.5300 24.6441 2.2813 10.1662 5.2626 23.4521 1.3450 5.9939

a The first atom label is the quantum atom, and the second one is the classical atom.

TABLE 2: Most Important Internal Coordinates for the Two Extremes of Ureaa C-O, Å C-N, Å N-C-N, deg O-C-N- Htrans, deg Gas-phase dipole, D Average liquid dipole, D a

Cp

Cnp

1.198 1.358 115.4 180 4.63 5.57

1.194 1.371 114.3 150.9 3.94 4.97

Bond lengths in Å, bond angles and dihedral angles in deg.

number of simulations of different geometries of the urea molecule has been done (vide infra). All simulations consist of 7.5 × 105 Monte Carlo steps for production; before production, the systems have of course been equilibrated. Every 80th step in the production run is collected for subsequent analysis. A total of 9375 configurations have therefore been stored from each simulation. The temperature and pressure in the simulation are 300 K and 1 atm, respectively. 3. Results and Discussion Seven different structures of the urea molecule are separately simulated. The structures are: (i) The optimal Hartree-Fock geometry in gas-phase with the same basis set as above, called Cnp. It is nonplanar. (ii) The optimal Hartree-Fock geometry in gas-phase under the condition that it is planar, called Cp. (iii) Five intermediate structures obtained by linear interpolation between the internal coordinates of the two previous structures. C(t) ) Cp‚(1 - t) + Cnp‚t

(2)

See Table 2 for the most relevant internal coordinates of Cp and Cnp. The values of the transformation parameter, t, are 0.15, 0.3, 0.48, 0.65, and 0.83. Because simulations have been done for all seven structures of urea, we can perform reliable freeenergy perturbation calculations to obtain the free-energy profile along t. We use the original method by Zwanzig,57 which for these small perturbations works very well. That is, G(t ) cn+1) - G(t ) cn) ) - kT ln〈e(U(t)cn)-U(t)cn+1))/kT〉t)cn (3) U(t ) cn) is the energy for transformation parameter t ) cn for a given solvent configuration; the Boltzmann average is estimated by the sampled configurations that belongs to t ) cn. By taking a backward step, that is stepping down the transformation parameter one level, we check that the perturbation is of a reasonable size. In the free energy obtained as above, energy contributions from the intramolecular energy for urea, from the intermolecular interactions between solute and solvent as well as solvent and solvent are included, together with the entropy

Planar or Nonplanar: What Is the Structure of Urea

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Figure 1. Free-energy profile of the different urea geometries along the transformation parameter (see text): at the HF level, calculated with QMSTAT including error bars and calculated with QMSTAT plus intramolecular MP2 correlation also including error bars. The error bars are the maximal error found in the free-energy perturbation, computed by taking the difference between a forward and backward step in the perturbation.

of the intermolecular degrees of freedom. Figure 1 shows the relative stability of the different configurations in gas phase and in solvated phase calculated with QMSTAT. As seen, the freeenergy profile undergoes a large change as urea is put into an aqueous environment. The most stable configuration is that corresponding to a value of 0.15 in the transformation parameter, a geometry quite similar to the planar configuration. However, the free-energy differences between the conformations are very small and are of the order of the maximal error in the perturbation calculation, as seen from the error bars. Consequently, for a Hartree-Fock description of urea in aqueous solution, no distinct structure along the transformation parameter t, exists. This mode is floppy. To study this mode in further detail and see if the above conclusion is maintained, we make two further types of calculations. First, it is possible to object that the linear interpolation covers a too small space of the urea conformation space; maybe there is a distinct minimum outside this line? A larger dipole moment will be favored by the solvent, and because the favorable increase in solute-solvent interaction initially will outweigh the unfavorable increase in intramolecular energy, we expect this to happen even more than already is the case along the transformation from nonplanar to planar (see Table 2 for dipole moments in t ) 0 and t ) 1). We therefore select the two minimum points, t ) 0.15 and t ) 0.83, and optimize the free energy with respect to the C-O and C-N bond distances, which we expect have the greatest impact on the dipole. We find a local minimum for both transition parameter values at 0.016 and -0.010 Å for the C-O and C-N bond distances, respectively; the free energies are respectively lowered by 1.61 and 1.57 kJ/mol for the two points. For the more stable structure at t ) 0.15, the average dipole moment increases to 5.81 D. From these results, we see that there certainly is some additional free energy to gain by relaxing the other internal coordinates of urea. However, it is less than the free-energy differences along t, which is roughly 6 kJ/mol, and further, it is nearly equal in magnitude in the two selected points t ) 0.15 and t ) 0.83. Thus, we conclude that the profile in Figure 1 is a good representation of the relative free-energy difference in the Hartree-Fock description along a mode that takes urea from a nonplanar to a planar structure. Second, it is reasonable to inquire whether the Hartree-Fock method is accurate enough.

Figure 2. Selected pair correlation functions in arbitrary units as a function of interatomic distance. Labels denote the quantum atom first, the solvent atom second. The solid line is for t ) 0.15, the dashed for t ) 0.83.

It should first be stated that QMSTAT requires a correct response density, which is much harder to obtain from a nonvariational method like second-order perturbation MøllerPlesset (MP2),58 than from the variational Hartree-Fock. Still, we can add a MP2 correction to the intramolecular energy along the transformation parameter. A free-energy profile with the intramolecular Hartree-Fock energy substituted with the intramolecular MP2 energy is also shown in Figure 1. This correction has a greater impact, and the nonplanar structures becomes more probable. However, the differences are still small. The two extremes are separated by slightly more than 2.5 kJ/ mol, which is of the order of kT at room temperature. Hence, even with this approximate MP2 correction added, the conclusion remains that the planar-to-nonplanar mode is floppy. To study the urea solvation structure, radial distribution functions, g(r), have been obtained from the simulations. In Figure 2 are some selected atom pair distribution functions for urea plotted; t is 0.15 or 0.83. The two hydrogen atoms on urea, which are placed in a trans position relative to the oxygen atom in the planar form, are denoted by Htrans, and the other two are denoted Hcis. Parts a and b of Figure 2 show the radial distribution around the oxygen atom in urea for both transformation parameters. The curves clearly show that there is hydrogen bonding to the carbonyl oxygen. On average, there are two water molecules in the first peak in Figure 2a,b. Figure 2c shows the distribution around the nitrogen atoms in urea for both values of the transformation parameter. There could be hydrogen bonding to this atom as well, but the distribution shows no sign of this, not even in the nonplanar structure, where presumably the nitrogen lone pairs become more concentrated on one side. Parts d and e of Figure 2 show the distribution around the two types of hydrogen atoms in urea. These are the distribution functions that show the greatest difference between the two simulations, but still no major differences. A slight accumulation of solvent oxygen atoms is seen, hence there is a weak hydrogen bonding to this side of urea. The total number

11514 J. Phys. Chem. B, Vol. 111, No. 39, 2007 of solvent molecules coordinated to urea (that is, in contact with the solute) is around 5.1 for the nonplanar structure and increases slightly to 5.5 for the planar one. Previous studies also find the peak of the urea oxygen-water hydrogen distribution around 2 Å, including experiment.19-22,59 Our peak is located at a separation slightly above 2 Å, while most previous studies find it at separations slightly below 2 Å. Dielectric relaxation experiments have been used to study the dipole moment and hydration number.60-63 To start with the latter, it is important to recognize the difference between hydration and coordination number. The former contains dynamical information, while the latter is mainly geometrical. The hydration number is found to be in the range of two. This is interpreted as a sign of two strongly bound water molecules to urea. Together with our results, this would suggest that the water molecules hydrogen bonded to the carbonyl oxygen atom are “strongly bound” from the perspective of dielectric relaxation experiments. The dipole moment of a molecule in solution is not an observable and hence not perfectly defined. The dipole a dielectric experiment measures is instead some effective dipole. It means that it can be the dipole of a larger complex, including some solvent molecules, which is measured.64 Therefore, the reported values for the dipole from the dielectric relaxation experiments (from 6.1 to 7.9 D) should be considered with some care; the fact that they are larger than our dipoles for urea in aqueous solution does not prove our simulations to be false. We note also that some combined experimental and theoretical estimates of the dipole moment of hydrogen-bonded urea in crystals are lower.65,66 Finally, we make comparisons with the previous study by Ishida et al.22 To start with, we should stress that the goal of our study and that of Ishida et al. differs slightly. We have used an accurate method to obtain a free-energy profile for a limited number of nuclear degrees of freedom for urea to evaluate the character of the planar-to-nonplanar mode; Ishida et al. have used a computationally less demanding method to make a freeenergy optimization of all nuclear degrees of freedom of urea to thus obtain the average structure of urea in solution. They find that a nonplanar structure is the average structure, and in this respect our results do not contradict each other because also our limited optimizations do not find the planar structure to be the dominant structure. Exactly which structure is the freeenergy optimum with our model is not determined, though, hence our study does not confirm the average structure of Ishida et al. There are two connected differences between our results. It is with respect to the dipole moment of urea in aqueous solution as well as the solvation structure. The gas-phase structure and dipole moment of Ishida et al. and the present study are very similar. But in solution, they obtain larger dipole moments than we do in this study. Presumably, the strong interactions, which follow from this high polarity, are the reason for the high coordination to the carbonyl oxygen, which Ishida et al. compute to 3.16. They suggest a physical explanation of the high coordination based on the hemispherical shape of the potential nearby the carbonyl oxygen. But as noted above, our quantum chemical methods give similar results in gas phase. More likely, the difference is thus found in the solute-solvent interaction and possibly in the statistical mechanical method. The large dipole could be an effect of the kind of excessive polarization that was discussed in the model section. Using diffuse basis sets for the solute, and a point-charge solvent model, can cause the density to “escape” into Pauli forbidden regions. Too-large dipole moments of the solute would then be obtained. There are other possibilities to explain the differences. For example, the relative strength of the solute-solvent and

Hermida-Ramo´n et al. the solvent-solvent interactions can be different on account of the different water models; this would lead to a different effective strength of the urea-water interaction. 4. Conclusions Our study of the free-energy profile for a planar-to-nonplanar mode in urea in aqueous solution shows that this is a floppy mode. That is, the thermal energy available at room temperature is of equal magnitude to all the free-energy differences between the different structures studied in this work. This means, in turn, that urea cannot be said to have one structure. In other words, the internal contributions to the entropy can be of importance. The question in the title is thus not exhaustive: urea is neither planar nor nonplanar in aqueous solution. Does this invalidate previous simulations, which have used a rigid structure of urea? Not necessarily. Force-fields greatly simplify the representation of molecular properties. The different energy terms will contain errors and the performance of a forcefield will rely on some cancellation of errors, which experience has shown can be managed quite well through parametrization; cancellations between repulsion and polarization is one such example.67 The structure can thus be considered as just another variable with some errors that cancel elsewhere in the model. The final result would then be a simulation that describes certain properties of the urea-water system very well. But it is possible to image situations where the flexibility of the planar-to-nonplanar mode can be of such importance that cancellation of errors is unsatisfactory. Because the flexibility is induced by the aqueous environment, it is obvious that a modification of the environment would in turn modify the flexibility. From our work, the formulation of the hypothesis that urea may assume a fixed structure (or at least much less flexible) as it approaches a nonpolar surface, such as a protein, seems justified. If there is any truth in that hypothesis, or whether the environment dependency of the flexibility is a property that is of relevance for the unresolved properties of urea outlined in the introduction, is left unanswered by the present study. Acknowledgment. J.M.H.-R. thanks the “Xunta de Galicia” for financial support as a researcher in the “Isidro Parga Pondal” program. A.O ¨ . and G.K. acknowledge financial support from the Swedish Research Council within the Linne´-project Organizing Molecular Matter. References and Notes (1) Wo¨hler, F. AdV. Chem. Phys. 1828, 12, 253. (2) Idrissi, A. Spectrochim. Acta, Part A 2005, 61, 1. (3) Creighton, T. E. Proteins: Structures and Molecular Properties, 2nd ed.; W. H. Freeman: New York, 1993. (4) Wetlaufer, D. B.; Coffin, R. L.; Malik, S. K.; Stoller, L. J. Am. Chem. Soc. 1964, 86, 508. (5) Brandts, J. F.; Hunt, L. J. J. Am. Chem. Soc. 1967, 89, 4826. (6) Frank, H. S.; Franks, J. J. Chem. Phys. 1968, 48, 4746. (7) Kuharski, R. A.; Rossky, P. J. J. Am. Chem. Soc. 1984, 106, 5786. (8) Tirado-Rives, J.; Orozco, M.; Jorgensen, W. Biochemistry 1997, 36, 7313. (9) Caballero-Herrera, A.; Nilsson, L. J. Mol. Struct. (THEOCHEM) 2006, 758, 139. (10) Tobi, D.; Elber, R.; Thirumalai, D. Biopolymers 2003, 68, 359. (11) Klimov, D. K.; Straub, J. E.; Thirumalai, D. Proc. Natl. Acad. Sci. U.S.A. 2004, 101, 14760. (12) Smith, L. J.; Berendsen, H. J. C.; van Gunsteren, W. F. J. Phys. Chem. B 2004, 108, 1065. (13) Ostenbrink, C.; van Gunsteren, W. F. Phys. Chem. Chem. Phys. 2005, 7, 53. (14) Lee, M.-E.; van der Vegt, N. F. A. J. Am. Chem. Soc. 2006, 128, 4949.

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