1. Introduction

The investigations on safe solvents that protect ecosystems nowadays have paved the way to the synthesis in 2001 by Abbott and coworkers [1-2] of novel mediums called deep eutectic solvents (DES) or low temperature transition mixtures (LTTM). Since then, these solvents have gained great interest and continuing research is done on their development and the understanding of the physical and chemical properties that they display. They are liquid over a certain range of temperatures, have negligible volatility as compared to traditional solvents such as organic solvents and show good thermal stability and electrical conductivity. As such, they are candidates for reaction mediums in the fields of material science, electrochemistry and biochemistry [3-7]. These important fields of application of DESs require that their geometric structures and their electronic charge distributions as well as their physico-chemical properties be well defined in order to offer optimal conditions for their use.

A deep eutectic solvent (DES) is defined as a mixture of two or more components which has a temperature of its eutectic point significantly below that of its ideal mixture. Studies done on the solid-liquid phase diagrams have shown that such mixtures present negative deviation from ideality at their eutectic point with specific ratio of the components and are liquid at operating temperatures over a certain range of composition [2,8-9]. They are mainly mixtures of Lewis or Bronsted acids and bases, which may be neutral or ionic. DESs that do not contain metal ions or metal free DES [10] are well established and an example of this category of solvents is the mixture of choline chloride and urea in a 1:2 ratio. This solvent contains a quaternary ammonium salt and urea as interacting agents. It is argued that the lowering of the eutectic point below the ideal one is due to interaction between the species through H-bonding so that the preparation of these solvents implies appropriate selection of the H-bond donor and acceptor.

For the particular case of the metal-free DES made of choline chloride (ChCl) and urea (U), several experimental and theoretical studies have been done in attempts to characterize it and to understand its properties. Abbot and al. [2] have studied the phase diagram constructed from measurements of freezing points and showed that the eutectic point of the solution has a temperature of 12°C with a composition of 1:2 ratio of respectively choline chloride and urea. At this composition, the mixture is referred to as reline. By using DSC technique, Morrisson et al. [11] have obtained an eutectic point of 17°C and a similar composition of the mixture. Later on, Meng and coworkers [12] have done a more extensive study on the phase diagram of this DES by measuring the melting point of different mixtures containing known amounts of water via DSC and optical microscopy techniques. Their results indicate that the presence of water greatly influences the interactions between the two components and therefore the physico-chemical properties of the DES. At the eutectic composition ratio of Abbot and al., their measured melting temperature was 25°C. The difference in the various measured eutectic temperatures is explained by the presence of water in the DES, as the constituents are hygroscopic. Water induces formation of new interactions with the polar constituents and therefore affects the density, viscosity and electrical conductivity of the mixture. These authors suggested that properties of DESs be measured on water free samples. The formation of H-bond in water free mixtures has been suggested from the liquid phase neutron diffraction measurements of isotopically substituted samples by Hammond et al. [13] and the IR and NMR investigations of Perkins et al. [14-15]. Ashworth et al. [16] have done a theoretical study of pairwise interactions between the constituents and of clusters of Cl^- with urea. This extensive work on conformers of pairs of species by DFT has revealed a network of H-bonding within the pairs of neutral and ionic species. They calculated interaction energies of these conformers in order to understand the basis of the H-bond formation. In this interesting analysis of the interactions of pairs of fragments of the DES, geometries and charge distributions have not been detailed to link the structures to the observed H-bonding. The present work is a continuation of the study on the interactions between choline chloride and urea based on model systems composed of several ratios of these constituents. We report calculated geometrical structures of urea, choline chloride and their associated compounds. We search for the gas phase optimal geometries and charge distributions of the constituents and the model compounds of reline that would enlighten our understanding of their structural, bonding and physico-chemical properties.

2. Computational Methodology

The work consists of a DFT [17] study of the geometries, energies and electronic structures of the fragments choline chloride and urea as well as those of their successive associations to form model compounds of reline. The GaussView06 software [18] was used to construct and visualize the various systems. Then optimized geometrical parameters, energies and charge distributions were carried out by the Gaussian 09 software package [19] by using the gradient corrected hybrid functional BYL3P [17] along with the standard 6-31+G(d,p) basis set which is a split valence band basis with polarization and diffuse functions to well describe bond formation and charge delocalization. No symmetry constraints were maintained during the optimization of the compounds. Vibrational frequencies were calculated at each optimized structure to characterize it as a minimum. The total energies are all ZPE corrected. The mechanism of charge delocalization through bonds in these systems was studied by performing NBO calculations on the optimized structures with the NBO codes provided by the Gaussian 09 package. Atomic charges were also calculated by using the NBO subroutine. The covalent nature of the bonds was analyzed by calculating Wiberg bond indices in the optimized species.

3. Results and Discussion

3.1. Geometries and Energies

The model compounds of the DES reline were investigated by starting with a search of the minimum structures of the fragments urea and choline chloride. Table 1-3 contain respectively the energies and optimized geometrical parameters of urea CO(NH₂)₂ (or U)_, its dimers, the choline cation [(CH₃)₃N(CH₂)₂OH]⁺ (or Ch⁺), choline chloride [(CH₃)₃N(CH₂)₂OH]Cl (or ChCl) and experimental results on urea. Figure 1-3 display their respective optimized structures.

a. Urea monomers and dimers

The equilibrium structure of urea is basis set dependent and our results in Table 1 and Figure 1a-c indicate that the conformation of C2 symmetry is its stationary structure while the others of C2V and Cs symmetries are respectively second and first order saddle points. The dihedral angles OCN₃H₄, OCN₃H₅ and N₆CN₃H₄ in the C2 minimal energy conformer have respective values of 11.8°, 152.3° and -168.2°. These parameters along with the calculated bond lengths and bond angles reproduce quite well the microwave results of Godfrey and al. [20] as well as the gas phase data obtained at the MP2/6-31G(d, p) and MP2/6-311G(d,p) by Raptis and coworkers [21]. This attests of the good quality of the basis set used in our approach. Oher experimental geometries of urea from neutron diffraction and X-rays analysis gave a planar structure with C-O and C-N bond lengths of 1.265Å and 1.349 Å respectively [22-24]. This CO bond length obtained in solid state is longer than our calculated gas phase value and may be due to intermolecular interactions. The structures of dimers of urea have been also explored and are shown on figure 1.d-f. They are true minima and the interaction energies, which range from -50.6 to -37.8 kJ.mol^-1 indicate that they are stable gas phase structures. One may notice that the interactions between two urea molecules cause elongation of the C-O and N-H bonds and opening of the C-N-H angles of interacting groups. The structural arrangements of these dimers in figure 1d-f well illustrate the proton donor and acceptor ability of urea through its N-H bonds and the lone pairs of electrons on its N and O atoms. One therefore expects urea to play a central role in the formation of compounds with choline chloride.

Table 1. Energies and geometries of optimized urea monomers and dimers

Torsional angles: OCN₃H₄ =0.0° and OCN₃H₅ =180.0° for urea C_2V;

Torsional angle: OCN₃H₄=11.836°and OCN₃H₅ =152.325°; N₆CN₃H₄ = -168.2 for urea C2

Torsional angle: OCN₃H₄= 164.594° and OCN₃H₅= 12.461° for urea Cs

Dimers:

- Conf 1 : d_O6---H13 = d_O14---H8 =1.859 Å

- Conf 2 : d_N3—H13 = 2.158Å; d_O14----H4 =1.990Å; d_O14----H7 = 2.708Å

- Conf 3 : d_N2---H13 =2.159 Å; d_O14---H4 = 2.676 Å; d_O14---H7 = 1.993 Å

Figure 1. Optimized structures of urea monomers and dimers

b. Choline cation and model compounds of choline chloride

Choline cation Ch⁺

Three conformations of the equilibrium structures of the choline cation noted Trans T1, Gauche G1 and Gauche G2 are found in our work and are pictured in Figure 2. The Trans conformer T2 with OH rotated is a first order saddle point. Table 2 presents their geometries and energies. The notation Trans and Gauche is related to the position of the C-O and C-N bonds with respect to the ethyl C-C chain. These conformational isomers differ also by the N-C-C-O torsional angle, which is 58.2° in the Gauche but 180° in the Trans suggesting that the C-N and C-O bonds are coplanar in the Trans isomers. The gauche conformers G1 and G2 are lower in energy and are found here as mirror images of one another as indicated by the opposite values of the dihedral angles C-N-C-C, C-C-O-H and N-C-C-O. The results for the bond length C-O (1.415-1.419Å), C-N (1.510-1.534 Å), C-C (1.523-1.534 Å), O-H (0.967 Å) and C-H (1.087-1.098 Å) and those of the bond angles obtained in these minimum structures are typical of standard organic compounds.

Table 2. Energies and geometries of optimized choline cation monomers

Figure 2. Optimized structures of Conformers of the cholinium cation

Choline chloride ChCl

Addition of the chloride ion by positioning it at different locations around the Ch⁺ cation of Trans and Gauche conformations has given five (5) minimum energy model compounds of choline chloride of each conformer noted T1a-e and G1a-e. Table 3 gives their geometrical parameters, energies, and figure 3 displays the minimum structures. These equilibrium structures of the choline chloride agree with the theoretical B3PYP/6-311+G(d, p) results of Ashworth and coworkers [16]. However, our study revealed two more minimum energy structures noted T1d and T1e. These conformational isomers of choline chloride are very close in energy and the most stable conformer G1a lies 40.288 kJ.mol^-1 below the least stable T1e. The position of Cl^- relative to the choline cation is crucial in the stabilization of each of these systems. As the geometrical parameters indicate, the most stable compounds are those where Cl^- interacts with the hydroxyl group along with its closed approach to H atoms of the methyl or ethyl groups. The closest d_OH---Cl distances are 2.079Å for G1a, 2.222 Å for G1b and 2.335Å for T1a. These OH---Cl interactions cause distortion of the dihedral angle N-C-C-O. In all these ten (10) structures, Cl^- sits at locations where it interacts closely with at least 3H atoms of the choline cation, causing the lengthening of the C-H and O-H bonds of the methyl, the ethyl and the hydroxyl groups relative to those found in the choline cation. However, contraction of the C-O bonds is observed where Cl---HO interactions occur. The reported B3LYP/6-31+G(d,p) value of 2.391 Å for CH_meth----Cl in choline chloride of Cs symmetry of Davis and coworkers [25] correlates well with the present values for T1b, T1c and G1e of C1 symmetry. The interaction energies of Cl^- with Ch⁺ are respectively -392.6 and -396.4 kJ.mol^-1 for the most stable compounds T1a and G1a (Table 6). As pointed out by other authors [26], these values are typical for gas phase ionic salts containing organic cations and have mainly coulombic contribution. Intramolecular interactions also exist within the choline cation involving its oxygen atom and surrounding nearest H atoms.as indicated by the O---H distances varying from 2.02 to 2.52Å.

Table 3. Energies and geometries of optimized choline chloride monomers (a)

Figure 3. Optimized structures of conformers of choline chloride

c. Model compounds of choline chloride and urea

Systems of one urea and one choline chloride

The present work explored several positions of one molecule of urea around the previous structures of choline chloride and this gave several model systems very close in energy. The conformers T1a and G1a, led to many minimal structures among which were the four most stable ones noted T1a-1, T1a-2, G1a-1 and G1a-2 shown in figure 4. Table 4 contains their ZPE corrected energies and geometrical parameters. The main NCCO backbone of Ch⁺ is retained. However, a main change occurs on the T1a-2 structure where the torsional N-C-C-O angle approaches that of the gauche conformers (-50.6° instead of -155.4° in T1a). One may also observe that urea assures a perfect link to each of the two ions by interacting with them via either its carbonyl or its amino end. The choline cation is associated to Cl^- through at least three H atoms and to urea by one or two H atoms. The pairwise interactions of the three fragments occur therefore through the H atoms. In the two lowest energy structures T1a-2 and G1a-2 for instance, one observes CO_ur---HO and CN_ur---HO respective close approach of 1.93Å and 1.91Å. The data in Table 6 show that the attachment energies of urea to choline chloride (DE) are respectively -70.631 and -59.972 kJ.mol^-1 for T1a-2 and G1a-2. The higher absolute value for T1a-2 may be due to the observed change in conformation.

Table 4. Energies and geometries of optimized systems of choline chloride and 1 urea

Figure 4. Optimized conformers of 1:1 complexes of choline chloride and urea

Systems of two urea molecules and one choline chloride

Experimental studies suggest that choline chloride and urea combine to form a complex of 1:2 ratio, used in liquid form as a green solvent for several purposes. We have therefore modelled this system and explored potential locations for H-bonding of urea with T1a-2 and G1a-2. Many optimized systems with positive vibrational frequencies were obtained and the two most stable in energy are displayed in Figure 5a-b. This shows that the first molecule of urea (by following the numbering of the atoms) interacts with the hydroxyl group of the choline cation Ch⁺ while the second urea is connected to it and Cl^-. The chain of fragments is closed by the interaction of Cl^- with three H atoms of the methyl groups of Ch⁺. These resulting two minimal structures of lowest energy formed from T1a-2 and G1a-2 with one additional urea molecule are mirror images as indicated by the NCCO, CO_ur2---CO_ur1 and OC_ur2---Cl---N_Ch torsional angles in Table 5. As previously noted, the Trans T1a conformer of choline chloride adopts a gauche conformation upon addition of a urea molecule (T1a-2). This may also result from the presence of the two mirror images G1 and G2 of the gauche choline cation shown earlier in Figure 2. All the traditional C-C, C-N, C-O and C-H bonds are equivalent in both structures. Interestingly, one may notice that H-bonding imposes the four fragments to interact in such a manner that the entire model has a « wheel » form. We found a third conformer pictured in Figure 5c lying just 6.59 kJ.mol^-1 above the two lowest energy structures and which has a geometry where Cl^- is « sandwiched » by the urea molecules and the choline cation through the NH and CH bonds with a C=O---OH link between Ch⁺ and one molecule of urea. The association energy of the second urea molecule to T1a-2 and G1a-2 are respectively -71.377 and -61.397 kJ.mol^-1 for the two most stable models of the DES and are very close to the previous ones of the 1:1 ratio model systems (Table 6).

Figure 5. Choline chloride complexes with 2 ureas

Table 5. Energies and geometries of optimized systems of choline chloride with 2 or 3 ureas (a)

Table 6. Reactions energies and quantum chemical parameters

Systems of three urea molecules and one choline chloride

To further our understanding of the composition of the solvent, the present study has also considered the 1:3 ratio model systems of choline chloride and urea by starting with the minimal energy structure of Fig.5b obtained from G1a-2. The reactions are also exoergic and Figure 6a-b show the two lowest minimum energy models. The geometry of the most energetically stable conformer (Figure 6a) shows an arrangement in which two of the urea molecules still interact with the choline cation. The third urea tends to form a second shell of urea molecules around choline chloride. In the second model compound, the third urea is just between the two formers, maintaining the « wheel » form. One therefore observes that in each of these two model compounds, the four main components of the solvent, that is, the choline cation Ch⁺, the chloride anion and two urea molecules remain in contact through H-bonding. These interactions of choline chloride with urea preserve the 1:2 ratio of these constituents in the solvent.

Figure 6. Choline chloride complexes with 3 ureas

3.2. Charge Distributions

a. Atomic charge

In the natural atomic orbital (NAO) basis, the natural population on an atom (A) is the sum over all contributing NAOs of the natural population q_i(A) of orbital φ_i(A). The difference between its atomic number and its natural population is its atomic charge Q(A). According to the Pauli principle, 0 ≤ q_i(A) ≤ 2. Table 7 displays the calculated atomic charges given by the present analysis. One may note the negative charge carried by the carbon atoms of the choline cation and which increases upon addition of Cl^- and urea due to the interactions. The results also indicate the charges on the electronegative elements N and O, which follow the same trend as the carbon atoms. Concurrently, there is a decrease in charge on the chlorine atom from -1.0 a.u to -0.856 au in the most stable 1:2 ratio model system. The H atoms are all polarized and those of the methyl groups nearest to the chloride ion have up to +0.305 au in the most stable model of reline.

Table 7. Atomic charges (in u.a) of the most stable compounds

b. Natural bond orbital (NBO) analysis

Natural bond orbitals (NBO) are localized orbitals constructed from natural atomic orbitals (NAO) and well describe the electron distribution in chemical substances. One often uses NBO analysis [27] to understand intra and intermolecular electronic charge transfer from occupied NBOs of an electron donor group into vacant ones of an acceptor. The second order perturbation energy E⁽²⁾ given by the analysis of the Fock matrix in the NBO basis provides an estimation of the strength of the interactions that lead to the charge delocalization and is expressed as:

(1)

F_ij, are Fock matrix elements, E_i and E_j are the NBO energies and q_i is the donor NBO occupancy. Table 8 presents the results of an NBO analysis with E⁽²⁾ ≥ 2 kcal.mol^-1 of the most stable model of the mixture containing ChCl and two molecules of urea. The data suggest that the interactions intra and inter fragments involve occupied C-H, N-H, O-H, C-O and C-N bonds, lone pairs on O, N and Cl with vacant antibonding C-C, C-H, C-O, N-C, N-H, and Rydberg orbitals of C atoms. The data also indicate that Cl^- interacts with Ch⁺ and the nearest urea U₂ through its lone pairs. Clearly, three C-H and two N-H empty acceptor orbitals receive electronic charge. The same observation is made of donor NBOs of the carbonyl group of urea U₂ with two vacant σ^*(N-H) of urea U₁ as well as for the donor lone pair LP(O) of U₁ with the empty σ^*(O-H) of Ch⁺. The stronger charge transfers of 10 to 60 kcal.mol^-1are mainly observed between the lone pairs of N, O and Cl with vacant antibonding NBOs that show some occupancy. The interactions through bonds contribute therefore to spread the electronic charge within the system and to stabilize it.

Table 8. Second order perturbation energy E(2) in kcal.mol-1 for the most important charge transfer interactions in the most stable model of choline chloride plus two urea (E(2) ≥ 2 kcal.mol-1)

c. Wiberg bond indices

The NBO analysis also provide Wiberg bond indices, which give estimates of the bond orders between pairs of atoms. Table 9-11 list these data for pure urea (C2), the conformers G1, G2 and T1 of the choline cation and of the most stable model of reline. They show that the formal covalent C-O, C-N, C-C, C-H, N-H and O-H bonds have calculated bond orders ranging from 1.6 for C=O in pure urea to 0.6 for O-H in the model of reline. It is important to note the formation of partial covalent bonds between the four fragments of the model of reline. The highest bond orders between H-bond acceptors and donors are respectively 0.0947 for C=O---H-O, 0.0541 and 0.0531 for Cl---H-N, 0.031, 0.0246 and 0.0236 for Cl---H-C and 0.0289, 0.0285 for C=O---H-N. One may also observe that these H-bonds join the pairs of fragments urea₁/Ch⁺, Cl^-/ urea₂, Cl^-/Ch⁺ and urea₁/urea₂. Even though these values of the calculated bond orders may contain errors, they correlate well with the strength of the through bond interactions presented in table 8. They may also explain the depletion of charge on the H atoms and the increase in charge on the C, N and O atoms involved in these H-bonds shown in table 7. The data show that the spread of the electronic charge in the compounds induces bond order between pairs of distant atoms. The bond orders also indicate that five closest H atoms of urea and Ch⁺ surround Cl^-. As expected, urea plays the double role of H-bond donor and acceptor in the formation of the DES.

Table 9. Wiberg bond Indices in the urea molecule (C2)

Table 10. Wiberg bond indices in the cholinium cation Gauche and Trans (C1)

Table 11. Wiberg bond Indices in choline chloride G1a et T1a plus 2 urea molecules (C1)

3.3. Quantum Chemical Parameters of the Model Compounds

The electronic chemical potential µ, the electronegativity χ, the chemical hardness η and the global electrophilicity index ω of the model compounds were determined in our study from the energies of the frontier orbitals E_HOMO and E_LUMO using the following expressions as suggested by other authors [28-30].

(2)

(3)

(4)

Electronic charge flows naturally from a substance of higher chemical potential to another of lower chemical potential or from an electron donor to an acceptor, which, beside this property has higher electronegativity and higher index of electrophilicity. Table 6 presents the calculated quantum chemical parameters. The choline cation has the lowest chemical potential (-8.0 eV for the conformer Gauche) compared to urea (-3.834 eV) and Cl^- (-2.562 eV). This favors the formation of choline chloride and its subsequent compounds with urea. Upon addition of two urea molecules, there is a notable decrease in the electrophilicity index of the mixture from that of the cation. However, this index starts to increase with the addition of a third molecule of urea and this may explain the combination ratio of 1:2 of choline chloride and urea in the solvent.

4. Conclusions

We report Density Functional Theory calculations for urea, Cl^-, the choline cation, choline chloride and model compounds of the DES reline that may result from their association. The total ZPE corrected energies; detailed structural parameters, interaction energies, charge distribution and some quantum chemical parameters of all these systems are presented. Our results predict minimum energy structures for the DES in which partial covalent H-bonds link the ions and the molecules of urea in accord with previous work. Our study reveals the presence in the model solvent of H-bonds of the type C=O---H-O, Cl---H-N, Cl---H-C and C=O---H-N that result from the interactions of the fragments. Formation of these H-bonds maximizes the intra and intermolecular interactions and stabilize the system. Our data do not show evidence of a specific speciation of Cl^- with urea although such geometries may minimize coulombic interactions. Our calculated quantum chemical parameters and the geometrical arrangement of the fragments in the model compounds also predict the 1:2 ratio in which choline chloride and urea combine in the DES.

ACKNOWLEDGEMENTS

The authors are grateful to Pr Jean-Marc Sotiropoulos at the CNRS of Pau in France for his contribution to this work.

Supplementary Material

Supplementary material choline chloride and urea compounds