Ionic Hydrogen Bonding Vibration in OH⁻(H₂O)_2-4

Abstract

Focusing on the OH⁻(H₂O)_2–4 clusters, we have theoretically studied the strongly red shifted ionic hydrogen bond (IHB) OH stretching vibration of water molecules directly bound to the hydroxide. Our calculations show that a systematic blue shift of the IHB OH peak is observed with the increase in the number of water molecules in the first solvation shell. Furthermore, we showed that the vibrational signature of the four coordinated hydroxide for OH⁻(H₂O)₄ will be observed in the 2800–3200 cm⁻¹ range.

1 Introduction

Due to the wide interest in acid base chemistry, the local hydration structure of aqueous hydroxide has been explored using many different experimental techniques [1,2,3,4,5,6,7,8] and theoretical simulations [9,10,11,12,13,14]. However, we still do not have a unified picture on the local hydration structure and transport mechanism of hydroxide in aqueous solutions. Specifically, we still do not have a consensus on the number of water molecules pinned to the O atom in OH⁻ at room temperature in aqueous solution. Ab initio molecular simulation [9], neutron scattering [2], and photoelectron emision [4] experiments for the aqueous phase have reported that 4 to 5 water molecules constitute the first solvation shell. Johnson and co-workers provided an answer from the gas-phase clusters by measuring the Ar-tagged predissociaiton spectra of OH⁻(H₂O)_n (n = 1–5) [15]. Due to the emergence of distinct peaks within the 3400–3600 cm⁻¹ region following the addition of the forth water to the OH⁻, they concluded that three waters constitute the first solvation shell in gas-phase OH⁻(H₂O)_n clusters. This gas-phase result contradicts with the liquid phase simulations and experiments. There have been many theoretical studies on small hydroxide water clusters [16,17,18,19,20], but there are no clear explanations for why the gas-phase and liquid phase differ.

In the present study we revisit this three and four coordinated water problem for OH⁻(H₂O)₄ and provide our interpretation from our theoretical calculations [21,22,23,24]. For anion hydration, due to the strong interaction between the excess electron and the hydrogen of the hydrating H₂O, the peak positions of this ionic hydrogen bond (IHB) OH, the OH directly bound to the anion, show very large anharmonicity. Therefore, the commonly used harmonic approximation fails miserably in calculating these systems. Furthermore, due to the quantum nature as well as the large anharmonicity of the IHB OH vibration, classical trajectory simulations fail to obtain accurate peak positions and intensity [25]. In addition, IHB causes strong couplings between several vibrational modes, which result in very broad spectra that cannot be assigned with simple quantum numbers [26,27,28,29,30]. This means that theoretical simulations have to take into account mode coupling as well as large anharmonicity, and provide the information beyond the stick spectra.

In the present paper, focusing on the OH⁻(H₂O)_2–4 clusters, we have theoretically studied the strongly red shifted IHB OH stretching vibration of water molecules directly bound to the hydroxide. After a brief review of the calculation methods, we summarize our findings which help us untangle some of the questions concerning the geometry of the hydrated hydroxide.

2 Methods

The vibrational spectra for OH⁻(H₂O)_2–4 were calculated by solving the multi-dimensional vibrational Schrödinger equation for the relevant vibrational modes. The potential energy surfaces (PESs) for the vibrational Hamiltonian and associated dipole moment functions (DMFs) were calculated with quantum chemistry methods. As reported in our previous papers [31,32], we used MP2[33]/6–311++G (3df,3pd) [34,35] for OH⁻ (H₂O)_2,3, and B3LYP[36,37]/6–31+G (d,p) forOH⁻(H₂O)₄. The vibrational calculations were carried out using the internal coordinates {s_i} with the following local mode (LM) vibrational Hamiltonian:   

$H=\sum _{i=1}^n\sum _{i=1}^n{G}_{ij}^{-1}\frac{\partial }{\partial s_i}\frac{\partial }{\partial s_j}+V\left(s_1, s_2,\cdots ,s_n\right)$

(1) ,where the $G_{ij}^{-1}$ is the inverse of the G-matrix of the internal coordinates [38]. Depending on the number of degrees of freedom that is considered explicitly, n, we will name the calculation LM-nD. Here we have ignored the rotational-vibrational coupling terms, as well as the mass dependent Watson terms but we believe that this will not cause great variation in the obtained results. Indeed, when we performed 2^nd order vibrational perturbation calculation [39] for the OH stretching vibration peak position for OH⁻(H₂O)₄ with and without rotational-vibrational couplings, we saw only a 1 cm⁻¹ shift. In the calculation of the PES and DMF, 20 grid points were employed for each degree of mode, and quartic polynomial interpolation is used to obtain the values of PES and DMF required for the vibrational calculation.

The vibrational spectrum is obtained by the diagonalization of the vibrational Hamiltonian matrix expanded by the basis obtained by taking the direct product of the discrete variable representation [40](DVR) of the harmonic oscillator basis functions. Thus, our calculation includes the mode coupling effects between active coordinates. We found that the convergence of 1 cm⁻¹ for the peak positions can be achieved by using 20 harmonic oscillator basis functions for each degree of freedom. We note that these basis functions are used to account for the anharmonic mode coupling effects as well as the anharmonicity of the stretching motions [22,31]. Using the obtained eigenvalues, eigenvectors, and DMF, the integrated absorption intensities (km mol⁻¹) between the initial ground state, ${\text{Ψ}}_0$, and the vibrational excited states, ${\text{Ψ}}_f$, were calculated by [41],   

$A=\frac{N_A\pi }{3{\in }_0\hslash c}{\left|⟨{\Psi }_0\text{|}\hat{\mu }\text{|}{\Psi }_f⟩\right|}^2{\tilde{\upsilon }}_{0f}=2.506{\left|{\mu }_{0f}\right|}^2{\tilde{\upsilon }}_{0f}$

(2) ,where $\hat{\mu }$ is the DMF in Debye, ${\tilde{\upsilon }}_{0f}$ is the transition energy in cm⁻¹ and $|{\mu }_{0f}{|}^2$ is the square of the absolute value of the transition moment vector.

To simulate the shape of the vibrational spectra we used the Voigt function [42], which requires the homogeneous and inhomogeneous widths. Based on our previous studies [21], we used the following simple power law relation between peak position ω and associated homogeneous linewidth Γ in cm⁻¹ unit,   

$\text{Γ}=0.11{\left({\omega }_{\text{ref}}-\omega \right)}^{1.22}$

(3) ,where ${\omega }_{\text{ref}}$ is the reference peak position of the OH stretching for the water (monomer) molecule with the local mode calculation. In this study, we use ${\omega }_{\text{ref}}$ = 3715 cm⁻¹ obtained with B3LYP/6-31G (d,p) for OH⁻(H₂O)₄, and ${\omega }_{\text{ref}}$ = 3772 cm⁻¹ obtained withMP2/6–311++G (3df,3pd) for OH⁻(H₂O)_n (n = 2–3). The inhomogeneous width is obtained from the direction of the transition moment with respect to the principal axes for inertia, and the temperature dependent rotation population. Here, because the experimental spectra lack rotational line structure, we only need to obtain an estimate on the temperature dependent rotational envelope. Uzer et al. [43], have used the following method to estimate the inhomogeneous width. First, at a given temperature using the Boltzmann distribution we obtain the most populated angular momentum J state, $J_{\text{max}}$,by assuming the symmetric top approximation. Then we approximate the inhomogeneous width Δ due to temperature dependent rotational broadening using   

$\text{Δ}=4\text{B}{J}_{\text{max}}$

(4) ,where B is the rotational B-constant of the cluster.

3 Results and discussion

For OH⁻(H₂O)₄, previous calculations have shown that the three coordinated isomer I and the four coordinated isomer II (see Figure 1) are isoenergetic using high level quantum chemistry calculations [11,21]. In Figure 1, we present the OH stretching modes which we explicitly coupled in our LM-nD calculation. For isomer I, the three IHB OH (light blue) in the first solvation shell; three OH stretching modes in the second solvation shell (purple); two free OH stretching vibration (light green) in the first solvation shell; and the hydroxide stretching vibrations. We will name the two waters on the left and right sides which are donating a hydrogen bond to the OH⁻ and accepting a hydrogen bond from the second solvation shell water as donor acceptor (DA) H₂O. On the other hand, for the water molecule in the center which is donating a hydrogen bond both to the OH⁻ and the second solvation shell water, we will use the notion DD H₂O. For isomer II, we used the four IHB OH (light blue); the four free OH (light green); and the hydroxide stretching vibration for LM-nD calculations. In this model, we ignore the intramolecular coupling of the two OH stretching vibrations in the same water molecule. In our first paper [21], we compared the simple LM-1D model, where all OH oscillators are independent, versus the local monomer unit model, where two OH stretching and one bending modes in a water molecular were explicitly coupled. It was shown that this intramolecular coupling only causes a 20 cm⁻¹ shift for the IHB OH stretching peaks in OH⁻(H₂O)₃ and OH⁻(H₂O)₄. On the other hand, in our second paper [31], we found that intermolecular coupling of the IHB OH stretching modes of different first solvation shell waters can cause the peaks to shift by 200 cm⁻¹ for OH⁻(H₂O)₃. Thereby in the present paper, we will directly couple the IHB OH on different water molecules and ignore the intramolecular coupling to the free OH in the same water. The obtained peak positions are summarized in Tables 1 and 2.

Figure 1.

 Schematics of OH⁻(H₂O)₄ (a) isomer I, and (b) isomer II. The OH vibrations that were explicitly coupled in the vibrational calculation are represented with color coded arrows.

Table 1.  Peak position in cm⁻¹ and absorption intensity, in km mol⁻¹, for OH⁻(H₂O)₄ isomer I were calculated using B3LYP/6-31+G (d,p).

Assignment	Peak position	Intensity
IHB OH (antisymmetric combination of two DA waters in the side)	2028	2471
IHB OH (symmetric combination of two DA waters in the side)	2233	1230
IHB OH (central DD water)	3112	826
Second solvation (symmetric)	3345	340
Second solvation (antisymmetric)	3378	180
Free OH (symmetric combination of two DA waters in the side)	3705	7
Free OH (antisymmetric combination of two DA waters in the side)	3705	8
OH−	3715	2

Table 2.  Peak position in cm⁻¹ and absorption intensity, in km mol⁻¹, for OH⁻(H₂O)₄ isomer II were calculated using B3LYP/6-31+G (d,p).

Assignment	Peak position	Intensity
IHB OH (B symmetry combination of four waters)	2875	0
IHB OH (E symmetry combination of four waters)	2893	1587
IHB OH (E symmetry combination of four waters)	2893	1587
IHB OH (A symmetry combination of four waters)	3102	1047
Free OH (A symmetry combination of four waters)	3669	22
Free OH (E symmetry combination of four waters)	3672	45
Free OH (E symmetry combination of four waters)	3672	45
Free OH (B symmetry combination of four waters)	3674	0
OH−	3711	0

For isomer I, we see that the IHB OH can be separated into two types, the strongly hydrogen bonded peaks of the DA H₂O which have large intensity in the 2028 and 2233 cm⁻¹ region and the weakly bonded peak of DD H₂O at 3112 cm⁻¹.The peaks for the second solvation shell water are calculated to be at 3345 and 3378 cm⁻¹ for the symmetric, and antisymmetric vibrations, respectively. On the other hand, the four first solvation shell waters for Isomer II have very strong peaks between 2900 to3100 cm⁻¹. The four IHB peaks can be assigned to the B, E, and A symmetry vibrations in the C₄ point group as given in Figure 2. Therefore the peak positions of dominant absorptions for the two isomers are very different. For free OH, we can see the large difference of the intensities between the isomers. Namely, isomer II has very strong intensity for the free OH stretching vibration. On the other hand, the hydroxide stretching vibration has very weak intensity for both isomers. This is similar to our previous study in which we saw weak intensities for hydroxide stretching vibration beyond n = 3 for OH⁻(H₂O)_n [23].

Figure 2.

 The top view schematic diagram for the four IHB vibrations for isomer II OH⁻(H₂O)_4.

In Figure 3, we present the experimental and theoretical vibrational spectra for OH⁻(H₂O)_2–4. To model the spectra, we must define a temperature which determines the population of the isomers or conformers. However, there are no clear definitions for the temperature in cluster experiments and previous studies have given estimates of within 50 to 150 K [44]. For OH⁻(H₂O)₄ we follow the previous energetics and assume equal population for each isomer. In our previous study [21] we calculated the zero point corrected MP2/6–311++G (3df,3pd) energy difference between isomer I and isomer II to be 0.6 kcal mol⁻¹, in favor of the former. However when we used the rigid rotor harmonic approximations to estimate the free energy difference at 150 K we obtained a smaller difference of 0.2 kcal mol⁻¹. Since such small energy difference is beyond the accuracy of our quantum chemistry methods, we decided to use equal population for each other. For OH⁻(H₂O)₃, since the temperature dependence was small, we used the results reported in our previous paper for 50 K. For OH⁻(H₂O)₂, in our previous study [32], we performed detailed studies on the population using path integral methods, but were not able to clarify the population of different isomers in this floppy system. Therefore, in the present paper we use equal population similar to our first paper [22] on OH⁻(H₂O)₂.

Figure 3.

 The theoretical and experimental vibrational spectra of (a) OH⁻(H₂O)₂, (b) OH⁻(H₂O)₃, and (c) OH⁻(H₂O)₄. The experimental spectra of Ar-tagged predissociaiton spectroscopy [15] are given in solid red lines and flipped for visual clarity. The theoretical results are given in solid black lines, while contributions from different isomers or conformers are given in dotted blue/green/pink lines. We define conformers as different structural isomers which can be obtained by simple rotations around a bond, while we use the term isomer if bonds must be broken to connect those two structural isomers.

As noted in the introduction, in going from OH⁻(H₂O)_2,3 to OH⁻(H₂O)₄, we notice new peaks emerging between 3400 to 3600 cm⁻¹. As can be seen from the light blue lines in the theory results given in Figure 3 for OH⁻(H₂O)₄, these peaks can be assigned to the three coordinated isomer I. This was the proof for the existence of the second solvation shell water in OH⁻(H₂O)₄. On the other hand, from our present calculation, we can understand the origin of the broad peak observed in the experiment at 2900 to 3100 cm⁻¹. Due to its large width it is hard to quantify it as an absorption peak, but from the close match with our calculation we tentatively assign the broad range as the IHB OH peak of the four coordinated isomer II. From this assignment, we show that both three and four coordinated clusters are observed in the experimental spectra for OH⁻(H₂O)₄. Furthermore, one can observe a constant blue shifting in the IHB OH stretching fundamental ($\text{Δυ}=1$) peaks as we increase the number of first solvation shell water (see the arrow in Figure 3). We note here that the spectra for OH⁻(H₂O)_2,3 are calculated using MP2 PESs while those for OH⁻(H₂O)₄ are from B3LYP PESs. In our previous paper [21], we showed that B3LYP overestimates the red shift compared to MP2 or CCSD (T). To confirm the extent of this overestimation of the red shift, we performed LM-1D calculation for one of the IHB OH in isomer II OH⁻(H₂O)₄ using MP2 and B3LYP. We found that B3LYP overestimates the red shift by 50 cm⁻¹ compared to MP2, which is much smaller than the large shift we observe for the IHB OH stretching peaks when we increase the number of first solvation shell waters: OH⁻(H₂O)₂, ∼2000 cm⁻¹, to OH⁻(H₂O)₃, ∼2400 cm⁻¹, to OH⁻(H₂O)₄, ∼2900 cm⁻¹. This blue shifting is consistent with the decrease in the binding energy of a water molecule as we increase the number of first solvation shell waters for OH⁻(H₂O)_n (see Table 3). As Bauer and Badger [45,46] noticed in 1937, the hydrogen bonding strength and the red shift of the OH stretching peak are correlated. The stronger the hydrogen bond the larger the red shift, and this correlation is also observed for OH⁻(H₂O)_n studied in this paper.

Table 3.  Zero point corrected binding energy, in kcal mol⁻¹, of a water molecule for OH⁻(H₂O)_n → OH⁻(H₂O)_n-1+H₂O calculated using B3LYP/6-31+G (d,p), and QCISD (T)/6-311++G (3df,3pd). The QCISD (T) energies are from our previous publication [23].

OH−(H2O)n	B3LYP	QCISD (T)
OH−(H2O)2	−20.13	−18.54
OH−(H2O)3	−17.09	−13.50
OH−(H2O)4	−11.90	−9.72

4 Conclusion

In this paper we presented the vibrational spectra forOH⁻(H₂O)_2–4 calculated using multi-dimensional vibrational calculations with potential energy and dipole moment obtained with quantum chemistry methods. Realistic spectra shape was simulated using the Voigt function based on the homogeneous and inhomogeneous widths, and also the possibility of coexistence of isoenergetic isomers or conformers was taken into account. Our calculations show that a systematic blue shift in the IHB OH is observed with the increase in the number of water molecules in the first solvation shell. Furthermore, we showed that the vibrational signature of the four coordinated hydroxide for OH⁻(H₂O)₄ can be observed in the 2800–3200 cm⁻¹ range. Previous experimental study on Ar-tagged OH⁻(H₂O)₄ observed a very broad feature in this region. We believe that a detailed experimental study using the IR-IR double resonance study [47,48] of this broad region will help us clarify the existence of the four coordinated isomer in gas-phase OH⁻(H₂O)₄.

5 Notes

The authors declare no competing financial interests.

Acknowledgment

This research is financially supported by Academia Sinica and the Ministry of Science and Technology of Taiwan (Grant: MOST102-2113-M-001–012-MY3). We would like to acknowledge the generous allocation of computational resources provided by National Center for High-performance Computing and Academia Sinica Computing Center. We thank Prof. Mark A. Johnson of Yale University for providing numerical data from previous experimental publications.

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