ARTICLE pubs.acs.org/JPCA
Hemibonding of Hydroxyl Radical and Halide Anion in Aqueous Solution Makoto Yamaguchi*,† Japan Atomic Energy Agency, 4-33 Muramatsu, Tokai-mura, Naka-gun, Ibaraki 319-1194, Japan
bS Supporting Information ABSTRACT: Molecular geometries and properties of the possible reaction products between the hydroxyl radical and the halide anions in aqueous solution were investigated. The formation of two-center three-electron bonding (hemibonding) between the hydroxyl radical and halide anions (Cl, Br, I) was examined by density functional theory (DFT) calculation with a range-separated hybrid (RSH) exchange-correlation functional. The long-range corrected hybrid functional (LC-ωPBE), which have given quantitatively satisfactory results for odd electron systems and excited states, was examined by test calculations for dihalogen radical anions (X2; X = Cl, Br, I) and hydroxyl radicalwater clusters. Equilibrium geometries with hemibonding between the hydroxyl radical and halide anions were located by including four hydrogen-bonded water molecules. Excitation energies and oscillator strengths of σσ* transitions calculated by the time-dependent DFT method showed good agreement with observed values. Calculated values of the free energy of reaction on the formation of hydroxyl halide radical anion from the hydroxyl radical and halide anion were endothermic for chloride but exothermic for bromide and iodide, which is consistent with experimental values of equilibrium constants.
1. INTRODUCTION Halide anions (Cl, Br, I) are ubiquitous in natural environment. They are the most reduced form of the elements (oxidation number 1), and their oxidation reactions via dihalogen molecules (oxidation number 0) to trioxide anion (oxidation number 5) play crucial roles in various photochemical and radiation chemical reaction processes. While the reaction mechanism is common for halide anions, their reactivity is largely different and thus results in significantly different consequences. For example, the addition of a small amount of bromide ion induces accumulation of hydrogen peroxide1 and molecular hydrogen2 under gamma radiolysis of water, while chloride ion does not show such pronounced effects. This may be relevant to geological disposal of spent nuclear fuel since the bromide ion contained in saline groundwater at low concentration would induce oxidative radiolytic dissolution of the spent nuclear fuel by the formation of hydrogen peroxide even under high concentration of dissolved molecular hydrogen.3 Oxidation of halide anions in aqueous solution under ionizing radiation is initiated by the reaction with the hydroxyl radical, which is a strong oxidant. Pulse radiolysis has successfully been applied for the study of reaction kinetics of the oxidation of halide anions by detecting the formation and decay of dihalogen radical anions due to their strong ultraviolet photoabsorption.4,5 Production of these dihalogen radical anions was dependent on pH, and the formation of dihalogen radical anions was almost complete in acidic solution after submicrosecond electron pulse irradiation. Such fast formation of dihalogen radical anion was explained by the formation and subsequent protonation of r 2011 American Chemical Society
hydroxyl halide radical anions (XOH): OH þ X ¼ XOH
ð1Þ
XOH þ Hþ ¼ X þ H2 O
ð2Þ
X þ X ¼ X2
ð3Þ
As for bromide aqueous solution, Zehavi and Rabani have determined reaction rate constants leading to the formation of Br2 including reactions 13 and following reactions of hydroxyl bromide radical anion (BrOH):6 BrOH ¼ Br þ OH
ð4Þ
BrOH ¼ Br þ OH
ð5Þ
BrOH þ Br ¼ Br2 þ OH
ð6Þ
The rate constants of reactions 4 and 5 are 3.3 10 and 4.2 106 dm3 mol1 s1, respectively, which are much smaller than that of reaction 1 (1.06 1010 dm3 mol1 s1) and consistent with the formation of BrOH in neutral aqueous solution. They derived the photoabsorption spectrum of BrOH with a maximum at λmax = 360 nm, and its molar absorption coefficient was εmax = 8000 dm3 mol1 cm1. The existence of BrOH was further supported by the studies at higher pH.7,8 7
Received: July 5, 2011 Revised: November 3, 2011 Published: December 05, 2011 14620
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In contrast to the case of bromide anion, the formation of Cl2 in neutral solution was observed only at high chloride ion concentration. Although this may be explained by reactions 13 due to locally high acidity in spurs,4 Hamill suggested that Cl2 is generated after hole migration from ionized water molecule H2O+ to chloride ion to form atomic chlorine and its subsequent reaction with another chloride ion.914 His idea and the effect of direct ionization of chloride ion at higher concentration was critically discussed in subsequent studies.1517 On the other hand, the formation of Cl2 in dilute acidic solutions was successfully analyzed with reactions 13, and their rate constants were derived by Jayson et al.17 They also derived a photoabsorption spectrum of ClOH with λmax = 350 nm and εmax = 3700 dm3 mol1 cm1, whose absorption maximum is located very close to that of Cl2 (λmax =340 nm), and its extinction coefficient is almost half of it (εmax = 8400 dm3 mol1 cm1). Hydroxyl iodide radical anion (IOH) was found to be in equilibrium with I2, as shown in reaction 7, and its photoabsorption spectrum was obtained by pulse radiolysis of highly alkaline aqueous solutions.19 IOH þ I ¼ I2 þ OH
ð7Þ
The observed photoabsorption maximum was blue-shifted to λmax = 340 nm from that of I2 (λmax = 390 nm), in contrast to the case of chloride and bromide ions. While the existence of hydroxyl halide radical anions as reaction intermediates in aqueous solutions have been well accepted,20 little progress has been made to explain their properties and reactivity based on theoretical calculation of their geometries and other properties in aqueous solution until recently. It is anticipated that two different interactions between the hydroxyl radical and the halide anion leads to two possible stable geometries: One is electrostatic in nature, and the dipole of the hydroxyl radical and negative charge of the halide anion would be stabilized in a linear conformation of OH 3 3 3 X type by the formation of a hydrogen bonding. The other is orbital interaction between two components by the formation of a two-center three-electron (2c3e) bond, which is coined “hemibonding” as its formal bond order is 0.5. Equilibrium geometries of the hydroxyl halide radical anions are governed by the relative strength of these two interactions between constituents. In the gas phase, a linear optimized geometry of OH 3 3 3 Cl type with hydrogen bonding was obtained.21 Although the geometry is consistent with observed photoelectron spectra, the electronic structure of the hydroxyl radical is a little perturbed by hydrogen bonding. A photoabsorption band due to the ΠΣ transition in the UV region is weak by symmetry, and the fairly strong ultraviolet photoabsorption observed in the aqueous phase cannot be attributed to this transition in the hydrogenbonded geometry. Based on the similarities of their ultraviolet photoabsorption spectra with those of dihalogen radical anions, which are unambiguously assigned to the σσ* transition of 2c3e bonds, the formation of such hemibonded structures is expected between the hydroxyl radical and the halide anions. Recently, Valiev et al. have performed ab initio quantum mechanical/molecular mechanics (QM/MM) calculation of the hydroxyl radical chloride anion complex in aqueous solution.22 A hemibonded optimized geometry was obtained by using the density functional theory (DFT) with the B3LYP hybrid functional23 in the QM
part, and it has a ClO distance of 2.46 Å and a ClOH angle of 89°. A hydrogen-bonded optimized geometry OHCl was found to be 3.3 kcal mol1 higher in free energy than ClOH. However, the free energy of ClOH became higher than that of OHCl by 1.7 kcal mol1 when the coupled cluster theory with full triples (CCSDT) was employed in the QM part. The σσ* transition of ClOH was calculated to be λmax = 346 nm at the EOMCCSDT/MM level, which was in good agreement with the observed value of λmax = 340 nm. Although this excellent agreement of the calculated and experimental values of photoabsorption maxima and the very small calculated difference in the free energies ClOH and OHCl by the high-level QM method support the existence of the hemibonded geometry ClOH, it should be mentioned that the geometry was optimized by the DFT method with the B3LYP hybrid functional. While the method and the functional are nowadays widely used as they give fairly accurate values of equilibrium geometries and their thermochemical properties, they still have difficulty in application to odd electron systems with 2c3e bonds, as semilocal exchange-correlation functionals give qualitatively incorrect results due to self-interaction error. For example, Braïda et al. have shown that homodimer radical cations X2+ with 2c3e bonds dissociate into two fractionally charged units X+1/2, and dissociation energies are too small.25 Although the B3LYP functionals give better results than pure gradient-correlated functionals, and the two parameter hybrid BH&HLYP functional24 gives excellent results for some cases, they have concluded that the DFT method is not appropriate for 2c3e bonds. Concerning to the present case, hemibonding formation the hydroxyl radical between a water molecule26 or a chloride anion27 in aqueous solution has been reported when semilocal functionals are employed in ab initio molecular dynamics (AIMD) calculations, but they seem to be artifacts as they have disappeared by making corrections for the self-interaction error in AIMD simulations.27,28 In contrast to the DFT method, dissociation of homodimer radical cations into X and X+ is properly described by HartreeFock theory, as it gives the exact exchange functional form in the dissociation limit. Thus a range-separated hybrid (RSH) functional was proposed in which the extent of the HartreeFock exchange is a smooth function of the distance between two electrons, and it converges to the pure Hartree Fock exchange in the dissociation limit. The standard error function was employed as a weight function to calculate the fraction of the HartreeFock exchange, as it requires only one adjustable parameter.29 This type of the RSH functional has been shown to greatly improve the accuracy of calculated values of molecular properties such as polarizabilities and electronic excitation energies.3032 Vydrov and Scuseria have shown that an RSH functional combined with the exchange correlation functional of Perdew, Burke, and Ernzerhof (PBE)33 denoted as LC-ωPBE gives excellent results on various properties including dissociation of symmetric radical cations.34 Recently, a systematic assessment of a large number of recently proposed exchangecorrelation functionals including RSH type was performed by Dumont et al. For application to disulfide and dihalogen radical anions, the LC-ωPBE was found to be one of the most accurate functionals for calculation of their equilibrium geometries and adiabatic electron affinities.35 On the basis of these successful results of the RSH functionals for systems relevant to the present study and molecular properties including excited states, this method was chosen in this study for 14621
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Table 1. Equilibrium Bond Lengths and Vibrational Frequencies of Dihalogen Radical Anions Cl2 method gas
LC-ωPBE
Br2
R (Å)
ω (cm1)
R (Å)
ω (cm1)
R (Å)
ω (cm1)
2.572
264
2.811
166
3.172
120
128
3.331
90
144
3.245
103
2.57 a B3LYP
2.82 a
2.709
204
2.952
2.71 a BH&HLYP
2.96 a
2.643
235
2.892
2.64 a MP2
2.90 a
2.570
268
2.60a 2.586 b
b
173
3.167
122
2.81a
156 b
3.186 b
113 b
264 b
2.836 b
2.603
257
2.823
165
3.209
116
CCSD(T)
2.60a
249 b
2.845a
147 b
3.221 b
107 b
160 c
3.205d
110 d 125
b
2.870
Exp.
2.56 c
255 c
2.82 c
b
LC-ωPBE
2.555
279
2.798
169
3.161
B3LYP
2.678
218
2.925
141
3.302
95
BH&HLYP
2.618
250
2.874
152
3.253
109
MP2
2.556
282
2.774
180
3.158
127
QCISD
2.586
272
2.809
169
3.196
122
273e
Exp. a
2.785
QCISD
2.619 water
I2
c
d
167 e
115 e
e
Reference 35. Reference 45. Reference 46. Reference 47. Reference 48.
the calculation of possible hemibonding formation of the hydroxyl radical and the halide anions and their molecular properties in aqueous phase.
2. COMPUTATIONAL METHOD All the calculations were performed by the Gaussian 09 program.36 The LC-ωPBE RSH functional was mainly used for calculation with the default value of parameter ω = 0.4 a01. Becke’s three- and two-parameter hybrid functionals denoted as B3LYP and BH&HLYP, respectively, and post-HartreeFock (post-HF) MP2 and quadratic CI with singles and doubles (QCISD)37 methods were also employed for comparison. Correlation corrected basis sets of triple-ζ type with augmentation functions denoted as aug-cc-pVTZ were used throughout this study.38,39 Pseudopotentials given by Peterson et al. were combined with this type of basis set for bromine and iodine.40,41 Optimized geometries were calculated by the GDIIS method with the default values of convergence criteria in the program. The effect of hydration was taken into account by placing two to four water molecules around the system. As for the DFT calculation, the same basis set used in the system was employed for the water molecules. On the other hand, in the post-HF calculation, the two-layer ONIOM method42 was applied, in which the water molecules were calculated at the HF level with a double-ζ type cc-pVDZ basis set. The polarizable continuum model43 was also employed in the calculation with the atomic radii of the default values of the simple united atom topological model (UA0) for the heavy atoms. Electronic transition energies and oscillator strengths were calculated by the time-dependent DFT (TDDFT) method. Optimized geometries and molecular orbitals were visualized by using the MOLDEN program package.44
Figure 1. Potential energy curves of Cl2.
3. RESULTS AND DISCUSSION 3.1. Dihalogen Radical Anions. Before starting calculation of the hydroxyl radical and halide anions in aqueous solution, the LC-ωPBE functional was applied for relevant chemical systems whose properties have already been extensively studied to confirm that the functional can give satisfactory results. First we have applied the functional for calculation of dihalogen radical anions to see whether their 2c3e bondings are properly described. Table 1 summarizes bond lengths and vibrational frequencies of dihalogen radical anions calculated with the DFT method as well as the post-HartreeFock methods without spinorbit coupling. Calculated values by Dumont et al.35 and Braïda and 14622
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Table 2. Calculated Properties of Photoabsorption Bands Due to σσ* Transition of Dihalogen Radical Anions in Aqueous Phase Cl2 λmax (nm)
337 (340)a 1
εmax/10 (dm mol 3
a
Br2
3
1
cm )
a
9.4 (8.4)
I2
366 (360)a
412 (380)a
a
10.7 (15)a
10.0 (12)
Experimental values from reference 20.
Hiberty45 and experimental values by Chen et al.46 for Cl2 and Br2 and Zanni et al. for I247 in the gas phase and Tripathi et al. in the aqueous phase are also listed for comparison.48 As for Cl2 and Br2, bond lengths calculated in this study are the same as the recently reported values by Dumont et al. with the same basis set and the computation method,35 although the effective core potential was employed for the calculation of the latter. The B3LYP and BH&HLYP functionals gave considerably longer bond lengths and much lower vibrational frequencies compared to the LC-ωPBE functional. It is interesting that the calculated values with the LC-ωPBE functional are very close to those calculated with the MP2 method, which Braïda and Hiberty have assumed as the only standard economical method for calculation of hemibonded systems.45 In the present study, the QCISD method was chosen to the most accurate values, while the calculated values with the coupled cluster method with singles and doubles and perturbative treatment of triples (CCSD(T)) were given as reference values in the literatures.35,45 The values with the QCISD and CCSD(T) are in good agreement with each other as well as with the experimental values, although the calculated bond length of Cl2 was slightly longer than the experimental value. It should be noted that the experimental values of the bond lengths and the vibrational frequencies were obtained by assuming Morse-type potential energy curves for both the neutral and the anionic states to simulate experimental data. While the values of I2 were obtained by simulating its photoelectron spectra, the values of Cl2 and Br2 were obtained by fitting to the cross sections of dissociative electron attachment to dihalogen molecules and the method may be less sensitive to slight changes in those parameters. Effect of hydration was examined by calculation with the polarizable continuum model without explicitly taking into account hydrating water molecules. All the equilibrium bond lengths were slightly shorter than the values in the gas phase, while vibrational frequencies are slightly higher than the experimental values derived from the peak positions in the resonance Raman spectra. Figure 1 shows potential energy curves of Cl2 in 2Σu+ and 2 + Σg states. Energy differences between total energies of Cl2 and Cl(2P3/2) + Cl are plotted by changing the bond length from 2 to 9 Å. The potential curve of the ground 2Σu+ state calculated with the LC-ωPBE functional approaches zero by increasing the bond length and 0.048 eV at r(ClCl) = 1000 Å. The excited 2Σg+ state energy calculated by the TDDFT method with the same functional also converges to zero in the dissociation limit. By contrast, the BH&HLYP and B3LYP functionals resulted in much lower energy in the ground 2Σu+ state, the potential energy curves do not approach zero in the dissociation limit, and the relative energy at r(ClCl) = 1000 Å was 0.69 eV and 2.32 eV, respectively. These features of the potential energy curves of Cl2 were also observed for Br2 and I2 without spin orbit coupling. While the relative energies at calculated with the LC-ωPBE were 0.095 eV in Br2 r = 1000 Å
Figure 2. Optimized geometry of hydrated hydroxyl radical (a) OH(H2O)3; (b) OH(H2O)4; (c) OH(H2O)7.
and 0.14 eV in I2, those corresponding values calculated with the BH&HLYP functional were 0.68 eV in Br2 and 0.64 eV in I2. These results clearly indicate the LC-ωPBE gives qualitatively correct and almost quantitatively satisfactory results on the potential energy curves of dihalogen radical anions while the BH&HLYP and B3LYP functionals fail in both aspects. Bond dissociation energies were calculated from the total energies at the equilibrium geometries and r = 1000 Å. Firstorder spinorbit corrections were made for Br and I in the dissociation limit, which amounted to 3.51 and 7.25 kcal/mol1, respectively.45 The calculated dissociation energies for Cl2, Br2 and I2 were 1.31, 1.16, and 0.97 eV, respectively. These values in the gas phase are in excellent agreement with experimental values in the literature for Cl2 (1.326 eV46), Br2 (1.19 eV46) and I2 (1.014 eV47). As for the aqueous phase, dissociation energies have been estimated from anharmonicity constants derived from overtones of resonance Raman peaks. Estimated values given by Tripathi et al. were 1.6, 1.3, and 0.9 eV for Cl2, Br2, and I2 . 48 However, Hynes and Wine gave the value for Cl2 as 1.3 eV, which seems more consistent with other experimental and calculated values in the literature and present calculation.49 Calculated and experimental values of σσ* transition energies and molar absorption coefficients are summarized in Table 2. The absorption maxima shift to the longer wavelength from Cl to I together with slight increase in molar absorption coefficients. These trends are in agreement with experimental values,20 although the extent of the changes in calculated values are larger for the absorption maxima and smaller for the molar absorption coefficients, respectively. It seems the agreement with the experimental and calculated values is less satisfactory in I2 compared with those of Cl2 and Br2. However, recently reported calculated absorption maxima of I2 3 nH2O (n = 1 to 8) by using the RSH functional were 386 to 382 nm, which are in better agreement with the experimental value of I2 in aqueous solution.50 3.2. Hydroxyl RadicalWater Complex. As noted above, although a hemibonded geometry of the hydroxyl radical in water was obtained by AIMD calculation,26 and such geometries have been invoked to explain photoabsorption of the hydroxyl radical in water,5153 the hemibonded structure of the hydroxyl radical in water was an artifact due to self-interaction error in the exchange correlation functional, and it has been shown that the hemibonding is absent by AIMD calculation with self-interaction correction.28 Thus the optimized geometries of the hydroxyl water systems were calculated to examine whether the LC-ωPBE functional can properly describe the interaction of the hydroxyl radical with water molecules. While cyclic geometries have been identified for small water clusters of the hydroxyl radical in the gas phase,54,55 recent AIMD calculations have shown that the hydroxyl radical forms both 14623
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Figure 3. Contour plots of potential energy surfaces of XOH calculated with four methods. (upper) ClOH (lower) BrOH. Zero values are set to the sum of total energies of OH and X, and values are in cm1. Contours with positive values are omitted in the plots.
hydrogen-donating and hydrogen-accepting bonds between water molecules.26,56 In addition, hemibonding formation with a water molecule has also been reported. A typical geometry of the hydroxyl radicalwater complex suggested by Vassilev et al. consists of an almost planar part of the hydroxyl radical with three hydrogenbonded water molecules to which one water molecule is perpendicularly hemibionded.26 Although hemibonding formation is possibly due to the self-interaction error, the hydroxyl radicalwater complex with hydrogen bondings is likely to be a stable structure even after the self-interaction error correction that may be a reactant to form other types of closed-shell molecules, including halide anions. Thus geometry optimization of a trihydrated hydroxyl radical was performed by referring to the estimated number of hydrogen-bonded water molecules to hydroxyl radicals in AIMD calculation. Figure 2a shows the optimized geometry of OH(H2O)3 with the LC-ωPBE functional. Its framework is almost planar, i.e., four oxygen atoms are located in the same plane. All the vibrational frequencies at this geometry were real values, indicating that the geometry corresponds to a local minimum. Optimized geometries of OH(H2O)3 were also performed by DFT (LC-ωPBE, BH&HLYP, and B3LYP) and post-HF methods. In the post-HF calculation, the ONIOM method was employed in which the hydroxyl radical was treated with the QCISD method, while three water molecules were treated at the HF level with a smaller basis set (cc-pVDZ). All the optimized geometries were planar in their framework of four oxygen atoms. Their Cartesian coordinates and vibrational frequencies are listed in the Supporting Information. Hemibonding formation of a water molecule with OH(H2O)3 was investigated by starting with a geometry in which the added water molecule was located above the oxygen atom of the hydroxyl radical. When the B3LYP functional was employed in the calculation, an optimized geometry was obtained, as shown in Figure 2b. The bond length between the oxygen atoms of the hydroxyl radical and the added water molecule was 2.389 Å,
which can be regarded as hemibonding. However, when the LCωPBE functional was employed in the geometry optimization calculation starting with this hemibonded optimized geometry of OH(H2O)4, the additional water molecule left from the initial position toward the water molecule accepts hydrogen bonding from the hydroxyl radical and finally forms a new hydrogen bond between these two water molecules. The formation of a hemibonded structure by LC-ωPBE functional was further sought by increasing the number of water molecules to prevent dissociation of the hemibonding. However, although several different initial geometries were tested and some of the geometries have become optimized, none of them showed apparent hemibonding. For example, Figure 2c shows an optimized geometry of OH(H2O)7 in which three water molecules were hydrogen bonded to the water molecules of the OH(H2O)3 unit while other ends of them were hydrogen bonded to a water molecule. Although in the beginning the bond length between the oxygen atoms in the hydroxyl and the water molecule was set to less than 3 Å, it was largely elongated to 4.1 Å in the optimized geometry in Figure 2c, which is too large to be regarded as hemibonding. Thus an optimized geometry of the hydroxyl water system with hemibonding has not yet been obtained by using the LC-ωPBE functional. This result is consistent with the results of the recent AIMD calculations with self-interaction energy-corrected functionals, and we suppose that interactions between the hydroxyl radical and water molecules are properly described with the LC-ωPBE functional. It should be mentioned that the absence of any optimized geometries in the present calculation does not mean total absence of hemibonding of the hydroxyl radical with a water molecule. If the total energy of a hemibonded configuration is only slightly higher than that of a dissociated configuration, the former would be thermally accessible at room temperature and consequently result in ultraviolet photoabsorption due to σσ* transition. In fact, the total energy of the geometry in Figure 2b 14624
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Table 4. Calculated HalogenOxygen Bond Lengths and Wavelengths of Photoabsorption Maxima of Optimized Geometries of Hydroxyl Halide Radical Anions with Different Configurations
Figure 4. Optimized geometries of hydroxyl halide radical anions with four water molecules. (a) ClOH(H 2O)4; (b) BrOH(H2O)4; (c) IOH(H2O)4.
Table 3. Calculated Properties of Hydroxyl Halide Radical Anions ClOH(H2O)4 BrOH(H2O)4 IOH(H2O)4
species ) r(XO) (Å a(XOH) (deg.) F(X)/F(O) XO stretching
2.417
2.402
2.485
88.5 0.286/0.783
93.5 0.489/0.581
98 0.66/0.418
162, 180
285
277
348 (350)a
343 (360)a
mode (cm1) λmax (nm) εmax/10
a
3
3
5.7 (3.7) 1
(dm mol a
7.1 (8)
a
324 (335)a 6.9 (4.5)a
1
cm )
Reference 20.
calculated with the LC-ωPBE functional was only 0.1 kcal mol1 higher than the total energy of OH(H2O)3 and H2 O, and a strong photoabsorption with λmax = 257 nm (f = 0.13) was predicted from TDDFT calculation. 3.3. Hemibonding between the Hydroxyl Radical and Halide Anions. Calculated results in the above sections have shown that the LC-ωPBE RSH functional gave satisfactory results on the odd electron systems relevant to the target of the present study. Thus the functional is then applied for calculation of possible equilibrium geometries with hemibonding between the oxygen atom in the hydroxyl radical and halogen atom. At first, the methods applied for those relevant open-shell systems were again compared for the hydroxyl radical-halide anion systems to confirm proper description of interaction between them. The effect of hydration was incorporated by the PCM model, and no water molecule was explicitly included in the calculation. Total energies were calculated at different geometries by changing XO bond lengths and XOH bond angles, while the OH bond length was fixed to 0.97 Å. Figure 3 shows contour plots of calculated energy surfaces of ClOH and BrOH by four methods. In the case of ClOH, energy minima appeared at a(ClOH) = 0° in all cases, which corresponds to a hydrogen-bonded linear OHCl configuration. Another energy minimum appeared at a(XOH) ∼ 90° only in the B3LYP calculation, which corresponds to a hemibonded geometry. As for the case of BrOH, the LC-ωPBE calculation also shows two energy minima at a(XOH) ∼ 0° and 90°, and a minimum at a(XOH) ∼ 0° disappeared in the B3LYP calculation. Although the other two calculations show only one minimum at a(XOH) ∼ 0°, contours are slightly stretched to the lower right corner of the plot in the QCISD calculation compared to the case of ClOH. In any case, while hemibonded geometries were located in the case of B3LYP, they
species
Cl
Br
I
XOH(H2O)4
2.417 (348)
2.402 (343)
2.485 (324)
2.417 (347)
2.403 (342)
2.486 (324)
2.496 (357)
2.424 (352)
2.481 (333)
2.413 (354)
2.405 (346)
2.483 (327)
2.340 (342)
2.387 (334)
2.488 (316)
XOH(H2O)2
were due to the error caused by the nonlocal XC functional, and the results indicate that explicit consideration of water molecules is necessary for description of hemibonded configurations of the hydroxyl radical and halide anions. As for the performance of the LC-ωPBE functional, there is a qualitative difference between the results by the QCISD method in the case of BrOH since a minimum corresponding to a hemibonded geometry appeared in the former while it is absent in the latter. However, in both methods, there is a tendency that the bent geometry becomes more favorable in BrOH than ClOH. Considering also its excellent performance for the dihalogen radical anions, the LC-ωPBE was employed for further calculations of hydroxyl halide radical anions. As discussed in the Introduction, if the hydroxyl radical is freely oriented toward a halide anion, they would become hydrogen bonded or form a linear configuration, unless hemibonding formation is overly stabilized, as in the case of the B3LYP functional. Hemibonding formation would become favorable if the relative motion of the hydroxyl radical is restricted by hydrogen bonds with surrounding water molecules. According to the results of the previous section, the hydroxyl radical with one hydrogen-donating and two hydrogen-accepting hydrogen bonds seems to be a favorable configuration in aqueous solution, and hemibonding formation was examined between this trihydrated hydroxyl radical and a halide anion, which was initially placed above the oxygen atom of the hydroxyl radical. Actually hemibonding was not formed by this setting as the halide anion moved toward a water molecule to form a hydrogen bond. To prevent migration of the halide anion, one water molecule was added to the system, which is hydrogen bonded to the halide anion while its oxygen atom accepts a hydrogen bond from the water molecule, which forms a hydrogen donative hydrogen bond toward the hydroxyl radical, thus forming cyclic square geometry by the halide anion, the hydroxyl radical, and two water molecules. Optimized geometries of such hydroxyl halide radical anions with four water molecules are shown in Figure 4, and their geometrical parameters and calculated properties are summarized in Table 4. Cartesian coordinates of the optimized geometries are listed in the Supporting Information. In all three halogen species, the halogen-oxygen bond lengths are less than 2.5 Å and the halogen atoms are located almost perpendicularly to the hydroxyl-water unit, as shown in Figure 4, and XOH(hydroxyl) angles are close to 90°. While r(IO) is longer than r(BrO), as expected from the ionic radii of the halogen atoms, r(ClO) is slightly longer than the latter. On the other hand, spin densities on the halogen atoms increase with atomic number, which is consistent with the order of their electron affinities. The halogen-oxygen 14625
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bond lengths and appreciably large spin densities on halogen atoms can be regarded as being due to hemibonding formation. All the vibrational frequencies were real at optimized geometries, and those values are available in the Supporting Information together with force constants, reduced masses, and infrared intensities, which help assignments of those vibrational modes. Of particular interest is halogen-oxygen stretching modes, which are characteristic to hemibondings. They can be identified from normal mode vectors in which displacements of the halogen atoms are large in addition to their fairly large reduced masses and force constants. In the case of Cl, two modes at 162 and 180 cm1 are assigned to asymmetric and symmetric stretching modes of the O(hydroxyl)ClH(water) bonds. By contrast, only one mode at 285 cm1 is assigned to the BrO stretching in the case of Br. This difference in the normal mode vectors may be due to different atomic weights of halogen atoms and weaker ClO hemibonding than that of BrO, as manifested by their bond lengths. The normal mode vector of the IO stretching mode is qualitatively the same as that of Br with slightly smaller frequency at 277 cm1. Table 3 also shows calculated and observed wavelengths and molar absorption coefficients of hydroxyl halide radical anions. Calculated values of photoabsorption maxima increase with atomic number of halogen species, while the order is reversed between chlorine and bromine in experiment. However, the differences between calculated and experimental values are fairly small. Iodine shows the shortest wavelength among hydroxyl halide radical anions, in contrast to the case of dihalogen radical anions as listed in Table 2. Agreement with the calculated and observed values is less satisfactory for molar absorption coefficients, possibly due to larger uncertainty in the experimental values and assumption made in the calculation on the spectral shape. However, it should be noted that calculation successfully reproduced the finding that molar absorption coefficients of hydroxyl halides are about less than half of the corresponding dihalogen radical anions. Other possible hemibonded geometries were sought by modification of XOH(H2O)4. In the optimized geometries shown in Figure 4, the hydrogen atom of the hydroxyl radical is included in the square cyclic structure. However, as suggested by an anonymous reviewer, another type of configuration in which the
hydrogen atom of the hydroxyl radical is not included in the square cyclic structure but forms a hydrogen bonding with a water molecule, which also does not constitute the cyclic motif. Such configurations were successfully optimized for all the halogen species, and an optimized geometry is shown in Figure 5a for the case of chlorine. Their total energies were only 1.51.6 kcal mol1 higher than those shown in Figure 4, and their geometrical parameters and other calculated properties are also very similar to those listed in Table 4. Successful geometry optimization of this type of configuration implies that molecular arrangements preventing rotation of the hydroxyl radical toward hydrogen bonding to halogen atoms are essential for hemibonding formation. Since the square cyclic motif seems to be effective for this constraint, geometry optimization calculations were performed for possible square cyclic configurations of XOH(H2O)2. There are several possible square cyclic configurations with different arrangements of hydrogen bonds: One is derived from the optimized geometries in Figure 4 by removing two water molecules hydrogen bonded to the hydroxyl radical, and the hydrogen atom of the hydroxyl radical is contained in the hydrogen bonding network of the square cyclic motif. However, this type of configuration did not converge to square cyclic optimized geometries for chloride and bromide. The second possible configuration is derived in the same manner from the optimized geometry in Figure 5a by removing two water molecules. In this case, the hydrogen atom of the hydroxyl radical does not form hydrogen bonding. Optimized geometries were obtained for all the halogen species as shown in Figure 5b for the case of chlorine. There is another possible square cyclic configuration in which the direction of the hydrogen bond between two water molecules is reversed, as shown in Figure 5c, which also resulted in optimized geometries for all the halogen species. Close examination of the optimized geometries of XOH(H2O)4 in Figure 4 reveals that the free OH bonds of the water molecules hydrogen bonded to the oxygen atom of the hydroxyl radical are directed upward, which may contribute to stabilization of the hemibonding to some extent due to electrostatic interaction between the hydrogen atoms and the halogen atom. In fact, optimized geometries, as shown in Figure 5d, derived by removing two water molecules in the square cyclic motif of Figure 4, were successfully obtained for all the halogen species. Among these three configurations, the square cyclic type of Figure 5b is the highest in its total energy, and the other two configurations of types c and d are 0.3 and 0.2 kcal mol1 more stable than the type b, respectively. Relative stability of types c and d are more enhanced in the case of bromine and iodine: Types c and d are 1.2 and 2.3 kcal mol1 more stable than the type (b) for bromine and 2.1 and 3.5 kcal mol1 for iodine, respectively. Table 4 shows calculated bond lengths of the halogen-oxygen bonds at optimized geometries of hydroxyl chloride radical anions shown in Figure 5 and their bromine and iodine analogues.
Figure 5. Optimized geometries of hydroxyl chloride radical anion with water molecules. (a) Another form of ClOH(H2O)4. (b) Square cyclic ClOH(H2O)2. (c) Another form of square cyclic ClOH(H2O)2. (d) ClOH(H2O)2 in which OH accepts two hydrogen bonds.
Table 5. Gibbs Free Energies of Reaction
E0 + Gcorr (Hartree)
Cl
Br
I
reactant
X OH(H2O)3+H2O
460.27720 381.42113
417.09101
295.93616
product
XOH(H2O)4
841.69477
798.51149
677.36946
2.24
1.78
7.63
1
ΔrG°(298 K) (kcal mol ) 14626
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While there are little differences between the calculated values at the two configurations of ClOH(H2O)4, the ClO bond lengths are changed with configurations of ClOH(H2O)2. In contrast, the IO bond lengths are almost constant regardless of the number of water molecules and their configurations. As shown in Table 4, Mulliken’s spin densities on the halogen atoms in XOH(H2O)4 increase with atomic number, and the iodineoxygen bonding is more covalent than the chlorine-oxygen bond and thus less susceptible to the arrangements of water molecules. Table 4 also shows calculated values of photoabsorption maxima of σσ* transition. Although the values are slightly shifted by changes in optimized geometries, their relative order of Cl > Br > I is unaffected. As noted above, reactivity toward oxidation in aqueous phase initiated by the hydroxyl radical is much lower in chloride than bromide and iodide. To explain this different reactivity, Gibbs free energies of reaction on formation were calculated for the following reaction: OHðH2 OÞ3 þ X þ H2 O ¼ XOHðH2 OÞ4
ð8Þ
To calculate free energies of the reactants or products, their partition functions are required. Results of vibrational analyses of OH(H2O)3 and XOH(H2O)4, at their optimized geometries as described above, were employed to calculate Gibbs free energy correction to total energies. As for other reactants, Gibbs free energy correction to total energies was calculated for a water molecule based on vibrational analysis at the optimized geometry. Total energies of halide anions in water were calculated with the polarizable continuum model without explicitly considering hydrating water molecules. Total energies with corrections of reactants and products as well as free energies of reaction are summarized in Table 5. The free energy of reaction was slightly endothermic for chloride, while calculated values of bromide and iodide were exothermic. As mentioned above, the formation of hydroxyl chloride radical anion is reversible, and the estimated equilibrium constant of the reaction 1 was 0.7, indicating that the reaction is slightly endothermic.18 On the other hand, reverse reaction of 1 was practically negligible for bromide and iodide, and dihalogen radical anions are formed as products of subsequent reaction 2 and 3. The calculated free energies are consistent with these experimental results and may suggest that the assumed reaction scheme of hydrated species is fortuitously appropriate.
’ CONCLUSION Geometries and properties of the hydroxyl radical and halide anions in aqueous phase were successfully calculated by using the LC-ωPBE RSH functional, which was further examined by calculation of dihalogen radical anions and hydrated hydroxyl radicals. Equilibrium geometries of the hydroxyl halide radical anions with four water molecules were successfully located, and they were confirmed to be local minima by vibrational analysis. Their photoexcitation energies and molecular absorption coefficients for σσ* transitions by the TDDFT method showed good agreement with experimental values. Calculated free energies of reaction on formation of the hydroxyl halide radical anions were consistent with the different reactivities of halide anions toward oxidation. Although this author believes that the present model of hydroxyl halide hydrated with four water molecules has captured the core of this species in aqueous phase, hydrogen bonds change
dynamically in actual systems, and it is highly hoped that the present model would be substantiated by AIMD calculation with self-interaction error correction or other methods that can treat open-shell systems with a larger number of water molecules. Most of the experiments hitherto performed indicated the formation of hydroxyl halide radical anions via transient photoabsorption measurement by pulse radiolysis. By contrast, resonance Raman spectra have been measured for dihalogen radical anions after pulse radiolysis, and potential energy curves were derived from the observed anharmonicity of peak positions. Unfortunately, no peaks of hydroxyl halide radical anions have ever appeared in the resonance Raman spectra, as most of the measurements were made at low pH to facilitate reactions 2 and 3 to generate dihalogen radical anions. However, judging from comparable molar absorption coefficients and estimated lifetimes at neutral to high pH conditions, the resonance Raman peaks of hydroxyl halide radical anions are expected to be detecable, and comparison with their peak positions would be a good test for the calculated vibrational frequencies of hydroxyl halide radical anions.
’ ASSOCIATED CONTENT
bS
Supporting Information. Optimized geometries in Cartesian coordinates and calculated vibrational frequencies at optimized geometries. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. Present Addresses †
Polymer Electrolyte Fuel Cell Cutting-Edge Research Center (FC-Cubic), Technology Research Association, 2-3-26 Aomi, Koto-ku, Tokyo 135-0064, Japan.
’ ACKNOWLEDGMENT The author thanks the anonymous reviewer who suggested possible hemibonded configurations of the hydroxyl halide complexes. This study is a part of the project for assessment methodology development of chemical effects on geological disposal systems funded by METI, the Ministry of Economy, Trade and Industry, Japan. ’ REFERENCES (1) Hochanadel, C. J. J. Phys. Chem. 1952, 56, 587. (2) LaVerne, J. A.; Ryan, M. R.; Mu, T. Radiat. Phys. Chem. 2009, 78, 1148. (3) Metz, V.; Loida, A.; Schild, B.; Dardenne, K. Radiochim. Acta 2008, 96, 637. (4) Anbar, M.; Thomas, J. K. J. Phys. Chem. 1964, 68, 3829. (5) Matheson, M. S.; Mulac, W. A.; Weeks, J. L.; Rabani, J. J. Phys. Chem. 1966, 70, 2092. (6) Zehavi, D.; Rabani, J. J. Phys. Chem. 1972, 76, 312. (7) Behar, D. J. Phys. Chem. 1972, 76, 1815. (8) Mamou, A.; Rabani, J.; Behar, D. J. Phys. Chem. 1977, 81, 1447. (9) Sawai, T.; Hamill, W. H. J. Phys. Chem. 1970, 74, 3914. (10) Khorana, S.; Hamill, W. H. J. Phys. Chem. 1971, 75, 3081. (11) Ogura, H.; Hamill, W. H. J. Phys. Chem. 1973, 77, 2952. (12) Fisher, M. M.; Hamill, W. H. J. Phys. Chem. 1973, 77, 171. 14627
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