Electric Field Effects on the Intermolecular Interactions in Water

Article pubs.acs.org/JPCA

Electric Field Effects on the Intermolecular Interactions in Water Whiskers: Insight from Structures, Energetics, and Properties Yang Bai,†,∥ Hui-Min He,† Ying Li,† Zhi-Ru Li,*,† Zhong-Jun Zhou,† Jia-Jun Wang,† Di Wu,† Wei Chen,† Feng-Long Gu,*,‡ Bobby G. Sumpter,§ and Jingsong Huang*,§ †

State Key Laboratory of Theoretical and Computational Chemistry Institute of Theoretical Chemistry, Jilin University, Changchun 130023, P. R. China ‡ Center for Computational Quantum Chemistry, South China Normal University, Guangzhou 510631, P. R. China § Center for Nanophase Materials Sciences and Computer Science & Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6493, United States ABSTRACT: Modulation of intermolecular interactions in response to external electric fields could be fundamental to the formation of unusual forms of water, such as water whiskers. However, a detailed understanding of the nature of intermolecular interactions in such systems is lacking. In this paper, we present novel theoretical results based on electron correlation calculations regarding the nature of H-bonds in water whiskers, which is revealed by studying their evolution under external electric fields with various field strengths. We find that the water whiskers consisting of 2−7 water molecules all have a chain-length dependent critical electric field. Under the critical electric field, the most compact chain structures are obtained, featuring very strong H-bonds, herein referred to as covalent H-bonds. In the case of a water dimer whisker, the bond length of the novel covalent H-bond shortens by 25%, the covalent bond order increases by 9 times, and accordingly the H-bond energy is strengthened by 5 times compared to the normal H-bond in a (H2O)2 cluster. Below the critical electric field, it is observed that, with increasing field strength, H-bonding orbitals display gradual evolutions in the orbital energy, orbital ordering, and orbital nature (i.e., from typical π-style orbital to unusual σ-style double H-bonding orbital). We also show that, beyond the critical electric field, a single water whisker may disintegrate to form a loosely bound zwitterionic chain due to a relay-style proton transfer, whereas two water whiskers may undergo intermolecular cross-linking to form a quasi-two-dimensional water network. Overall, these results help shed new insight on the effects of electric fields on water whisker formation.

1. INTRODUCTION Water is vital to the existence of all forms of life and plays a critical role in many physical and chemical processes due to its polar nature and propensity to form hydrogen bonds (Hbonds).1 As such, fundamental studies of water have long attracted both experimental and theoretical interests.2−5 During the late 1960s, whether water that condensed from vapor inside a narrow quartz capillary tube was a new allotropic form of water6 not only motivated an intense interest among professional scientists7 but also stimulated considerable excitement in the general public,8,9 due to its anomalous properties different from those of ordinary water. During this surge of studies, scientist coined the name of “polywater” to suggest a polymeric structure for water.7 However, in 1971 it was proven that the condensed water in the capillary tube was actually ordinary water, and the hypothesized “polywater” was then dismissed as an artifact simply caused by the presence of impurities.10−14 The scientific controversy over “polywater” quickly died down after the short-lived journey of anomalous water. Albeit a misnomer, the term of “polywater” may still prompt one to wonder about the polymeric structures of water. Would © XXXX American Chemical Society

it be possible for water to undergo polymerizations with an external assistance, e.g., in the presence of an external electric field? Investigations of the effect of external electric fields on water structures actually date back to 1960s, when protonated water clusters were first observed in field ionizations by mass spectrometers.15,16 Anway proposed a model for the water layer condensed on the field ionization tip, suggesting long whiskers of water molecules oriented dipole-to-dipole and neighboring whiskers having essentially no interaction with one another.17 It is noteworthy that, although there was no evidence that these chains are covalently bonded, the whisker formation was still referred to as polymerization at that time. The studies of high electric field effects (≈1 V/Å) on the structures of adsorbed water layers stimulated further interests in the 1980−1990s. Block et al. studied the field-induced structural changes in adsorbed water layers using photon-stimulated desorption with tunable synchrotron radiation.18−21 It was found that the metal field emitter tips exposed to water vapor led to the growth of Received: November 16, 2014 Revised: January 19, 2015

A

DOI: 10.1021/jp511460c J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

Dunning’s correlation-consistent basis set (aug-cc-pVDZ)39 were employed. The structures of both (H2O)n water clusters with water molecule number n = 2−5 under zero electric field and water whiskers with n = 2−7 under external electric fields of various strengths up to 600 × 10−4 au (3.09 V/Å) were fully optimized. Vibrational frequency calculations were performed for all of the optimized structures to verify that the geometries correspond to minimum structures instead of saddle points on the potential energy surface. The MP2 results for the dimer case were further supported by additional calculations for the evolution of water dimer under external electric fields of various strengths using the coupled cluster single and double substitutions (CCSD) method. The energetic and geometrical trends agree well between the two electron correlation theories as the strength of external electric field increases gradually from 0 to a critical electric field where the most compact dimer whisker forms. More specifically, the critical electric field strength of the water dimer whisker at the MP2 level is only 6% smaller than that at the CCSD level. Since the convergence for geometry optimizations under an external electric field is more easily achieved at the MP2 compared to the CCSD level, the more practicable MP2 method was adopted in the calculations for the rest longer whiskers. In the calculations of H-bond interaction energies (ΔE) between two water fragments, the counterpoise procedure was used to eliminate basis set superposition errors (BSSE).40,41 Natural bond orbital (NBO) analyses were performed to assess the covalent characteristics of the strengthened H-bonds under external electric fields. All of the calculations were carried out using the Gaussian 09 program package.42 Molecular orbitals were visualized with the GaussView program.43

water whiskers on the surface, before they were photodesorbed giving protonated water clusters. In recent years, numerous additional experimental and theoretical investigations have been conducted on water confined in nanoscale one-dimensional channels, which is of great interest to biologists, geologists, and materials scientists.22−26 Thus, far, it has been found that water molecules trapped inside the cavities of carbon nanotubes are still very similar to those in the bulk due to their normal H-bonds.22−24 However, strong H-bonds were found to occur in water wires or chains confined together with protons or other ions in carbon nanotubes.25,26 It is worth noting that, if the electric field is too strong, the H-bonded system may undergo disintegration, as illustrated in the acid−base chemistry between HCl and NH3. Experiments revealed that the proton transfer in the H-bonded ClH···NH3 complex on the molecular scale does not happen to form the ionic salt NH4+Cl− unless an excess electron is present.27 Ab initio calculations showed that a critical electric field of 54 × 10−4 au is needed for the proton transfer to take place, and the external electric field induced by the excess electron is equivalent to 125 × 10−4 au.28 In the past decade, extensive theoretical efforts have been devoted to rationalize the formation of water whiskers in external electric fields. Using density functional theory (DFT) and perturbation theory, Kim and co-workers studied the electric field effects on smaller water clusters (H2O)n with n = 3−5 and the formation of water wires.29 James et al. investigated the energy landscapes of water clusters (H2O)n with n = 2−5 and n = 8 in a uniform electric field by using three related rigid-body models.30 Rai et al. used DFT to examine larger water clusters (H2O)n with n = 6−8 and found that the overall effect of the external electric field is to open up threedimensional morphologies of water clusters to form linear, branched, or netlike structures.31 Very recently, Kreuzer’s group presented a detailed theoretical analysis on the basis of DFT for long whiskers with up to 12 water molecules, which substantiates the formation of water whiskers in high electric fields.32,33 Despite these pioneering studies on the structural conversion from water clusters to water whiskers under the influence of external electric fields, a fundamental understanding of the nature of intermolecular interactions is still lacking. The main questions are as follows: Is the nature of H-bonds in water whiskers different from that in water clusters? Does it change in water whiskers with increasing electric field strength? With this motivation, herein we perform high fidelity electron correlation calculations to study the evolution of water whiskers from the perspective of H-bonds. Based on our structure, energetics, and property studies as a function of external electric field strength, we found that the water whiskers have a chain-length dependent critical electric field. Under the critical electric field, the most compact chain structures are obtained, featuring very strong H-bonds that we refer to as covalent H-bonds. Below the critical electric field, H-bonding orbitals display a gradual evolution in the orbital energy, orbital ordering, and orbital nature with increasing field strength. Beyond the critical electric field, water whiskers may break down forming zwitterionic chains or become cross-linked to form a quasitwo-dimensional water network.

3. RESULTS AND DISCUSSION Figure 1 shows the linear chain structures of water whiskers containing 2−7 water molecules optimized with MP2/aug-ccpVDZ under respective critical electric fields (Fc). It can be seen that the strength of Fc gradually decreases from 535 × 10−4 to 225 × 10−4 au with increasing chain lengths as indicated

Figure 1. Linear chain structures of water whiskers with 2−7 water molecules, under respective critical electric fields (Fc). The Fc decreases with increasing chain length. The linear chain (n = 2) and cyclic structures (n = 3−5) of typical (H2O)n water clusters are also shown for comparison. All structures were optimized at the level of MP2. The green lines represent the H-bonds whose covalent characteristics were focused in this study. The inset illustrates the atomic and bond labels.

2. COMPUTATIONAL DETAILS For the theoretical calculations, quantum chemical secondorder Møller−Plesset perturbation theory (MP2)34−38 with B


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Table 1. Hydrogen Bond Length R (H1−O1 in Å), the O−H Bond Length r (H1−O2 in Å), the Hydrogen Bond Angle θ (∠O1H1O2 in Degree), the Hydrogen Bond Interaction Energy ΔE (kcal/mol), the Covalent Bond Order (WBI), and the Charges (q) on the Three Atoms Involved in the H-Bond (Figure 1 Inset) Calculated at the MP2 and CCSD Levels during the Conversion from a (H2O)2 Water Cluster to a Water Dimer Whisker with Increasing Electric Field Strength F (in10−4 au) until the Critical Field Strength (Boldface) MP2 CCSD

MP2 CCSD MP2 CCSD

F

R

r

θ

ΔE

WBI

q(O1)

q(H1)

q(O2)

0 1.982 100 1.982 200 1.985 300 1.967 400 1.889 500 535 535 571

1.951 0.970 1.939 0.970 1.926 0.977 1.887 0.983 1.791 0.994 1.615 1.654 1.466 1.478

0.973 171.77 0.977 171.81 0.983 147.52 0.991 141.19 1.007 141.69 1.047 1.038 1.103 1.097

171.69 −4.26 161.84 −4.29 151.30 −6.32 146.48 −7.88 147.54 −10.25 154.16 151.39 160.26 159.23

−4.46 0.017 −5.40 0.017 −6.79 0.017 −8.64 0.021 −11.52 0.034 −17.09 −16.8 -23.16 -23.22

0.019 −0.976 0.018 −0.993 0.022 −1.025 0.030 −1.047 0.050 −1.068 0.104 0.097 0.170 0.170

−0.976 0.510 −1.004 0.508 −1.025 0.541 −1.047 0.555 −1.066 0.573 −1.077 −1.085 -1.063 -1.068

0.511 −0.995 0.530 −0.976 0.545 −1.032 0.561 −1.059 0.579 −1.091 0.598 0.598 0.601 0.604

−0.998

by the number of molecules in the water whiskers. The wellstudied (H2O)n water clusters with n = 2−5 featuring cyclic structures (except for n = 2 which is linear) are also shown for comparison. All of these structures have been verified to be minima due to the absence of any imaginary frequencies from vibrational frequency calculations. As will become clear in subsequent analyses, the difference in the linear versus cyclic geometries for the water whiskers and water clusters resides in the nature of the H-bonds that bind the water molecules together. In the following, we will first illustrate the structural variations of the water whiskers under external electric field and address the different strengths of critical electric fields as a function of the chain length in different water whiskers. Then we will elaborate on the strong covalent characteristics of the H-bonds in the water whiskers and compare their differences with those in the water clusters. Finally, we will show the breakdown of water whiskers and the consequent formation of either a zwitterionic chain or a quasi-two-dimensional whisker network under an external field of strength that exceeds the critical electric field for the specific water whisker. 3.1. Water Whisker Evolution and the Critical Electric Field. We first examine the structural variations of water whiskers under external electric field. In line with previous studies,29−33 all of the optimized geometries for the water clusters are found to be cyclic under zero electric field, except for the water dimer, which is linear. In contrast, under high external electric fields, the initially cyclic water clusters are all converted to water whiskers that are characterized by compressed linear chain structures. These linear chains are considered “compressed” because the H-bond lengths are shortened by the external electric fields. As a matter of fact, we found that each compressed linear chain structure and its Hbonds are continually compacted with increasing external electric field strength. This can be illustrated with the shortest water dimer case. As shown in Table 1, the H-bond length R is gradually reduced from the initial 1.951 to the final 1.466 Å at the MP2 level (or from 1.982 to 1.478 Å at the CCSD level). Obviously, the chain structure is the most compact for the water dimer whisker under the critical external electric field Fc. As can be seen from Figure 2, accompanied by the compression of the linear chain structure, the variations of H-bond energy

−1.011 −1.035 −1.063 −1.097 −1.142 −1.142 -1.169 -1.176

Figure 2. Λ-shaped curves calculated at the levels of MP2 and CCSD for the interaction energy (ΔE) of (H2O)2 and the covalent bond order in terms of Wiberg bond index (WBI) of the O1−H1 bond (Figure 1). Both levels of theory give consistent results indicating increasing ΔE and WBI with the external electric field until the critical field strength, clearly revealing an evolution from a (H2O)2 cluster with a normal H-bond to a water dimer whisker with a covalent Hbond.

and covalent bond order (Wiberg bond index, WBI) with the external electric field strength display Λ-shaped curves at both the MP2 and CCSD levels of theory. The strongest bonding energy and bond order are found at the two critical Λ points, which correspond to the critical electric field Fc. If the external electric field is further increased to be greater than the critical field, the water whisker will be converted to new structures due to the ionization of a water molecule or the cross-linking of water whiskers (see section 3.3). Note that the two Λ points for the two levels of theory are very close to each other. Therefore, the discussions for other whiskers are only based on the MP2 calculations. The structures for all of the water whiskers with different number of water molecules n = 2−7 under zero and the critical electric field are given in Table 2, all showing the compressed linear chain structures under respective Fc. Additionally, similar to the dimer case, the bonding energies and bond orders are significantly enhanced under respective Fc. It is not surprising that different critical field strengths Fc are required for the formation of the most compact water whiskers C


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Table 2. Hydrogen Bond Length R (H1−O1 in Å), the O−H Bond Length r (H1−O2 in Å), the Bond Angle θ (∠O1H1O2 in Degree), the Hydrogen Bond Interaction Energy ΔE (kcal/mol), the Covalent Bond Order in Terms of Wiberg Bond Index (WBI), for Selected H-Bonds (as Highlighted by the Green Line Segments in Figure 1) and the Charges (q) on the Three Atoms Involved in the H-Bond (as Labeled in Figure 1 Inset) Calculated at the MP2 Level for Water Clusters (n = 2-5) under Zero Electric Field and Water Whiskers (n = 2−7, in Boldface) under Respective Critical Electric Fields Fc (in 10−4au) n

F/Fc

R

r

θ

ΔE

WBI

q(O1)

q(H1)

q(O2)

2

0 535 0 413 0 325 0 277 245 225

1.951 1.466 2.00 1.416 1.776 1.393 1.743 1.446 1.422 1.428

0.973 1.103 0.971 1.095 0.985 1.103 0.987 1.071 1.080 1.074

171.69 160.26 164.86 173.73 167.62 175.92 175.67 176.23 176.88 176.09

−4.46 -23.16 −3.47 -26.07 −8.81 -30.66 −10.18 -28.19 -31.36 -31.65

0.019 0.170 0.016 0.186 0.044 0.197 0.049 0.166 0.178 0.174

−0.976 -1.063 −0.990 -1.034 −1.031 -1.081 −1.036 -1.073 -1.087 -1.079

0.511 0.601 0.506 0.609 0.541 0.601 0.546 0.598 0.596 0.595

−0.998 -1.169 −0.992 -1.127 −1.031 -1.036 −1.035 -1.101 -1.114 -1.097

3 4 5 6 7

the internal self-attractive interaction (the precompression) effect, the critical external electric field thus decreases with increasing number of water molecules in the water whiskers. A relevant question concerns whether the mean value of the equivalent electric field compensated by the self-attractive interactions is the same for every increased water molecule in various water whiskers of different chain lengths. This quantity can be evaluated by [Fc(2) − Fc(n′)]/(n′ − 2), where the water dimer whisker with n = 2 is taken as a reference. As can be seen in Figure 3, along with the increased number of water molecules, the mean value of the equivalent electric field per increased water molecule decreases from 122 × 10−4 (n = 3) to 62 × 10−4 au (n = 7). The reason that each additional water molecule contributes less equivalent electric field in a longer chain than in a shorter chain can be ascribed to the onedimensional chain structure of water whiskers where the chain lengths of water whiskers are elongated by the increased number of water molecules. In turn, with the elongated chain length, the additional water molecules may contribute less to the self-attractive interactions due to their more distant separations, especially for those at the two terminals. Consequently, although the critical external electric field decreases with increasing chain length, the rate of change is found to decrease with increasing length. Figure 3 shows a trend of Fc that asymptotically approaches ca. 200 × 10−4 au for longer water whiskers (n > 7). 3.2. Covalent Characteristics of H-Bond. Next we elaborate on the nature of intermolecular bonding interactions during the evolution from a water cluster to a most compact water whisker with increasing external field strength. We first illustrate the evolution of the smallest system, i.e., the water dimer. The structural parameters, the H-bond interaction energy, and the covalent bond order (WBI) are used to represent the covalent characteristics of the H-bond. As can be seen from Table 1, under zero external electric field, the (H2O)2 water cluster44 has a normal H-bond structure with a H-bond length (R = 1.951 Å) and a H-bond angle (θ = 171.69°). In addition, the water cluster has a small H-bond interaction energy (ΔE = −4.46 kcal/mol) and a negligible covalent bond order (WBI = 0.019). As the (H2O)2 cluster evolves to the water dimer whisker, the H-bond length (R) decreases significantly with increasing electric field strength. Meanwhile, both the interaction energy (ΔE) and the WBI of the H-bond increase significantly. These indices representing the covalent characteristics of the H-bond are also shown in

with different numbers of water molecules. One would expect that it is more difficult to form a longer water whisker (with more water molecules) than a shorter one; therefore, a higher critical electric field would be needed for a longer chain. However, counterintuitive results are obtained. As can be seen from Figure 3, the critical external field strength does not

Figure 3. Unexpected relationship between the critical field (Fc) and the degree of polymerization (n) for the water whiskers with n = 2−7 where Fc decreases with increasing n. Due to the contribution of selfinteraction, the average equivalent electric field per increased water molecule decreases from 122 × 10−4 (n = 3) to 62 × 10−4 au (n = 7) with respect to the water dimer whisker.

increase but on the contrary decreases with increasing number of water molecules in the water whiskers. Such an unexpected observation may be understood as follows. The formation of the one-dimensional water whiskers depends not only on an extrinsic effect from the compression of external electric fields but also on an intrinsic effect from the self-attractive interactions among the water molecules. Due to their polar nature, water molecules have inherent dipole moments which may exert dipole electric fields and produce self-attractive interactions. Such mutual attractions among the water molecules mainly include long-range dipole−dipole interactions, induced interactions, and short-range H-bond interactions. The H-bond interactions have directionality, saturability, and charge-transfer properties. The resulting selfattractive interactions in water whiskers may partially compensate the compression effect from an external electric field, thus reducing the needed strength of the external field. Since the increased number of water molecules helps to enlarge D


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n = 5 is close to that of 0.170 for n = 2, while the remaining WBI values for n = 3, 4, 6, and 7 are even greater than that for n = 2. All of these results showing strong covalent characteristics clearly indicate the presence of covalent H-bond characteristics in these longer water whiskers (n = 3−7). Similar to the case of the water dimer whisker, the enhanced atomic charges in these longer water whiskers under respective Fc may also contribute to the Coulomb interactions on top of the covalent H-bond. To further clarify the nature of the new covalent H-bonds in the water whiskers, we examine the evolution of selected bonding molecular orbitals for the water dimer with increasing external field strength. As can be seen in Figure 5, under zero

Figures 2 and 4. As mentioned above, the (H2O)2 water cluster has evolved into the most compact water dimer whisker with

Figure 4. Variations of the H-bond length (R) and covalent bond order in terms of the Wiberg bond index (WBI) calculated by MP2 as a function of the external electric field during the course of the evolution from a (H2O)2 cluster to a water dimer whisker.

considerably stronger covalent characteristics when the electric field increases to the critical value of 535 × 10−4 au. For this structure, the new H-bond has its bond length shortened by 25%, its covalent bond order increased by 9 times, and its Hbond energy strengthened by 5 times compared with the normal H-bond in the (H2O)2 cluster (see Table 1). These novel results indicate that the H-bond interaction has extraordinarily strong covalent characteristics in the water dimer whisker. In analogy with the scenario that a covalent bond with polarity is named as a polar covalent bond, we have named this kind of extraordinarily strong H-bond a covalent Hbond (as a new intermolecular interaction) due to its strong covalent characteristics. Interestingly, under external electric field, the atomic charges are also enhanced (see Table 1), which may contribute to the Coulomb interactions on top of the strengthened H-bond. Similar trends are also observed in longer water whiskers with higher number of water molecules (n = 3−7). For these systems, the structural parameters, H-bond interaction energies ΔE, covalent bond orders (WBI), and charges (q) on the atoms of interested (as labeled in Figure 1 inset) under zero and respective critical electric fields Fc are compared with those of the water dimer case in Table 2. Note that the calculations are presented for the selected H-bonds as highlighted by the green line segments in Figure 1. For the structural characteristics, these water whisker molecules also have shortened H-bond lengths R = 1.393−1.446 under respective Fc, which are even shorter than the R = 1.466 Å in the water dimer whisker (n = 2). It is also interesting to note that the shortening of R(H1− O1) is accompanied by the elongation of r(H1−O2), both directly involved in the H-bonds (Tables 1 and 2). Taking n = 4 for instance, the difference between R and r is 0.29 Å for the water whisker, much smaller than that of 0.79 Å for the water cluster. Additionally, the H-bond angle θ values in water whiskers with n = 3−7 are found to increase slightly with n, and meanwhile all are larger than the 160.26 degree in water dimer whisker by 13.47 to 16.62 degrees. For other characteristics of the H-bonds highlighted in Figure 1, the H-bond interaction energies in the range of −26.07 to ∼−31.65 kcal/mol are larger than the value of −23.16 kcal/mol for the water dimer whisker. The covalent bond index (WBI) values are in the range of 0.166−0.197. Among these, the smallest WBI value of 0.166 for

Figure 5. Visualizations of HOMO−3 through HOMO−5 for (H2O)2 along with the orbital energies as a function of the strength of external electric field. The increasing strength of the external electric field causes the H-bond orbital energies to decrease with increasing field strength (red and pink lines). The H-bond orbitals connected by the red lines display a distinct characteristic of a double H-bond orbital. In comparison, the non-H-bond orbitals connected by the light blue lines have nearly constant energies, independent of the field strength. The stabilization of the H-bond orbitals with the external field strength is responsible for the formation of the water dimer whisker.

external electric field, the H-3 (HOMO−3) orbital appears to have an ordinary π-style H-bonding nature. With increasing external electric field strength, it gradually evolves to an unusual σ-style double H-bonding orbital, in which both H’s s-orbitals contribute simultaneously to the H-bonding orbital. Such a double H-bonding orbital may be ascribed to the reduced R length and θ angle (Table 1), which can facilitate the orbital overlap of both H’s orbitals with the O’s orbital on the neighboring molecule. In comparison, the H-4 orbital only shows the characteristic of a σ-style single H-bonding orbital, regardless of the strength of external electric field. It is noteworthy that the H-5 orbital is a nonbonding orbital, and therefore its energy remains nearly constant under the external field strength from 0 to the critical field strength. In comparison, the energies of both of the H-3 and H-4 orbitals are lowered remarkably by the external field. Under the critical electric field, their energies become even lower than that of the H-5 orbital, making the H-5 orbital the highest level among the three. It is quite interesting that, with increasing external field strength, normal H-bonding orbitals can evolve not only in the orbital energy and orbital ordering but also in the orbital nature (from the typical π-style orbital to unusual σ-style double Hbonding orbital). Based on the insight obtained from these E


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chain. Taking the water whisker (n = 4) as an example, under an external field of 330 × 10−4 au that is stronger than the corresponding critical field Fc = 325 × 10−4 au, a relay-style proton transfer along the H-bonded chain occurs in the direction of the external field (from right to left, in Figure 7).

orbital visualizations, it can be concluded that the evolution of H-bonding orbitals with external electric field are the fundamental cause for the formation of the covalent H-bond. It is worth noting that the covalent H-bonds observed in this work are asymmetric H-bonds. In the example of the water dimer whisker, the two H−O distances are R(H1−O1) = 1.466 and r(H1−O2) = 1.103 Å, exhibiting an asymmetric H-bond under the critical external field. It was assumed in an early work that the H-bond in polywater resembles the strong symmetric H-bond in the [F···H···F]− ion.45 Symmetric H-bonds only occur in systems where the middle H atom is located in a symmetric environment. These systems include [F···H···F]− for HF2−, [HO···H···OH]− for H2O···HO−, and so on. For the water whiskers studied herein, the structure of [HO-H···OH2] does not allow a symmetric environment for the middle H atom, so the symmetric H-bond cannot be formed in the water whiskers. Although the difference of the two H−O distances involved in the covalent H-bond is significantly reduced by the increased electric field strength (Table 1), the water dimer whisker still has a difference of R − r = 0.363 Å under the critical field. As the external field increases to above the critical value, the one-dimensional water whisker will disintegrate (section 3.3), and a symmetric H-bond still cannot be formed. Therefore, the intermolecular interactions in the water whiskers studied here mainly involve asymmetric covalent H-bonds. Interestingly, the formation of covalent H-bonds is found to cause different vibrational properties. This can be expected based on the significant change of the H-bond lengths and strengths. Figure 6 illustrates the vibrational spectra of the

Figure 7. For a water whisker with n = 4, under an external field of 330 × 10−4 au that is greater than the critical field of 325 × 10−4 au, a relaystyle proton transfer from one H2O to the next H2O occurs along the chain (from right to left), forming a loosely bound zwitterionic chain of H3O+···(H2O)n···HO−.

Each water molecule in the middle of the H-bonded chain accepts a proton from its right-side neighboring H2O and meanwhile donates a proton to the left-side neighboring H2O. In contrast, the rightmost water molecule loses a proton and the leftmost water molecule gains a proton, giving a cation and an anion at the two terminals, respectively. Consequently, the one-dimensional water whisker structure is changed into a loosely bound zwitterionic cluster H3O+··· (H2O)2 ···HO‑. A second situation that occurs beyond the critical electric field is that the one-dimensional water whiskers undergo intermolecular cross-linking. This has not been observed experimentally, probably because in a brush of water whiskers, the one-dimensional water whisker chains are fixed on the tip of a metal field emitter.32 However, based on our MP2/aug-ccpVDZ calculations, a cyclic equilibrium structure formed from two water whiskers of n = 4 is obtained under the external field of 330 × 10−4 au (Figure 8). This structure has been verified by vibrational calculations that show all real frequencies. Thus, this result indicates that it is possible for water whiskers to form a quasi-two-dimensional water network through intermolecular cross-linking under an external field that is higher than the critical field of the constituent single water whisker. This

Figure 6. Vibrational spectra of the (H2O)2 cluster and the water dimer whisker with n = 2. Two strong characteristic peaks at 1293 and 1927 cm−1 only appear in the water dimer whisker due to its strong covalent H-bond characteristics.

(H2O)2 cluster and the water dimer whisker. Due to the formation of the water dimer whisker, two very strong characteristic peaks show up at 1293 and 1927 cm−1, which correspond to the two vibrational modes of the covalent Hbond in the water dimer whisker. These two vibrational modes come from the strong O−H stretching vibrations in the Hbond due to its strong covalent characteristics. However, such vibrational modes do not exist in the (H2O)2 cluster. Consequently, the distinctive structures between the (H2O)2 cluster and water dimer whisker are characterized by these distinctive vibrational spectra. 3.3. Disintegration and Cross-Linking of Water Whisker. As pointed out previously, under an external field with a strength exceeding the critical value Fc, a single water whisker may undergo disintegration leading to a zwitterionic

Figure 8. Two water whiskers of n = 4 cross-link to form a cyclic water whisker under an external field of 330 × 10−4 au that is greater than the critical field of 325 × 10−4 a.u for one water whisker with n = 4. F



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observation invites further experimental work to explore the formation of quasi-two-dimensional water networks.

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Corresponding Authors

*E-mail: [email protected]. Phone: 86-431-8498964. *E-mail: [email protected]. *E-mail: [email protected].

4. CONCLUSIONS In this work, we have performed electron correlation calculations on the evolution of anomalous water whiskers consisting of 2−7 water molecules under external electric fields of various strengths. We have focused on the H-bond characteristics of the water whiskers in terms of structural variations, covalent bond orders, H-bond interaction energies, and the H-bond effects on the vibrational properties, in order to gain a fundamental understanding of the intermolecular interactions responsible for their formation. Based on the theoretical findings revealed through these studies, we have gained new insight into the nature of H-bonds in water whiskers. (1) Every water whisker is found to have a chainlength dependent critical electric field for its formation. Counterintuitively, the strength of the critical external electric field shows a monotonic decrease with increasing chain length of the water whiskers. This unusual relationship may be explained by the self-attractive interaction effect among the water molecules in the water whiskers. (2) The critical electric field leads to the most compact chain structure with the strongest H-bond, which is a novel covalent H-bond due to its strong covalent characteristics. In the example of a water dimer whisker, the strong covalent characteristics of the H-bond manifest in that its bond length is shortened by 25%, its covalent bond order is increased by 9 times, and accordingly its H-bond energy is strengthened by 5 times compared to the normal H-bond in the (H2O)2 cluster. (3) Below the critical electric field, it is found that, with increasing field strength, Hbonding orbitals display gradual evolutions in the orbital energy, orbital ordering, and orbital nature (i.e., from ordinary π-style orbital to unusual σ-style double H-bonding orbital). It can be concluded that the evolutions of H-bonding orbitals with external field are the fundamental cause for the formation of the covalent H-bonds. (4) The presence of covalent Hbonds under the critical electric field is found to give an extraordinary vibrational spectrum showing two very strong characteristic peaks (1293 and 1927 cm−1) that correspond to the vibrational modes for the covalent H-bond. (5) Beyond the critical electric field, a single water whisker may disintegrate to form a loosely bound zwitterionic chain due to a relay-style proton transfer, whereas two water whiskers may undergo intermolecular cross-linking to form a quasi-two-dimensional water network. The results presented in this work are expected to shed further light on the effects of electric fields on the formation of water whiskers. They also prompt us to question the possibility of reviving the term of “polywater”, which implies a polymeric structure for the water whiskers. Indeed, the strong H-bonds caused by the critical electric fields have extraordinarily strong interaction energies in the range of −20 to −30 kcal/mol and high bond orders close to 0.2. These covalent H-bond characteristics are much stronger than those in ordinary water clusters under zero external electric field. In addition, the exceedingly strong structural variations from cyclic water clusters to linear water whiskers may be considered a stretch−shrink transformation, which can be switched backand-forth by external electric fields. Therefore, these findings may also inspire research on molecular machines and molecular muscles based on the electric field effects on the structures of water clusters/whiskers.

Present Address ∥

College of Chemistry and Chemical Engineering, Jinzhong University, Jinzhong 030619, P. R. China. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was financially supported by the National Natural Science Foundation of China (Nos. 21173098, 21173095, 21103065, 21403083, and 21043003) and by the Center for Nanophase Materials Sciences (CNMS), which is sponsored at Oak Ridge National Laboratory by the Scientific User Facilities Division, Office of Basic Energy Sciences, U.S. Department of Energy. Z.R.L. thanks Prof. Jia-Li Gao for the helpful discussions.

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Electric Field Effects on the Intermolecular Interactions in Water

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