The hydrogen bond interaction between CH3CHO, CH2FCHO, and CH3CFO and two water molecules is investigated at the B3LYP/6-311++G(d,p) level. The results are compared with the complexes involving the same carbonyl derivatives and one water molecule. The calculations involve the optimization of the structure, the harmonic vibrational frequencies, and relevant NBO (natural bond orbital) parameters such as the NBO charges, the occupation of antibonding orbitals, and intra- and intermolecular hyperconjugation energies. Two stable cyclic structures are predicted. The two structures are stabilized by C=OHO hydrogen bond. The A structures are further stabilized by CHO bond involving the CH3 (CH2F) group. This bond results in an elongation of the CH bond and red shift of the ν(CH) vibration. The B structures are stabilized by CHO interaction involving the aldehydic CH bond. The formation of this bond results in a marked contraction of the CH bond and blue shift of the ν(CH) vibration indicating the predominance of the lone pair effect in determining the CH distances. The total interaction energies range from −12.40 to −13.50 kcal mol−1. The cooperative energies calculated at the trimer geometry are comprised between −2.30 and −2.60 kcal mol−1.

1. Introduction

Cooperative interactions involving three or more molecules are an important component of intermolecular interactions, particularly those involving hydrogen bonds. The cooperativity of hydrogen bonds plays an important role in controlling and regulating the processes in living materials. This has been recognized since a long time and quantitative aspects of cooperativity have been discussed [17]. Cooperativity can be positive or negative. It has been shown that a first hydrogen bond involving a given site of a molecule weakens the reactivity of the neighboring sites of the same nature whereas it enhances the electron donor power of the adjacent sites of opposite nature [4]. Cooperativity between water molecules is particularly important, because in liquid water at room temperature, the great majority of the molecules are hydrogen-bonded to each other, the concentration of “free” OH groups being very low [8]. For this reason, extensive theoretical calculations have been carried out on the cooperativity in water [913]. In recent works, the interaction between proton acceptors (or donors) and two (or more) water molecules has been discussed [1421].

In a recent work [22], the complexes between acetaldehyde and some of its monofluorinated derivatives and one water molecule have been investigated by theoretical methods. It was shown in this work that water acts as a proton donor toward the C=O bond forming C=OHO hydrogen bonds but that water can also act as a proton acceptor forming weak CHO hydrogen bonds. It seemed to us interesting to investigate the interaction between some of these carbonyl derivatives (CH3CHO, CH2FCHO, and CH3CFO) and two water molecules in order to discuss the effect of cooperativity in these hydrogen-bonded systems. To the best of our knowledge, no experimental data are available for these systems.

This paper is arranged as follows. The first step of our study deals with the structure of the complexes. In the second section, the intramolecular distances, some vibrational frequencies and the results of a natural bond orbital (NBO) analysis are discussed. A special attention is paid to the NBO charges, occupation of antibonding orbitals, and hyperconjugation energies. In the last section, the cooperative energies are discussed.

2. Computational Methods

Calulations of the properties of CH3CHO, CH2FCHO, and CH3CFO, complexed with two water molecules were carried out using the density functional B3LYP method [23] and the Gaussian suite of programs [24]. The basis set 6-311++G(d, p) was invoked. The second-order Mǿller-Plesset MP2/aug-cc-PVTZ method was also used to calculate some of the structures or binding energies. The computed interaction energies were corrected for the basis superposition error (BSSE) [25].

The cooperativity in a molecular trimer containing A, B, and C molecules is given by the three-body term Δ𝐸coop which can be defined as the difference between the total interaction energy 𝐸int(ABC) and the sum of the pairwise or two-body interaction energies 𝐸2(AB), 𝐸2 (BC), 𝐸2 (AC). Δ𝐸coop=𝐸int(ABC)𝐸2(AB)𝐸2(BC)𝐸2(AC).(1) Here, the 𝐸2 values correspond to the two-body contributions at the trimer geometry [2628] calculated with the same basis set.

The harmonic vibrational frequencies were calculated to characterize the stationary points. No scaling factor was used. The charges on individual atoms, orbital occupancies, and hyperconjugation energies were obtained by an NBO analysis [29].

3. Results and Discussion

3.1. Structure of the Complexes between CH3CHO, CH2FCHO, and CH3CFO with Two Water Molecules

Figure 1 illustrates the structure of the 1-2 complexes between CH3CHO, CH2CHO, and CH3CFO with two water molecules calculated with the B3LYP functional. The distances calculated with the MP2 method are somewhat shorter. The structure of the complexes with one water molecule taken from a previous work [22] is shown for the comparison. As shown in this work, the 1-1 complexes are characterized by two stable structures. In both A and B structures, the molecules are held together by a C=OHO hydrogen bond. The A complexes are cyclic and stabilized by a weak C4H5O interaction and they are slightly more stable than the B complexes. These structures have been established by considering the intermolecular H5O distances and some NBO parameters such as the weak intermolecular charge transfer from the O atom of water to the 𝜎*(C4H5) orbital. In none of the 1-1 complexes the C1H3 bond was involved in the formation of a cyclic structure. Let us notice that CH3CFO is also able to form a cyclic complex with two water molecules, one of the OH bonds of the water dimer being bonded to the F atom. This complex will not be considered here.

In none of the 1-2 complexes the second water molecule is bonded to the second electron pair of the carbonyl O atom. This structure is anticooperative, both electron donor sites having the same nature [4]. As shown in Figure 1, the intermolecular C=OHO distances are shortened with respect to their values in the 1-1 complexes by amounts ranging from 0.081 to 0.109 Å. Further, the O9…H11 distances ranging from 1.840 to 1.866 Å are shorter than in the water dimer (1.933 Å). The most spectacular indication of a positive cooperativity is the shortening of the H5O distances by 0.212 Å in CH3CHO (A1-2), 0.585 Å in CH2FCHO (A1-2), and 0.194 Å in CH3CFO (A1-2). The short H3O distances of 2.319 Å in CH3CHO (B1-2), and 2.255 Å in CH2FCHO(B1-2) also indicates that the trimer is stabilized by a C1H3O interaction. This will be further confirmed by the NBO data. Therefore, the hydrogen bond pattern appears to be different in the B(1-1) and B(1-2) complexes. We note also an increase in the angles, the C4H5O bond becoming almost linear in both A(1-2) complexes involving CH3CHO and CH3CFO and increasing by 40–50° in the other structures. The OHO angles decrease by 10 to 17° from its value in the water dimer (175°).

3.2. Geometrical and NBO Properties of the Complexes

Tables 1, 2, and 3 list some relevant geometrical properties of the complexes, namely the C1H3, C4H5, C=O, and HO distances in the isolated monomers, in the 1-1 and in the 1-2 complexes with water. The corresponding vibrational frequencies are indicated as well. Tables 1, 2, and 3 also indicate important NBO parameters, namely, the occupation of σ*(C1H3) or σ*(C4H5) antibonding orbitals, the NBO charges along with some intra- or intermolecular hyperconjugative interactions.

Inspection of the results of Tables 1, 2, and 3 shows that the elongation of the C=O bonds and the decrease of the ν(C=O) vibrational frequencies are larger for the 1-2 than for the 1-1 complexes. Both parameters are linearly related [30] and suggest a reinforcement of the C=OHO interaction in the 1-2 complexes. These data will no more be discussed hereafter, the main scope of this section being the discussion of the properties of the CH bonds.

Let us at first discuss the properties of the C1H3 bond in the CH3CHO and CH2FCHO complexes. As discussed in [22], the contraction of the C1H3 bond and the increase of the corresponding vibrational ν(C1H3) frequencies in the A(1-1) and B(1-1) complexes results from the classical lone pair effect [3140]. The C1H3 distances, the σ*(C1H3) occupation and the intramolecular LPO2σ*(C1H3) hyperconjugation energies are almost identical in the A(1-1) and A(1-2) complexes. The intramolecular hyperconjugation energies decrease by 1.42 kcal mol−1 (CH3CHO(1-2) and by 1.61 kcal mol−1 (CH2FCHO(1-2) from the isolated molecules. As discussed in the first section, the short intermolecular H3O distances suggest that the C1H3 bond is involved in the formation of the cyclic structure in the two B(1-2) complexes. This is in full agreement with the relatively large intermolecular charge transfer from the O12 atom of water to the σ*(C1H3) orbital (2.70 and 3.40 kcal mol−1). Despite this charge transfer, the σ*(C1H3) occupation decreases. This can be explained by the large variation of the LPO2σ*(C1H3) hyperconjugation which decreases by 4.8 kcal mol−1 in both B(1-2) complexes. This illustrates the predominance of the lone pair effect in determining the C1H3 distances. These distances are linearly related to the σ* (C1H3) occupation as follows: 𝑟C1H3Å=0.448𝜎C1H3(e)+1.0801(𝑟=0.961).(2) The small increase of the s-character of the C1(H3) atom in the B(1-2) complexes does not influence the C1H3 distances to a great extent.

Parallel to the decrease of the C1H3 distances, the large blue shift of the ν (C1H3) vibration must be noticed (93 cm−1 and 61 cm−1). Let us notice that the blue shift of 93 cm−1 in the CH3CHO (B1-2) system is one of the largest ones predicted in CHO hydrogen bonds involving neutral molecules [4148]. In the present cases, the cooperativity results in an increase of the blue shift. This increase has also been found for other systems. For H2C=O complexed with one and two water molecules, the blue shifts of the 𝜈𝑠(CH) vibration are 45 and 66 cm−1, respectively, [17]. For CH3Cl complexed with one and two water molecules, the blue shifts are 13 and 25 cm−1, respectively [19]. Further, the increase of the polarity of the C1H3 bond in the B(1-2) complexes is also worth noticing, the positive charge on the proton being about 0.06e larger than in the isolated molecules.

In a next step, we will discuss the properties of the C4H5 bond in the three carbonyl complexes. As shown in our previous study [22], the C4H5 bonds in the CH3 or CH2F groups are weakly sensitive to the formation of a hydrogen bond with the O atom of water. In the acetone·1H2O complex as, for example, the two CH bonds which do not participate in the interaction show a greater sensitivity to hydrogen bond formation than the CH bond involved in the interaction. This was rather unexpected and was explained by the orbital interaction between the bonding σ (CH) orbital and the antibonding σ*(C=O) and π*(C=O) orbitals [22]. For the 1-2 complexes considered here, the value of this interaction remains almost constant. For the C4H5 bond of CH3CHO, the value of this orbital interaction is equal to 0.81 kcal mol−1 in the isolated molecule, 0.71 kcal mol−1 in the A(1-2) complex, and 0.86 kcal mol−1 in the B(1-2) complex. In contrast with the A(1-1) complexes, there is a significant elongation of the C4H5 bond in the A(1-2) complexes equal to 0.0012 Å in CH3CHO, 0.0022  Å in CH2FCHO and 0.0024  Å in CH3CFO. The corresponding red shifts of the ν(C4H5) vibration are 11, 20 (average value of the 𝜈as and 𝜈s vibrations), and 22 cm−1. It may be interesting to note that the C4H5 bond contracts by 0.006  Å when we consider the A(1-1) complex with the C4H5O bond at the trimer geometry and this is mainly due to the increase in % s-character of C4(H5) by almost 1.3%. In fact, at the optimized geometry considered here, the cooperativity markedly enhances the LPO12σ*(C4H5) charge transfer, resulting in an elongation of the C4H5 bond. Indeed, in CH3CHO, this charge transfer is equal to 0.46 kcal mol−1 in the A(1-1) complex and 2.95 kcal mol−1 in the A(1-2) complex. This increase is larger in the CH2FCHO system, being 0.10 kcal mol−1 in the A(1-1) complex and 4.56 kcal mol−1 in the A(1-2) complex. In agreement with this charge transfer, the σ*(C4H5) occupation increases by amounts ranging from 0.0025e (CH2FCHO), and 0.0070e (CH3CFO) with respect to the A(1-1) complexes.

In these cases also, the hybridization of the C4(H5) atom slightly increases by ca 1.5% when the C4H5 bond is involved in the A(1-2) interaction, and this increase does not influence the C4H5 distances to a great extent.

The C4H5 distances are linearly correlated to the σ*(C4H5) occupation as follows: 𝑟C4H5Å=0.371𝜎C4H5(e)+1.0886.(𝑟=0.973).(3)

It should be noticed that in all the systems the C4H5 distances where the C4(H5) atom has an sp3 hybridization are smaller than the C1H3 distances when the C1(H3) atom has hybridization between sp2.1 and sp2.3. This in contrast with the usual trend for the CH distances: C(sp3)–H > C(sp2)–H. Let us notice that the intercept of (2) (1.0801) is smaller than the intercept of (3) (1.0886). This possibly reflects the larger CH distances in C (𝑠𝑝3)–H than in C (𝑠𝑝2)–H bonds when the σ*(CH) occupation tends to zero.

We may also notice that the increase of linearity of the intermolecular O9H8O2 and C4H5O12 bonds may also contribute to the stability of the trimers.

We will now briefly discuss the changes induced in the water molecules. It is known that the OH bond of the water dimer (O9H8 bond in the present systems) is a better proton donor and the O atom (O12 atom in the present systems) is a better proton acceptor than in the water monomer [913]. For NBO charges on H and O atoms in the monomer, dimer, and complexes, see S.I.).

As previously mentioned, the intermolecular O9H11 distances do not markedly differ in the 1-2 complexes. From this, it can be anticipated that the properties of the water dimer considered as subsystem will not vary on a spectacular way. For all the complexes, the results indicate that the bonds between the two water molecules is stronger than in the water dimer. Further, as indicated in Tables 1, 2, and 3, the C=OHO bond in the 1-2 complexes is stronger than in the 1-1 complexes. This is shown by the larger elongation of the O9H8 bond, the larger decrease of the corresponding vibrational frequencies, and the larger LPO2σ*(O9H8) hyperconjugation.

The elongations of the OH bond are linearly related to frequency shifts of the 𝜈𝑠(OH) vibration of water as follows: ÅΔ𝑟(OH)=5.105Δ𝜈s(OH)cm1+0.0029(𝑟=0.978).(4) This correlation includes all the 1-1 and 1-2 complexes.

Other water properties such as the σ*(OH) occupation are summarized in S.I. These results indicate a large positive NBO charge of the bonding protons H8 and H11, a larger negative charge on the O9 or O12 atoms, and a larger σ*(O9H8) or σ*(O11H12) occupation than in the 1-1 complexes. It should be also noticed that in the 1-1 complexes, the water molecule acts as an electron acceptor, with the charge transfer from the carbonyl derivative to the water molecule ranging from 0.008 to 0.017e. In the 1-2 complexes, the sum of the charge on the H8O9H10 molecule remains weak (positive or negative), the charge being transferred to the second water molecule which always bears a negative charge.

3.3. Binding Energies

Table 4 reports the total binding energies in the trimer, E(ABC); the binding energies between the AB, BC, and AC molecules at the trimer geometry along with the cooperative energies, Δ𝐸coop, calculated by (1).

The % cooperativity defined as the ratio Δ𝐸coop/𝐸ABC ranges between 18% and 20% and is almost constant for the five systems considered here. This percentage is slightly larger than in the H2C=O·2H2O system (16%) [27] but smaller than in the NH2CHO·2H2O system (26%) where the C=O HO and CHO bonds are formed [20].

The binding energies between the two water molecules are almost the same for all the systems, between −4.50 and −4.62 kcal mol−1. These results are in line with the small differences in intermolecular distances and the NBO parameters in the two bonded water molecules discussed in the previous section.

The binding energies 𝐸AB vary between −4.73 and −3.60 kcal mol−1. They are ordered according to the proton affinities of the O atom of the carbonyl group which vary from 170.1 to 185.3 kcal mol−1 (Table 4) 𝐸HBkcalmol1=0.0786PAkcalmol19.83(𝑟=0.998).(5) The slope of this correlation is slightly larger than the slope of the correlation calculated for the 1-1 complexes (0.061) [22]. This conclusion must be taken with caution owing to the small range of considered energies. In a broad energy range, the cooperativity effects are usually nonlinear [49].

Let us also notice that the C4H5 bonds characterized by deprotonation enthalpies between 357 and 364 kcal mol−1 are better proton donors that the C1H3 bonds having much larger deprotonation enthalpies, between 382 and 391 kcal mol−1. The binding energies 𝐸AC are weak but do not reflect the differences in acidity of the CH bonds. The same remark also holds for the % of cooperativity which is almost constant.

4. Conclusions

The present work deals with a theoretical investigation of the cooperativity in CH3CHO·2H2O, CH2FCHO·2H2O, and CH3CFO·2H2O systems. The results are compared with the complexes involving one water molecule. The main conclusions of our work are the following ones.(1)For the three systems, two stable cyclic structures are predicted. Both structures are stabilized by C=OHO interaction. In the A structures, the system is stabilized by a CHO interaction involving the CH3 (or CH2F) group. In the B structures, the CH bond of the HC=O group participates to the CHO interaction. The optimized structures indicate shorter intermolecular distances than in the 1-1 complexes or than in the water dimer.(2)Formation of the A(1-2) complexes results in an elongation of the CH bond of the CH3 or CH2F group involved in the CHO interaction, a red shift of the ν(CH) vibration, and an increase in occupation of the σ*(CH) orbitals. This elongation is negligible in the A(1-1) complexes. In contrast, formation of the B(1-2) complexes results in a contraction of the aldehydic CH bond and a marked blue shift of the ν(CH) vibration, which are both larger than in the B(1-1) complexes. This effect is explained by a large decrease of the intramolecular LPO → σ*(CH) hyperconjugation energy and illustrates the predominance of the lone pair effect in determining the CH distances.(3)The elongation of the OH bonds in the water molecules, the red shifts of the ν(OH) vibrations are larger than in the water dimer. The same remark also holds for the variation of the NBO charges on the H and O atoms.(4)Quantitative correlations between the CH distances and the σ*(CH) occupations or between the frequency shifts of the ν(OH) stretching vibrations and the elongations of the OH bond of water are presented.(5)The total binding energies in the ternary systems range between −12.41 and −13.48 kcal mol−1. The two-body interaction energies are calculated at the trimer geometries. At this geometry, the interaction energies between the carbonyl derivative and the considered water molecules slightly increase with the basicity of the C=O group. The cooperative energies are comprised between −2.32 and −2.59 kcal mol−1.


A. K. Chandara thanks CSIR India for financial assistance through Project no. 01(2494)/11/EMR-II. T. Z. -Huyskens thanks the Department of Chemistry, University of Leuven for computer facilities.