DFT Study of Hydrogen-Bonding Interaction, Solvation Effect, and

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A DFT Study of Hydrogen-Bonding Interaction, Solvation Effect, and Electric Field Effect on Raman Spectra of Hydrated Proton Ran Pang, Li-Juan Yu, Meng Zhang, Zhong-Qun Tian, and De-Yin Wu J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b07064 • Publication Date (Web): 30 Sep 2016 Downloaded from http://pubs.acs.org on October 2, 2016

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The Journal of Physical Chemistry

A DFT Study of Hydrogen-Bonding Interaction, Solvation Effect, and Electric Field Effect on Raman Spectra of Hydrated Proton Ran Pang, Li-Juan Yu, Meng Zhang, Zhong-Qun Tian, De-Yin Wu* State Key Laboratory of Physical Chemistry of Solid Surfaces, Collaborative Innovation Center of Chemistry for Energy Materials, Department of Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, 361005, China

ABSTRACT: Strong hydrogen-bonding interaction and Raman spectra of hydrated proton have been investigated using hybrid density functional theory method B3LYP. The solvation model of density (SMD) approach is employed in the present calculation to simulate hydrated protons in aqueous solution. Focusing on the different hydrogen bonded Eigen-water and Zundel-water interactions, we present a better assignment of Raman signals of hydrated proton on the basis of vibrational analysis in different environments. Our results showed that B3LYP calculations could give a good prediction for characteristic vibrational frequencies of Eigen and Zundel isomers in liquid phase. The O-H stretching vibrational frequencies from Eigen and Zundel units are very sensitive to hydrogen-bonding interaction with solvent water molecules. Moreover, the solvation effect and the external electric field effect lead to the proton deviating from the central position of Zundel structure, and finally resulting in a transition to Eigen one in aqueous solution.

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Furthermore, by combining theoretical prediction and Raman scattering theory, we calculate absolute Raman intensities of characteristic signals based on the polarizability tensor derivatives of hydrated proton clusters. This is very helpful to infer the microstructure of hydrated protons in aqueous solution by using Raman measurements.

Introduction Hydrated proton plays an important role in many chemical processes in life, energy and material science.1-5 The excess proton in water is involved in extremely strong hydrogen bonds and anomalously high mobility along the hydrogen-bonded networks in aqueous solution.6-10 Not only energies but also spectroscopic and dynamic properties of the hydrogen-bonded networks provide important information for the fingerprint of the hydrogen-bonding topology. Even so, there is a challenge to clearly understand the corresponding relationship of vibrational spectroscopic signals and dynamic hydrogen-bonded networks at present. Therefore, quantum chemical methods are significantly helpful to understand the nature of hydrated proton through depicting the hydrogen-bonding (HB) interaction of the excess proton in bulk water. It is generally accepted that, in aqueous solution, the proton shuttle mechanism involves fast interconversions between two distinct proton hydration structures, namely, the Eigen

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and

Zundel 12 cations. A number of experimental and theoretical results support that the Eigen cation is the dominant form for the hydrated proton in water.7,8,13-16 Knight and Voth proposed that the most likely solvation structure for the hydrated proton is a distorted Eigen-type complex.5 In the process of proton solvation, the proton hopping involves the neighboring water hydrogenbonding network fluctuation and structure rearrangements. Besides, the hydrated proton interacting with surrounding water in finite size clusters is also presented in various isomers with


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different HB structures.17-21 The complexity of the observed vibrational spectra indicates that several isomers are necessary to be further investigated on the basis of experimental conditions. Raman spectroscopy provided fingerprint signals of hydrated protons in aqueous solutions.22-26 Previously, ones extensively explored the O-H stretching bands of water more than 3000 cm-1,2628

because the O-H stretching vibration is believed to sensitively reflect the local structures and

interactions of hydrogen-bonded networks.19,26 However, in middle and low wavenumber regions, vibrational signals are very important in characterizing the structure of complex molecular systems. For hydrated protons, the libration and bending vibrational signals are very sensitive to the intermolecular interaction and electrolytes. Giguère et al. reported that the Raman band at ca. 1100 ~ 1200 cm-1 for symmetric bending of hydronium ion could be used to characterize hydrated protons in concentrated acid solution.23 Nevertheless, the exact assignment of Zundel ions is lack in Raman measurements in acidic solution. A number of ab initio calculations have been carried out in order to investigate the geometry and energetic properties, and the correlation of structures and their infrared spectra for protonated water clusters.18,20,29-31 Several groups performed molecular dynamics (MD) simulation to investigate the diffusion of hydrated proton in aqueous solution and the detailed molecular mechanism of proton transfer.5,14,32 However, few theoretical studies reported on Raman spectra of water and hydrated species in hydrogen-bonded systems so far. Cybulski et al. calculated Raman spectra of small water clusters.33 In their results, the Raman intensities of stretching vibrations for the three-coordinated single donor-double acceptor (DAA) molecules are higher than the double donor-single acceptor (DDA) molecules, showing that there is a correlation between the hydrogen-bonding topology of water-containing clusters and their Raman spectra. Wu et al. investigated the influence of hydrogen bonding interaction on


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vibrational Raman spectra of water in the three kinds of anionic complexes, i.e. anionic water clusters, water-halide anionic complexes, and water metal anionic complexes.34 Their results showed that the HB interaction can induce the vibrational frequency shifts significantly and the relative Raman intensity increases when water molecules directly binding to various anions with large polarizability. As for the hydrated proton, Domcke and coworkers simulated the electronic and Raman spectra of hydrated hydronium radical (H3O)aq.35,36 They suggested that (H3O)aq could be the carrier of the hydrated electron in liquid water. Recently, our calculated preresonance Raman spectra of protonated water clusters (H15O7+) adsorbed on negatively charged silver clusters are in consistence of surface-enhanced Raman scattering (SERS) spectra of interfacial water.37 All these studies focused on the Raman signals of water molecule itself, but there are a few of theoretical studies investigated the two units of hydrated protons. Further study is, however, much needed to gain a better understanding of Raman spectra of hydrated protons in special HB interactions. The goal of the present work is to explore the influence of the HB interaction, the solvation effect, and the external electric field on Raman spectra of different hydrated proton species in aqueous solution. To consider the solvation effect, we employed the solvation model of density (SMD) approach in the present calculation. On the basis of the optimized structures and simulated Raman spectra, vibrational frequency analysis provides assignments of characteristic Raman bands from Eigen and Zundel ions, as well as the influence of surrounding water. To explore the significant change of vibrational frequency shifts and Raman intensity of hydrated protons, we investigate the HB interaction, the electric field effect, and the polarizability tensor derivatives of interesting vibrational modes in Eigen isomers (H3O+Wn) and Zundel ones (H5O2+Wn) separately. Here, n is the number of water molecules involved in HB networks.


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Finally, we propose that characteristic Raman signals can be used to infer the microstructure of hydrated proton in aqueous solution by using Raman measurement.

Computational Details In this article, we use two methods to considering the solvation effect on the structure fluctuation of hydrated protons. One is the explicit model by adding localized water molecules around the protons as shown in Figure 1a. In this model, the proton HB interaction with surrounding water plays an important role in shaping the structure of clusters. Another method is using the SMD solvation model for the implicit solvent calculation of hydrated proton clusters in aqueous solution.38 The SMD model considers the non-electrostatic terms and is recommended to predict solvation Gibbs free energies (∆G) of ions and molecules. As shown in Figure 1b, we choose water with a static dielectric constant (ε = 78.3) as the solvent. Furthermore, we also considered the influence of the external electric effect on the structure deformation of Zundel ions as shown in Figure 1c. All the density functional calculations, including geometry optimization, vibrational analysis and thermodynamic energies, were carried out by using Gaussian 09 program.39 The hybrid exchange-correlation functional B3LYP approach

40,41

is

used for geometry optimizations and electronic energies calculations of hydrated protons in the gas phase and aqueous solution. As for O and H atoms, we use the augmented triplet-zeta splitting Dunning’s correlation consistent basis set aug-cc-pVTZ.42 The charge population on these hydrogen-bonded networks is estimated on the basis of natural bonding orbital (NBO) analysis.43 In a recent work, Marković et al. reported the thermodynamic values obtained at this theoretical level were in very good agreement with the existing literature values for proton and electron in solvents.44 Meanwhile, the validity of the theoretical methods on the prediction of


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Raman spectra has been demonstrated in our previous studies.34,37,45 These successes encourage us to further explore the HB interaction and the solvation effect on Raman spectra of hydrated protons in the gas phase and aqueous solution. To compare the significant change of vibrational frequency shifts of hydrated protons, we try to do normal mode analysis. On top of the optimized structures, harmonic force constant matrix and vibrational frequencies are calculated at the same theoretical level. Based on the force constant matrix of optimized structures in the Cartesian coordinate, the scaled quantum mechanical force field (SQMF) procedure is used to do normal mode analysis.46 The procedure can effectively correct the defect in the theoretical methods, basis set effect, and the anharmonic effect so that it properly reproduces experimental frequencies. To obtain information of absolute Raman intensity, we need to calculate the differential Raman scattering cross section (DRSCS) at a given excitation wavelength. First, the atomic polarizability derivative tensor (PDX) in the Cartesian coordinate can be further converted to the polarizability derivative tensor (PDQ) in the normal coordinate frame by using the following expression.47 PDQ = PD X ALS

(1)

Then the absolute Raman intensity of a given vibrational mode is,48,49

( v%0 − v%i ) h I = 2 ⋅ S 8π cv%i 45 1 − exp ( − hcv%i k BT )  i 4

R i

(2)

Where Si = 45α i′2 + 7γ i′2

α i′ =

(3)

1 (PDQXX,i + PDQYY,i + PDQZZ,i ) 3


(4)

6

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[( + 3[(PD

) ( ) ( ) + (PD ) + (PD ) ]

v%0

denote the frequency of the incident light and the vibrational frequency of the ith

γ i′2 =

2 2 1 PDQXX, i − PDQYY, i + PDQXX, i − PDQYY,i + PDQXX,i − PDQYY, i 2 YX 2 Q ,i

where

and

v%i

ZX 2 Q,i

)] 2

ZY 2 Q,i

(5)

mode. The Raman scattering factor Si in Eq. 3 is calculated from the mean polarizability tensor derivative,

αi′ , and the anisotropic polarizability derivative, γ i′2 , of the ith vibrational mode, as

seen in Eqs. (4) and (5). In this paper, the Raman intensity presented in simulated Raman spectra is in the DRSCS with the Lorentzian expansion in a line width of 10 cm-1 at laser line 514.5 nm. The unit of cm2.sr-1.mole-1 means the effective scattering cross section cm2 per steradian per molecule.

Results and Discussion Hydronium Ion H3O+ For comparison of the influence of the HB interaction and the solvation effect on the Raman spectra, we selected a free hydronium ion as a reference. Its equilibrium structure and Raman spectrum are first calculated at the B3LYP/aug-cc-pVTZ level. The predicted O-H bond distance and the HOH angle are 0.980 Å and 112.8°, respectively, which are in agreement with 0.983 Å and 111° calculated at the level of CCSD(T)/aug-cc-pVDZ.50 The hydronium ion has six fundamentals, as shown in Table 1, i.e. the symmetric bending mode (v1: a1), degenerate scissoring ones (v2 and v3: e), the symmetric stretching one (v4: a1), and degenerate asymmetric stretching ones (v5 and v6: e). By using the SQMF procedure, these fundamentals are predicted to be 806.3, 1640.6/1641.1, 3440.2, and 3524.7/3525.0 cm-1, respectively. Two scaling factors were used here for the B3LYP harmonic frequencies, 0.927 for O-H stretching coordinates and 0.963


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for the HOH bending modes. Thus, except for the v1 mode, these scaled frequencies agree well with experimental frequencies in the gas phase high-resolution infrared spectra.51-53 For the v1 mode, the experiment shows two frequencies at 526 and 954 cm-1 due to the tunneling splitting effect of the double-well potential,54 while our B3LYP calculations (∼800 cm-1) did not consider the effect. As for H3O+ ion in aqueous solution, we employ polarizable continuum model (PCM) and SMD models for considering the water solvent calculations. As shown in Table 1, the vibrational frequencies change sharply with different methods and solvation models. This clearly implies that the solvation effect plays an important role in the system of hydrated proton. In the experimental measurement, it is generally accepted that the H3O+ ion exists when the ratio of acid : water = 1 : 1.21 The Raman frequencies of the H3O+ ion are firstly reported at 1095, 1600, 3510, and 3560 cm-1 in solution containing H3O+SbCl6- in CH2Cl2.22 In an equimolar mixture of H2O-HBr system, the Raman band observed at 1050 cm-1 was assigned to the symmetric bending (v1) of H3O+.23 These experimental results indicate that the present B3LYP calculation with the SMD model may underestimate the frequency of the v1 mode. Other fundamental frequencies as shown in Table 1 showed that the frequencies calculated at the B3LYP with the SMD model are the best ones among these four calculation tests. Next we move on to the absolute Raman intensity of hydronium presented in the DRSCS at laser line 514.5 nm. The DRSCS predicted at the B3LYP/aug-cc-pVTZ level are 0.03 (v1), 0.05 (v2 and v3), 0.70 (v4) and 0.10 × 10-30 (v5 and v6) cm2.sr-1.mole-1 for a free hydronium ion in the gas phase. The absolute Raman intensities of hydronium were enhanced more significantly for stretching vibrations than the bending ones when considering the solvation effect. In order to quantitatively estimate the polarization effect, we derive the polarizability derivatives with


8

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respect to the normal coordinates. Based on Eqs. 3, 4, and 5, our calculated results are presented in Table 2 for the isotropic and anisotropic polarizability derivatives and Raman scattering factors of the six normal coordinates. The results show that the solvation effect causes an increase in both polarizability derivatives for the symmetric stretching mode (v4). As for the asymmetric stretching modes (v5 and v6), their anisotropic polarizability derivatives were enhanced twice compared with that in the gas phase.

Stable Structures of Hydrated Proton Figure 2 presents optimized structures of hydrated proton (H+(H2O)n, n = 1 ~ 10) clusters with the SMD model. The parameters of optimized geometries in the gas phase are showed in Figure S1 (see supporting information). For n = 4, larger difference in energy is presented in the two isomers, in which that the Eigen one is 3.26 kcal/mol more stable than the Zundel one in the gas phase, and 2.42 kcal/mol in aqueous solution. While for n = 6 ~ 10, the energy difference between Eigen and Zundel isomers is between 0.03 and 0.65 kcal/mol, indicating that different isomers are coexisting in the gas phase. Here, we focus on open hydrogen-bonded networks consisted of Eigen-water and Zundel-water complexes, whereas ring and cage configurations29,55 are not considered here. We compare the differences in geometries between Eigen-water and Zundel-water HBs in the gas phase. As shown in Figure S1(a), Eigen ion can form three very strong hydrogen bonds with surrounding water in the form of H9O4+(H3O+W3). Our DFT calculations show that the bonding energy is about 25.8 kcal/mol, which agrees with 23.0 kcal/mol estimated from previous mass spectrometer measurement.56 The O…O distances are 2.563 Å in the gas phase, which is comparable to the O…O distance of 2.57 Å from the experimental measurement57 and previous


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theoretical calculations.50,58 On the other hand, the Zundel ion forms four hydrogen bonds in the fully hydrated form of H13O6+(H5O2+W4). B3LYP predicts that in the gas phase the distances are 2.401 and 2.674 Å for the central and peripheral O…O bonds, respectively. Our results agree with the X-ray detection of ∼2.39 Å and ∼2.52 Å in Zundel-type H5O2+.4H2O ion for the central and peripheral O⋯O separations, respectively.59 Therefore, the HB interaction plays a more significantly role in H3O+ than H5O2+ of hydrated protons in the solvent shell. In aqueous solution, the structures of Eigen and Zundel isomers present a certain degree of distortion as shown in Figure 2. For example, in aqueous H9O4+(H3O+W3), the O…O distances are extended to 2.582 Å, which is comparable to 2.57 Å obtained within the MS-EVB approach.7 As for Zundel isomers, the structural distortions due to the solvation effect are more obvious. In the Zundel isomer of H9O4+(H5O2+W2), the O…O distances from 2.399 Å in the gas phase extended to 2.469 Å in aqueous solution. Our results by using the SMD model are slightly larger than the distances of 2.43 Å calculated with the COSMO model.60 The change in geometries of the proton solvation leads to obvious frequency shifts and Raman intensity changes, and we discussed Raman spectra in the next section.

Raman Spectra of Eigen Isomers in the Gas Phase In the gas phase, a significant influence of Eigen-water HB interactions on infrared spectra was widely discussed in previous studies.19,20 Here we mainly focus on characteristic peaks in Raman spectra of different Eigen isomers H3O+Wn (n = 3 - 9) presented in Figure 3. Table 3 summarizes the bond lengths and vibrational frequencies of the H3O+ moiety in different Eigen clusters. These data can be considered from three points as follows. First, we inspect the Raman spectral feature in symmetric Eigen-water HBs microstructures. For example, the clusters H3O+W3,


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H3O+W6 and H3O+W9 are in an approximate C3 symmetry with an equal OE…On distance. Here, OE and On denote the oxygen atom in the Eigen unit and in the surrounding Wn water molecules. The O…O distance shows a decreasing trend with values of 2.562, 2.543 and 2.529 Å in H3O+W3, H3O+W6, and H3O+W9, respectively, indicating that the size effect strengthens the inside HB interaction.56 Meanwhile, this leads to a red shift of H3O+ stretching vibrations presents in Raman spectra, as shown in Table 3. Our results are in good agreement with simulated infrared peaks predicted at 2758 and 2863 cm-1,50 and 2665 cm-1 in argon predissociation spectrum of H3O+W3.19 The red shift of Raman bands of H3O+ is due to the negative charge transfer from the lonepaired orbitals of outer oxygen atoms to the anti-bonding orbital of the center O-H bonds. The NBO analysis obviously supports the data. The net transferred charges amounts from the outer water molecules to the H3O+ moiety are estimated about 0.059e (H3O+W3), 0.071e (H3O+W6), and 0.081e (H3O+W9), respectively. The stabilization energies due to the orbital interaction increase to 19.46, 22.57, and 25.02 kcal/mol, indicating that the arrangement of outer water molecules has a significant influence on the vibrational frequency shift of H3O+ moiety. Secondly, the asymmetric arrangements (Cs symmetric) of outer water also lead to obvious changes of Raman bands in H3O+ moiety. For example, in H3O+W4, the H3O+ moiety exhibits asymmetric geometries with shortened OE…O1 and elongated OE…O2 and OE…O3 bonds with respect to H3O+W3. Correspondingly, Raman peaks appear at 2252.7, 2918.9 and 2981.4 cm-1. The latter two peaks correspond to 2879 and 2967 cm-1 observed in high-frequency predissociation spectrum.31 After a new O2…O5 HB formed in H3O+W5, the length of the OE…O2 bond shortens to 2.517 Å. In Raman spectrum of H3O+W5, the OE…O2 stretching vibration red shifts to 2579.1 cm-1, while vibrations for OE…O1 and OE…O3 blue shift to 2428.0


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and 3025.6 cm-1, respectively. As shown in Table 3, similar trend is observed in the change from H3O+W6 to H3O+W9. The present results indicate that not only the direct HB interaction could influence the Raman shifts of the H3O+ moiety, but also the solvent water molecules in the outer second shell also play an important role in their Raman spectra. Thirdly, we presented the assignment of OH vibrational frequency from solvent water molecules in the range of 3200 and 3800 cm-1. The peaks were ascribed to stretching vibrations of HB O-H in water Wn (n = 1 – 3) present a blue shift from 3230 to 3500 cm-1 as shown in Figure 3 (brown dashed box). They agree with previous calculations

20,28,50

and observations in

the gas phase predissociation spectra.19,31 This is due to the weakening HB interaction between the first and second water molecules with increasing the size. The free O-H stretching vibrations in the second shell exhibit the Raman signals at around 3660 and 3750 cm-1, as observed in the gas phase infrared spectra.27,33 Finally, our results show that the size effect has little influence on Raman intensities of the H3O+ moiety. Bending modes have very weak Raman intensities of around 2 × 10-32 cm2.sr1.

mole-1 in the excitation line of 514.5 nm, which are about 1 percent of the Raman intensity of

the stretching ones. This is similar to the case of pure water.61 Raman intensities of the symmetric O-H stretching peaks increase slightly with increasing the size, and the DRSCS increases from 2.18 to 2.60 × 10-30 cm2.sr-1.mole-1 for that in H3O+W3 and H3O+W9, respectively. This can be explained due to the positive excess charge dispersion in larger clusters though the enhancement effect is not significant. For example, NBO analysis shows that the positive charge distributes around the central H3O+ ion from 0.77 au in H3O+W3 decreasing to 0.70 au in H3O+W9.


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Raman Spectra of Aqueous Eigen Isomers Spectroscopic properties of hydrated proton in condensed phase have been observed substantially different from that in the gas phase. Figure 4 presents simulated Raman spectra of Eigen isomers in aqueous solution by using the SMD model. Compared with that in the gas phase, Raman intensities increase about 2 fold for both bending and stretching vibrations, but their intensity ratio is still close to 0.01. The Raman bands of bending and libration vibrations provide rich information on the proton clusters. The symmetric bending frequency was observed at about 1220 cm-1 in Raman spectra of 4:1 mixture of H2O-HBr system.23 Our calculations show that the frequency of the symmetric bending vibration (v1) is at 1230.2 cm-1 in H3O+W3 under the SMD model. As shown in Figure 4, the vibrational frequencies of bending modes are not sensitive to environment factors, with frequency of v1 is around 1250 cm-1 in fully hydrated clusters. The asymmetric bending modes (v1 and v2) of H3O+ give a very weak Raman peak around 1660 cm-1. The peaks appeared around 1560 cm-1 are from the HOH bending vibration of water in the first solvation shell. The frequencies are underestimated due to the SMD model, compared with the observed Raman band of water at about 1620 cm-1 in the presence of dissolved HCl.62 For the O-H stretching frequencies in the H3O+ moiety, the shift trend in Figure 4 is similar to the case observed in Figure 3. The O-H stretching frequencies of hydronium are in the range of 2200 and 2800 cm-1. This is in consistence with a broad and diffuse band observed between 2460 and 3000 cm-1 assigned to the OH stretching band of H3O+ ion.25 Besides, in Raman measurement of acid solution, the characteristic bands at around 3200 cm-1 drew much attentions.26,62 In these previous studies, this is believed as a characteristic band of the H3O+ ion in acid solution. Actually, our DFT calculations show that the broad bands at 3200 cm-1 should be assigned to the O-H stretching vibration of solvent water molecules, which are hydrogen


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bonded with other water molecules. Figure 4 shows this band is slightly sensitive to the environment water, locating in the region of 3200 and 3300 cm-1. The bands at 3635 and 3710 cm-1 can be assigned to the free O-H bonds of water molecules in the second shell. For water with few HB interaction in aqueous solution, the bands should appear at around 3400 cm-1 in Raman measurement.23,62

Raman Spectra of Zundel Isomers in the Gas Phase The Raman spectrum of the free Zundel ion is significantly different from the Eigen one. Table 4 lists vibrational frequencies and Raman intensities for all vibrational modes of the free Zundel ion. It is worth nothing that the O－H+－O moiety has two coupling stretching modes (v6 and v7) at 596.6 and 910.6 cm-1 assigned to the symmetric and asymmetric O-H stretching vibrations, respectively. Only the lower frequency has slightly strong Raman activity in the gas phase, which is comparable with the most intensive Raman band at 637 cm-1 in H5O2+ClO4- crystal.63 While the higher frequency at 910.6 cm-1 owns very strong IR intensity (See Table S1 in supporting information), which agrees with previous theoretical predictions19,50 and infrared measurements.58,64,65 When the Zundel clusters increase to H5O2+W2, H5O2+W4, and H5O2+W6, the fundamental frequencies and Raman intensities are sensitive to the symmetric arrangement of surrounding water (C2 symmetry). Table 5 lists the O…O distances, and vibrational frequencies and Raman intensities of v6 and v7 of O－H+－O moiety in Zundel isomers. The O…O distance of O－H+－ O moiety keeps in a constant of 2.400 Å in these isomers, which is in a good agreement with 2.40 Å experimentally measured by X-ray technique,66 and 2.400 Å calculated at the


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CCSD(T)/aug-cc-pVDZ level.50 Therefore, the v6 and v7 Raman bands have some slight shifts due to surrounding water molecules. While in H5O2+W8, the O…O distance slightly increases to 2.420 Å with asymmetric O-H distances of 1.123 and 1.297 Å, and the frequency of v7 blue shift to 1265.6 cm-1. This is due to a slight asymmetric arrangement of eight water molecules arranged in the surrounding of Zundel ion, resulting in the central proton deviation from the C2 symmetry obviously. It is worth noting that in H5O2+W5 and H5O2+W7, the asymmetric arrangements of surrounding water lead to large structural distortion. The distances of O－H+－O significantly increase to about 2.450 Å, which is significantly different from the typical structure of Eigen or Zundel ion. This indicates that there are more complex intermediates in the process of proton transfer. In their Raman spectra, the v7 vibration further blue-shifts to around 1900 cm-1. Meanwhile, the Raman intensities are enhanced more than 30-fold referring to that in the free Zundel ion. Similarly, this perturbation from weak interactions is enough to result in a significant change in configuration and infrared spectra of the Zundel ion.67,68

Raman Spectra of Aqueous Distorted Zundel Isomers For the Zundel ions, the sensitivity of structures and spectral properties to the solvent environment is very remarkable. By using the SMD model in aqueous solution, the solvation effect leads to the central proton deviation from the central position, and the increase of the O…O distance to 2.418 Å, which is in agreement with a previous calculation about 2.41~2.44 Å with the PCM model.69 The symmetry breaking causes a significant change in Raman spectra of the Zundel ions closely related to the polarity of solvent molecules. Table S2 (see supporting information) lists the structural features, stretching frequencies, and Raman intensities of the v6


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and v7 vibrations in the H5O2+ ion in different solvents with their dielectric constants in an ascending sequence. The calculated results indicate that the H5O2+ ion presents a significant asymmetry in the central structure with unequal O-H bonds in the O－H+－O moiety when the dielectric constants of solvents are larger than 24, such as ethanol and methanol. Meanwhile, the two vibrations v6 and v7 are decoupled. The asymmetric v7 frequency blue-shifts to 773.6 cm-1 with a slight stronger Raman intensity. Table 4 also lists isotropic and anisotropic polarizability derivatives of H5O2+ under the SMD model. This is used to quantitatively analyze the influence on Raman intensity the ion in aqueous solution. In H5O2+, the most intense band is assigned to the symmetric stretching modes (v13) of the outer water moiety. Although the anisotropic part is enhanced about 3 fold due to the solvation effect, the absolute Raman intensity of the v13 mode increases slightly. This means that the isotropic polarizability derivatives dominate the absolute Raman intensity of symmetric stretching ones. In aqueous solution, the asymmetric v7 vibration is enhanced to 1.46 × 10-30 cm2.sr-1.mole-1, which is about 50 fold larger than that in the gas phase. Our results show that the solvation effect causes an increase in both polarizability derivatives for the v7 mode. Finally, the Raman intensities of bending vibrations (v8 ~ v11), however, are still relatively weak. The arrangement of localized solvent water molecules leads to a further deformation of Zundel isomers in larger size. This leads to the transition of Zundel structural to the Eigen one under the SMD model. For example, when the SMD model was used, the O…O distance of the central O －H+－O moiety increases from 2.418 Å in H5O2+ to 2.498 Å in H5O2+W4, which is comparable to the O…O distance in Eigen isomers. These obvious deformation of Zundel isomers in aqueous solution can be regard as that symmetric Zundel structure is a unstable structure with an existing times about 50 fs for proton transfer in the Eigen-Zundel-Eigen mechanism proposed in recent


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studies.5,8,32 Correspondingly, the characteristic v7 vibrational frequency exhibits a significant blue shift. As shown in Figure 5, the v7 frequency blue-shifts from 773.6 cm-1 in H5O2+, to 1785.6 cm-1 in H5O2+W2, and further to 2034.8 cm-1 in H5O2+W4. The large fluctuation in vibrational frequency shifts makes the assignment much more difficult for proton transfer in aqueous solution. Also in dilute acidic solution, the Raman spectra of Zundel isomers with large size (H5O2+Wn, n = 5 – 8, see Figure S2 in supporting information) are similar to that of Eigen ones. Therefore, this interprets why the exact assignment of Zundel ions is lack in Raman measurements in acidic solution.

Polarizability tensors To further consider the change of absolute Raman intensities in proton-water HBs, we calculated the polarizability tensor (αρσ) changes along the normal coordinates for bending and stretching vibrations of proton-water HBs. Figure 6 presents the variation of the six polarizability tensor components of these normal modes. For the Eigen isomer H3O+W3, the three Eigen-water HBs are in the xy plane. The components αxx and αyy have the largest values among the six components, while the values of anisotropic polarizability components αxy, αxz and αyz are almost zero. For symmetric bending (v1) modes of H3O+ moiety in H3O+W3, as shown in Figure 6a, the polarizability increases dramatically when the proton is far away from the plane xy, although the Raman intensity is very weak and the polarizability derivatives are almost zero at the equilibrium position. This indicates that the proton movement has significant influence on the molecular polarizability and Raman intensity. Figure 6b presents the variation of polarizability tensor components of the symmetric stretching one (v4) in H3O+W3. As the proton moves from the H3O+ to outer water molecules, the polarizability increases remarkably due to the HB


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interaction and the fluctuation of charge center that the electrons move in the opposite direction. In the case, the slopes of αxx and αyy increase significantly, showing that there will be an enhancement of Raman intensity during the process of proton transfer. For the Zundel ion H5O2+, we calculate the polarizability tensors along the asymmetric stretching (v7) coordinate in the O － H+ － O moiety as shown in Figure 6c. There the polarizability value of αxx along the O－H+－O bond in the x axis is larger than the other five components, indicating the derivative of αxx values is the decisive factor of the Raman intensity. For H5O2+ in the gas phase, Figure 6c presents the largest polarizability at the equilibrium position, which agrees with the extremely polarizable property of HB and high polarizability found in Zundel ions.70 However, the derivative of polarizability tensor component αxx is almost zero at the equilibrium position, indicating the Raman intensity of the v7 mode is very weak in the gas phase. Due to the solvation effect, the proton leaves from the central position moving to one side. Thus, the potential energy curve of the solvated H5O2+ ion also forms a symmetric double-well curve. As shown in Figure 6d, the maximum of the polarizability tensor is no longer at the equilibrium position. Thus, the larger derivative of αxx is estimated about 1.52 Å2.amu-1/2 at the equilibrium position. This explains that the Raman intensity of the v7 mode increases in aqueous solution. No only the solvation effect, the electric field effect also leads to the transition of the Zundel structure to an Eigen one. Table S3 (see supporting information) lists the geometric parameters of O－H+－O moiety in H5O2+, and vibrational frequencies and Raman intensities of the two stretching modes, when an external electric field is applied along the x axis. As the electric field changes from 0.001 to 0.010 au, the O…O distance of O－H+－O moiety in H5O2+ increases


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from 2.405 Å to 2.487 Å, approaching the O…O distance in Eigen isomers. Here, the proton moves along the opposite direction of electric fields. Meanwhile, the two stretching vibrations of O－H+－O moiety decoupled so that the frequency of the v6 mode is decreased, while the v7 frequency presents an increasing trend from 962.7 to 2192.6 cm-1. This is similar to the change of the v7 frequency in the different solution. Also, the Raman intensity of the v7 mode is enhanced with increasing the electric field. Figure 7 presents the change of the polarizability tensors. The electric field also leads to a significant increase in the derivative of the polarizability tensor component αxx at the equilibrium position. For example, the derivative of αxx is increased to 1.79 Å2.amu-1/2 when the applied electric field is very high to 0.010 au. Therefore, combining theoretical prediction and Raman scattering theory, the analysis of polarizability tensor derivatives is very helpful to understand the structural relaxation of hydrated proton under the perturbation of external fields.

Conclusion We have investigated the influence of the hydrogen bonding (HB) interaction, the solvation effect and the electric field effect on Raman spectra of hydrated protons. The proton-water HB interaction plays an important role in shaping the microstructures of hydrated proton and determining the Raman shifts in different concentrations of proton environments. Our results show that not only the direct HB interaction could influence the Raman shifts, but also the solvent water molecules in second-shell have an influence on their Raman spectra. Therefore, characteristic Raman signals can be used to infer the microstructure of hydrated proton by using Raman measurement.


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Besides, the solvation effect has influence on vibrational frequency shift and Raman intensity enhancement of O-H characteristic bands in Eigen isomers. In particular, the solvation effect leads to the proton leaving from the central position, and finally results in a transition of Zundel structure to Eigen one in aqueous solution when the solvent polarity increases. The transition process presented in the Raman spectra has a significant blue shift and Raman intensity enhancement of asymmetric O-H stretching vibrations in the O－H+－O moiety. By analyzing the variation of polarizability tensors of the Zundel ion, our calculated results show that the asymmetric structure leads to that the maximum of the polarizability tensor is no longer at the equilibrium position. Thus, a larger derivative appeared at the equilibrium position explains a stronger Raman signal possibly to be observed in aqueous solution. Finally, we also consider the electric field effect on the structures and Raman spectra of the Zundel ions. Similar to the solvation effect, an electric field applied along the x direction also leads to the proton deviation to one side. By combining theoretical prediction and Raman scattering theory, our results suggested that the analysis of Raman spectra based on the polarizability tensor derivatives is very helpful to understand the structural relaxation of hydrated proton under the perturbation of external fields. This work is closely associated to application of surface-enhanced Raman spectroscopy in electrochemical interfaces.

ASSOCIATED CONTENT Supporting Information. This material is available free of charge via the Internet at http://pubs.acs.org.


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Optimized structures of hydrated proton in the gas phase, simulated Raman spectra of Zundel isomers, vibrational frequencies and infrared intensity of the free Zundel ion, structural parameters and frequencies and Raman intensities of the H5O2+ ion in different solvents, structural parameters and frequencies and Raman intensities of the H5O2+ ion in an electric field.

AUTHOR INFORMATION

Corresponding Author De-Yin Wu Address: State Key Laboratory of Physical Chemistry of Solid Surfaces, Collaborative Innovation Center of Chemistry for Energy Materials, and Department of Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China. Phone Number: +86-592-2189023 Fax number: +86-592-2186979 E-mail address: [email protected]

Acknowledgements National Natural Science Foundation of China (21321062, 21533006 and 21373712), National Key Basic Research Program of China (No. 2015CB932303), and Funds of State Key Laboratory of Physical Chemistry of Solid Surfaces.


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TABLE 1. Experimental and Theoretical Vibrational Frequencies (cm-1) and Raman Intensity (IR, 10-30 cm2.sr-1.mole-1) of Vibrational Modes of Hydronium Ion. H 3O

Freq (g)

+

Freq (l) CCSD(T)/

Modes

CCSD(T)

B3LYP

CCSD(T)/

B3LYP/

IR B3LYP/

Expt.(g)

B3LYP/

B3LYP/

PCM

SMD

B3LYP PCM

SMD

PCM

SMD

v1

889

806.3

954, 526d

1030.4

1075.9

934.0

992.3

0.03

0.03

0.03

v2

1620

1640.6

1626b

1706.0

1674.5

1655.9

1616.9

0.05

0.06

0.07

v3

1620

1641.1

1639b

1715.1

1687.7

1659.2

1636.0

0.05

0.06

0.07

v4

3426

3440.2

3390, 3491e

3627.3

3633.0

3476.9

3484.1

0.70

0.97

1.28

v5

3537

3524.7

3513c

3706.0

3706.3

3546.0

3541.1

0.10

0.14

0.20

v6

3537

3525.0

3530 c

3712.2

3709.6

3547.8

3545.5

0.10

0.14

0.20

a

Vibrational frequencies and Raman intensities are calculated at the B3LYP and CCSD(T)/augcc-pVTZ level. Note that the vibrational frequencies by using the B3LYP method were scaled. (g) and (l) denote the frequencies in the gas phase and in liquid solution, respectively. b Ref52, c Ref51, d Ref54, and e Ref53.


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TABLE 2. Isotropic Polarizability Derivatives (Å2/amu1/2), Squared Anisotropic Polarizability Derivatives (Å4/amu) and Raman Scattering Factors (Å4/amu) of Hydronium Ion. H3O+

B3LYP

B3LYP/PCM

B3LYP/SMD

Modes

α′

γ ′2

SR

α′

γ ′2

SR

α′

γ ′2

SR

v1

-0.07

0.01

0.31

-0.07

0.02

0.41

-0.08

0.03

0.46

v2

0.00

0.20

1.40

0.00

0.25

1.74

0.00

0.27

1.91

v3

0.00

0.20

1.40

0.00

0.25

1.76

-0.01

0.27

1.89

v4

1.14

0.63

62.82

1.36

0.73

89.27

-1.58

0.79

117.80

v5

0.00

1.37

9.62

0.00

2.01

14.19

0.02

2.71

18.95

v6

0.00

1.37

9.62

-0.05

2.01

14.11

0.06

2.71

19.15


27


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Page 28 of 38

TABLE 3. Bond Lengths (lOE…On/Å) and Vibrational Frequencies (FOE…On/cm-1) of H3O+ Moiety in Eigen Isomers (H3O+Wn, n = 2 – 9) in the Gas Phase Calculated at B3LYP/aug-cc-pVTZ Level. Eigen Isomers

lOE…O1

lOE…O2

H3O+W2

2.499

2.494

H3O+W3

2.562

2.562

H3O+W4

2.483

H3O+W5

lOE…O3

FOE…O1

FOE…O2

FOE…O1

2300.2

2479.1

3659.1

2.562

2754.2

2757.3

2879.9

2.595

2.597

2252.7

2918.9

2981.4

2.516

2.517

2.620

2428.0

2579.1

3042.6

H3O+W6

2.543

2.543

2.543

2602.1

2602.2

2786.0

H3O+W7

2.476

2.569

2.569

2157.9

2774.0

2871.7

H3O+W8

2.506

2.507

2.591

2319.6

2487.5

2917.3

H3O+W9

2.529

2.529

2.529

2486.9

2487.3

2703.8

a

On the basis of vibrational frequencies analysis, the vibrational frequencies were scaled through the SQMF procedure. OE and On denote the oxygen atom in the Eigen unit and in the surrounding Wn water molecules.


28

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


TABLE 4. Vibrational Frequencies (cm-1), Raman Intensity (IR, 10-30 cm2.sr-1.mole-1), Isotropic Polarizability Derivatives (Å2/amu1/2) and Squared Anisotropic Polarizability Derivatives (Å4/amu) of All Vibrational Modes of the Free Zundel ion in the Gas Phase and Aqueous Solution Calculated at the B3LYP/aug-cc-pVTZ (SMD) level. H5O2+

Aqueous Solution

Gas Phase

Assignment

Modes

Freq(g)

IR

α′

γ ′2

Freq(l)

IR

α′

γ ′2

v1

171.3

0.76

0.00

0.13

254.4

0.16

0.02

0.10

tors.

v2

351.5

0.08

0.00

0.05

633.5

0.04

-0.01

0.04

oop

v3

423.0

0.13

-0.03

0.09

486.5

0.03

0.02

0.03

oop+line

v4

492.9

0.04

0.00

0.03

691.7

0.11

-0.01

0.03

rocking

v5

507.1

0.04

0.00

0.04

437.1

0.04

-0.04

0.04

rocking

v6

596.6

0.54

-0.24

0.22

248.1

0.30

0.06

0.15

s. stre. O－H+－O

v7

910.6

0.03

0.00

0.06

773.6

1.46

0.41

1.12

a. stre. O－H+－O

v8

1419.8

0.02

0.00

0.06

1330.6

0.03

0.00

0.09

linear

v9

1488.1

0.09

0.11

0.22

1550.7

0.09

-0.04

0.34

linear

v10

1649.7

0.04

0.03

0.14

1632.0

0.04

-0.04

0.13

bend

v11

1709.9

0.02

0.00

0.08

1661.0

0.04

-0.03

0.07

bend

v12

3593.5

0.13

-0.05

1.73

3583.9

1.15

1.46

1.65

s. stre. of HOH

v13

3601.7

1.36

-1.70

0.52

3603.4

1.68

1.86

1.88

s. stre. of HOH

v14

3678.6

0.18

0.05

2.58

3643.2

0.71

0.01

4.42

as. stre. of HOH

v15

3679.4

0.18

0.07

2.59

3668.3

0.34

0.02

4.97

as. stre. of HOH

a

The vibrational frequencies were scaled through the SQMF procedure. tors., oop, linear, bend, and stre. denote torsion, out-of-plane, linear, bending, and stretching vibrations, respectively. s. and as. denote symmetric and asymmetric, respectively.


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Page 30 of 38

TABLE 5. The O…O distances (Å) of O－H+ －O moiety, Vibrational Frequencies (cm-1), Raman Scattering Factors (SR, Å4/amu), and Raman Intensity (IR, 10-30 cm2.sr-1.mole-1) of Central O-H Stretching Vibrations in Zundel Isomers (H5O2+Wn, n = 2, 4 – 8) in the Gas Phase Calculated at B3LYP/aug-cc-pVTZ level. Zundel Isomers

lO…O

F6

SR,6

IR,6

F7

SR,7

IR,7

H5O2+W2

2.399

589.7

1.96

0.26

816.4

0.90

0.08

H5O2+W4

2.401

618.8

3.30

0.41

965.3

0.19

0.01

H5O2+W6

2.403

596.7

2.29

0.30

863.3

0.89

0.07

H5O2+W8

2.420

502.6

0.77

0.13

1265.6

15.12

0.76

H5O2+W5*

2.450

439.4

0.61

0.12

1941.2

33.14

0.93

H5O2+W7*

2.451

441.4

0.49

0.10

1932.6

35.99

1.02

a

On the basis of vibrational frequencies analysis, the vibrational frequencies were scaled through the SQMF procedure. *denote the structures with asymmetric surrounding water arrangement.


30

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 1. schematic diagram of HB interaction, the SMD solvation model, and external electric field on hydrated protons.


31


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Page 32 of 38

Figure 2. Optimized structures of Eigen (a) and Zundel (b) hydrated proton clusters calculated at the B3LYP/aug-cc-pVTZ level with SMD model.


32

Page 33 of 38

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Figure 3. Simulated Raman spectra of Eigen-type ions H3O+Wn (n = 3 ~ 9) in the gas phase calculated at the B3LYP/aug-cc-pVTZ level. The Lorentzian line shape was used in the expansion of the DRSCS value with the linewidth of 10 cm-1. The excitation wavelength of 514.5 nm was used. The red and blue arrows denote the frequency shifts, respectively. The peaks in brown dashed box and in black dot lines are assigned to the hydrogen-bonded and free O-H stretching vibrations of water, respectively.


33


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Page 34 of 38

Figure 4. Simulated Raman spectra of Eigen isomers H3O+Wn (n = 3 ~ 9) in aqueous solution calculated at the B3LYP/Aug-cc-pVTZ level with SMD model. The Lorentzian line shape was used in the expansion of the DRSCS value with the linewidth of 10 cm-1. The excitation wavelength of 514.5 nm was used. The red and blue arrows denote the frequency shifts. The peaks in brown dashed box and in black dot lines correspond to the hydrogen-bonded and free OH stretching vibrations of water, respectively.


34

Page 35 of 38

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 5. Simulated Raman spectra of Zundel isomers H5O2+Wn (n = 0, 2, 4) in the aqueous solution calculated at the B3LYP/Aug-cc-pVTZ level with the SMD model. The Lorentzian line shape was used in the expansion of the DRSCS value with the linewidth of 10 cm-1. The excitation wavelength of 514.5 nm was used. The blue arrows denote the frequency shifts.


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Page 36 of 38

Figure 6. Definition of Cartesian coordinates and the polarizability tensor components

αxx, αyx, αyy, αzx, αzy, αzz along normal coordinates of symmetric bending (a) and stretching (b) vibrations of the H3O+ moiety in H3O+W3, and asymmetric stretching vibrations of O－H+－O moiety in H5O2+ in the gas phase (c) and aqueous solution (d), respectively.


36

Page 37 of 38

0.000 au 0.001 au 0.002 au 0.003 au 0.004 au 0.005 au 0.006 au 0.007 au 0.008 au 0.009 au 0.010 au

23

3

Polarizability/(Bohr )

22 21 20 19 18 17 16 15 -0.6

-0.4

-0.2

0.0

0.2

····

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.4

0.6

1/2

Normal coordinate/(Å amu ) Figure 7. The polarizability tensor component αxx along normal coordinates of the asymmetric stretching vibrations of O－H+－O moiety in the Zundel ion H5O2+ in an applied electric field from 0.000 to 0.010 au (Black to Red) in the x direction.


37


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Page 38 of 38

TOC:


38

DFT Study of Hydrogen-Bonding Interaction, Solvation Effect, and

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