Comparison of Hydrated Hydroperoxide Anion (HOO–)(H2O)n

ARTICLE pubs.acs.org/JPCA

Comparison of Hydrated Hydroperoxide Anion (HOO
)(H2O)n Clusters with Alkaline Hydrogen Peroxide (HOOH)(OH
)(H2O)n
1 Clusters, n = 1
8, 20: An ab Initio Study David J. Anick McLean Hospital, Harvard Medical School, 115 Mill Street, Centre Building, 11 Belmont, Massachusetts 02144, United States

bS Supporting Information ABSTRACT: Hydroperoxide anion (HOO
), the conjugate base of hydrogen peroxide (HOOH), has been relatively little studied despite the importance of HOOH in commercial processes, atmospheric science, and biology. The anion has been shown to exist as a stable species in alkaline water. This project explored the structure of gas phase (HOO
)(H2O)n clusters and identified the lowest energy configurations for n e 8 at the B3LYP/6-311þþG** level of theory and for n e 6 at the MP2/aug-cc-pVTZ level of theory. As a start toward understanding equilibration between HOO
and HOOH in an alkaline environment, (HOOH)(OH
)(H2O)n
1 clusters were likewise examined, and the lowest energy configurations were determined for n e 8 (B3LYP/6-311þþG**) and n e 6 (MP2/aug-cc-pVTZ). Some studies were also done for n = 20. The two species have very different solvation behaviors. In low energy (HOOH)(OH
)(H2O)n
1 clusters, HOOH sits on the surface of the cluster, is 4-coordinated (each O is donor once and acceptor once), and donates to the hydroxide ion. In contrast, in low energy (HOO
)(H2O)n clusters, (HOO
) takes a position in the cluster center surrounded on all sides by water molecules, and its optimum coordination number appears to be 7 (one O is donor
acceptor
acceptor while the other is a 4-fold acceptor). For n e 6 the lowest (HOOH)(OH
)(H2O)n
1 cluster lies 1.0
2.1 kcal/mol below the lowest (HOO
)(H2O)n cluster, but the lowest clusters found for n = 20 favor (HOO
)(H2O)20. The results suggest that ambient water could act as a substantial kinetic brake that slows equilibration between (HOOH)(OH
) and (HOO
)(H2O) because extensive rearrangement of solvation shells is necessary to restabilize either species after proton transfer.

’ INTRODUCTION Hydrogen peroxide (H2O2 or HOOH) plays important roles in atmospheric science,1 in biology,2 and in many commercial processes.3 About hydrogen peroxide there is an extensive literature, including ab initio studies of the type that are the focus of this article. The free HOOH molecule has C2 symmetry with an HOOH torsional angle of 112.5°, OOH angles of 100°, and O
O separation of 145.4 pm.4 Its full 6-variable PES has been computed at a high level of theory,5 leading to an understanding of energy flow among its vibrational modes.6 The energy barrier for the “cis” form of the molecule (C2v symmetry) in the gas phase is 7.3 kcal/mol. Gas phase (HOOH)(H2O)n clusters were considered by Ju et al.7 for n e 3, who noted their preference for cyclic structures, and by Kulkarni et al.8 for n e 6, who noted their overall similarity to (H2O)nþ2 clusters. Kulkarni and co-workers also looked at clusters with more than one HOOH and either one or two H2O’s.9 Martins-Costa and Ruiz-Lopez10 performed a mixed quantum/classical molecular dynamics simulation of HOOH in water. They noted a similarity between the radial distribution functions of HOOH and hydroxide radical; that HOOH is a better H-bond donor but poorer acceptor than H2O; that the H
O
O
H torsional angle distribution peaks around (110° and essentially never attains r 2011 American Chemical Society

the “cisoid” (near 0°) configuration; and the propensity for HOOH to be 4-coordinated (each O being single-donor-singleacceptor or “da”). The neutral hydroperoxy radical (HOO•) in water has likewise been the subject of many studies.11
18 The reaction of HOOH with hydroxide radical OH• to form H2O and hydroperoxide radical HOO• was studied in detail by Ginovska et al.19 In contrast, hydroperoxide anion (HOO
), the conjugate base of hydrogen peroxide, has been relatively little studied. A classical work by Evans20 determined that the pKa of HOOH is 11.65, and the Kirk-Othmer Encyclopedia quotes 11.75.21 Experimental results for the gas-phase acidity of HOOH are 375.5 ( 3.3 kcal/mol22 and 369.5 ( 0.4 kcal/mol.23 Experimental results for the electron affinity of (HOO•) are 26.7 ( 3.4 kcal/mol22 and 24.86 ( 0.14 kcal/mol.23 UV spectroscopic studies of HOOH after addition of sodium hydroxide were undertaken by Chlistunoff and Simonin,24 who showed that the spectra could best be explained by postulating that both hydrated HOO
and NaþHOO
complexes were present. Their work included ab Received: November 4, 2010 Revised: April 21, 2011 Published: May 23, 2011 6327

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Table 1. Summary of Methods Used for Generating (HOO
)(H2O)n and (HOOH)(OH
)(H2O)n
1 Clusters (1)Adjoin another (H2O) unit to a low energy (HOO
)(H2O)n
1 (respectively (HOOH)(OH
)(H2O)n
2) cluster. [This was particularly effective when a “d” H2O donating to o2 of (HOO
) was attached.] (2)Start with the monomers arrayed randomly within a finite space (subject to keeping them at least a certain distance apart) and optimize using B3LYP/6-31G**. [The majority of structures found this way were 10 kcal/mol or more above the bottom of the range, but a few structures were potentially useful, especially when further massaged (cf. no. 5).] (3)(For (HOOH)(OH
)(H2O)n
1 only) Replace a dda H2O of (OH
)(H2O)n by a d/da HOOH, or replace a ddaa H2O of (OH
)(H2O)nþ1 by a da/da HOOH. There are two ways to make the substitution, based on which O the acceptor(s) are assigned. [Overall this method was not particularly efficacious for generating low energy isomers.] (4)(For (HOOH)(OH
)(H2O)n
1 only) Replace a dda
daa dimer of (OH
)(H2O)nþ1 by a da/da HOOH. The concept also works to replace a dda
ddaa dimer of (OH
)(H2O)nþ1 by a da/daa HOOH, or to replace a da
daa dimer of (OH
)(H2O)nþ1 by a d/da HOOH. [This turned out to be the single most efficacious way to find the lowest energy isomers for n e 6, provided the dimer is “trans” and the daa donates to the OH
.] (5)Alter structures found by any of the above methods, using cyclic proton transfers, flipping of the orientation of a free H on a “da”, repositioning of free H’s, or other modifications. [This method was responsible for about half the entries in Tables 2
5.] (6)Apply deductive graph-theoretic logic to determine all isomer topologies satisfying certain empirical principles that characterize low energy structures. [This was particularly useful for n g 7, and for any n for assuring that the list of low energy isomers was comprehensive.]

initio modeling of HOO
and Naþ(HOO
). However, the author is unaware of any experimental studies of gas phase (HOO
)(H2O)n clusters, AIMD studies of HOO
, or previous estimates of aqueous coordination of HOO
. The aqueous behavior of HOO
turns out to be very different from that of HOO•. The reaction of HOO• and H2O19 is contextually relevant but does not predict at all the interaction of HOO
and water. This project explored the structure of gas phase (HOO
)(H2O)n clusters and identified the lowest energy configurations for n e 6 at the B3LYP/6-311þþG** and MP2/augcc-pVTZ levels of theory, and for n = 7 and 8 at the B3LYP and MP2//B3LYP levels. The goal chosen was to find the isomer with the lowest computed binding energy, or “computational global minimum” (CGM), for each n, as well as all isomers coming within 1 kcal/mol of the minimum. As a start toward understanding equilibration between HOO
and HOOH in an alkaline environment, (HOOH)(OH
)(H2O)n
1 clusters were likewise examined, and the low energy configurations were determined for n e 8. Both types of clusters can be compared and contrasted with (OH
)(H2O)n clusters,25
28 and generalizations can be drawn about the structural properties of the low energy clusters. Some studies were also done for n = 20. The idea behind using n = 20 was to get closer to modeling bulk water while taking advantage of some theory and past work that is specific to n = 20.29

’ METHODS Density functional and second order Møller
Plesset calculations were done on a Parallel Quantum Solutions (PQS) QuantumCube, using PQS parallel software.30 Becke’s 3-parameter hybrid functional31 and the correlation functional of Lee, Yang, and Parr (B3LYP)32 were used for all DFT calculations. All clusters discussed here were optimized via B3LYP/ 6-311þþG**, and those whose electronic energy (E0) came within about 3 kcal/mol of the bottom of the energy range for their value of n were recalculated via MP2. For n e 6 the MP2 calculation was MP2/aug-cc-pVTZ, and for n > 6 it was MP2/ aug-cc-pVTZ//B3LYP/6-311þþG**. (For n e 6, screening of clusters at the MP2//B3LYP level made it possible to eliminate the majority as very unlikely to come within 1 kcal/mol of the lowest-lying cluster, and unless such clusters held particular interest they were not studied further.) Where no basis is specified, in this article “B3LYP” means B3LYP/6-311þþG**,

and “MP2” means MP2/aug-cc-pVTZ. For all B3LYP calculations, and for MP2 calculations with n e 6, basis set superposition error (BSSE) was computed, in the usual way.33,34 Vibrational frequencies, zero point energy (ZPE), and thermal corrections to ΔH and ΔS were computed analytically using the harmonic approximation, and were only computed using B3LYP/6-311þþG**. For all clusters discussed or mentioned in this article, the vibrational frequencies calculation confirmed that the cluster was a local minimum (no imaginary frequencies). Because anharmonicity can introduce significant error for water cluster O
H stretch mode frequencies, all normal modes for clusters with n e 6 were recalculated via the vibrational selfconsistent field (VSCF) method.35
37 The implementation of VSCF in NWCHEM38 was used. The VSCF method is known to be significantly inaccurate for some torsional modes39,40 whereas a recent study by Miller et al. of anion-water complexes found that for modes below 1800 cm
1 the harmonic calculation gives results that agree well with experimental values.41 On the basis of these reports, the method with the best trade-off between accuracy and computational feasibility for n e 6 was deemed to be a “hybrid” ZPE obtained by using VSCF frequencies for O
H stretch modes (i.e., for modes above 1800 cm
1) and harmonic frequencies for all other modes. To do VSCF calculations for a large set of clusters for n > 6 would become prohibitively long. Instead, for n > 6, harmonically computed ZPE was scaled by 0.986 in accord with the scaling factor recommended for B3LYP.42 The notations “harZPE”, “hybZPE”, and “scaZPE” designate respectively the pure harmonic, hybrid, and scaled ZPE values. A variety of methods were used to generate (HOO
)(H2O)n and (HOOH)(OH
)(H2O)n
1 cluster topologies. These are listed in Table 1. The first method was to consider ways that another H2O unit could be adjoined to low energy clusters that were found for n
1. Second, in lieu of a full Monte Carlo simulation, optimization using B3LYP/6-31G** was done starting from a configuration consisting of random initial orientations and positions for the components distributed in a bounded region of space. Some 20
30 initial random configurations were tried, for each value of n = 5
7. Third, to make an (HOOH)(OH
)(H2O)n
1, one can start with a low energy (OH
)(H2O)n cluster and replace one H2O by HOOH, forcing a slight adjustment of its neighbor’s positions. Low energy (OH
)(H2O)n clusters for n e 3 were determined by Chaudhuri 6328

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Figure 1. MP2-optimized geometries for low energy (HOO
)(H2O)n clusters, 2 e n e 6. See Supporting Information for a complete figure.

Figure 2. B3LYP-optimized geometries for low energy (HOO
)(H2O)n clusters, n = 7, 8. See Supporting Information for a complete figure.

Figure 3. MP2-optimized geometries for low energy (HOOH)(OH
)(H2O)n
1 clusters, 1 e n e 6. See Supporting Information for a complete figure.

et al.,26 for n = 4
6 by Lee et al.,27 and for n = 7 by Kuo and coworkers.43 Likewise, HOOH can be substituted for an (H2O)2 dimer embedded in (OH
)(H2O)nþ1, provided that the acceptor H2O of the dimer has one free (non-H-bonded) H. Starting from geometries obtained through any of these means, further geometries could be obtained by cyclic proton transfers, flipping of the position of the free H on “da” H2O units,44
46 or other rearrangements that appeared judicious to try. Finally, after examining what topological properties were shared by many low energy clusters, it was possible to use graph theoretic deductive reasoning to generate and study the set of all clusters that had those properties. These methods are summarized in Table 1.

’ RESULTS A. (HOO
)(H2O)n Clusters, n = 1
8. To talk about HOO
, it

is convenient to give the oxygen atoms names: the O that is covalently bonded to the H is o1, and the other O is o2. When an HOO
molecule embeds in an (HOO
)(H2O)n cluster so that o1 is a donor in one H-bond and an acceptor in one H-bond, and o2 is an acceptor in three H-bonds, the notation for this will be da/aaa; i.e., the xxx part of an “xxx/yyy” notation will describe the H-bonding of o1 and the yyy part gives the H-bonding of o2. The notation “
/aa” means o1 has no H-bonds and o2 is a double acceptor. For an H2O unit embedded in a cluster, the standard notation is used; i.e., “dda” means it is a double donor and single acceptor, “daa” is donor
acceptor
acceptor, etc.

For n = 1, (HOO
)(H2O) has a local minimum with H2O donating to o2 of HOO
when computed by B3LYP, but there is no (HOO
)(H2O) local minimum when computed by MP2. Instead, (HOO
)(H2O) converts barrierlessly to (HOOH)(OH
). For n g 2 local minima for (HOO
)(H2O)n exist. Figures 1 and 2 display the lowest energy isomer for each n along with other local minima that fall within 1 kcal/mol of the lowest, and various other clusters that were deemed to be of interest. Because a total of 136 clusters are listed in the tables, the full Figures 1
5 are relegated to Supporting Information. In the printed article these figures display only a sampling. The structures depicted in Figure 1 (n e 6) are MP2-optimized geometries, and in Figure 2 (n = 7, 8), B3LYP optima. For a handful of clusters, it occurred that two O’s that were not H-bonded at the B3LYP level drew enough closer together at the MP2 level to form a new H-bond. Otherwise, there is not much difference between MP2 and B3LYP optimized geometries. Coordinates for all depicted structures, optimized via B3LYP (any n) and via MP2 (n e 6), are listed in the Supporting Information. For Figures 1
4, cluster names consist of either “hoo-w[n]” or “hoohw[n
1]oh” followed by a letter symbol and a number. The letter symbols are the same when two isomers have topologically equivalent O-skeleta. The O-skeleton is the undirected graph obtained by drawing a vertex for each O and an edge between each pair of O’s that are H-bonded.29 Another way to say this is that if two clusters were given the same letter symbol, then they have the same connectivity except for H-bond directions and free H positions. For n = 2, there is an a/a local minimum for B3LYP that is unstable when optimized by MP2. The Cs-symmetric
/aa 6329

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Figure 4. B3LYP-optimized geometries for low energy (HOOH)(OH
)(H2O)n
1 clusters, n = 7, 8. See Supporting Information for a complete figure.

Figure 5. B3LYP-optimized geometries for lowest energy 512-based (HOO
)(H2O)20 cluster(s) found for each of several coordination patterns: (a) daa/aaaa; (b) daaa/aaaa; (c) da/aaaa, lowest for MP2//B3LYP; (d) da/aaaa, lowest for B3LYP; (e) daaa/aaa; (f) daa/aaa. See Supporting Information for a complete figure.

Figure 6. B3LYP-optimized geometries for lowest energy (HOOH)(OH
)(H2O)19 cluster found for each of four types of O-skeleton. (a) Derived via dimer replacement from O-skeleton of TIP4P global minimum (H2O)22. (b) Variant of lowest energy (H2O)20 . (c) Two fused polyhedra. (d) Cage with single interior H2O.

arrangement, hoo-w2B1 of Figure 1, has the lowest energy when computing with B3LYP, but MP2 prefers the d/aa configuration hoo-w2A1. For n = 3, a Cs-symmetric d/aa setup, hoo-w3B1 of Figure 1, has the lowest electronic energy (E0) by MP2, but with ZPE correction the d/aaa arrangement hoo-w3A1 is lower. When there is a choice, the preference is for donors to o2 to be da and donors to o1 to be dd, rather than the reverse. That is, having free H’s situated on donors to o2 is more stable than to have those free H’s on donors to o1. When a donor H2O is “d”, i.e., single-donor-no-acceptor, its preferred alignment generally has its free OH bond approximately parallel to the o2—o1 bond.

Tables 2 and 3 list the coordination of HOO
for each structure in Figures 1 and 2, along with the total number of H-bonds. Also listed are their B3LYP electronic energy (E0), BSSE, harZPE, and either hybZPE (n e 6) or scaZPE (n > 6) . Electronic energies are given relative to positing that a configuration consisting of one HOO
and n H2O’s that are widely separated has “zero” energy. For n e 6, MP2 electronic energy and BSSE are also computed, and (E0)MP2 þ BSSEMP2 þ hybZPE is the expression that was used to rank clusters for the “computational global minimum” (CGM). For n > 6, MP2// B3LYP electronic energies are provided, and clusters are ranked by according to the formula (E0)MP2//B3LYP þ BSSEB3LYP þ scaZPE. On the basis of a regression analysis of the clusters with 3 e n e 6, MP2//B3LYP electronic energies correlate very strongly with MP2 electronic energies and predict them with an rms error of 0.2 kcal/mol, and BSSEB3LYP correlates with BSSEMP2 and predicts it with an rms error of 0.1 kcal/mol. Thus the formula for n > 6 is not decisive, but it is a reasonable approximation that clearly has relevance for locating low lying clusters. For each value of n, the lowest values found for E0, binding energy (BE), and ΔG at 25 °C (ΔG298) are highlighted in each table. Like other anion-containing small water clusters, (HOO
)(H2O)n local minima often include some H-bonds in the first solvation shell that are long and weak, and it can become a judgment call whether to consider the O’s to be H-bonded. For H-bond counts, cutoffs for H-bonding were set at RHO < 270 pm and O
H--O angle >110°. It occurred often for n e 5, that a single water molecule could serve as both an acceptor from o1 and a donor to o2 (cf. hoo-w2A1, hoo-w3A1, hoo-w4A1, hoo-w5C1; the motif also occurs for n = 7 in the cube-based hoo-w7Ex). For n g 4, it is energetically favorable for o2 to be at least a triple acceptor and for o1 to be a donor. Geometries in which the HOO
lies on the surface and several H2O’s are not H-bonded to it tend to convert spontaneously to (HOOH)(OH
)(H2O)n
1 clusters. That is why clusters with surface HOO
are absent from 6330

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Table 2. HOO
Coordination, Number of H-Bonds, Electronic Energies, Basis Set Superposition Errors, Harmonic and Hybrid Zero Point Energies, Binding Energies, and Free Energy for the (HOO
)(H2O)n Isomers of Figure 1a B3LYP n

a

geometry




HOO coord

no. of HB

E0

BSSE

harZPE

MP2 hybZPE

BE

E0

BSSE

BE

ΔG(25 °C)

2

hoo-w2B1


/aa

2


46.92

2.16

38.93

38.76


40.61


46.90

2.18


40.56


25.92

2

hoo-w2A1

d/aa

3


47.00

2.31

39.17

37.28


42.02


47.79

2.38


42.74


27.23

3 3

hoo-w3C2 hoo-w3F1

da/aa
/aa

5 4


63.77
64.15

3.59 3.60

55.38 55.62

54.78 54.99


53.37
53.54


63.92
64.13

3.28 3.23


53.83
53.88


29.84
29.20

3

hoo-w3D2

d/aa

5


64.34

4.05

56.10

55.76


52.51

-66.11

3.82


54.49


28.66

3

hoo-w3E1

a/aa

4


64.22

3.54

55.39

53.52


55.13


63.60

3.09


54.97


31.22

3

hoo-w3D1

d/aa

5


63.74

4.10

55.97

54.60


53.01


65.43

3.83


54.97


29.27

3

hoo-w3C1

da/aa

5


64.05

3.60

55.62

53.76


54.67


64.26

3.32


55.16


30.84

3

hoo-w3B1

da/aa

6


63.71

3.86

56.11

53.65


54.17


64.51

3.44


55.38


30.30

3

hoo-w3A1

d/aaa

5


64.43

3.45

54.99

54.19


54.76


65.41

3.19


56.00


33.06

4 4

hoo-w4D2 hoo-w4C2

da/aaa d/aaa

7 6


80.01
80.75

4.64 5.11

71.34 71.95

70.26 71.33


66.44
65.64


80.62
82.32

4.12 4.52


67.57
67.80


35.71
34.43

4

hoo-w4D1

da/aaa

7


79.88

4.64

71.31

69.91


66.66


80.58

4.14


67.87


34.62

4

hoo-w4C1

d/aaa

6


80.21

5.07

71.79

70.50


65.97


81.68

4.51


68.00


34.78
34.05

4

hoo-w4B1

da/aaa

8


79.71

4.84

71.90

70.10


66.10


81.61

4.38


68.46

4

hoo-w4A1

da/aaa

7


80.05

5.09

71.92

69.58


66.72


80.91

4.19


68.48


35.46

5

hoo-w5E1

d/aa

9


94.67

7.02

87.96

86.92


75.43


96.29

6.23


77.84


33.43

5

hoo-w5D1

d/aaaa

8


93.67

6.12

88.07

86.85


75.40


96.38

5.44


78.80


36.72

5 5

hoo-w5C2 hoo-w5B4

da/aaa da/aaa

9 9


95.37
95.44

6.09 6.65

88.72 89.13

86.88 87.60


77.11
75.89


96.73
97.97

5.36 5.79


79.19
79.28


36.58
35.61

5

hoo-w5B3

da/aaa

9


96.10

6.66

89.15

87.75


76.40


98.34

5.75


79.54


35.76

5

hoo-w5C1

da/aaa

9


95.51

6.02

88.63

86.84


77.35


97.25

5.49


79.63


37.46

5

hoo-w5B2

da/aaa

9


96.34

6.62

89.13

87.45


76.97


98.66

5.76


80.15


36.34

5

hoo-w5B1

da/aaa

9


96.12

6.63

89.20

87.35


76.85


98.62

5.80


80.17


36.38

5

hoo-w5A2

d/aaa

8


94.04

6.35

87.64

84.66


77.72


95.55

5.62


79.97


37.71

5

hoo-w5A1

d/aaa

8


94.66

6.31

87.90

84.92


78.13


96.39

5.66


80.52


37.98

6 6

hoo-w6E1 hoo-w6D1

da/aa d/aaa

11 10


110.85
109.68

8.26 7.88

105.22 104.20

104.21 102.88


86.44
86.98


112.70
111.26

7.40 6.85


89.15
89.59


34.93
37.68

6

hoo-w6C1

da/aaaa

11


108.52

7.47

104.89

103.64


85.47


111.88

6.62


89.68


38.11

6

hoo-w6A4

da/aaaa

11


109.09

7.64

105.30

103.91


85.60


112.56

6.73


89.98


37.55

6

hoo-w6A3

da/aaaa

11


109.12

7.67

105.23

103.72


85.79


112.37

6.68


90.03


37.67

6

hoo-w6B3

da/aaa

11


109.53

7.86

105.30

103.00


86.74


111.72

6.74


90.04


37.04

6

hoo-w6B2

da/aaa

11


109.77

7.75

105.50

103.24


86.84


112.42

6.88


90.36


37.30

6

hoo-w6A2

da/aaaa

11


109.52

7.70

105.23

103.45


86.43


112.86

6.69


90.77


38.47

6 6

hoo-w6B1 hoo-w6A1

da/aaa da/aaaa

11 11


109.90
109.49

7.73 7.67

105.49 105.12

102.90 103.16


87.33
86.72


112.62
112.81

6.88 6.70


90.91
91.01


37.86
38.84

All energies are reported in kcal/mol. Bold: lowest energy.

Figure 2, and there are just three for n g 4 in Figure 1. The coordination of HOO
in the computational global minimum cluster for n = 4
6, respectively, is da/aaa, d/aaa, and da/aaaa. For n = 7, the lowest three clusters (hoo-w7A1, hoo-w7B1, hoo-w7B2) are da/aaa. The next lowest (hoo-w7C1) is daa/aaaa and lies 0.94 kcal/mol above hoo-w7A1. It is likely that the true free energy minimum has one of these two coordination patterns. For n = 8, the top fifteen clusters are all da/aaaa, spread over six O-skeleta. Then comes the first daa/aaa (hoo-w8G1), just 0.66 kcal/mol above hoo-w8A1. The first cluster with 7-coordinated HOO
, hoo-w8H1, lies 0.97 kcal/mol above hoo-w8A1. Clusters with 5-fold coordination at o2 were also examined, to see if this arrangement is possible. There exist local minima for n = 7 and 8 that are da/aaaaa and daa/aaaaa, respectively, depicted

in Figure 2 as hoo-w7X1 and hoo-w8Yx, but they have substantially higher energy. A search was also made for daaa/aaaa isomers at n = 8. There is aesthetic appeal in the idea of a daaa/aaaa isomer consisting of H2O’s bonding alternately to o1 and to o2 forming a collar around the O
O bond, but there is no local minimum of this sort (for B3LYP). The “daaa/aaaa collar” can be stabilized with the addition of one more monomer: see hoo-w9X1 of Figure 2. Of the methods in Table 1 for generating (HOO
)(H2O)n clusters, (1) and (5) were the most effective for finding the CGM. Method (6) was helpful for achieving a comprehensive search. The method of random initial setups was not particularly effective. Only two of the isomers in Table 2 were found this way, and none of the CGM’s. About a third of the optimizations 6331

dx.doi.org/10.1021/jp110558y |J. Phys. Chem. A 2011, 115, 6327–6338

The Journal of Physical Chemistry A

ARTICLE

Table 3. HOO
Coordination, Number of H-Bonds, Electronic Energies, Basis Set Superposition Error, Harmonic and Scaled a Zero Point Energies, Binding Energies, and Free Energy for the (HOO
)(H2O)n Isomers of Figures 2 and 5 B3LYP

MP2//B3LYP

HOO coord

no. of HB

E0

BSSE

harZPE

scaZPE

BE

E0

BE

ΔG(25 °C)

hoo-w7  1

da/aaaaa

14


118.76

8.74

121.23

119.53


91.91


123.20


96.35


35.21

hoo-w7F2

da/aaaa

13


122.07

8.92

121.22

119.52


95.05


124.93


97.91


36.58

7

hoo-w7H1

da/aaaa

12


122.50

8.87

121.36

119.66


95.39


125.24


98.14


36.74

7

hoo-w7G1

d/aaaa

13


122.14

9.11

121.69

119.98


94.48


125.68


98.01


35.57

7

hoo-w7C6

daa/aaaa

13


121.57

8.92

121.23

119.53


94.54


125.26


98.24


36.75

7

hoo-w7C5

daa/aaaa

13


121.80

8.96

121.44

119.74


94.52


125.54


98.26


36.56

7

hoo-w7E2

daa/aaa

13


124.73

8.94

121.68

119.97


97.24


125.77


98.28


36.43

7

hoo-w7F1

da/aaaa

13


122.29

8.82

121.18

119.49


95.41


125.19


98.31


36.91

7

hoo-w7E1

daa/aaa

13


124.78

8.90

121.61

119.91


97.40


125.91


98.52


36.75

7

hoo-w7C4

daa/aaaa

13


122.57

8.94

121.65

119.95


95.10


126.02


98.56


36.69

7

hoo-w7C3

daa/aaaa

13


122.03

8.90

121.24

119.54


95.02


125.68


98.66


37.11

7

hoo-w7D1

d/aaaa

13


122.59

9.02

121.49

119.79


95.20


126.15


98.77


36.73

7

hoo-w7C2

daa/aaaa

13


122.85

8.95

121.89

120.18


95.15


126.56


98.85


36.84

7

hoo-w7C1

daa/aaaa

13


122.81

8.93

121.70

120.00


95.30


126.37


98.87


36.95

7

hoo-w7B2

da/aaa

13


124.78

9.29

121.72

120.01


96.90


127.13


99.25


36.74

7

hoo-w7B1

da/aaa

13


124.95

9.35

121.64

119.93


97.10


127.40


99.54


37.04

7

hoo-w7A1

da/aaa

12


125.51

9.16

121.13

119.44


98.34


126.97


99.80


38.07

8

hoo-w8Y2

daa/aaaaa

16


131.96

10.06

137.84

135.91


100.78


136.82


105.63


35.04

8

hoo-w8Y1

daa/aaaaa

16


131.90

10.02

137.75

135.83


100.85


136.77


105.72


35.23

n

geometry

7 7

8

hoo-w8G3

daa/aaa

14


137.13

10.35

137.27

135.35


106.22


138.51


107.59


37.08

8

hoo-w8J2

daa/aaaa

15


136.08

10.45

138.11

136.18


104.24


139.51


107.67


36.44

8

hoo-w8J1

daa/aaaa

15


136.06

10.42

138.07

136.14


104.29


139.56


107.78


36.53

8

hoo-w8H2

daa/aaaa

15


135.66

10.19

137.76

135.83


104.43


139.18


107.95


37.33

8

hoo-w8F3

da/aaaa

15


134.85

10.29

137.81

135.88


103.47


139.43


108.05


36.97

8

hoo-w8F2

da/aaaa

15


135.16

10.45

137.86

135.93


103.57


139.65


108.06


37.07
37.07

8

hoo-w8H1

daa/aaaa

15


135.75

10.10

137.95

136.02


104.42


139.41


108.07

8

hoo-w8G2

daa/aaa

14


137.55

10.31

137.18

135.26


106.77


139.02


108.24


37.79

8

hoo-w8B5

da/aaaa

16


135.67

10.48

138.24

136.30


103.67


140.32


108.32


36.46

8

hoo-w8G1

daa/aaa

14


137.63

10.27

137.26

135.34


106.81


139.20


108.38


37.82

8

hoo-w8B4

da/aaaa

16


135.56

10.43

138.11

136.18


103.74


140.21


108.39


36.77

8

hoo-w8E2

da/aaaa

14


136.54

10.14

137.23

135.31


105.88


139.13


108.47


38.50

8

hoo-w8B3

da/aaaa

16


135.67

10.44

138.25

136.31


103.70


140.45


108.48


36.79

8

hoo-w8F1

da/aaaa

15


135.30

10.26

137.92

135.99


103.84


139.95


108.49


37.33

8

hoo-w8E1

da/aaaa

14


136.60

10.18

137.31

135.38


105.83


139.26


108.49


38.43
38.03

8

hoo-w8A6

da/aaaa

14


136.05

10.16

137.31

135.39


105.29


139.35


108.59

8

hoo-w8D1

da/aaaa

15


135.99

10.05

137.27

135.35


105.38


139.20


108.60


38.77

8

hoo-w8B2

da/aaaa

16


136.18

10.41

138.62

136.68


103.87


141.09


108.79


36.74

8

hoo-w8C1

da/aaaa

15


135.31

10.24

137.44

135.52


104.33


139.77


108.79


37.95

8

hoo-w8A5

da/aaaa

14


136.16

10.12

137.24

135.32


105.51


139.46


108.81


38.99

8

hoo-w8A4

da/aaaa

14


136.34

10.26

137.27

135.35


105.53


139.64


108.83


38.31

8

hoo-w8A3

da/aaaa

14


136.20

10.21

137.30

135.38


105.40


139.72


108.92


38.68

8

hoo-w8B1

da/aaaa

16


136.40

10.45

138.49

136.55


104.19


141.14


108.93


36.98

8

hoo-w8A2

da/aaaa

14


136.96

10.29

137.66

135.73


105.73


140.22


108.98


38.04

hoo-w8A1

da/aaaa

14


137.04

10.38

137.60

135.67


105.78


140.31


109.04


38.12

hoo-dod33-A1

daa/aaa

36


290.40

28.77

333.98

329.31


207.47


297.86


214.92


29.16

8 20

a




20

hoo-dod43-A1

daaa/aaa

37


292.49

28.60

334.74

330.05


208.98


298.50


214.99


28.90

20

hoo-dod24-B1

da/aaaa

36


294.51

28.74

334.79

330.10


210.82


299.84


216.15


29.95

20

hoo-dod24-A1

da/aaaa

36


294.41

28.78

334.79

330.10


210.68


300.01


216.27


30.09

20

hoo-dod44-A1

daaa/aaaa

38


293.84

28.26

335.45

330.75


209.97


301.41


217.54


31.21

20

hoo-dod34-A1

daa/aaaa

37


297.51

28.85

335.33

330.64


213.16


303.57


219.22


32.97

All energies are reported in kcal/mol. Bold: lowest energy. 6332

dx.doi.org/10.1021/jp110558y |J. Phys. Chem. A 2011, 115, 6327–6338

The Journal of Physical Chemistry A

ARTICLE

Table 4. HOOH Coordination, Number of H-Bonds, Electronic Energies, Basis Set Superposition Errors, Harmonic and Hybrid Zero Point Energies, Binding Energies, and Free Energy for the (HOOH)(OH
)(H2O)n
1 Isomers of Figure 3a B3LYP n

a

geometry

HOOH coord

no. of HB

E0

BSSE

harZPE

MP2 hybZPE

BE

E0

BSSE

BE

ΔG(25 °C)

1

hooh-oh

d/d

2


26.99

2.87

24.07

23.84


21.53


29.68

1.55


25.53


17.44

2

hooh-w1ohA2

d/d

3


45.97

4.01

39.38

36.96


39.61


48.05

2.82


42.87


26.01

2 2

hooh-w1ohB1 hooh-w1ohA1

d/d d/d

3 3


47.81
47.29

4.20 4.06

39.50 39.45

38.30 36.93


39.91
40.91


49.10
49.21

2.41 2.86


43.00
44.03

-28.13
26.97

3

hooh-w2ohE1

d/d

5


63.30

5.34

55.31

53.55


52.39


64.55

3.83


55.14


29.63

3

hooh-w2ohD1

d/d

5


63.44

5.46

56.02

53.88


52.08


65.04

3.50


55.63


30.66

3

hooh-w2ohC1

d/d

5


64.01

5.46

55.84

54.53


52.00


65.44

3.24


55.64


31.78

3

hooh-w2ohB1

d/d

4


65.66

5.12

55.57

53.98


54.53


66.76

3.54


57.21


32.80

3

hooh-w2ohA1

d/da

6


65.18

5.36

56.19

54.22


53.57


67.24

3.71


57.29


31.99

4

hooh-w3ohE1

d/d

6


80.12

6.44

71.92

69.54


65.47


81.24

4.54


68.49


34.70

4 4

hooh-w3ohD2 hooh-w3ohD1

d/da d/da

7 7


81.01
81.01

6.59 6.57

72.77 72.70

70.73 70.12


65.03
65.66


83.00
83.02

4.83 4.84


68.78
69.40


33.67
34.55

4

hooh-w3ohC1

d/da

7


79.53

6.91

72.11

68.81


65.14


81.92

5.01


69.43


34.67

4

hooh-w3ohB1

da/da

8


81.74

6.51

72.75

71.16


65.41


84.17

4.92


69.43


34.92

4

hooh-w3ohA1

d/da

7


81.14

6.86

72.71

69.95


65.67


83.09

4.90


69.58


34.58

5

hooh-w4ohE1

d/da

8


97.33

7.87

89.09

88.94


75.22


99.35

6.02


79.10


34.92
35.52

5

hooh-w4ohB2

d/da

8


95.97

7.98

88.85

86.90


75.79


97.72

5.96


79.55

5

hooh-w4ohD1

d/da

8


95.99

8.40

88.73

86.49


75.79


98.01

6.10


80.12


35.97

5 5

hooh-w4ohC1 hooh-w4ohB1

d/da d/da

9 8


95.94
96.92

8.22 8.07

89.67 89.00

87.76 86.86


74.67
76.69


99.36
98.79

6.01 6.00


80.29
80.62


36.02
36.51
36.89

5

hooh-w4ohA1

da/da

10


97.09

8.28

89.90

87.48


76.03


100.41

6.06

-81.57

6

hooh-w5ohA3

da/da

11


110.90

9.73

105.43

104.28


84.95


113.32

7.52


89.58


35.47

6

hooh-w5ohD1

da/da

11


109.78

9.65

105.92

103.66


84.53


113.13

7.12


90.41


36.84

6

hooh-w5ohC1

da/da

11


110.84

9.53

106.20

104.61


84.76


114.23

7.19


90.50


36.64

6

hooh-w5ohB1

da/da

12


111.91

9.56

106.11

104.87


85.54


115.59

7.25


91.52


38.04

6

hooh-w5ohA2

da/da

11


112.15

9.41

105.56

103.02


87.78


114.60

7.50


92.14


37.82

6

hooh-w5ohA1

da/da

11


113.24

9.47

105.67

102.95


88.88


115.44

7.39


93.16


38.91

All energies are reported in kcal/mol. Bold: lowest energy.

from random initial setups had spontaneous conversion to (HOOH)(OH
)(H2O)n
1. Overall, the study of (HOO
)(H2O)n for n e 8 shows a strong preference for the hydroperoxide ion to assume a position at the center of the cluster, surrounded on all sides by water. Coordination at o2 equals or exceeds coordination at o1. Oxygen o1 serves well as an H-bond donor but only after o2 is a multiple acceptor. The trend is toward total coordination of up to 7 or 8, with 7 as most likely to be optimal for larger n. However, for n = 7 and n = 8 the preference appears to be for filling in part of the second shell before completing the first solvation shell. B. (HOOH)(OH
)(H2O)n
1 Clusters, n = 1
8. Like above, the notation “da/daa” will refer to an HOOH in which one O is a single donor and single acceptor and the other O is a single donor and double acceptor. Hundreds of (HOOH)(OH
)(H2O)n
1 clusters were generated and optimized, using the methods outlined in Table 1. Tables 4 and 5 are the analogs of Tables 2 and 3, respectively, and they display the corresponding data. Tables 4 and 5 list, for n = 1
8, the (HOOH)(OH
)(H2O)n
1 cluster with lowest computed binding energy, all clusters whose binding energies came within 1 kcal/mol of the minimum, and various others of interest. Their HOOH coordination and total number of H-bonds are listed, as well as B3LYP and either MP2 (for n e 6) or MP2//

B3LYP (for n > 6) energies. For ease of comparison with Tables 2 and 3, the reference or “zero” for binding energy is the same as in Tables 2 and 3; i.e., “zero” is again the energy of a configuration consisting of n H2O’s and one HOO
, at infinite separation. All clusters listed in Tables 4 and 5 are illustrated in Figures 3 and 4, respectively. Again, the full figures are in the Supporting Information and the printed version contains representatives. The number of possible (HOOH)(OH
)(H2O)n
1 clusters grows very rapidly with n because there are two solutes, HOOH and OH
. Certain patterns emerged at small values of n, which allowed the search at larger n to be somewhat better focused. Extrapolation of the patterns to larger n was supported by comparing otherwise similar examples as test cases. First, as Lee et al.27 found for (OH
)(H2O)n clusters, there is some preference for OH
to be 4-coordinated with the H of OH
being free (i.e., non-H-bonded). On the whole this preference applies to (HOOH)(OH
)(H2O)n
1 clusters also. Second, as MartinsCosta and Ruiz-Lopez found for HOOH in bulk water, HOOH is a stronger donor than acceptor.10 This meant that HOOH was always at least d/d in the computational global minimum, and that adding more acceptors beyond “da” at either O tended to be less favorable than alternatives where additional acceptor O’s were in H2O units. Third, it costs about 2
3 kcal/mol if the torsional angle H
O
O-H is close to 0° rather than 80° to 130°. This 6333

dx.doi.org/10.1021/jp110558y |J. Phys. Chem. A 2011, 115, 6327–6338

The Journal of Physical Chemistry A

ARTICLE

Table 5. HOOH Coordination, Number of H-Bonds, Electronic Energies, Basis Set Superposition Error, Harmonic and Scaled Zero Point Energies, Binding Energies, and Free Energy for the (HOOH)(OH
)(H2O)n
1 Isomers of Figures 4 and 6a B3LYP n

HOOH oord

no. of HB

E0

BSSE

harZPE

scaZPE

BE

E0

BE

ΔG(25 °C)

7

hooh-w6ohA3

da/da

12


122.93

10.50

121.21

119.51


94.35


125.16


96.57


33.68

7

hooh-w6ohC3

da/da

13


123.77

10.94

121.92

120.21


94.05


126.53


96.80


33.64

7 7

hooh-w6ohE1 hooh-w6ohC2

da/da da/da

13 13


124.16
125.43

10.68 10.90

122.07 122.42

120.36 120.71


94.54
95.24


127.19
128.11


97.57
97.92


34.93
34.68

7

hooh-w6ohD1

da/da

13


125.59

10.91

122.16

120.45


95.66


128.12


98.18


35.00

7

hooh-w6ohC1

da/da

13


125.72

10.84

122.44

120.73


95.57


128.45


98.30


35.08
35.35

7

hooh-w6ohA2

da/da

12


125.32

10.36

121.64

119.93


96.44


127.24


98.36

7

hooh-w6ohB1

da/da

13


126.09

11.02

122.45

120.73


95.76


128.76


98.43


35.01

7

hooh-w6ohA1

da/da

12


125.22

10.33

121.56

119.86


96.45


127.27


98.51


35.48

8

hooh-w7ohD3

da/da

14


138.36

11.95

137.64

135.71


105.49


139.80


106.92


34.39

8 8

hooh-w7ohG1 hooh-w7ohF1

d/da da/da

14 14


138.62
138.50

12.36 11.87

138.36 137.83

136.43 135.90


104.62
105.50


141.01
140.00


107.01
107.01


34.60
34.48

8

hooh-w7ohD2

da/da

14


138.68

12.03

137.82

135.89


105.54


140.20


107.07


34.29

8

hooh-w7ohE1

da/da

14


138.17

12.30

138.35

136.42


104.24


141.16


107.23


34.94

8

hooh-w7ohD1

da/da

14


139.14

11.86

137.92

135.99


106.08


140.74


107.67


35.05

8

hooh-w7ohC1

da/da

14


139.00

12.10

138.55

136.61


105.09


141.71


107.80


35.48

8

hooh-w7ohB1

da/da

14


138.99

12.01

138.63

136.69


105.08


141.72


107.81


35.39

8

hooh-w7ohA1

da/da

14


139.33

12.09

138.58

136.64


105.39


142.23


108.29


36.00

hooh-w19ohN1 hooh-w19ohM1

da/daa da/da

35 36


290.57
294.60

29.63 28.92

333.99 334.36

329.32 329.68


206.77
211.15


294.56
295.49


210.75
212.04


24.99
26.52

20 20

a

geometry

MP2//B3LYP

20

hooh-w19ohL1

da/daa

36


291.86

28.10

333.72

329.05


209.85


294.55


212.55


27.09

20

hooh-w19ohK1

da/da

37


292.85

28.23

335.06

330.37


209.39


297.80


214.34


28.64

All energies are reported in kcal/mol. Bold: lowest energy.

means that solvation blunts the height of the barrier (compared to 7.3 kcal/mol for isolated HOOH) but still, low energy isomers for n g 4 are essentially certain to have torsional angles g70° for the H
O
O
H. Fourth, a pattern also emerged that in the lowest energy clusters, the HOOH is one of the donors to the hydroxide. Lastly, there is a strong preference for HOOH to lie on the surface of the cluster. For HOOH to have a “surface” location can be defined as follows: there exists a plane containing the O
O bond that has all of the other atoms of the cluster lying on one side of the plane. See Figures 3 and 4 for illustration of these principles. The most efficacious way to find CGM’s and other low energy isomers turned out to be method 4 of Table 1: replace an embedded dimer of (OH
)(H2O)nþ1 with HOOH. The best dimers to replace consist of a dda donating to a daa that in turn donates to the hydroxide, and where the embedded dimer has a “trans” setup for its two H’s that make bonds to other H2O’s. (Replacing a “cis” dimer yields a higher energy cis HOOH.) For each n e 6, the lowest-energy (HOOH)(OH
)(H2O)n
1 is obtainable from the lowest-energy (OH
)(H2O)nþ1 cluster by means of dimer replacement. The lowest-energy (OH
)(H2O)nþ1 clusters have not been established for n þ 1 > 7. For n = 7 and n = 8, the most efficacious method was (6) of Table 1, using the principles outlined in the prior paragraph. The energetics of (HOOH)(OH
)(H2O)n
1 and (HOO
)(H2O)n show that for 2 e n e 6, the (HOOH)(OH
)(H2O)n
1 CGM is energetically preferred over the (HOO
)(H2O)n CGM, by 1.0
2.1 kcal/mol. The largest spread of 2.1 kcal/mol occurs only for the cube-based (HOOH)(OH
)(H2O)5 cluster, suggesting that this cluster may be a “magic number” as is true of the

neutral (H2O)8 cube. Those figures are for 0 K. At 25 °C, the range is
0.3 to 1.1 for n g 3, so the thermal corrections favor (HOO
)(H2O)n. For n = 7 (respectively n = 8) the admittedly approximate calculation finds that ΔG298 is lower for (HOO
)(H2O)n by 2.6 (respectively 3.0) kcal/mol. Looking at ΔG298 as a function of n, for both (HOO
)(H2O)n and (HOOH)(OH
)(H2O)n
1 it decreases with n up to n = 6, then rises for n = 7, and decreases again for n = 8. Morrell and Shields47 found the same behavior of ΔG-vs-n for ammonia
water clusters and discussed the implications for atmospheric formation of water droplets. Overall, the study of (HOOH)(OH
)(H2O)n
1 for n e 8 shows that HOOH has a strong preference to be “trans” and to lie on the surface of the cluster. For every isomer in Figures 3 and 4, a plane can be drawn containing the O
O bond of HOOH with the property that all the other cluster atoms lie on one side of the plane. This is rarely true of the low energy (HOO
)(H2O)n clusters (for n g 4). The HOOH is always at least d/d, because it is a better donor than acceptor, and for n g 5 the lowest-lying cluster is consistently da/da. There are local minima that are da/ daa but by studying these it is clear that adding a second donor to an O of HOOH is less energetically favorable than having a second donor at the O of an H2O somewhere else in the cluster. Once there are enough H2O’s, the hydroxide prefers to be 4-coordinated, with the interesting exception of the cube-based (HOOH)(OH
)(H2O)5 discussed above. For n = 7 it is a virtual tie between the lowest cluster with 3-coordinated OH
(hoohw6ohA1) and the lowest cluster with 4-coordinated OH
(hoohw6ohB1). 6334

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Figure 7. OH-stretch region of predicted IR spectrum of lowest energy (HOOH)(OH
)(H2O)n
1 clusters: (a) hooh-w6ohA1 (n = 7); (b) hoohw7ohA1 (n = 8).

C. (HOO
)(H2O)20 and (HOOH)(OH
)(H2O)19 Clusters. The

number of isomers for n = 20 is so huge that an exhaustive study would be impossible. A starting point is to enclose either HOO
or HOOH in the 512 dodecahedral cage, which can be thought of as mimicking the solute being surrounded by water.16 The number of H-bonds between the solute and the cage is a parameter that approximates solute coordination in the bulk phase. This arrangement works well for HOO
. Various other geometries for (HOO
)(H2O)20 were tried, and all had substantially higher energy. A large number of isomers consisting of HOO
inside the 512 cage were then optimized at the B3LYP/ 6-311G** level, of which the best were reoptimized using B3LYP/6-311þþG**. O-topology theory29 suggested choosing configurations with no daa
daa bonds and the fewest possible daa
ddaa bonds. Experimenting confirmed the validity of this approach for (HOO
)(H2O)20, which greatly reduced the number of structures that needed to be considered. For each of five coordination patterns (da/aaaa, daa/aaa, daa/aaaa, daaa/ aaaa, and daaa/aaa) the lowest examples found for B3LYP were also compared via MP2//B3LYP. See Table 3 and Figure 5 for the results. Lowest energy occurred for a 7-coordinated HOO
(daa/aaaa). Putting HOOH inside a 512 cage with one surface H2O replaced by OH
has much higher energy than some other (HOOH)(OH
)(H2O)19 geometries. This is not surprising because the HOOH-inside-a-cage setup has multiple unfavorable motifs: HOOH not on surface, OH
is 3-coordinated rather than 4-coordinated, and HOOH does not donate to OH
. Various setups were explored that have surface HOOH donating to 4-coordinated OH
. These included cages with a single interior H2 O, two fused cages, a 3-fused-cages variant of the lowest-energy (H 2 O)20 isomer, and isomers using

the “network” O-skeleton of the TIP4P global minimum (H 2 O)22 . 48 Of these, a “network” isomer had the lowest energy, followed by “three fused cages” (cf. Table 5 and Figure 6). Its scaZPE- and BSSE-corrected energy lies 4.88 kcal/ mol higher than the lowest (HOO
)(H2O)20 (4.03 kcal/mol at 25 °C). One can ask how well these ab initio data predict the pKa of HOOH. A general purpose calculation finds that if an (A
)(H2O)n cluster has free energy GA and an (HA)(OH
)(H2O)n
1 cluster has free energy GHA, and the clusters are taken to be representative of bulk solution, then the predicted pKa is pK a ¼ 14:0 þ log10 ½H2 O þ log10 ðeÞðGA
GHA Þ=RT ð1Þ At T = 298.15 K this becomes pK a ¼ 15:74 þ ð0:733ÞðGA
GHA Þ

ð2Þ

assuming the units of energy are kcal/mol. Substituting
4.03 for (GA
GHA) yields a prediction of 12.78 for the pKa of HOOH, just 1 pKa point higher than the measured value of about 11.7. To get 11.7, (GA
GHA) would have to be
5.51 kcal/mol, so the error is around 1.5 kcal/mol. While there have been many approximations made, one of them is to allow HOOH to sit on the surface of its cluster. In actual bulk water most of the HOOH and OH
molecules would be forced into the interior and the corresponding GHOOH would increase somewhat, making (GHOO
GHOOH) more negative. D. Infrared Spectra. Predicted IR spectra were computed via B3LYP for all the structures discussed herein, as well as for many others of higher electronic energy. Figures 7 and 8 show the O
H stretch region of the calculated IR spectrum for the lowestenergy isomer for n = 7 and 8. These spectra are similar to other 6335

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Figure 8. OH-stretch region of predicted spectrum of lowest energy (HOO
)(H2O)n clusters: (a) hoo-w7A1 (n = 7); (b) hoo-w8A1 (n = 8).

water cluster spectra in several respects: there is a distinct but low amplitude peak near 3880 cm
1 (unscaled) for non-H-bonded H’s on daa’s; the majority of peaks can be assigned unambiguously to a single stretch mode but strong coupling is sometimes observed between modes of very close frequency; having a daa as donor (respectively dda as acceptor) red-shifts a stretch mode’s frequency relative to ddaa, while a daa donor (respectively daa acceptor) blue-shifts it; the peak layout approximately mirrors the distribution of covalent O
H bond distances for protons in the structure; and there is a trend for peak intensity to correlate inversely with frequency. Figure 7 shows two (HOOH)(OH
)(H2O)n
1 spectra. Starting with Figure 7a for the (HOOH)(OH
)(H2O)6 spectrum, the lowest 4 stretch modes, in increasing order, are for protons in bonds that are (along with [wavenumber/intensity]) daa
OH
[2369/1995], daa
OH
[2837/1950], HOOH
OH
[2976/788], and HOOH
dda [3322/472]. The protons that donate to the hydroxide are provide the lowest frequency modes, with the lowest two occurring when the donor is daa and the third lowest occurring when the donor is HOOH. The next lowest is HOOH
dda. A similar pattern occurs for the (HOOH)(OH
)(H2O)7 spectrum, Figure 7b: the sequence is daa
OH
[2726/1489], HOOH
OH
[3099/1316], da
OH
[3225/452], HOOH
dda [3253/ 732], and dda
OH
[3386/722]. The pattern that emerges from these and many other examples is daa
OH
< HOOH
OH
< ddaa
OH
< dda
OH
 HOOH
dda daa
dda < HOOH
dda < ddaa
dda < dda
dda

ð3Þ Actual stretch frequencies are difficult to predict accurately from connectivity data alone because factors such as 3- vs

4-coordination of OH
, the types of neighboring O’s, the magnitude and direction of the total cluster dipole, and mode coupling also affect stretch frequencies. Still, taken together, these and other similar observations indicate that HOOH is a stronger donor than ddaa and a slightly weaker donor than daa. This is consistent with previous observations that in bulk water, HOOH is a stronger H-bond donor than H2O. The (HOO
)(H2O)n spectra in Figure 8 have the property that the protons that donate to o2 have the reddest stretches, followed by the o1-dda mode. In each case this accounts for either the four lowest or the five lowest stretch modes, depending on the coordination of o2. For Figure 8b, the spectrum of hoow8A1, the fourth and fifth lowest stretch modes are coupled. As expected, the ordering is daa
o2 < ddaa
o2 ≈ da
o2 < dda
o2. Altogether, it is safe to infer the following generalizations: bonds to o2 will represent the reddest stretches of an (HOO
)(H2O)n spectrum, with the possible exception of daa
dda bonds, with o1-dda close behind; coupling is common among these modes; and o2 is a much stronger acceptor than o1. Oxygen o1 is not a particularly strong acceptor.

’ DISCUSSION We have noted patterns for the low energy clusters that probably transfer, at least to some degree, to properties of these solutes in aqueous solution: HOOH is da/da, avoids H-bonds on one side, is stronger donor than acceptor, and donates to OH
. HOO
tends to be daa/aaaa and prefers to be surrounded on all sides by H-bonds. For n e 8 the (HOOH)(OH
)(H2O)n
1 clusters are energetically favored, but this is reversed at n = 20. This can be understood as follows. HOOH prefers surface, which is plentiful for small n, and the disruption of the H-bond network from the 6336

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The Journal of Physical Chemistry A “one-sidedness” of both HOOH and OH
is not a problem until n gets large enough for the cluster to want to expand toward that space. Conversely, hydroperoxide features tolerance of high coordination and nestles nicely into the middle of a water network. These properties work against (HOO
)(H2O)n at small n but become strengths at larger n. Extrapolating from static to dynamical behavior for (HOO
)(H2O)n, the data predict it will be fairly difficult to replace the H2O’s that donate to o2. In addition to these bonds being relatively strong (as measured by short bOH and low stretch frequencies) to start with, notice that the easiest achieved conversions from daa/aaaa, which is expected to be most prevalent setup, are to da/aaaa or daaa/aaaa. Neither of these provides an opportunity to replace an H2O of o2's first shell. Replacement would require temporary conversion to daa/aaa, requiring substantially higher energy, or to the likewise unfavorable daa/aaaaa setup. As a result, dwell time of an H2O bonded to o2 is expected to be quite long relative to other anion first shell dwell times, though a quantitative prediction at this point is not possible. Using the same reasoning, dwell time for first shell H2O’s at o1 should not be particularly long, both because bonds to o1 are not especially strong to start with and because of the relative ease of temporarily losing or gaining one bond at o1. Another dynamical question, difficult to answer from static data alone, concerns switching of the roles of o1 and o2 in bulk water. This could occur starting from daaa/aaaa if there were simultaneous transfer of h1 (the proton covalently bonded to o1) along a water wire away from o1 and transfer of one of o2’s solvating protons to o2 (think “daaa/aaaa” becomes “aaaa/daaa”). What about conversion of HOOH to HOO
or vice versa? A key take-home message of this article is that solvation of HOOH and of HOO
are very different. One cannot simply transfer a proton in either direction, to make one species from the other. Proton transfer results in a high energy unfavorable setup: enclosed daa/daaa for HOOH, or “surface” da/aa for HOO
. Either of these will push the transferred proton back where it came from. In terms of Tuckerman’s “presolvation” concept,49,50 multiple high energy shifts in the solvation shell have to occur before HOOH can become HOO
or vice versa. This phenomenon, which might be called “solvation shell inertia”, explains why the reaction of hydride ion with water can be slower with more solvation than with less solvation.51 Extrapolating from the results presented here, solvation shell inertia might also slow significantly the equilibration of HOOH and HOO
in alkaline aqueous solution.

’ CONCLUSIONS Although gas phase calculations cannot replace molecular dynamical modeling and experiments, they do provide some insight into the behavior of (HOO
) and HOOH in alkaline aqueous solution. Specifically: • Optimal coordination for HOOH is 4 (da/da) whereas for (HOO
) it is 7 (daa/aaaa). Other patterns that occur in relatively low energy clusters are d/da and da/daa for HOOH, and da/aaaa and daaa/aaaa for (HOO
). • (HOO
) is a probable kosmotrope; i.e., it enhances the H-bonding network and increases H-bond density by supporting the formation of bonds around it in all directions. • HOOH is a likely chaotrope; i.e., it can disrupt the H-bonding network due to its tendency to prefer an H-bond-free “surface” in one direction. Being a larger molecule that still

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• • • •

•

has just 4 H-bonds, HOOH would reduce the density of H-bonds. When solvated, HOOH prefers a configuration with torsional angle of 80
120°. An angle near 0° adds 2
3 kcal/mol. There may be a tendency for HOOH to associate with (i.e., to be a donor to) hydroxide ions, more often than would occur by chance. Typically, HOOH’s strength as a H-bond donor lies between that of H2O’s that are daa and ddaa. Dynamically, 4-fold coordination at the o2 oxygen of HOO
is predicted to be by far the dominant pattern, with relatively long dwell times for the first shell water molecules at o2. Coordination at o1 will show more variation among daa, da, and daaa, with shorter dwell times. While equilibration between A
and HA þ OH
is normally very rapid for a weak acid HA in alkaline solution, these results predict that “solvation shell inertia” could substantially slow equilibration between (HOO
) and HOOH þ (OH
). This effect might be able to be detected experimentally.

’ ASSOCIATED CONTENT

bS

Supporting Information. Coordinates in xyz format for all B3LYP-optimized structures listed in Tables 2
5. Coordinates in xyz format for all MP2-optimized structures listed in Tables 2 and 4. Complete Figures 1
5, consisting of highprecision images of these clusters. Figures 6
8 are complete in the main article. This material is available free of charge via the Internet at http://pubs.acs.org.

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