Article pubs.acs.org/JPCA
Features in Vibrational Spectra Induced by Ar-Tagging for H3O+Arm, m = 0−3 Jheng-Wei Li,†,‡ Masato Morita,†,§ Kaito Takahashi,*,† and Jer-Lai Kuo*,† †
Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 10617, Taiwan Department of Physics, National Taiwan University, Taipei 10617, Taiwan
‡
S Supporting Information *
ABSTRACT: Understanding the spectral features for solvated hydronium has been hindered due to the strong and complex vibrational couplings that lead to broad bands in the aqueous phase. In this work, utilizing ab initio vibrational calculations, we determine how the vibrational couplings induced by the Ar microsolvation in H3O+Arm m = 0−3 affect the observed spectra. With theoretical peak intensities and peak positions, we assign the experimental spectra. We also show that an increase in the number of Ar atoms results in an anticooperative blue shifting in the Ar-tagged OH stretching bands. This change in peak position of the OH stretching fundamental modulates the Fermi resonance with the bending overtone. This is observed as a distinct doublet feature at 3200 cm−1 with varying intensities for H3O+Ar2 and H3O+Ar3. The coupling between the in-plane rotation of the hydronium and the bending modes of H3O+ leads to the existence of a strong association bands around 1900 cm−1. experimental spectra from 1500 to 3800 cm−1 have been obtained by Johnson’s group.23,27 In our theoretical simulations, both the peak positions and absorption intensities can be evaluated directly by solving the quantum vibrational Schrödinger equation using the potential energy and the dipole moment obtained from ab initio methods. From the detailed assignments of the observed peaks, which show very interesting intensity variations, we glean into the couplings among the vibrational modes of H3O+ and see how these couplings can be modulated by the attachment of Ar atoms. The rest of the paper is organized in the following manner. In section 2, the details for the theoretical methods will be given. In section 3, we present the detailed analysis of the theoretical calculations and discussion in comparison with experimental results. Lastly, we provide a brief conclusion in section 4.
1. INTRODUCTION Solvated proton (H+) in aqueous phase has many applications in chemistry and biology.1−3 Highlighted by the recent study on H+(H2O)21 by Johnson’s group,4 molecular level understanding of the hydrated proton can be obtained from the vibrational spectra of H+(H2O)n.5−10 Dominant peaks in these spectra have been assigned on the basis of the scaled harmonic vibrational calculation using quantum chemistry methods.5−13 However, for these and other hydrated ionic species anharmonic couplings among vibrational modes result in overtones and combination bands that cannot be assigned using the normal-mode analysis based on the double harmonic approximation.14−17 Because these vibrational couplings are sensitive to the solvation environment, it provides a good testing ground to confirm the structures as well as the accuracy of the computational studies. Furthermore, a very broad absorption feature is observed in aqueous acidic solutions in the range 1800−3400 cm−1, but assignments of these features are still under active debate.18 The simplest solvated proton, the hydronium ion, H3O+, has been studied experimentally in its bare case as well as with the messenger tagging technique.19−24 In one of the early studies, vibrational spectra of H3O+(H2)n above 3000 cm−1 were measured by Lee’s group.21 Recently, ab initio molecular dynamics simulations have been utilized to study these clusters, but understanding on the effect of messengers toward the observed vibrational spectra is still far from complete.25,26 Duncan’s group examined the OH stretching vibrations of H3O+(N2)n=1−3 by measuring the spectra above 2600 cm−1 and performed harmonic calculations to assist their assignments.24 In the present paper, we focus on both the stretching and the bending motions of hydronium for H3O+Arm, m = 1−3, because © 2015 American Chemical Society
2. METHODS Theoretical Methods. The vibrational spectra for H3O+Arm, m = 0−3, were calculated by solving the reduceddimensional vibrational Schrödinger equations. The potential energy surface (PES) for the vibrational Hamiltonian and associated dipole moment functions (DMF) were calculated at the MP2/aug-cc-pVDZ level using Gaussian 09 program.28−30 We selected this ab initio method because McCoy et al. had success analyzing the spectra of H3O+Ar3 using this method.27 The reduced-dimension PES was constructed as a function of normal modes {qi} of the embedded H3O+, while all other Received: September 12, 2015 Revised: October 13, 2015 Published: October 15, 2015 10887
DOI: 10.1021/acs.jpca.5b08898 J. Phys. Chem. A 2015, 119, 10887−10892
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Table 1. Peak Position, cm−1, of the Fundamental Vibration of H3O+ Obtained by the 5-Dimensional Vibrational Calculation at the MP2/aug-cc-pVDZ Level as Well as Previous Full Dimension Calculations by Huang et al.a
degrees of freedom were kept at the equilibrium values. The expression of the vibrational Hamiltonian is as follows: n
H=
∑− i=1
1 ∂2 + V (q1 , q2 ,... ,qn) 2mi ∂qi2
(1)
averageb
where the mi is the reduced mass of each mode. 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. Schematics of the six normal modes (NM) selected for the present analysis, the three OH stretching modes, two HOH bending modes, and hindered rotation of the hydronium, are given in the Supporting Information (Figure S1). For the present calculation we use the Cartesian representation of the NM. NM coordinates were extracted from the Gaussian09 output using the freq=hpmodes keyword. In the calculation of the PES and DMF, nine grid points were employed for each degree of freedom, and quartic polynomial interpolation is used to obtain the values required for the vibrational calculation. Therefore, we performed 96 = 531441 single point calculations for each H3O+Arm system. 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 representation31 of the harmonic oscillator basis functions. Thus, our calculation includes the mode coupling effects between active normal modes. We used nine harmonic oscillator basis functions for each degree of freedom to obtain a convergence of 1 cm−1 in the peak positions. Using the obtained eigenvalues, eigenvectors, and DMF, the integrated absorption intensities (km/mol) between the initial ground state, ψ0, and the vibrational excited states, ψf, were calculated by32 A=
NAπ |⟨ψ |μ|̂ ψ ⟩|2 υ0f̃ = 2.506 |μ0f |2 υ0f̃ 3ϵ0ℏc 0 f
vibrational mode bending symmetric OH stretching asymmetric OH stretching a b
present 5D
MM/PES-2c
experimentc
1609 1609 3373 3473 3473
1629 1629 3383 3523 3517
1632.24 3440.41 3527.25
The experimental values are also presented in the last column. Average values for the tunneling splitting doublets. cFrom ref 33.
using MP2 underestimate the experimental values by ∼50 cm−1. This not only gives us an estimate on the error of the present method but also gives us confidence that the general trend for H3O+Arm, m = 0−3, in the range 1500−3800 cm−1, can be calculated by this computational method. In Figure 1, we plot the 5D results of H3O+ as well as the 6D results of H3O+Arm obtained by adding the hindered rotation of the H3O+ inside the Ar cage. The peaks with dominant contribution from fundamentals and overtones of the bending modes, free and Ar-tagged OH stretching modes, and combination band of the bending fundamental and hindered rotation are presented with different colors. The last band has been recognized as the association band in the condensed phase community27,35,36 so we will also follow this notation in this text. Experimental spectra of H3O+Arm from Johnson’s group are shown in gray for comparison. The values for the peak position and intensities are given as tables in the Supporting Information. One can clearly see that our calculated stick spectra account for the dominant features of the experimental spectra. Compared to the bare H3O+, the most noticeable change is the ∼300 cm−1 red shift in the peak position and increase in the intensity of the Ar-tagged OH stretching band. Although the bending peak positions are not sensitive to the presence of Ar, their intensity gradually decreases upon the addition of Ar. This has been previously discussed by McCoy and co-workers as due to the charge sloshing effect, where increase in the charge delocalization results in a weakening of the bending intensity.27 Furthermore, one can see two additional distinct differences by the addition of the Ar atom: (1) existence of the association bands (light green) and (2) the increased intensity of the bending overtones (red). Consistent with previous assignments27,36 the two main peaks in the 1600−2000 cm−1 region are assigned to the bend fundamentals (νHOH) and the association bands (να). One can see that peak positions of the bending fundamentals (shown as pink sticks in Figure 1, also see Tables S1−S3) only shift slightly ∼10 cm−1, with the increase in number of Ar atoms. Accordingly, the overtones, ΔνHOH = 2 (shown as red sticks in Figure 1), also do not show much shifting in peak positions. In Table 2, we compare the m dependence of the peak splittings and the intensity ratio between these two peaks for H3O+Arm. Both theoretical and experimental peak splittings increase with m. This is similar to what McCoy et al. observed for the fully solvated H3O+X3 (X = Ar, N2, CH4, H2O). In that case the splitting between the bend fundamental and association band increased with strengthening the interaction by changing the messenger. In the present case by increasing the number of
(2)
where μ̂ is the DMF in Debye, υ̃0f is the transition energy in cm−1 and |μ0f|2 is the square of the absolute value of the transition moment vector. Experimental Spectra. The numerical data for the H3O+Arm m = 1−3, spectra were obtained from Johnson’s group.23,27 To obtain the intensity of the peaks, we performed numerical integration of the spectral region from 1601 to 1800 cm−1 and from 1801 to 2000 cm−1 for the bending fundamental and the association bands (see section 3 for the definition), respectively.
3. RESULTS AND DISCUSSIONS To justify the use of reduced dimensional vibrational calculation with MP2/aug-cc-pVDZ, we first compare our bare hydronium results obtained by the 5-dimensional coupled normal modes (5DNM) calculations (including three OH stretching modes and two bending modes) with the previous full dimensional vibrational calculation by Huang et al. as well as the available experimental values.33,34 If one includes the umbrella motion, the OH stretch and HOH bend peaks split into doublets. However, in the Ar-tagged spectra of H3O+Arm these tunneling splittings are quenched. Therefore, we performed the calculation ignoring this mode and compared our results with the averaged values of the doublets. As given in Table 1, the peak positions of the bending and the stretching modes calculated by the present reduced dimension method 10888
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Figure 1. Stick spectrum for (a) H3O+, (b) H3O+Ar, (c) H3O+Ar2, and (d) H3O+Ar3 calculated by the 5-dimensional or 6-dimensional vibrational calculation using MP2/aug-cc-pVDZ. The peaks that have a dominant contribution from the fundamental and overtone transitions of the bending modes are given in pink and red, respectively. Peaks with large contributions from the free and Ar-tagged OH stretching fundamentals is given in black and blue. The combination band of the bending fundamental band and hindered rotation are given in light green. The combination band of the bending overtone and hindered rotation is given in dark green. To compare the two spectral regions, the calculated intensities for peaks below 2600 cm−1 are scaled by 10 times. The experimental spectra by Johnson’s group are given in gray.
intensity of the association band (Figure 1 light green) increases with m. As seen in Table 2, the intensity ratio of the association band is only one-third of the bending fundamental at m = 1 but becomes nearly equal at m = 3. This variation is consistent with the experimental values. In the 3000−3800 cm−1 region, for H3O+Arm we obtain strong peaks corresponding to the Ar-tagged OH stretching modes (shown as blue sticks in Figure 1). These peaks show a consistent blue shift with the addition of Ar to H3O+Ar. The Ar-tagging to the H3O+ species causes the Ar-tagged hydrogen of H3O+Ar to have a larger positive charge compared to H3O+ species. However, further addition of Ar atoms to the H3O+Ar causes this excess positive charge on the original Ar-tagged hydrogen to delocalize to other Ar-tagged hydrogen atoms. This weakens the local binding strength between OH and Ar atom for H3O+Ar2 and H3O+Ar3 compared to H3O+Ar. In the
Table 2. Comparison of the Calculated and Experimental Trends between the “Association Band” να and HOH Bend νHOHa να − νHOH H3O+Ar1 H3O+Ar2 H3O+Ar3
Iα/IHOH
exp
calc
exp
calc
195 266 312
195 262 323
0.33 0.49 0.82
0.22 0.43 0.89
The peak splittings are in cm−1, and the intensity ratios are given in the right and left columns, respectively.
a
messengers, we strengthen the total interaction between the hydronium and the messengers; thus, we see an increase in the splitting between the bend fundamental and association bend. In accord with the stronger coupling, the relative integrated 10889
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Figure 2. Contour plots of the two-dimensional cut of the vibrational wave functions along one of the bending coordinates (q2) and along one of the stretching coordinates (q3) for (a) (b) H3O+Ar3, (c) (d) H3O+, and (e) (f) noncoupled harmonic oscillator of H3O+. See Figure S1, for the definition of the coordinates.
seen, and then in H3O+Ar3 a weak peak is seen to the red, 3210 cm−1. The doublet in m = 2 was originally assigned as symmetric and asymmetric Ar-tagged OH stretching fundamentals.23 However, in a following paper, the authors assigned it as the Fermi resonance between the Ar-tagged OH stretching fundamental and the OH bend overtone.27 Our present results support this latest assignment. We note that for H3O+(N2)2 there are no such doublet features.24 We believe that this is due to the fact that N2-solvated OH stretching peaks at 2975 cm−1 are detuned from the bend overtone, ∼3200 cm−1; thus no intensity sharing is observed. Sensitivity of Fermi resonance on peak positions has recently been discussed for hydrated benzene by Zwier and Sibert’s groups,38 as well as for Cl−H2O by Johnson’s group.39,40 Furthermore, for the water
vibrational spectra this results in a blue shift of the Ar-tagged OH stretching peaks with increasing m. Here we note that although binding between each OH bond and Ar atom is weakened, the total interaction between H3O+ and the Arm messenger increases with m. Duncan’s group also observed similar blue shifting due to the increase in the number of messengers in H3O+(N2)m, m = 1−3.24 Such a general trend known as the anticooperative effect of the messenger was also seen and analyzed in protonated methanol−water mixed clusters previously.37 Furthermore, one observes additional peaks next to the strong OH stretching band in the experimental spectra. In H3O+Ar, only a very weak peak to the blue at 3325 cm−1 is seen experimentally, in H3O+Ar2 two nearly equal intensity peaks are 10890
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the spectral range 1500−3800 cm−1. We have shown that bending mode frequencies are insensitive to the number of solvating Ar atoms. McCoy et al. have shown that compared to the bare case, the attachment of different messengers can cause bending modes to shift by ±50 cm−1.27 Therefore, if the solvated OH stretching vibration falls in the 3200 ± 100 cm−1 range, a significant Fermi resonance feature with the bend overtone should be observed.38−41 Furthermore, the strength of the solvation environment not only modulates the peak splitting between the bending and its association modes but it also greatly affects their intensity ratios. All in all, these anharmonic calculations provide evidence that microsolvation by messengers in H3O+Mm can effectively modulate the coupling between the intense proton stretching modes and other weaker combination and overtone bands. Therefore, if used properly, one can utilize such a mechanism to “turn on” some dark states by changing the solvation environments.
hexamer, recent theoretical simulations by Bowman’s group have shown that this Fermi resonance coupling is important for reproducing the experimental spectra.41 As discussed previously, the addition of Ar atom causes minimal effect on the peak position of bending modes (Figure 1 pink); thus, the overtone of the HOH bend (Figure 1 red) is insensitive to m. Therefore, the anticooperative effect on the Ar-tagged OH stretching mode causes the two states to cross as we increase the number of Ar atoms. This causes the spectra intensity to vary as we go from m = 1 to m = 3. Consistent with the experimental spectra, the weaker bend overtone is to the blue of OH stretching peak for m = 1 but is to the red for m = 3. For H3O+(H2)m; the fine-tuning of the Fermi resonance with messengers has been speculated from molecular dynamics simulations without concrete proof.25,26 In our case we can plot the vibrational wave functions to confirm the strong mixing between the Ar-tagged OH stretching and HOH bending modes. In Figure 2, we present the calculated vibrational wave function projected onto the bending and stretching coordinates. First, because there is no coupling between the two modes, one can clearly see node structures along the bending and stretching coordinate in Figure 2e,f. This allows one to assign the transitions to these states from the ground vibrational state as the bend overtone and stretching fundamental, respectively. For the H3O+ wave functions given in Figure 2c,d, the general features still persist, thereby allowing one to assign transitions to these states as the bend overtone and stretching fundamental, respectively. However, for the H3O+Ar3 wave function given in Figure 2a,b, the mixture between the two coordinates makes it hard to give simple assignments. This shows that the attachment of the Ar messenger increases the Fermi resonance coupling strength between the bending overtone (Δν = 2) and stretching fundamental (Δν = 1). This strong mixing results in the observed doublet in the H3O+Ar3 spectrum. In other words, the number of Ar messengers can be interpreted as a tuning parameter on the strength of mode couplings. Such messengerinduced fluctuation of Fermi coupling has been mentioned for Cl−H2O39,40 before, but we believe that this is the first time one was able to simulate variations in intensity for the spectra in the very wide range of 1500−3800 cm−1. It is very interesting to note that for the experimental H3O+Ar2 spectra, one can notice a doublet peak around 3550 cm−1. Considering that there is only one free OH for this system, it is quite puzzling to see a doublet feature in this region. From our calculation given in Figure 1, we assign the additional peak (shown the dark green stick) to the combination band of the bending overtone and the hindered rotation. For the H3O+Ar2 species, this combination band accidentally lies in the vicinity of the free OH stretching band and thus can effectively borrow intensity. For H3O+Ar and H3O+Ar3, similar combinational modes exist but are not in the vicinity of any strong bands; thus, their intensities are weak (Tables S1−S3). We believe that this is the first time an association combination band was shown to borrow intensity from the free OH stretching motion. Further studies are required to see if this type of interaction can be seen in the spectra of other systems.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b08898. Schematic diagram of the vibrational normal modes considered in the present study, the theoretical peak positions and intensities, the full ref 30, as well as the Cartesian geometries of H3O+Arm m = 0−3 are given in the Supporting Information (PDF)
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AUTHOR INFORMATION
Corresponding Authors
*K. Takahashi. E-mail:
[email protected]. *J.-L. Kuo. E-mail:
[email protected]. Present Address §
Department of Chemistry, Durham University, South Road, Durham DH1 3LE, U.K. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This research is financially supported by Academia Sinica and the Ministry of Science and Technology of Taiwan (Grants: MOST102-2113-M-001-012-MY3, MOST101-2113-M-001023-MY3, and MOST 104-2113-M-001-017). We thank the generous allocation of computational resources provided by National Center for High-performance Computing and Academia Sinica Computing Center. We acknowledge Prof. Mark A. Johnson of Yale University for providing the experimental data that enabled a direct comparison between experimental and theoretical results.
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REFERENCES
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