Hemibonding between Hydroxyl Radical and Water - The Journal of

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Hemibonding between Hydroxyl Radical and Water Daniel M. Chipman* Radiation Laboratory, University of Notre Dame, Notre Dame, Indiana 46556-5674, United States ABSTRACT: The ultraviolet absorption peak commonly used to identify OH radical in liquid water is mainly due to a charge-transfer-from-solvent transition that is prominent when OH is hemibonded, rather than more stable hydrogen bonded, to H2O. This work computationally characterizes the hemibonding interaction and the extent of the geometrical region over which it is significant. Hemibonding is found to be associated with an enlarged energy separation between the two lowest-lying electronic states, which are otherwise always quite close to one another. The lower state, wherein the hemibonding occurs, retains an attractive interaction energy between OH and H2O that can be as much as one-half as strong as the optimum hydrogen-bonding interaction, while the enlarged separation between the states is mainly due to the upper state becoming repulsive over most of the hemibonding region. Hemibonding also leads to a considerable drop in the energy and a considerable increase in the oscillator strength of the characteristic charge-transfer transition. The region of significant hemibonding is found to lie within a moderate range of O-O azimuthal angles and over quite wide ranges of O-O separation distances and hydroxyl OH tilt angles. In particular, significant hemibonding interactions can extend down to surprisingly short O-O distances, where the oscillator strength for the charge-transfer-from-solvent transition becomes very large.

’ INTRODUCTION Interactions of hydroxyl radical (OH) with water are of importance in radiation chemistry,1,2 atmospheric chemistry,3 advanced oxidation processes for environmental remediation,4-6 and oxidative stress in cell biology.7 Hydroxyl radical interacting with a single water molecule has been the subject of a number of experimental8-18 and computational16,17,19-30 studies. Further computational investigations have also been reported on interactions of OH with larger clusters of water molecules,12,24,27,29,31-34 on OH in aqueous solution,35-40 and on OH at aqueous interfaces.41-46 Most computational studies of the OH 3 H2O complex have focused on the global minimum geometry, wherein OH donates a hydrogen bond to H2O.16,17,20-30 Some studies have also examined a higher energy local minimum geometry wherein OH accepts a hydrogen bond from H2O.16,19-24,27-30 One study27 has further examined the potential energy surface of interaction more globally. A few studies have also considered hemibonding interactions between OH and H2O.24,29,30,47 The hemibond in this case can be qualitatively described as a 2-center 3-electron interaction with a formal bond order of 1/2 that exists between the singly occupied local-π orbital on OH and the doubly occupied local-π lone pair on H2O when these orbitals are favorably disposed for significant overlap. Density functional theory calculations typically show a hemibonded OH 3 H2O complex to be a local minimum on the potential energy surface24 and to be persistent in molecular dynamics simulations.36 However, density functional theory calculations that include correction for self-interaction error47 indicate that even while there is a significant attractive hemibonding interaction, there is in fact no hemibonded local minimum. Higher level ab initio methods have further confirmed an overstabilization of the hemibonding interaction by ordinary density functional theory.47 It has previously been demonstrated that the strong ultraviolet absorption band of OH radical in aqueous solution peaking near r 2011 American Chemical Society

or below 235 nm48,49 that is often used to monitor its reaction kinetics50 is mostly due to a strong charge-transfer-from-solvent transition.29,30,51,52 This characteristic transition has further been identified as coming mainly from hemibonded interactions,30 where a large oscillator strength associated with the transition more than makes up for the (presumably) relatively small transient population of hemibonded OH 3 H2O species. In light of their importance in the ultraviolet spectrum of aqueous OH, and perhaps elsewhere as well, we report here electronic structure calculations that further elucidate the nature and extent of hemibonding interactions between OH and H2O. The next section describes the computational methods used and also reports on some tests that validate the methods. After that follow three results sections. To provide a point of reference, the first of these describes the optimum hydrogen-bonding geometries and energies. Then comes a section describing how varying the O-O azimuthal angle with constrained optimizations causes a qualitative change from hydrogen-bonding to hemibonding interactions and further proposes specific criteria to define when significant hemibonding interactions are present. After that a section describes the influence of scans over the O-O separation distance and hydroxyl OH tilt angle within the range that is favorable for hemibonding. The paper ends with a brief summary and conclusion section.

’ COMPUTATIONAL METHODS Methods for Low-Lying States. We limit consideration to geometries having the OH bond axis and the H2O symmetry axis lying in a common plane that is perpendicular to the Received: October 26, 2010 Revised: December 21, 2010 Published: January 27, 2011 1161

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The Journal of Physical Chemistry A

Figure 1. Intermolecular parameters defining the OH 3 H2O geometry. The structure is shown at a typical hemibonding geometry.

H2O molecule, giving the complex Cs symmetry, as shown in Figure 1. The two lowest energy states are expected and found to be closely spaced since they derive from the two states of free OH that are degenerate in the absence of spin-orbit splitting. These are labeled here as 1A0 for the ground state and 1A00 for the lowest-lying excited state. A hemibonding interaction can occur when the unpaired electron distribution lies in the mirror plane, corresponding to the 1A0 state. Energies of the 1A0 and 1A00 states were calculated with the NWChem program53 using the spin-unrestricted CCSD(T) method (coupled cluster single and double excitations with noniterative treatment of triplet excitations),54,55 together with the augcc-pVTZ basis set56,57 that is triple-ζ in the valence space and also has polarization and diffuse functions on all atoms. These two states can each be individually described with CCSD(T) by virtue of lying in different symmetry subspaces. Interaction energies (Eint) in the 1A0 and 1A00 states are given with respect to zero for separated OH and H2O and include correction for basis set superposition error (BSSE) by the counterpoise method.58 No corrections have been applied for vibrational motions. Since analytic gradients are not available for the CCSD(T) method, scans and constrained geometry optimizations were laboriously carried out manually on each of the 1A0 and 1A00 states. To simplify this process, intramolecular parameters in the two monomers were held rigid at their noninteracting equilibrium geometries. The monomer geometries used were taken from literature CCSD(T)/aug-cc-pVTZ calculations that used a spinrestricted reference,27 giving 0.97330 Å for the bond distance in OH, 0.96160 Å for the bond distance in H2O, and 104.186° for the bond angle in H2O. Under these restraints of rigid monomers and a mirror plane of symmetry, three intermolecular parameters remain to complete the geometry specification. With expensive electronic structure methods such as those used here it is not feasible to do a comprehensive examination over the full 3D space. We therefore limit ourselves to lower dimensional searches and scans that are expected to demonstrate the main features of hemibonding interactions. These are carried out in terms of intermolecular parameters corresponding to the O-O distance R, the hydroxyl OH

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tilt angle R, and the O-O azimuthal angle χ, as shown in Figure 1. Some conventions are necessary to specify the sense of each angle.The OH radical bond axis and the water OX axis, with X being the midpoint of the two water hydrogens, are in a trans arrangement with respect to the line connecting the two O atoms if both χ and R are in the interval (0°,180°), which is the situation depicted in Figure 1. This arrangement becomes cis if one of χ or R is in the interval (-180°,0°) or (180°,360°) while the other remains in the interval (0°,180°). The arrangement is again trans if both χ and R are outside the interval (0°,180°), being instead in either the (-180°,0°) or the (180°,360°) interval. A series of constrained geometry optimizations in the lowlying 1A0 and 1A00 states was carried out as a function of the angle χ. For this, χ was stepped from 0° to 180° in increments of 10° and at each fixed value of χ the energy was minimized with respect to both R and R. This minimization was done from single-point energy calculations carried out over a grid of points with spacing of 0.01 Å for R and 1° for R, determining the constrained-χ minimum energy position by fitting low-order polynomials to energies obtained at the nearest R and R grid points bracketing it. For the most part these constrained-χ optimizations were carried out on interaction energies obtained without correction for BSSE, even though BSSE correction was applied at the final optimum geometry so determined. However, in addition to shifting the interaction energies at a given geometry the BSSE correction could also change the shapes of the potential energy surfaces. To evaluate the possible influence of this effect on the geometries obtained, in a few strategic instances analogous constrained-χ optimizations were also carried out after correction for BSSE. In the 1A0 state, as χ reaches 180° the constrained optimum value of R reaches 0°, i.e., the hydrogen bond becomes exactly linear, and as χ reaches 0° the constrained optimum value of R reaches 180°. Consequently, the regions of χ above 180° and below 0° are redundant with regions in the (0°,180°) interval. In the 1A00 state, as χ reaches 180° the constrained optimum value of R again reaches 0° so the regions of χ above 180° are again redundant with regions below 180°. However, as χ reaches 0° in the 1A00 state the value of R does not quite attain 180°, so in this case the region of χ below 0° is distinct. The constrained optimizations were therefore further stepped in 10° increments for χ below 0° to examine this distinct region in the 1A00 state. At several particular χ values for which the constrained-χ geometry was found to have significant hemibonding interactions in the 1A0 state, additional scans were made at fixed χ and R over a grid of R values with a spacing of 0.05 Å and also at fixed χ and R over a grid of R values with a spacing of 10°. In all cases, results that are reported at points not specifically calculated come from estimation by cubic spline interpolation. Methods for Higher-Lying States. At each of the geometries described above, calculations were also made to obtain vertical transition energies (ΔEexc) to the next two higher-lying vertical excited states, which are labeled as 2A0 and 3A0 . Previous calculations using the EOM(equations of motion)-CCSD and EOM-CCSDT methods30 on representative OH 3 H2O structures found that while triple excitations have only a minor effect on ΔEexc(2A0 r 1A0 ), triples can have a large effect on ΔEexc(3A0 r 1A0 ). The triples were found to provide a lowering of 0.46 eV for ΔEexc(3A0 r 1A0 ) in a representative hemibonded structure and even more (0.75 eV) in a representative H-bond acceptor structure. Due to the computational expense, it is not feasible to include triple excitations in calculations on a large number of structures 1162

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Table 1. Excitation Energies (ΔEexc), Wavenumbers (λ), and Oscillator Strengths ( f ) Calculated for the 2A0 r 1A0 and 3A0 r 1A0 Transitions of a Hemibonded Structure of OH 3 H2Oa ΔEexc (eV)

λ (nm)

f

4.41

281

0.0010

“EOM-CCSDT/aug-cc-pVTZ”

4.39

282

EOM-IP-CCSD/aug-cc-pVTZ

4.39

283

0.0004

method

Table 2. Intermolecular Geometrical Parameters χ, R, r, and Interaction Energies, Eint, Characterizing Optimum Hydrogen-Bonding and Constrained Optimum Hemibonding Interactionsa 1A0 hydrogen bondb

2A0 r 1A0 transition EOM-CCSD/aug-cc-pVTZ b

EOM-CCSD/aug-cc-pVTZ “EOM-CCSDT/aug-cc-pVTZ”b

5.88 5.42

211 229

0.0876

EOM-IP-CCSD/aug-cc-pVTZ

5.36

231

0.1038

a

The geometry used here is labeled as structure C2 in ref 30 and corresponds to the hemibonded local minimum found in the DFT calculation of ref 24. b The method labeled “EOM-CCSDT/aug-ccpVTZ” is an approximation to EOM-CCSDT/aug-cc-pVTZ, obtained by assuming additivity of separate corrections due to inclusion of triple excitations and to extension from a smaller basis set, as described in ref 30.

even with a small basis set, much less than with the large basis set adopted in this work. Fortunately, a solution to this difficulty was described to us by Dr. Anna Krylov, who found essentially the same problem in calculations on (H2O)2þ.59 It seems that in open-shell systems some intermediate stages of EOM-CCSD methods can be subject to very serious spin contamination effects, even when carried out with a spin-restricted open-shell reference state. This problem is solved in the EOM-IP-CCSD (EOM-ionization potential-CCSD) method60-62 that uses a Hartree-Fock calculation on the closed-shell anion as a reference state and thereby provides a procedure that is automatically spin restricted throughout. In general, triple excitations may also be necessary in cases where the open-shell reference state does not correctly localize the spin in the right place, but that does not seem to be a problem in the present work. With EOM-IP-CCSD we find that there is no need to treat triple excitations in the present problem. This is clearly demonstrated by the results shown in Table 1, where the large discrepancy of 0.46 eV in ΔEexc(3A0 r 1A0 ) at the EOM-CCSD/ aug-cc-pVTZ level, as compared to an estimate of the true EOMCCSDT/aug-cc-pVTZ result, is reduced to only 0.06 eV with EOM-IP-CCSD/aug-cc-pVTZ. The 2A0 state is mainly localized on OH. The hole comes mainly by removing an electron from the nominal doubly occupied local-σ bonding orbital on OH, and the excited electron fills what was previously the valence hole in the nominal local-π system on OH. This transition therefore corresponds closely to the valence A ~rX ~ transition of free OH, which is seen experimentally at 4.05 eV63 (306 nm) with an oscillator strength (f number) of 0.0011.64 An EOM-IP-CCSD/aug-cc-pVTZ calculation on free OH at the geometry used in this work finds it very close to there, at 4.12 eV (299 nm) with f of 0.0017. The 3A0 state will be shown below to be the result of a chargetransfer transition wherein essentially a full electron jumps from the water molecule to the hydroxyl. The hole comes mainly by removing an electron from the nominal local-π lone pair orbital on H2O, which corresponds to the HOMO of an isolated water molecule, and the excited electron fills what was previously the valence hole in the nominal local-π system on OH.

1A0 hemibondd

χ

142.6 (146.2)

136.9 (140.2)

47.2 (47.2)

R

2.8894 (2.9147)

2.9167 (2.9424)

2.6810 (2.7179)

R

3A0 r 1A0 transition

1A00 hydrogen bondc

1.5 (1.4)

1.7 (1.5)

74.4 (73.9)

Eint(1A0 )

-5.37 (-5.38)

-5.36 (-5.37)

-2.70 (-2.71)

Eint(1A00 )

-5.04 (-5.07)

-5.07 (-5.08)

0.73 (0.30)

a

Distances are given in Angstroms, angles in degrees, and energies in kcal/mol. Results in parentheses are obtained from optimizations carried out after correction for BSSE. b Optimum hydrogen-bonding interaction found from minimum Eint in the 1A0 state. c Optimum hydrogenbonding interaction found from minimum Eint in the 1A00 state. d Optimum hemibonding interaction found from minimum R of constrained optimizations in the 1A0 state.

All calculations on the 2A0 and 3A0 vertical excited states using the EOM-IP-CCSD/aug-cc-pVTZ method were performed with the QChem program.65

’ OPTIMUM HYDROGEN-BONDING GEOMETRIES In both the 1A0 and 1A00 states the minimum energy geometry is characterized by hydrogen-bonding interactions. The optimum geometrical parameters and energies are summarized in the first two numerical columns of Table 2. The global energy minimum is found in the 1A0 state, with Eint of -5.37 kcal/mol. This energy and the optimum geometry reported for the 1A0 state in Table 2 are in excellent agreement with the energy and geometry found previously in a very similar optimization27 also carried out with rigid monomers. A QCISD/ 6-311þþG(2d,2p) optimization9 that allowed monomer relaxation also found a similar energy of -5.69 kcal/mol, indicating that monomer relaxation is not a very significant factor. There is also a secondary local minimum structure corresponding to OH accepting a hydrogen bond from H2O, with a calculated energy of -3.51 kcal/mol.9 This latter structure, which has OH and H2O lying in a common plane, is far from the geometries considered in the present work and will not be further considered The results in Table 2 show that energy minimization in the 1A00 state leads to Eint only 0.33 kcal/mol higher than in the 1A0 state. The optimum hydrogen-bonding geometries are very similar in the two states, with χ of about 140° that is near where a putative water lone pair in tetrahedral sp3 hybridization would point, R near 2.9 Å, and R of about 0° corresponding to a nearly linear hydrogen bond. The influence of carrying out these geometrical optimizations after rather than before correction for BSSE (as seen with the parenthetical results in Table 2) is generally minor, increasing χ by only about 3-4°, increasing R somewhat by 0.025-0.026 Å, decreasing R by only 0.1-0.2°, and lowering Eint(1A0 ) and Eint(1A00 ) by only 0.01-0.03 kcal/mol. ’ DEPENDENCE ON AZIMUTHAL ANGLE Χ Figure 2 shows results from constrained-χ optimizations carried out in the 1A0 state, and Figure 3 shows results from constrained-χ optimizations carried out in the 1A00 state. The bottom panel of each figure shows Eint(1A0 ) and Eint(1A00 ), the 1163



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Figure 2. Results from constrained-χ optimizations in the 1A0 state. The region of significant hemibonding interaction is enclosed by vertical dashed lines, excepting for clarity such lines in the redundant region below χ of 0°.

next to bottom panel shows R, the middle panel shows R, the next to top panel shows ΔEexc(2A0 r 1A0 ) and ΔEexc(3A0 r 1A0 ), and the top panel shows f(2A0 r 1A0 ) and f(3A0 r 1A0 ). Note that the results in Figure 3 show a break as χ extends below -50°. This is because attempting a constrained optimization at χ of -60° by starting from the parameter values obtained at χ of -50° (where R is 179.5°), the constrained-χ optimization process takes R past 180°, that is the hydroxyl hydrogen changes from a trans to a cis orientation with respect to the midpoint of the water hydrogens. After that point the constrained optimization then undergoes a catastrophic change and collapses to the much stronger interaction corresponding to R of 300°. Thus, somewhere in the regions from at least -50° to -60° and equivalently from at least 300° to 310° there are two local minima in the constrained-χ optimization. To show this break in smooth behavior, we make the plot in Figure 3 extend over the range from -60° to 300°. For consistency and to allow for facile comparisons we also employ this same range in Figure 2, even though this leads to display of redundant regions in that case. 1A0 and 1A00 States. In Figures 2 and 3 over the range of about 90-270° in χ the 1A0 and 1A00 states lie close together, never differing by more than 0.38 kcal/mol, and have substantial interaction energies Eint below -4.1 kcal/mol. Hydrogen bonding dominates the hydroxyl-water interaction over this range in both states and is almost as strong at 1A00 -optimized geometries as at the respective 1A0 -optimized geometries. More discordant behavior between Eint(1A0 ) and Eint(1A00 ) is found over the remaining range of χ. In Figure 3 it is seen that as

χ decreases below 90° the 1A0 and 1A00 states remain closely spaced and have weaker interaction energies, indicating that the hydrogen-bonding interaction is gradually being broken as χ decreases. In Figure 2, however, as χ decreases below 90° the 1A0 state retains a significant Eint that always remains below -1.9 kcal/mol. In stark contrast, the 1A00 state rises sharply and even becomes repulsive over the range of 26-55° in χ. This produces a substantial Eint(1A00 ) - Eint(1A0 ) difference that has a maximum of 3.43 kcal/mol at χ = 46.8° and then drops down to a smaller value of 0.68 kcal/mol at χ = 0°. Taken together, these results are indicative that as χ decreases the nature of the interaction in the 1A0 state gradually changes over from hydrogen bonding to hemibonding in character, until the hemibond is ultimately broken as χ nears 0°. These energetic behaviors can be correlated with changes in the R and R geometric parameters shown, respectively, in the next to bottom and middle panels of Figures 2 and 3. In the region above 90° in χ where significant hydrogen-bonding interactions dominate, R is nearly constant at 2.89-2.92 Å in Figure 2 and at 2.92-2.96 Å in Figure 3. At the same time R remains below 17° in Figure 2 and below 14° in Figure 3, indicating a nearly linear hydrogen bond. As χ falls below 90° in Figure 3 there is an increase in R and a concomitant increase in R that leads to a gradual weakening of the hydrogen bond as the two monomers separate. However, as χ falls below 90° in Figure 2 there is instead a sharp decrease in R accompanied by an increase in R. Near the optimum hemibonding region in χ the value of R is near 90°, indicating that the hydroxyl OH axis has swung away 1164



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Figure 3. Results from constrained-χ optimizations in the 1A00 state.

from pointing toward the water oxygen to now instead be more nearly parallel to the water plane, thereby breaking the hydrogen bond and allowing the hemibond to form instead. As χ finally reaches 0°, a substantial increase of R to 3.080 Å makes the interaction energy weaker and allows R to increase to 180°. Geometries and energies characterizing the optimum hemibonding interaction are summarized in the third numerical column of Table 2. The optimum interaction in this case is defined to be the point where R takes on its minimum value in the constrained-χ optimizations for the 1A0 state. It is notable that this minimum value of R in the hemibonding region is more than 0.2 Å shorter than the corresponding R at the geometry corresponding to optimum hydrogen-bonding interaction. The χ of 47.2° at which R takes on this minimum value is less than one-half a degree away from the χ noted above that maximizes Eint(1A00 ) - Eint(1A0 ). The influence of carrying out this optimization after correction for BSSE (as seen with the results in parentheses in the third column of Table 2) is again generally minor, leaving χ essentially unchanged, increasing R somewhat by 0.037 Å, decreasing R by only 0.5°, lowering Eint(1A0 ) by only 0.01 kcal/mol, and lowering Eint(1A00 ) somewhat more by 0.43 kcal/mol. Quantification of the Hemibonding Region. To facilitate discussion of trends, it is useful to be more specific at this point about just when a significant hemibonding interaction is present. Since there is no convenient direct measure of hemibonding, we must rely on circumstantial indicators. While recognizing that any quantitative stipulation is necessarily somewhat arbitrary, after considering the results presented above as well as further

Figure 4. Density differences between various excited states and the ground state. Blue isosurfaces enclose the hole where electron density has been depleted, and shaded white isosurfaces enclose the excited electron where electron density has accumulated upon excitation. The isosurfaces correspond to (0.025 e/a30.

results yet to be presented below we can make a reasonable characterization that seems appropriate for this particular system. To wit, we specify that a significant hemibonding interaction occurs between OH and H2O when two criteria are simultaneously satisfied. First, the strength of the hemibond should be significant. We satisfy this by stipulating that Eint(1A0 ) should be below -1.5 kcal/mol. Second, to distinguish regions dominated 1165



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Figure 5. Results from scans over R and R at χ = 30°. The region of significant hemibonding interaction is enclosed by vertical dashed lines.

by hemibonding from those dominated by hydrogen bonding, the interaction energy in the low-lying state that does not allow hemibonding to occur should be substantially higher than in the other low-lying state that does allow it. We satisfy this by stipulating that Eint(1A00 ) - Eint(1A0 ) should be above 1.5 kcal/mol, which can be compared to the separation of at most 0.4 kcal/mol found between these states at geometries that are clearly dominated by hydrogen bonding. In the constrained-χ results of Figure 2, the first criterion is satisifed for all χ while the second criterion limits the significant hemibonding region to the range of 20.3-59.7° in χ. The behavior in Figure 2 in which R is relatively short and R is closer to 90° than to either 0° or 180° further substantiates the claim of significant hemibonding over this range of χ. Thus, over the range of 20-60° in χ it is seen that R is always below 2.87 Å and R varies from 50° to 112°. These values should be compared with the R of 2.89-2.92 Å and R of 0-17° that pertain at χ above 90° where hydrogen bonding clearly dominates. 2A0 and 3A0 States. Vertical excitation energies to the 2A0 and 3A0 states are shown in the next to top panels of Figures 2 and

3 and the corresponding oscillator strengths in the top panels. Properties of the 2A0 state are rather insensitive to χ, with ΔEexc lying in the range of 3.74-4.18 eV in Figure 2 and 3.76-4.10 eV in Figure 3, while f is small, lying in the range of 0.0000-0.0043 in Figure 2 and 0.0008-0.0026 in Figure 3. These results are similar to the ΔEexc of 4.12 eV and f of 0.0017 calculated for free OH, indicating that this transition essentially retains its local OH character albeit with some perturbation due to nearby H2O. Over the range of about 90-270° in χ properties of the 3A0 state are also rather insensitive to χ. In Figure 2 ΔEexc ranges over 7.07-7.58 eV and f over 0.0033-0.0081, while in Figure 3 ΔEexc ranges over 7.12-7.58 eV and f over 0.0026-0.0053. However, properties of the 3A0 state are found to be much more sensitive as χ decreases below 90°. In Figure 3, ΔEexc becomes as low as 5.39 eV at χ of 1.0° and f becomes as high as 0.0101 at χ of 39.7°. The changes are even more dramatic below χ of 90° in Figure 2, where hemibonding becomes possible. There ΔEexc drops below 5.88 eV and f rises above 0.0127 throughout the putative hemibonding range. ΔEexc becomes as low as 4.71 eV (263 nm) at χ of 25.4°, and f becomes as high as 0.0507 at χ of 50.2°. Thus, 1166



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Figure 6. Results from scans over R and R at χ = 47.2°. The region of significant hemibonding interaction is enclosed by vertical dashed lines.

hemibonding allows the 3A0 state to fall well into the range of the observed maximum ultraviolet absorption of OH in liquid water and to do so with very high oscillator strength. Density Changes upon Transition. Figure 4 provides a convenient visual picture of the changes in electron density upon transition. The bottom row depicts states at the optimum hydrogenbonding geometry, while the top row depicts states at the constrained optimum hemibonding geometry. The hole, which is the region where electron density is depleted upon transition, is shown in blue and the excited electron, which is the region where electron density accumulates upon transition, is shown in shaded white. The qualitative nature of each transition is seen to be essentially the same at hydrogen bonding as at hemibonding geometries. The low-lying 1A00 r 1A0 transition moves an electron from one nominal local-π orbital on OH to the other nominal local-π orbital on OH. The 2A0 r 1A0 transition moves an electron from the nominal local-σ bonding orbital on OH to fill the previously incomplete nominal local-π shell on OH. The 3A0 r 1A0 transition mainly involves charge transfer to move an electron from the nominal local-π bonding orbital on H2O,

which corresponds to the HOMO of an isolated water molecule, to fill the previously incomplete nominal local-π shell on OH and also has smaller contributions of donut shape about the waist of each oxygen atom. In summary, at either geometry the three transitions are mainly distinguished by each having a very different characteristic hole, whereas the excited electron is qualitatively similar in each transition. However, the detailed shape of the excited electron density does vary somewhat depending on which particular transition is involved. For any given transition the shape of neither the excited electron nor the hole shows much change with χ, other than for closely following the fragment on which it is localized. The charge-transfer character of the 3A0 r 1A0 transition is further confirmed by the large dipole moments of 15.9 and 9.1 D calculated for the 3A0 excited states at the hydrogen-bonding and hemibonding geometries, respectively. To put these in perspective, we note that two charges of (e separated by a distance of 1 Å would produce a dipole moment of 4.8 D. Thus, the 3A0 r 1A0 transition leads to a very substantial charge separation in the 3A0 excited state. 1167



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Figure 7. Results from scans over R and R at χ = 60°. The region of significant hemibonding interaction is enclosed by vertical dashed lines.

’ DEPENDENCE ON O-O SEPARATION R AND TILT ANGLE R To further explore the hemibonding region we now consider simple scans over slices with varying either R or R. These explorations are done for three particular values of χ selected in light of the results discussed above and are shown in Figures 5-7. In Figure 6 χ is fixed at 47.2° to probe the optimum hemibonding region, while Figures 5 and 7, respectively, have χ fixed at 30° and 60° to probe the edges of the hemibonding region. The bottom three panels of each figure show the dependence on R, with R fixed at its value found in the respective constrained-χ optimization. Similarly, the top three panels of each figure show the dependence on R, with R fixed at its value found in the respective constrained-χ optimization. Within each group of three panels the lowermost panel shows Eint in the 1A0 and 1A00 states, the middle panel shows ΔEexc in the 3A0 and 4A0 states, and the top panel shows f in the 3A0 and 4A0 states. We note that the scans over R are shown only over the interval (0°,180°). This is because even though the (180°,360°) interval of R is unique, it is not of particular interest since Eint(1A0 ) and Eint(1A00 ) are both somewhat repulsive there.

1A0 and 1A00 States. Figures 5-7 indicate that hemibonding

is significant over considerable ranges of R and R. Table 3 summarizes the particular regions of R and R over which the two criteria specified for significant hemibonding are satisfied in Figures 5-7. In all the R scans the boundary at small R is dictated by the Eint(1A0 ) < -1.5 kcal/mol criterion while the boundary at large R is dictated by the Eint(1A00 ) - Eint(1A0 ) > 1.5 kcal/mol criterion. On the other hand, in all the R scans the boundary at small R is dictated by the Eint(1A00 ) - Eint(1A0 ) > 1.5 kcal/mol criterion while the boundary at large R is dictated by the Eint(1A0 ) < -1.5 kcal/mol criterion. The region of significant hemibonding is seen to be for R values that are always slightly to considerably shorter than what is typical of optimum hydrogen bonding. In fact, the significant hemibonding region extends down to surprisingly small R, as low as 2.387 Å in the scan at fixed χ of 47.2°. We surmise that allowing relaxation of monomer geometry, particularly allowing for stretching of the hydroxyl bond, would probably further stabilize the hemibonding interaction in this region. The scans also show that hemibonding is significant for a wide range of R, for example, ranging from about 42° to 123° in the scan at fixed χ of 47.2°. 1168



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Table 3. Range of R with Fixed χ and r and Range of r with Fixed χ and R over which Significant Hemibonding Interactions Occura χ (deg)

range of R (Å)

fixed R (deg)

30

2.498-2.892

91.4

47.2

2.387-2.919

74.4

60

2.483-2.796

49.1

χ (deg)

fixed R (Å)

range of R (deg)

30 47.2

2.750 2.681

52.5-136.8 41.8-123.3

60

2.810

50.4-120.6

In the upper portion of the table the range of R is given while R is fixed at its constrained-χ optimum value. In the lower portion of the table the range of R is given while R is fixed at its constrained-χ optimum value. a

2A0 and 3A0 States. Properties of the 2A0 state do not vary

much over the significant hemibonding region. Throughout all the panels in Figures 5-7 ΔEexc ranges only from 3.76 to 4.23 eV and its variation within any one panel is considerably less than that while the f numbers vary only from 0.0000 to 0.0050. These results are similar to the ΔEexc of 4.12 eV and f of 0.0017 calculated for free OH, indicating that this transition essentially retains its local OH character albeit with some perturbation due to nearby H2O. Properties of the 3A0 state do change considerably over the significant hemibonding region. Throughout all the panels in Figures 5-7 ΔEexc ranges from 4.45 to 5.90 eV, while the f numbers vary from 0.0001 to 0.0824. We first consider the significant hemibonding regions in the R scans, where ΔEexc ranges from 4.45 to 4.98 eV at χ of 30°, from 5.00 to 5.41 eV at χ of 47.2°, and from 5.87 to 5.90 eV at χ of 60°, with ΔEexc always decreasing with decreasing R. The corresponding f numbers range from 0.0204 to 0.0464 at χ of 30°, from 0.0307 to 0.0824 at χ of 47.2°, and from 0.0327 to 0.0588 at χ of 60°, with f always increasing with decreasing R. This general lowering of ΔEexc and increasing of f indicates that hemibonding becomes more pronounced with decreasing R. Next, we consider the significant hemibonding regions in the R scans, where ΔEexc ranges from 4.78 to 5.26 eV at χ of 30°, from 5.04 to 5.81 eV at χ of 47.2°, and from 5.43 to 5.88 eV at χ of 60°, with ΔEexc always decreasing with increasing R. Meanwhile f ranges from 0.0114 to 0.0276 at χ of 30°, from 0.0202 to 0.0521 at χ of 47.2°, and from 0.0331 to 0.0492 at χ of 60°, with f always always achieving a maximum roughly in the middle of the R range. This suggests, not surprisingly, that hemibonding generally becomes most pronounced near R = 90°.

’ SUMMARY AND CONCLUSION It has been previously established30 that the major ultraviolet absorption peak of the OH radical in liquid water arises mainly from transitions occurring when the OH is hemibonded to H2O, which allows an intense excited state of charge-transfer character29,30,51 to become accessible. In this work the nature and extent of the hemibonding interaction is examined in more detail. Although there is no local minimum hemibonded structure, hemibonding interactions can be quite significant over a fairly wide range of geometries. To quantify the matter for purposes of discussion, it is proposed somewhat arbitrarily that hemibonding should be considered significant when the interaction energy

between OH and H2O in the lowest electronic state is under -1.5 kcal/mol and when simultaneously the separation between the two lowest electronic states is above 1.5 kcal/mol. To delineate the hemibonding ranges, scans are made over three relevant intermolecular parameters corresponding to the O-O azimuthal angle χ, the O-O distance R, and the hydroxyl OH tilt angle R. A plane of symmetry containing both OH and the symmetry axis of H2O is maintained throughout to allow clear distinction of the ground state 1A0 , wherein the nominal local-π orbital on OH that points toward the H2O is singly occupied, from the low-lying excited state 1A00 , wherein that same orbital is doubly occupied. A constrained optimum scan over χ, in which both R and R are varied at each fixed χ to minimize Eint(1A0 ), shows that the global minimum occurs at a hydrogen-bonding geometry with χ of about 143°. At that point Eint(1A0 ) is -5.37 kcal/mol, with Eint(1A00 ) being only slightly higher at -5.04 kcal/mol. An analogous constrained-χ optimization carried out in the 1A00 state leads to a very similar hydrogen-bonding geometry and only slightly higher energies of the two lowest states. As χ decreases from the hydrogen-bonding region a hemibond gradually forms in its place. The criteria specified for significant hemibonding interaction are found to be satisfied for χ over the range of about 20-60°. The hemibonding interaction is maximized on this scan at χ of 47.2°, where the constrained optimum value of R is over 0.20 Å shorter than at the optimum hydrogenbonding configuration. At this point Eint(1A0 ) is still substantially attractive at -2.70 kcal/mol, which is about one-half as strong as the maximum hydrogen-bonding interaction, Eint(1A00 ) is repulsive at þ0.73 kcal/mol, ΔEexc(3A0 r 1A0 ) has a relatively low value of 5.13 eV (242 nm), and f(3A0 r 1A0 ) has a relatively high value of 0.0493. As χ decreases still further below about 20° the hemibond becomes broken as R increases to values even higher than in optimum hydrogen-bonding geometries and R increases up to 180°. For further investigation, values of 30°, 47.2°, and 60° are selected for χ as being representative of the approximate range of values over which significant hemibonding interactions are obtained in the constrained optimization scan. At these fixed χ values, scans vary either R or R while the other is held fixed at its constrained optimum value. The scans with fixed χ and R show that significant hemibonding interactions can occur over a quite wide range of R values. Thus, at χ of 47.2° (with R of 74.4°) the specified hemibonding criteria are met down to R of 2.39 Å, which is more than 0.50 Å shorter than the optimum hydrogen-bonding distance! At short R the ΔEexc(3A0 r 1A0 ) remains relatively low and f(3A0 r 1A0 ) increases to quite high values. Although not quite as dramatic, similar behavior with respect to R is also seen at χ = 30° and 60°. The scans with fixed χ and R show that significant hemibonding interactions can also occur over a quite wide range of R values. Thus, at χ = 47.2° (with R of 2.681 Å) the specified hemibonding criteria are met for R of 42-123°, with ΔEexc(3A0 r1A0 ) remaining relatively low and f(3A0 r 1A0 ) remaining relatively high over most of this region. A similar behavior with respect to R is also seen at χ = 30° and 60°. In conclusion, this work serves to characterize the nature and extent of the hemibonding region and thereby points to where further studies on the matter should concentrate. Even for interaction of hydroxyl radical with just one water molecule, it is still necessary to explore how hemibonding interactions drop off with changes in intermolecular parameters that break the mirror plane 1169


The Journal of Physical Chemistry A of symmetry that was invoked in this work. To be more relevant to the condensed phase, the influence on hemibonding of additional nearby water molecules, which may or may not be directly hydrogen bonded to the hydroxyl, needs to be considered. It is clear that much additional work on hemibonding interactions is necessary to ultimately achieve a successful quantitative interpretation of the major ultraviolet absorption band of hydroxyl radical in water.

’ AUTHOR INFORMATION Corresponding Author

*Phone: 574-631-5562. Fax 574-631-8068. E-mail chipman.1@ nd.edu.

’ ACKNOWLEDGMENT Helpful discussions with Dr. A. Krylov and Dr. P. Cabral do Couto are gratefully acknowledged. The research described herein was supported by the Office of Basic Energy Sciences of the Department of Energy. This is Contribution No. NDRL4870 from the Notre Dame Radiation Laboratory. ’ REFERENCES (1) Spinks, J. W.; Woods, R. J. An Introduction to Radiation Chemistry, 3rd ed.; J. Wiley and Sons: New York, 1990. (2) Garrett, B. C.; Dixon, D. A.; Camaioni, D. M.; Chipman, D. M.; Johnson, M. A.; Jonah, C. D.; Kimmel, G. A.; Miller, J. H.; Rescigno, T. N.; Rossky, P. J.; Xantheas, S .S.; Colson, S. D.; Laufer, A. H.; Ray, D.; Barbara, P. F.; Bartels, D. M.; Becker, K. H.; Bowen, H.; Bradforth, S. E.; Carmichael, I.; Coe, J. V.; Corrales, L. R.; Cowin, J. P.; Dupuis, M.; Eisenthal, K. B.; Franz, J. A.; Gutowski, M. S.; Jordan, K. D.; Kay, B. D.; LaVerne, J. A.; Lymar, S. V.; Madey, T. E.; McCurdy, C. W.; Meisel, D.; Mukamel, S.; Nilsson, A. R.; Orlando, T. M.; Petrik, N. G.; Pimblott, S. M.; Rustad, J. R.; Schenter, G. K.; Singer, S. J.; Tokmakoff, A.; Wang, L. S.; Wittig, C.; Zwier, T. S. Chem. Rev. 2005, 105, 355. (3) Seinfeld, J. H.; Pandis, S. N. Atmospheric Chemistry and Physics: From Air Pollution to Climate Change; J. Wiley and Sons: New York, 1998. (4) Buxton, G. V.; Greenstock, C. L.; Helman, W. P.; Ross, A. B. J. Phys. Chem. Ref. Data 1988, 17, 513. (5) Pignatello, J. J.; Oliveros, E.; MacKay, A. Crit. Rev. Environ. Sci. Technol. 2006, 36, 1. (6) Pignatello, J. J.; Oliveros, E.; MacKay, A. Crit. Rev. Environ. Sci. Technol. 2007, 37, 273. (7) Halliwell, B.; Gutteridge, J. H. C. Free Radicals in Biology and Medicine, 3rd ed.; Oxford University Press: New York, 1999. (8) Langford, V. S.; McKinley, A. J.; Quickenden, T. I. J. Am. Chem. Soc. 2000, 122, 12859. (9) Cooper, P. D.; Kjaergaard, H. G.; Langford, V. S.; McKinley, A. J.; Quickenden, T. I.; Schofield, D. P. J. Am. Chem. Soc. 2003, 125, 6048. (10) Engdahl, A.; Karlstrom, G.; Nelander, B. J. Chem. Phys. 2003, 118, 7797. (11) Autrey, T.; Brown, A. K.; Camaioni, D. M.; Dupuis, M.; Foster, N. S.; Getty, A. J. Am. Chem. Soc. 2004, 126, 3680. (12) Dong, X.; Zhou, Z.; Tian, L.; Zhao, G. Int. J. Quantum Chem. 2005, 102, 461. (13) Brauer, C. S.; Sedo, G.; Grumstrup, E. M.; Leopold, K. R.; Marshall, M. D.; Leung, H. O. Chem. Phys. Lett. 2005, 401, 420. (14) Marshall, M. D.; Lester, M. I. J. Phys. Chem. B 2005, 109, 8400. (15) Ohshima, Y.; Sato, K.; Sumiyoshi, Y.; Endo, Y. J. Am. Chem. Soc. 2005, 127, 1108. (16) McCabe, D. C.; Rajakumar, B.; Marshall, P.; Smith, I. W. M.; Ravishankara, A. R. Phys. Chem. Chem. Phys. 2006, 8, 4563.

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Hemibonding between Hydroxyl Radical and Water - The Journal of

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