Theoretical Characterization of the Structures and Vibrational Spectra

The Wn clusters are π-hydrogen-bonded to the benzene ring, with the strength of this interaction being greatest for BW2. ..... The Journal of Physica...
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J. Phys. Chem. 1996, 100, 7810-7821

Theoretical Characterization of the Structures and Vibrational Spectra of Benzene-(H2O)n (n ) 1-3) Clusters Sharon Yee Fredericks and Kenneth D. Jordan* Department of Chemistry, UniVersity of Pittsburgh, Pittsburgh, PennsylVania 15260

Timothy S. Zwier* Department of Chemistry, Purdue UniVersity, West Lafayette, Indiana 47907-1393, and The Joint Institute for Laboratory Astrophysics, The UniVersity of Colorado, Boulder, Colorado 80309 ReceiVed: December 4, 1995X

The (H2O)n and benzene-(H2O)n (n ) 1-3) clusters have been characterized by means of the MP2 and density functional methods. The minimum-energy structures were optimized, and the harmonic frequencies were calculated for both the benzene-water clusters (BWn) and the free water clusters (Wn). The Wn clusters are π-hydrogen-bonded to the benzene ring, with the strength of this interaction being greatest for BW2. The geometries of the Wn portions of the BWn clusters are found to be close to those of the free water clusters, with the perturbation due to the interaction with the benzene being greatest for BW3. For the OH stretching modes good agreement is found between the calculated and measured OH stretch IR spectra for both Wn and BWn clusters. Both geometric and electronic (i.e., charge transfer/polarization interactions) effects are responsible for the significant changes in the OH stretch IR spectra brought about by the complexation of the water clusters with the benzene molecule.

I. Introduction Understanding the properties of water in environments different from the bulk is important in a wide range of problems including protein-water interfaces, water entrapped in cavities, aerosols, and surface wetting phenomena. Gas-phase water clusters, with their high surface area and preponderance of unoccupied hydrogen-bonding sites, can serve as model systems for understanding water at interfaces. Gas-phase water clusters have received much experimental attention. High-resolution measurements in the microwave,1-4 near-infrared (near-IR),5 and far-infrared (FIR)6,7 regions are now available for the water dimer. Some ambiguities in the vibrational assignments of the OH stretch vibrations still remain, however, because not all bands are rotationally resolvable. The recent work of Huisken et al.8 summarizes the current status of these assignments. FIR measurements have recently been extended to larger water clusters as well and hold out great promise for characterizing the structures and tunneling dynamics of these species.9,10 The corresponding near-IR studies of the larger (H2O)n (abbreviated as Wn), n g 3, clusters in the OH stretch region are both tantalizing and difficult. The frequencies, intensities, and breadths of the OH stretch vibrations are particularly sensitive probes of hydrogen bonding and of the cooperative effects which play such an important role in hydrogen-bonded aggregates. However, the loss of rotational resolution which accompanies many of these transitions presents difficulties in assigning absorption features to a given Wn cluster.11,12 Huisken et al.8 have used collisions with a secondary rare gas beam to disperse Wn clusters by size. These studies have provided data on Wn clusters up to n ) 5. In the trimer, tetramer, and pentamer clusters, two OH stretch transitions have been resolved, one assigned to free OH stretch and the other to excitation of the OH ring vibrations in cyclic structures. Other bands are either not resolved due to the near degeneracy of some of the modes or are too low in intensity to be observed. * Authors to whom correspondence should be addressed. X Abstract published in AdVance ACS Abstracts, April 15, 1996.

S0022-3654(95)03571-4 CCC: $12.00

A molecular-scale understanding of solute-solvent interactions in aqueous solution benefits from the study of solute(H2O)n clusters. Benzene-(H2O)n clusters (hereafter referred to as BWn for short) in particular have been studied by a wide range of spectroscopic techniques, including electronic absorption spectroscopy, in which the benzene acts as an electronic chromophore,13-16 microwave,17,18 Raman,19 and IR20-22 spectroscopies. The recently recorded microwave spectra of BW1 and its isotopomers have provided insight to the structure and internal dynamics of this complex. Raman spectra of sizeselected BWn clusters with n ) 1-5 have provided information on the intermolecular vibrations of these clusters.19 Finally, Zwier and co-workers20-22 have recently extended the study of BWn clusters to the near-IR region using resonant ion-dip infrared spectroscopy (RIDIRS) to record OH and CH stretch infrared spectra of size-selected BWn clusters with n ) 1-7. The OH stretching frequencies and intensities observed in the studies of Pribble et al.20-22 indicate that the BWn clusters are comprised of a benzene molecule attached to the surfaces of Wn clusters, with the structures of the Wn portions of the BWn clusters being quite similar to those of the corresponding free water clusters. This has been confirmed by force-field calculations.23 Characteristic absorptions due to “free OH”, “single-donor OH”, “double-donor OH”, and “π-hydrogenbonded OH” groups have been identified. On the basis of these considerations, Pribble and Zwier20,21 concluded that the water portions of the BW3, BW4, and BW5 clusters have cyclic (i.e., ring-like) structures, whereas the water portions of BW6 and BW7 clusters have more compact, noncyclic structures incorporating double-donor water molecules. The experimental studies and force-field calculations indicate that in BW1 both hydroxy hydrogens have significant interactions with the benzene ring in a nominally π-hydrogen-bonded configuration. The water molecule undergoes large-amplitude internal rotation and in-plane torsion even in the zero-point level, and 6-fold symmetry is retained on a vibrationally averaged basis. For BWn clusters, with n g 2, the water cluster is bonded to the benzene ring primarily through a single OH group, and the © 1996 American Chemical Society

Benzene-(H2O)n Clusters interaction of the Wn cluster with the benzene molecule is sufficiently strong that even on a vibrationally averaged basis lower than 3-fold symmetry results. Although the general picture that emerges from these studies is that the Wn hydrogen-bonded structure is not greatly affected by the presence of benzene, the consequences of the interactions with benzene on the Wn OH stretch spectra are nevertheless significant. The frequencies, degeneracies, and, mostly notably, the intensities of the OH stretch transitions of the Wn aggregate are all changed to some degree by the presence of benzene. In order to better understand these effects, we have undertaken ab initio calculations of the geometries and vibrational frequencies and intensities of BWn and Wn (n ) 1-3). The calculations were carried out using both the MP2 and density functional (DFT) methods. The utility of the MP2 method for describing small water clusters is well-documented.24-36 The DFT calculations employed the Becke3LYP functional37 which combines the “Becke3” hybrid-exchange functional38 and a combination of the local and nonlocal correlation functionals of Vosko, Wilk, and Nusair39 and Lee, Yang, and Parr,40 respectively. Prior studies have shown that the Becke3LYP functional provides a good description of the structures and vibrational frequencies of water clusters.35,41,42 In the case of the “bare” water clusters, we have also optimized the structures and calculated the frequencies using the QCISD method,43 a coupled-cluster type method which includes the contributions of certain classes of excitations to infinite order. The BW1 complex has been studied previously by means of the Hartree-Fock44-46 and MP218 methods. However, none of the previous studies reported vibrational frequencies, and the study using the MP2 method did not carry out a complete geometry optimization. The BW2 and BW3 clusters have not been the subject of prior ab initio calculations. MP2-level and QCISD-level (or, closely related, CCSD-level) structures and vibrational frequencies have been reported previously for W1W3.24,25,27,30-35 The main reason for carrying out new calculations on W1-W3 is to have results for these species with the same basis set as employed for BW1-BW3. This is essential for determining the influence of benzene on the structure of the water clusters. The vibrational frequencies and IR intensities of W1-W3 were calculated using both the optimized structures of the free water clusters as well as the geometries of the Wn portions of the BWn clusters. This allows us to estimate the extent to which the frequency shifts are due to the geometrical distortions of the Wn species brought about by interaction with the benzene ring. II. Computational Details All results reported in this study were obtained using for the water molecules a basis set formed by adding to the 6-31+G basis set47 the two oxygen d functions and the tight hydrogen p function from the aug-cc-pVDZ basis set of Kendall et al.48 This basis set, designated as 6-31+G[2d,p], has been found28,41 to be superior to the 6-31+G(2d,p) basis set, which employs the standard Gaussian 92 polarization functions, and to give results (geometries and vibrational frequencies) for the water monomer and dimer similar to those obtained with the more computationally demanding aug-cc-pVDZ basis set. Two different basis setss6-31G*47 and 6-31+G*47swere employed for benzene. This resulted in two hybrid basis sets, one combining the 6-31+G[2d,p] basis set for water and the 6-31G* basis set for benzene, referred to simply as 6-31+G[2d,p], and the other combining the 6-31+G[2d,p] basis for water and the 6-31+G(2d,p)47 for benzene, referred to as 6-31+G{2d,p}. As will be shown below, the 6-31+G[2d,p] basis is adequate for

J. Phys. Chem., Vol. 100, No. 19, 1996 7811 accounting for the trends in the OH stretching frequencies of the BWn and Wn (n ) 1-3) clusters. The larger 6-31+G{2d,p} basis set was introduced in order to obtain more reliable estimates of the binding energies of the BWn clusters. The geometries and normal-mode vibrational frequencies of the BWn and Wn (n ) 1-349) clusters were calculated at both the MP2 and Becke3LYP levels of theory and using the 6-31+G[2d,p] basis set. In addition, calculations were also performed on the “bare” water clusters at the QCISD level, again using the 6-31+G[2d,p] basis set. Geometries were optimized using analytical gradients. The MP2 and Becke3LYP vibrational frequencies were calculated using analytical second derivatives, whereas the QCISD frequencies were obtained by use of numerical differentiation of the analytical first derivatives. The calculations were carried out using the Gaussian 92 program.37 The results presented here for the BW1 and BW2 clusters are from calculations with the benzene ring constrained to be planar. The geometry of BW3 was optimized in the presence and absence of this constraint. The geometries, energies, and vibrational frequencies obtained for BW3 from the calculations with the ring constrained to be planar and in the absence of constraints are nearly identical, showing that the forced planarity of the benzene ring does not introduce significant errors in the properties of interest. As will be seen below, the inclusion of higher-order correlation effects is especially important for the calculation of the frequencies of the single-donor OH stretching modes of W2 and W3. Higher-order correlation effects are expected to be of comparable importance for the single-donor OH stretching modes of BW2 and BW3. Although QCISD-level calculations on the BWn (n ) 1-3) clusters would be computationally prohibitive, it is possible to estimate QCISD frequencies for these clusters by combining the MP2 frequencies for a given BWn cluster with the differences between the MP2 and QCISD frequencies of the corresponding Wn cluster. This correction procedure is complicated by the fact that there is not always a one-to-one correspondence between OH stretch modes of the BWn and Wn clusters. In particular, modes that are delocalized in a Wn cluster can acquire considerable localized character in the corresponding BWn cluster. The localization is most pronounced in BW3, and in this case, the frequencies of the three free OH groups were corrected by the mean of the QCISDMP2 frequency differences of the three free OH groups of W3, and the frequencies of the three single-donor OH groups were corrected by the mean of the QCISD-MP2 frequency differences of the three single-donor OH groups of W3. III. Results and Discussion A. Structures. The key geometrical parameters obtained from the geometry optimizations of the Wn and BWn (n ) 1-3) clusters are reported in Figure 1-3. Additional information on the geometrical parameters is reported in Table 1. For the Wn clusters the structures and the vibrational frequencies obtained from the MP2 calculations using the 6-31+G[2d,p] basis set are close to those obtained from MP2 calculations with larger basis sets.24,31,35 The calculated and, where known, experimental rotational constants and dipole moments of the various clusters are summarized in Table 2. 1. W1 and BW1. The MP2/6-31+G[2d,p] calculations give for H2O and OH bond length of 0.964 Å, a HOH angle of 104.3°, and a dipole moment of 2.00 D. Similar structural parameters and dipole moment values are obtained for the Becke3LYP and QCISD calculations. The experimental val-

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Fredericks et al.

Figure 1. MP2-optimized structures of BW1. X indicates the inversion center of the benzene molecule; distances are in angstroms. (a) Global minimum and (b) symmetric (C2V) transition-state structure.

Figure 3. MP2-optimized structures of (a) W3 at its optimized geometry, (b) BW3 at its optimized geometry, and (c) a higher-energy local minimum of BW3. X indicates the inversion center of the benzene molecule; distances are in angstroms. The dotted lines represent hydrogen bonds, and the dashed lines are used to indicate the OO distances.

Figure 2. MP2-optimized minimum-energy structures of (a) W2 and (b) BW2. X indicates the inversion center of the benzene molecule; distances are in angstroms. The dotted lines represent hydrogen bonds, and the dashed lines are used to indicate the OO distances.

ues50 of the OH bond length and HOH angle are 0.957 Å and 104.5°, respectively, and the experimental value51 for the dipole moment is 1.85 D. The overestimation of the dipole moment and OH bond length in the present calculations is due to the use of the moderate-sized 6-31+G[2d,p] basis set. Given the large-amplitude motion in the BW1 complex,22 the connection between the minimum-energy structure determined from the ab initio calculations and the experimentally deter-

mined structure is less direct than for complexes with more rigid structures. Both the MP2 and Becke3LYP calculations give a minimum-energy structure for BW1 in which the water interacts more strongly with the benzene ring through one of the hydroxy hydrogen atoms than the other (Figure 1a). On the other hand, the symmetric transition-state structure (Figure 1b) for the interchange of the H atoms through the “rocking” motion is predicted to lie only 50 cm-1 (MP2 level) above the local minimum. These features of the MP2 intermolecular potential are consistent with previous MP2 calculations of Suzuki et al.,18 with the model potential calculations of Augspurger et al.,23 and with the deductions of Pribble et al.22 from their experimental OH stretch infrared spectra of C6H6-H2O and C6H6HOD. In the MP2-optimized structure of BW1, the distance from the center of the benzene ring to the H-atom π-bonded to the ring is 2.302 Å, and the benzene center-of-mass (c.m.) to water c.m. separation is 3.210 Å, in fair agreement with the experimentally determined value17,18 of 3.32 Å. The earlier MP2

Benzene-(H2O)n Clusters

J. Phys. Chem., Vol. 100, No. 19, 1996 7813

TABLE 1: Internal Coordinates of the (H2O)n and C6H6-(H2O)n (n ) 1-3) Clustersa Becke3LYP cluster n

coordinatesb

1

R(O-H2) R(O-H3) θ(H2-O-H3) R(O1-X) R(H3-X) φ R(O1-H3) R(O1-H4) R(O2-H5) R(O2-H6) R(O1-O2) R(O2‚‚‚H4) θ(H2‚O1-H3) θ(H5-O4-H6) R(H6-X) R(O1-O2) R(O2-O3) R(O1-O3) R(O1-H4) R(O1-H5) R(O2-H6) R(O2-H7) R(O3-H8) R(O3-H9) R(O1‚‚‚H8) R(O2‚‚‚H4) R(O3‚‚‚H6) θ(H4-O1-H5) θ(H6-O2-H7) θ(H8-O3-H9) R(O1-H4-O2) R(O2-H6-O3) R(O3-H8-O1) δ(H4-O1-O2-O3) δ(H6-O2-O3-O1) δ(H8-O3-O1-O2) δ(H5-O1-O2-O3) δ(H7-O2-O3-O1) δ(H9-O3-O1-O2) R(H5-X)

2

3

a

Wn 0.963 0.963 105.0

0.963 0.972 0.964 0.964 2.906 1.942 105.4 105.3 2.794 2.804 2.795 0.979 0.963 0.978 0.963 0.979 0.963 1.893 1.893 1.919 106.0 106.2 106.2 151.8 149.2 151.8 179.2 -167.6 178.5 115.8 -117.5 -125.1

MP2 BWn

0.963 0.967 104.8 3.617 2.688 56.16 0.962 0.975 0.964 0.969 2.879 1.912 105.1 105.1 2.641 2.850 2.817 2.766 0.976 0.967 0.978 0.963 0.983 0.963 1.840 1.971 1.917 105.6 105.9 106.0 155.9 151.7 155.9 177.9 -170.1 -179.7 107.6 -116.7 -121.3 2.542

Wn 0.964 0.964 104.3

0.963 0.972 0.965 0.965 2.917 1.950 104.6 104.6 2.804 2.812 2.805 0.978 0.964 0.977 0.963 0.978 0.963 1.907 1.906 1.933 105.2 105.5 105.5 151.4 148.3 151.4 178.7 -165.7 178.9 117.2 -119.7 -127.9

BWn 0.963 0.967 104.0 3.257 2.302 49.29 0.964 0.975 0.965 0.970 2.898 1.926 104.4 104.0 2.243 2.894 2.835 2.776 0.974 0.969 0.978 0.964 0.983 0.964 1.843 2.027 1.924 103.8 105.0 105.0 147.0 153.9 157.2 -176.8 -171.1 -177.7 101.7 -119.0 -119.0 2.291

QCISD Wn 0.963 0.963 104.5

0.962 0.969 0.964 0.964 2.944 1.979 104.7 104.8 2.837 2.845 2.837 0.973 0.962 0.973 0.962 0.973 0.962 1.945 1.948 1.973 105.3 105.7 105.6 150.8 148.0 151.2 180.6 -167.2 178.8 117.5 -123.0 -128.7

Bond lengths are in angstroms and angles in degrees. b X denotes the center of the benzene ring.

calculations of Suzuki et al.18 gave a c.m. to c.m. separation of 3.195 Å. The angle F, giving the tilt of the water molecule relative to the C6 axis of the benzene ring (see Chart 1), is calculated to be 49.3° at the MP2 level of theory. This is close the F value deduced from a model of the experimental data21 but is 25° larger than that of the structure obtained in the earlier theoretical study of Suzuki et al. However, because the potential energy surface is very shallow along the F coordinate, we do not attribute much significance to this difference in F values. The interaction of the water monomer with the benzene ring causes the two OH bond lengths to become unequal in the minimum-energy structure (although averaging over the zeropoint vibrational level apparently restores the equivalency of the two bonds21,22). At the MP2/6-31+G[2d,p] level of theory, the OH bond associated with the H atom π-bonded to the ring is about 0.003 Å longer and the other OH bond is about 0.001 Å shorter than in the free water molecule. The Becke3LYP calculations place the water monomer about 0.39 Å further from the benzene ring than do the MP2 calculations. (Here we are using the separation between the H atom π-bonded to the ring and the center of the ring.) As will be seen later, this is consistent with a weaker binding between the benzene and water molecules at the Becke3LYP level of theory. The F value obtained from the Becke3LYP calculations is 56.2°, about 7° greater than that obtained from the MP2 calculations.

2. W2 and BW2. The structure of the water dimer is wellcharacterized experimentally1 and theoretically,24,30-35 and the present calculations give geometrical parameters in good agreement with those from prior theoretical studies. As shown in Figure 2a, the water dimer has a Cs structure, in which the two monomers can be distinguished as “donor” and “acceptor”. In the donor monomer, the two OH groups can be further distinguished as “donor” and “free”. The present Becke3LYP and MP2 calculations give for the dimer OO separations of 2.906 and 2.917 Å, respectively. These are significantly shorter than the experimentally derived OO separation of 2.98 Å.1 This discrepancy between theory and experiment has two origins: (i) the neglect in the calculations of higher-order correlation effects and (ii) the vibrational averaging1 inherent to the spectroscopic data, with the latter being somewhat more important. The QCISD/6-31+G[2d,p] calculations give an OO separation of 2.944 Å, close to that obtained by other researchers31,33 using the QCISD or coupled-cluster methods. At each level of theory, the OH bond lengths of the acceptor monomer of W2 are nearly the same as those in the isolated water monomer. On the other hand, the bond length of the donor OH group (O1H4) of W2 is appreciably longer than the OH bond lengths of the water monomer (by 0.009, 0.008, and 0.006 Å at the Becke3LYP, MP2, and QCISD levels of theory, respectively). The variation with level of theory of the donor

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Fredericks et al.

TABLE 2: Rotational Constants (GHz) and Dipole Moments (D) molecule W1

W2

W3

BW1j

BW2

BW3

A B C µ A B C µ A B C µ A B C µ A B C µ A B C µ

Becke3LYP

MP2

821.5728 428.9023 281.7924 1.98 212.6205 6.4431 6.4425 2.58 6.8994 6.7869 3.4921 1.17 3.0378 1.8248 1.7503 2.51 2.6577 0.9730 0.9034 2.42 1.7737 0.7204 0.6809 0.39

806.4500 432.7952 281.6454 2.00 214.1366 6.3891 6.3882 2.70 6.8478 6.7393 3.4629 1.14 2.8388 2.0911 2.0885 2.46 2.4609 1.2358 1.1580 2.11 1.8294 0.9338 0.8549 0.53

MP2(corr)a

2.8367 1.9359 1.9347 2.41 2.3771 1.1741 1.0866 2.14 1.7846 0.8766 0.8156 0.57

QCISD

expt

812.4733 432.3768 282.1983 1.99 215.7908 6.2729 6.2725 2.70 6.6921 6.5896 3.3805 1.08

835.7313b 435.0587b 278.3572b 1.85c 227.5804d 6.177d 6.151d 2.60e 6.6469f 6.6469f 3.0885f 2.84g 1.995h 1.995h 2.35i 1.56i 1.40i

a MP2 geometries corrected for BSSE. b Herzberg, G. Molecular Spectra and Molecular Structure; Krieger: Malibar, 1991; Vol. III, 584. c Reference 51. d Reference 3. e Reference 1a. f Reference 9c. Rotational constant C is for (D2O)3. Fit is to a symmetric top. g Reference 13. Rotational constant A is for benzene-D O. h Reference 2 17. Fit is to a symmetric top. i Reference 13. j Good agreement is found between experiment and the rotational constants for BW1 optimized at the MP2/6-31+G{2d,p} level of theory (A ) 2.8432, B ) 1.9863, C ) 1.9760).

CHART 1: Definition of the Angle G

OH bond length of W2 is consistent with that noted above for the OO separations (i.e., as the OO separation decreases, the single-donor OH bond length increases). The ab initio calculations give a minimum-energy structure of BW2 with the W2 entity bound to the π cloud of benzene via one of the H atoms of the acceptor water molecule (Figure 2b). The structure of the W2 portion of BW2 is similar to that of the free W2 molecule. This is consistent with the predictions of MMC calculations23 and with the analysis of the experimental data.20,21 The MP2 calculations give for BW2 a distance of 2.243 Å between the center of the ring and the H atom π-bonded to the ring. This is 0.06 Å shorter than the corresponding distance in BW1. Moreover, the OH bond length associated with the H

atom π-bonded to the ring is 0.003 Å longer than that in BW1. These results are indicative of a stronger H atom π-bond in BW2 than in BW1, as might be expected given the larger dipole moment of W2 compared to W1 (2.601 Vs 1.85 D51). The MP2 calculations predict the OO axis of the W2 species to be tilted about 10° toward the benzene ring (away from the parallel). This is precisely the result obtained from analysis of the rotational band contour by Gotch and Zwier.13 These workers have argued that this tilting is accompanied by enhanced interaction of the donor water molecule with the benzene ring. At the MP2 level the interaction of the water dimer with the benzene ring causes a 0.02 Å decrease in the OO separation of W2. In contrast, Gotch and Zwier deduced from their spectroscopic results that the OO separation decreased by 0.20 ( 0.10 Å in going from W2 to BW2. The origin of this discrepancy between theory and experiment is unknown. The O1H4 singledonor bond length is predicted to be 0.003 Å longer in BW2 than in W2, consistent with the above-noted decrease in the OO separation. The Becke3LYP calculations give a structure for BW2 similar to that obtained from the MP2 calculations. However, as for BW1, the distance between the π-bonded H atom and the center of the ring is appreciably greater (= 0.40 Å) in the Becke3LYP than in the MP2 calculations. 3. W3 and BW3. The global minimum of the water trimer is a cyclic structure (Figure 3a), with each water molecule acting as a single H atom donor and with the H atoms of two of the free OH groups lying on one side of the OOO plane and the H atom of the other free OH group lying on the other side of this plane.9,24,25,27,36 The present MP2 optimized structure of W3 has OO distances of 2.804, 2.812, and 2.805 Å, with the longest OO distance being that with the associated free OH protons lying on the same side of the OOO plane. The three singledonor OH bond lengths are predicted to be nearly equal (0.9770.978 Å) as are the three free OH bond lengths (0.963-0.964 Å). These results are in close agreement with those of prior MP2 calculations on W3.24,25,27,36 Given the low barrier for flipping one of the free hydrogens to the other side of the plane of the three oxygen atoms, the vibrationally averaged experimental structure9 is expected to have equal OO bond lengths as well as equal single-donor and equal free OH bond lengths. Consistent with the results for the water dimer, the Becke3LYP calculations give for the water trimer slightly shorter OO distances and slightly longer single-donor OH bond lengths than obtained from the MP2 calculations. More pronounced changes are found upon inclusion of higher-order electron correlation effects: most noticeably, the OO distances are 0.032-0.033 Å longer and the single-donor OH bond lengths are 0.004-0.005 Å shorter in the QCISD than in the MP2 calculations. The bond length changes brought about upon inclusion of higher-order correlation effects are greater for W3 than for W2. Our QCISD structure for W3 is very close to the CCSD(T) structure reported recently by Fowler and Schaefer.25 As shown in Figure 3b,c, two structurally inequivalent local minima were located for BW3. Both structures retain the cyclic structure for the W3 entity. They differ in terms of which free OH group is π-bonded to the ring. In the lower energy structure, the H5 atom is π-bonded to the ring, whereas in the higher energy structure the H9 atom is π-bonded to the ring. The two structures can be interconverted by a flip of one of the remaining free OH groups.52 For the free W3 species, the two structures in question are of identical energy, but in the BW3 complex they differ by 217 cm-1 in energy (at the MP2 level of theory). The ensuing discussion will focus on the lower energy structure.

Benzene-(H2O)n Clusters

J. Phys. Chem., Vol. 100, No. 19, 1996 7815

TABLE 3: Binding Energies (kcal/mol)a of Wn to Benzene Becke3LYP

MP2

n

6-31+G[2d,p] uncorr corr

6-31+G{2d,p} uncorr corr

6-31+G[2d,p] uncorr corr

6-31+G{2d,p} uncorr corr

1 2 3

-3.02 -4.37 -3.31

-1.79 -2.84 -1.60

-5.23 -8.01 -7.77

-3.65 -6.09 -5.73

-1.91 -2.93 -1.69

-1.46 -2.40 -1.20

-2.49 -4.02 -3.04

-2.48 -4.38 -3.62

MP2 6-31+G[2d,p] reopt

MMC ref 23

-2.83 -4.63 -3.44

-3.80 -6.58 -5.70

a The uncorrected (uncorr) binding energies and the corrected (corr) binding energies exclude and include, respectively, the counterpoise correction for BSSE. The results labeled “reopt” were obtained by reoptimizing the benzene-water separation including the counterpoise correction.

At the MP2 level of theory the distance between the center of the benzene ring and the H-atom π-bonded to the ring (2.291 Å) is 0.011 Å shorter in BW3 than that in BW1 but 0.048 Å longer than in BW2. This trend suggests that the interaction between the water cluster and the benzene ring is strongest for BW2, smallest for BW1, and of intermediate strength for BW3. This is indeed the case, as will be seen in the next subsection. On the other hand, the O1H5 bond length (0.969 Å) in BW3 is closer to the bond length of the OH group π-bonded to the ring in BW2 than in BW1. There is an overall expansion of the W3 cycle brought about by the interaction with the benzene molecule. At the MP2 level of theory, the average OO distance increases from 2.807 Å in free W3 to 2.835 Å in BW3. More importantly, the interaction with the benzene induces significant asymmetry in the water trimer. Whereas all three OO distances are about 2.807 Å in W3, the individual O1O2, O1O3, and O2O3 distances in the BW3 cluster are calculated to be 2.894, 2.776, and 2.835 Å, respectively. These changes are in the direction expected based on simple electrostatic considerations. The charge transfer/ polarization interaction with the benzene ring causes the oxygen atom of the OH group π-bonded to the ring (O1) to become more negatively charged, thereby making it a better H-bond acceptor and the associated single-donor group a poorer H-bond donor. This is reflected in the changes in the O1O2 and O1O3 distances and in the changes in the lengths of the single-donor OH bonds. The Becke3LYP calculations give a structure for BW3 similar to that obtained from the MP2 calculations, with the main difference being the 0.25 Å greater separation between the benzene ring and W3 in the Becke3LYP calculations. For BW1 and BW2 the increase in the benzene-Wn separation (as measured by the separation between the π-bonded H atom and the center of the benzene ring) in going from the MP2 to Becke3LYP optimized structures was 0.38-0.40 Å. B. Trends in Binding Energies. Table 3 summarizes the binding energies of benzene to the Wn clusters, calculated from E(BWn) - {E(B) + E(Wn)}. Binding energies with and without counterpoise corrections for basis set superposition error (BSSE)53 are reported. The BSSE contribution to the interaction energy between two species A and B results from the improved description of each species due to the presence of the basis functions centered on the other and, hence, acts so as to artifically increase the binding energies. For the BWn clusters the counterpoise corrections are obtained by performing calculations on benzene in both the presence and absence of the basis functions on the water molecules and also on the water clusters in both the presence and absence of the basis functions on the benzene molecule. The results of the MP2 calculations using the 6-31+G[2d,p] basis set are considered first. These calculations, without corrections for BSSE, give binding energies of -5.23, -8.01, and -7.77 kcal/mol for BW1, BW2, and BW3, respectively. These binding energies are clearly overestimated in magnitude since the benzene-water binding energy should be appreciably

weaker than the water-water binding energy, which recent estimates place near -4.7 kcal/mol.30-33,35 When the MP2/631+G[2d,p] results are corrected for BSSE, binding energies of -2.49, -4.02, and -3.04 kcal/mol are obtained for BW1, BW2, and BW3, respectively. Not surprisingly, the contribution of BSSE to the binding energy grows with increasing size of the water cluster. Nonetheless, both the calculations with and those without the BSSE corrections predict binding energies (in an absolute value sense) in the order E(B‚‚‚W1) < E(B‚‚‚W3) < E(B‚‚‚W2), consistent with the trends in the benzene-Wn separations. MP2 calculations with the larger 6-31+G{2d,p} basis set, but retaining the MP2/6-31+G[2d,p] optimized geometries, give binding energies of -3.65, -6.09, and -5.73 kcal/mol for BW1, BW2, and BW3, respectively. These binding energies are 1.62.0 kcal/mol smaller in magnitude than those obtained with the 6-31+G[2d,p] basis set. This is largely a result of the reduction in the BSSE upon the adoption of the more flexible basis set for the benzene molecule. With the inclusion of the correction for BSSE, the corresponding binding energies are -2.48, -4.38, and -3.62 kcal/mol. These BSSE-corrected binding energies, which agree to within 0.6 kcal/mol of those obtained with the smaller 6-31+G[2d,p] basis set, are expected to be close to the true binding energies and are 1.3-2.2 kcal/mol smaller in magnitude than those predicted by the MMC calculations. The presence of BSSE causes a shortening of the distance between the benzene molecule and the water cluster. In order to estimate the magnitude of this effect on the MP2 geometries, we carried out for each of the BWn (n ) 1-3) clusters singlepoint MP2/6-31+G[2d,p] calculations for several values of the benzene-Wn separation (as measured by the distance between the π-bonded H atom and the center of the benzene ring), keeping all other geometrical parameters fixed at their MP2optimized values and applying at each separation the counterpoise correction for BSSE. For each of the three BWn clusters considered, this approach led to about an 0.2 Å increase in the separation between the benzene ring and the water cluster (as measured by the distance between the center of the benzene ring and the H atom π-bonded to the ring). The BSSE-corrected MP2/6-31+G[2d,p] binding energies at these new geometries are 0.3-0.6 kcal/mol larger in magnitude than at the original geometries, obtained without correction for BSSE, with the largest increase being for BW2 and the smallest for BW1. These changes, while nonnegligible, are sufficiently small that the impact of BSSE on the OH stretching frequencies should be relatively minor. In the case of BW1, we have also reoptimized the geometry and calculated the normal-mode vibrational frequencies at the MP2/6-31+G{2d,p} level of theory with no constraints other than the forced planarity of the benzene ring. This calculation gave a value of the benzene-water separation only 0.024 Å smaller than that obtained from the above-described grid search including the correction for BSSE. Moreover, the MP2/631+G{2d,p} optimization gave a benzene-water c.m. to c.m. separation within 0.02 Å of that determined experimentally. The

7816 J. Phys. Chem., Vol. 100, No. 19, 1996

Fredericks et al.

TABLE 4: Vibrational Frequenciesa (cm-1) and Intensitiesb of Wn and BWn, n ) 1-3 n 1 2

3

labelc BWn

Wn

Becke3LYP Wnd

BWn

Wn

MP2 Wnd

BWn

QCISD Wn BWne

ν3 ν1 O2, F O1, F O2, π O1, S F F O1, π O1, S O2, S O3, S

3922 (56) 3814 (6) 3909 (79) 3890 (81) 3805 (13) 3679 (345) 3886 (48) 3884 (94) 3880 (88) 3603 (548) 3589 (602) 3525 (18)

3910 (53) 3793 (9) 3890 (68) 3890 (79) 3770 (19) 3648 (364) 3884 (64) 3882 (77) 3834 (98) 3632 (441) 3581 (461) 3482 (271)

3902 (94) 3780 (108) 3884 (102) 3887 (67) 3739 (195) 3631 (389) 3883 (60) 3881 (71) 3813 (249) 3637 (351) 3582 (412) 3473 (315)

3966 (67) 3833 (9) 3950 (90) 3930 (108) 3823 (15) 3723 (294) 3920 (85) 3918 (111) 3914 (109) 3663 (454) 3651 (507) 3590 (16)

3953 (64) 3815 (11) 3930 (82) 3919 (94) 3787 (21) 3677 (338) 3907 (90) 3903 (91) 3858 (130) 3693 (293) 3627 (410) 3521 (289)

3947 (114) 3813 (78) 3920 (120) 3916 (77) 3773 (141) 3662 (307) 3906 (77) 3901 (79) 3836 (220) 3699 (219) 3625 (328) 3507 (286)

3958 (50) 3844 (6) 3950 (70) 3931 (98) 3840 (11) 3772 (233) 3928 (91) 3926 (92) 3922 (82) 3728 (356) 3720 (394) 3674 (15)

3939 3824 3920 3917 3790 3711 3914 3909 3844 3772 3698 3580

expt Wn

BWn

3756f 3657f 3745h 3730h (3650)i,l 3600i 3720i

3731g 3634g 3722j 3708j 3608k 3550k 3716k 3657k 3550k 3508k 3423k

3533i

a The theoretical frequencies were obtained in the harmonic approximation, whereas the experimental frequencies include anharmonicities. b The intensities are in parentheses. c The “F” and “S” labels refer to free OH and single-donor OH groups, respectively. The frequency associated with the OH group π-bonded to the ring is designated by “π”. In some cases there is not a 1:1 correlation between modes of BWn and Wn due to the localization of the modes brought about by the benzene. See text for further discussion. d Wn geometry taken from BWn. e Determined as described in the text. f Reference 50. g Deduced from analysis of the spectrum in reference 22. h Reference 5. i Reference 8. j Experiment (refs 20 and 21) does not establish which of these modes is the O2H free and which is the O1H free stretch. k References 20 and 21. l The water dimer acceptor symmetric stretch, predicted to occur at 3650 cm-1, has not been experimentally observed.

OH stretching frequencies obtained with this basis set are nearly the same as those obtained with the smaller 6-31+G[2d,p] basis set, even though the BSSE is appreciably larger with the smaller basis set. This confirms our expectation that the OH stretch vibrational frequencies are reliably predicted in spite of the sizable BSSE when using the 6-31+G[2d,p] basis set. The Becke3LYP/6-31+G[2d,p] calculations, without BSSE corrections, give binding energies of -3.02, -4.37, and -3.31 kcal/mol for BW1, BW2, and BW3, respectively. After inclusion of the counterpoise correction for BSSE, the corresponding binding energies become -1.91, -2.93, and -1.69 kcal/mol. With the adoption of the more flexible 6-31+G{2d,p} basis set, the Becke3LYP binding energies, calculated at the Becke3LYP/ 6-31+G[2d,p] geometries and without BSSE corrections, are 1.2-1.7 kcal/mol smaller in magnitude, but the BSSE-corrected results remain nearly the same as those obtained with the 6-31+G[2d,p] basis set. With both basis sets used, the magnitudes of the BSSE-corrected binding energies are appreciably smaller at the Becke3LYP than at the MP2 level of theory. It appears that the DFT calculations with the Becke3LYP functional underestimate by 1-2 kcal/mol the magnitude of the interaction energies between benzene and Wn clusters. C. Vibrational Frequencies and Intensities. The primary comparison of the present theoretical results with experiment is via the frequencies and intensities of the OH stretch fundamentals of the Wn and BWn clusters. The experimental frequencies include anharmonic contributions, while the computed frequencies are harmonic. A more useful comparison between experiment and theory can be made via frequency shifts associated with the differences between the OH stretch frequency and ωo, defined as the average of the symmetric and asymmetric stretch frequencies of the water monomer. The frequency shifts are calculated from ∆ωi ) ωi - ωo where ωi is the frequency of mode i. In obtaining the theoretical values of the shifts, harmonic frequencies are employed (for both ωi and ωo). On the other hand, anharmonicity effects are included in the experimental values of the frequency shifts. However, because the anharmonicities for the OH stretch modes have similar values in the clusters as in water monomer, use of the frequency shifts thereby facilitates comparison between theory and experiment. The calculated (harmonic) and experimental (anharmonic) OH stretching frequencies and the calculated IR intensities of the Wn and BWn clusters are reported in Table 4, and the

TABLE 5: Frequency Shiftsa (cm-1) Becke3LYP

MP2

QCISD

Exptb

n

Wn

BWn

Wn

BWn

Wn

BWn

Wn

BWn

1

+54 -54 +41 +22 -63 -189 +18 +16 +12 -265 -279 -343

+34 -88 +16 +19 -129 -237 +15 +13 -55 -231 -286 -395

+66 -66 +50 +30 -76 -177 +20 +18 +14 -237 -249 -310

+47 -87 +20 +16 -127 -238 +6 +1 -64 -201 -275 -393

+57 -57 +49 +30 -61 -129 +27 +25 +21 -173 -181 -227

+38 -77 +19 +16 -111 -190 +13 +8 -57 -129 -203 -321

+50 -50 +39 +24 (-56)c -106 +14

+25 -72 +16 +2 -98 -156 +10

2

3

-173

-49 -156 -198 -283

a Shifts are reported relative to the mean of the two OH stretching frequencies from theory or experiment, as appropriate. b References for the experimental values are found in Table 4. c The water dimer acceptor symmetric stretch, predicted to occur at 3650 cm-1, has not been experimentally observed.

corresponding frequency shifts are reported in Table 5. The former table includes theoretical results both for the optimized free Wn clusters as well as for structures generated by “cutting out” the Wn portions of the BWn complexes. 1. W1 and BW1. For W1 the harmonic frequencies calculated at MP2, Becke3LYP, and QCISD levels are all in excellent agreement with the experimental values of the harmonic frequencies, with a maximum discrepancy of 23 cm-1 between theory and experiment. At the MP2/6-3+G[2d,p] level, the splitting between the two OH stretching modes in water is 133 cm-1, which is appreciably larger than the experimentally observed splitting (99 and 111 cm-1 for the anharmonic and harmonic frequencies, respectively). However, with the inclusion of higher-order correlation effects by means of the QCISD/ 6-31+G[2d,p] procedure, the splitting between the two harmonic OH stretching frequencies of W1 drops to 114 cm-1, which is in excellent agreement with the results of experiment and prior QCISD and CCSD calculations.31 The Becke3LYP calculations also give a splitting between the two OH stretching frequencies nearly identical to that obtained experimentally. Both the MP2 and Becke3LYP calculations predict that the OH stretching frequencies decrease upon complexation of a water monomer with benzene, consistent with the water molecule acquiring a partial negative charge in the BW1 complex. At the MP2 level of theory, the decrease is about 20

Benzene-(H2O)n Clusters cm-1 for both the asymmetric and symmetric OH stretching modes, in excellent agreement with the corresponding experimentally observed decreases of 25 and 23 cm-1.22 For the water monomer, the experimental IR intensity of the asymmetric OH stretching mode is 14.5 times that of the symmetric stretch.54 This is a direct manifestation of the nonlinearity of the OH stretch dipole moment derivative, since purely geometrical considerations predict Iasym/Isym ) 3.5.55 The MP2, Becke3LYP, and QCISD calculations with the 6-31+G[2d,p] basis set give intensity ratios ranging from 7.4 to 9.3. The disparity between the theoretical and experimental intensity ratios reflects the need to use more flexible atomic basis sets. There is a remarkably large change in the water monomer’s asymmetric to symmetric stretch intensity ratio upon complexation to benzene. The experimental IR spectrum of BW1 gives Iasym/Isym ) 1.5. While part of this change could be ascribed to saturation effects in the experiment, the present calculations suggest a more fundamental source. Both the MP2 and Becke3LYP calculations predict that the two OH stretching modes are of comparable intensity at the minimum-energy configuration for the BW1 complex (Table 4). In going from W1 to BW1, the calculated intensity of the asymmetric OH stretching mode increases by a factor of about 1.7 in both the MP2 and Becke3LYP methods, while that of the symmetric OH stretching mode undergoes a much larger increase (by factors of 8.7 and 18 at the MP2 and Becke3LYP levels of theory, respectively). In an earlier publication,22 it was suggested that partial localization of the OH stretch vibrations due to the complexation of H2O with benzene might be the source of the observed intensity changes, and in fact, the calculations at the asymmetric minimum-energy configuration do indeed show partial localization in these vibrations. To explore this possibility further, we have calculated, at the MP2 level of theory, the vibrational frequencies and the IR intensities for the symmetrical transition state structure of BW1 for which the vibrations are necessarily pure symmetric and asymmetric stretches. The intensities obtained for this transition state structure are very close to those calculated for the minimum-energy structure. Furthermore, MP2 calculations for the distorted water model, in which the water monomer is fixed at the geometry that it has in the minimumenergy BW1 structure, also give intensities nearly identical to those of the undistorted W1. It follows, therefore, that the large increase in the intensity of water’s symmetric stretch fundamental brought about by complexation with benzene is not the result of symmetry breaking (and acquisition of local-mode character) in the complex. An alternative possibility is that the intensity changes arise from charge transfer/polarization interactions between the benzene and water molecule. This interaction is surprisingly large, causing a 0.5 D increase in the dipole moment relative to that of the water monomer, with the dipole moment change consistent with transfer of electron charge from the benzene to the water molecule. Although the ab initio calculations do not allow one to uniquely separate the dipole moment change into charge-transfer and polarization components, the fact that the MMC calculations23 gave a similar dipole moment change upon complexation of a water molecular with benzene suggests that polarization rather than charge transfer probably dominates the dipole moment change. 2. W2 and BW2. In the Wn (n g 2) clusters there can be both localized and delocalized OH stretch modes. This is illustrated by W2. In the acceptor water molecule of W2, the two OH stretch modesssymmetric (ν1(A)) and asymmetric (ν3(A)) stretchsare delocalized over the two OH groups, while in

J. Phys. Chem., Vol. 100, No. 19, 1996 7817

Figure 4. Experimental and calculated vibrational frequency shifts for the OH stretch vibrations of W2 and BW2. (a) MP2 and QCISD results for W2 and (d) MP2 results for BW2. The zero of the relative frequency scale is set at the average of the OH stretch vibrational frequencies for the water monomer at the same level of theory. (b) Experimental results for W2. In W2, the two high-frequency modes have been assigned in ref 5, while the band at -106 cm-1 is assigned as the H-bonded OH stretch in ref 8. The band at -55 cm-1 has not been experimentally observed but is believed to be in this region (refs 8, 56, and 57). (c) Experimental results for BW2 from refs 20 and 21. The zero of the relative frequency scale is set at the average of the OH stretch vibrational fundamentals for the water monomer (3706 cm-1).

the donor water the asymmetry imposed by the hydrogen bond causes the vibrations to be more nearly local-mode stretches (free OH and H-bonded OH stretch). The lowering of the force constant for the donor H-bonded OH relative to the intrabond coupling is thus sufficient to effectively localize the donor molecule’s OH stretch modes. This is confirmed by the computed normal modes. Figure 4a,b compares the calculated (MP2 and QCISD) and experimental OH stretch frequency shifts and intensities for W2. At the MP2 level of theory, the frequency shifts of the asymmetric and symmetric OH stretching modes of the acceptor water of W2 are +50 and -76 cm-1, respectively. These are 16 and 10 cm-1 lower than the corresponding frequency shifts calculated for the water monomer. Qualitatively similar results are obtained from the Becke3LYP and QCISD calculations. All three theoretical methods predict a splitting between the acceptor asymmetric and symmetric stretching modes slightly (2-6 cm-1) smaller than in the free water monomer. Not surprisingly, the frequency shift of the free OH stretch mode of the donor water molecule in W2 is similar in the three theoretical methods, ranging from +22 to +30 cm-1. The corresponding shifts for the donor H-bonded OH span a larger range: -129 (QCISD), -177 (MP2), and -189 cm-1 (Becke3LYP). The smaller magnitude of the frequency shift of the donor H-bonded OH stretch in the QCISD calculations is consistent with the increase in the OO separation and the accompanying decrease in the donor OH bond length brought about by inclusion of higher-order correlation effects.

7818 J. Phys. Chem., Vol. 100, No. 19, 1996 Comparison of these results with experiment is clouded by uncertainties in the experimental assignments of the water dimer OH stretch modes. The high-resolution spectra of Huang and Miller5 unambiguously assign the acceptor asymmetric stretch (3745 cm-1) and donor free OH stretch (3730 cm-1). These authors also assigned a partially resolved band at 3600 cm-1 to the acceptor symmetric stretch. Earlier studies11,12 had associated this mode with a band at 3530 cm-1. However, Huisken et al.8 have recently reassigned the 3600 cm-1 mode to the donor OH stretch, in keeping with the assignments by Nelander56 and Forney et al.57 based on matrix isolation infrared spectra (3590 cm-1). These authors8,56,57 suggest that the weak acceptor symmetric stretch has not yet been detected but should occur near 3650 cm-1. The theoretical results presented in Tables 4 and 5 support the assignment of the H-bonded OH stretch and acceptor symmetric stretch modes suggested by these groups.8,56,57 First, one difficulty with the earlier assignment5 of the 3600 cm-1 band to the acceptor symmetric stretch is that it would result in a 145 cm-1 separation between the symmetric and asymmetric OH stretch modes of the acceptor molecule. This is 35 cm-1 larger than predicted by the present calculations. It is also 46 cm-1 larger than the measured splitting between the symmetric and asymmetric OH stretch modes of a free water molecule. It seems unlikely that the intrabond coupling in the acceptor water molecule would undergo a 50% change due to hydrogen bonding. Second, the -129 cm-1 frequency shift predicted by the highest level of calculation employed here (QCISD) is much more in keeping with the assignment of the 3600 cm-1 band as the H-bonded OH stretch (with observed shift of -106 cm-1). Finally, as will be seen below, this reassignment is also more consistent with the results for BW2. Figure 4c,d compares the experimental and calculated OH stretch infrared spectra of BW2. The correspondence between the experiment and calculation is excellent in two important respects. First, the calculated frequency shifts are close to those measured, with the estimated QCISD shifts for the four OH stretch vibrations of BW2 differing from the experimental values on average by only 16 cm-1. Second, the calculations adequately reproduce the observed similar strengths of all four transitions. The calculations on BW2 also suggest important changes in the form of the OH stretch normal modes of the water dimer upon complexation with benzene. As noted above, at the minimum-energy structure for BW2, the acceptor water molecule is π-H-bonded to the benzene ring via one of its OH groups (Figure 2b). This results in a partial localization of the acceptor water molecule’s vibrations (with the localization being somewhat greater than in the OH stretch modes of BW1). At the MP2 level the changes in the frequency shifts are greater in going from W2 to BW2 than from W1 to BW1. These results are consistent with a stronger interaction between W2 and the benzene ring than between W1 and the benzene ring. For the donor molecule in W2 the interaction with the benzene ring causes the frequency of the modes localized on the free OH and donor H-bonded OH groups to decrease at the MP2 level by 14 and 61 cm-1, respectively. The large decrease in the frequency of the latter mode is consistent with the decrease in the OO separation and the sizable (0.003 Å) increase in the donor OH bond length in the BW2 complex. For the most part, the changes in the OH stretching frequencies in going from W2 to BW2 are “recovered” by the distorted W2 model, in which the geometry of W2 is extracted from that of the BW2 complex. Of the four OH stretching modes of W2 only that associated with the acceptor symmetric stretch has a

Fredericks et al.

Figure 5. Experimental and calculated vibrational frequency shifts for the OH stretch vibrations in W3 and BW3. (a) MP2 and QCISD results for W3 and (d) MP2 results for BW3. The zero of the relative frequency scale is set at the average of the OH stretch vibrational frequencies for the water monomer at the same level of theory. (b) Experimental results for W3 from ref 8. (c) Experimental results for BW3 from refs 20 and 21. The zero of the relative frequency scale is set at the average of the OH stretch vibrational fundamentals for the water monomer (3706 cm-1).

very different IR intensity in BW2. This intensity change is not described by the distorted W2 model, indicating that, as was the case for BW1, it is due to charge transfer/polarization interactions. The strength of the transition in the experimental spectrum (Figure 4c) suggests that such interactions are indeed important in BW2. 3. W3 and BW3. The OH stretch modes of cyclic water trimer divide into two groups of three: three high-frequency modes that are predominantly free OH stretch in character and three low-frequency modes that are predominantly single-donor OH stretch in character.20,21 As shown in the stick spectrum of Figure 5a, the three free OH stretching modes are nearly degenerate (3914-3920 cm-1, in the MP2 approximation), whereas the triad of single-donor OH stretching modes is composed of a nearly degenerate pair with large intensity and a single mode of lower frequency and low intensity. Both the free and single-donor modes are highly delocalized over all three water molecules. This is shown in Figure 6 for the single-donor modes. As has been suggested by Honegger and Leutwyler,58 these modes can be viewed as “longitudinal phonons” with different numbers of nodes in the phonon motion. The delocalized form of the single-donor modes indicates that coupling of the donor OH groups across the hydroen bonds exceeds the intramolecular OH/OH coupling with a water molecule.58 The lowest frequency OH stretching mode (Figure 6a) involves the “in-phase” motion of the three single-donor OH groups and, due to the near cancellation of the dipole moment derivatives from the individual OH groups, has a very low IR intensity. (It would be strictly IR forbidden in C3h symmetry.)

Benzene-(H2O)n Clusters

J. Phys. Chem., Vol. 100, No. 19, 1996 7819

Figure 6. MP2-level single-donor OH stretch modes in W3 at (a) 3590, (b) 3651, and (c) 3663 cm-1. The arrow lengths represent the relative contributions of the various OH groups.

Figure 7. MP2-level single-donor OH stretch modes in BW3 at (a) 3507, (b) 3625, and (c) 3699 cm-1. The arrow lengths represent the relative contributions of the various OH groups.

The experimental infrared spectrum of W3 (Figure 5b) observed by Huisken et al.8 has two resolved bands, one near 3720 cm-1 and a second at 3600 cm-1. The former is due to the three free OH stretching modes and the latter to the two degenerate or nearly degenerate single-donor OH stretching modes. The third single-donor mode, that with the low IR intensity, is not observed in the infrared spectrum. The frequency shifts (relative to the mean of ν1 and ν3 of H2O) predicted for the free OH stretching modes (+14 to +20 cm-1 at the MP2 level) are in good agreement with that observed experimentally (+14 cm-1). In contrast, in the MP2 and Becke3LYP approximations, the shifts calculated for the singledonor OH stretching modes are 60-90 cm-1 larger in magnitude than those observed (see Table 5). This is remedied by the QCISD method which gives frequency shifts for both the free and single-donor OH stretching modes in excellent agreement with experiment. As Figure 5c,d shows, the OH stretch IR spectrum calculated at the MP2 level is in qualitative agreement with the experimental spectrum, and that obtained at the QCISD level (estimated as described above) is in near quantitative agreement with experiment. The interaction of the benzene ring with the W3 cluster has several important consequences for the OH stretch infrared spectrum. In the free OH stretch region, the near degeneracy of the free OH modes is broken as a result of formation of the π-hydrogen bond with the benzene ring. At the MP2 level of theory, the frequency of the OH group π-bonded to the ring is shifted -64 cm-1, whereas the frequency

shifts of the two remaining free OH groups are +6 and +1 cm-1. These results are in fairly good agreement with the observed frequency shifts of -49 and +10 cm-1 (two unresolved bands). In addition, the calculations indicate that even the two nearly degenerate free OH stretch modes of BW3 are localized, though this localization is a product more of the weak coupling between the free OH groups than of a significant change in the force constants of the two OH groups in question. The interaction of the W3 cluster with the benzene ring has an even more dramatic effect on the single-donor OH stretch region of the spectrum (Figure 5c,d). First, whereas the lowest frequency single-donor OH stretch transition is essentially forbidden in W3, in BW3 it carries an intensity comparable to that of the other single-donor modes. The reason for this intensity increase can be seen from a comparison of the lowest frequency single-donor OH stretch modes in W3 (Figure 6) and BW3 (Figure 7). In W3 the lowest frequency single-donor OH stretching mode is highly delocalized with nearly equal contributions from O1H4, O2H6, and O3H8 stretches, whereas in BW3 it is largely localized on the O3H8 group (Figure 7a). This has the obvious consequence of turning on intensity in this mode, as observed experimentally. Second, the degeneracy of the two higher frequency single-donor modes is broken, with a benzeneinduced splitting of 74 cm-1 at the MP2 level. This is also borne out by experiment, where the two modes are split by 42 cm-1. From Figure 7b,c it is seen that the highest frequency OH stretch mode of BW3 is well described as the O1H4 stretch, with the remaining mode being the O2H6 stretch. Third, at the

7820 J. Phys. Chem., Vol. 100, No. 19, 1996 MP2 level the calculated spread in the frequencies of the singledonor modes increases from 73 cm-1 in the free W3 cluster to 192 cm-1 in BW3. The observed spread in the frequencies of the single-donor OH stretch modes of BW3 is 127 cm-1. Thus for BW3, as for W3, the frequency shifts calculated in the MP2 approximation are in qualitative but not quantitative accord with experiment. However, the shifts obtained from the estimated QCISD procedure are in excellent agreement with experiment. There is a strong correlation between the frequency of a mode and the length of the OH bond with which it is associated (i.e., on which it is largely localized). In particular, in the MP2 approximation, the 3507, 3625, and 3699 cm-1 modes are associated with the single-donor OH bonds of lengths 0.983, 0.978, and 0.974 Å, respectively. (The corresponding OO distances are 2.776, 2.835, and 2.894 Å.) As for BW1 and BW2, the effect of benzene on W3 has been explored by carrying out calculations of the vibrational frequencies and intensities for a distorted W3 in which its geometry is fixed at that for the W3 portion of BW3. To a large extent, both the frequency shifts and intensity changes in going from W3 to BW3 are accounted for by the distorted W3 model. In particular, for both the distorted W3 model and BW3, the intensity of the lowest frequency single-donor OH stretching mode is calculated in the MP2 approximation to be 18 times larger than that of W3. Since the net intensity of the three singledonor OH stretching modes is nearly the same for the optimal and distorted W3 structures, the main impact of the geometrical distortions is a redistribution of the intensities among the three modes. The intensity of the OH stretching mode associated with the OH group π-bonded to the ring is about twice that of the free OH stretching modes of W3. As for BW1 and BW2, most of the intensity change in this mode is due to an electronic interaction between the distorted W3 and the benzene ring rather than to the geometrical distortion. IV. Conclusions In this work MP2 and Becke3LYP calculations were carried out to characterize the BWn (n ) 1-3) clusters. The interaction with the benzene ring is found to induce small structural changes in the W1 and W2 clusters and somewhat larger structural changes in the W3 cluster. Most of the changes in the OH stretching frequencies brought about by the interaction with the benzene ring can be understood in terms of the geometrical distortions induced on the Wn cluster by the Wn-benzene interactions. In the case of BW3 the geometrical distortions cause a significant redistribution of the intensities among the three single-donor OH stretching modes. The nearly forbidden OH stretch mode of W3 (a delocalized in-phase stretch of all three single-donor OH groups in the W3 cycle) becomes strongly allowed in BW3, and the degeneracy of the other two singledonor OH stretches is broken by the asymmetry induced by the benzene molecule. In addition, these modes are much more localized in BW3 than in W3. The effect of benzene on the OH stretch modes of BWn is also observed in the π-hydrogenbonded OH stretch. For each of the BW1, BW2, and BW3 clusters the intensity of this mode is increased significantly due to charge transfer/polarization interactions, with these intensity changes being more pronounced for BW1 and BW2 than for BW3. Overall, the IR spectra of BW1-BW3 calculated at the MP2 level of theory are in good agreement with experiment. The largest discrepancies between theory and experiment are for the frequency shifts of the single-donor OH stretching modes. This is due to the tendency of the MP2 (and also the Becke3LYP) calculations to give OO distances that are too short and single-

Fredericks et al. donor OH bond lengths that are too long. This is remedied by inclusion of higher-order correlation effects, accomplished in this work by means of QCISD calculations. Acknowledgment. This research was carried out with the support of grants (to T.S.Z. and K.D.J.) from the National Science Foundation. K.D.J. also acknowledges grants of computer time at the Pittsburgh Supercomputing Center and the National Center for Supercomputing Applications. T.S.Z. also gratefully acknowledges the support of a JILA visiting fellowship for 1994-1995, and K.D.J. acknowledges Jack Simons’ hospitality during a sabbatical stay at the University of Utah for 1994-1995. References and Notes (1) Dyke, T. R.; Mack, K. M.; Muenter, J. S. J. Chem. Phys. 1977, 66, 498. Odutola, J. A.; Dyke, T. R. J. Chem. Phys. 1980, 72, 5062. (2) Fraser, G. T. Int. ReV. Phys. Chem. 1991, 10, 189 and references therein. (3) Zwart, E.; Ter Meulen, J. J.; Meerts, W. L. J. Mol. Spectrosc. 1991, 147, 27. (4) Coudert, L. H.; Lovas, F. J.; Suenram, R. D.; Hougen, J. T. J. Chem. Phys. 1987, 87, 6290. (5) Huang, Z. S.; Miller, R. E. J. Chem. Phys. 1989, 91, 6613. (6) Busarow, K. L.; Cohen, R. C.; Blake, G. A.; Laughlin, K. B.; Lee, Y. T.; Saykally, R. J. J. Chem. Phys. 1989, 90, 3937. (7) Pugliano, N.; Cruzan, J. D.; Loeser, J. G.; Saykally, R. J. J. Chem. Phys. 1993, 98, 6600. (8) Huisken, F.; Kaloudis, M.; Kulcke, A. J. Chem. Phys. 1996, 104, 17. (9) Pugliano, N.; Saykally, R. J. Science 1992, 257, 1937. Liu, K.; Elrod, M. J.; Loeser, J. G.; Cruzan, J. D.; Pugliano, N.; Brown, M. G.; Rzepiela, J.; Saykally, R. J. Faraday Discuss. 1994, 97, 35. Liu, K.; Loeser, J. G.; Elrod, M. J.; Host, B. C.; Rzepiela, J. A.; Pugliano, N.; Saykally, R. J. J. Am. Chem. Soc. 1994, 116, 3507. (10) Liu, K.; Brown, M. G.; Cruzan, J. D.; Saykally, R. J. Science 1996, 271, 929. Cruzan, J. D.; Braly, L. B.; Liu, K.; Brown, M. G.; Loeser, J. G.; Saykally, R. J. Science 1996, 271, 62. (11) Vernon, M. F.; Krajnovich, D. J.; Kwok, H. S.; Lisy, J. M.; Shen, Y. R.; Lee, Y. T. J. Chem. Phys. 1982, 77, 47. (12) Coker, D. F.; Miller, R. E.; Watts, R. O. J. Chem. Phys. 1985, 82, 3554. (13) Gotch, A. J.; Zwier, T. S. J. Chem. Phys. 1992, 96, 3388. Garrett, A. W.; Zwier, T. S. J. Chem. Phys. 1992, 96, 3402. (14) Ergdahl, A.; Nelander, B. J. Phys. Chem. 1987, 91, 2253. (15) Wanna, A. J.; Menapace, J. A.; Bernstein, E. R. J. Chem. Phys. 1986, 85, 1795. (16) Bornsen, K. O.; Selzle, H. L.; Schlag, E. W. Z. Naturforsch. A 1990, 45, 1217. (17) Gutowsky, H. S.; Emilsson, T.; Arunan, E. J. Chem. Phys. 1993, 99, 4883. (18) Suzuki, S.; Green, P. G.; Bumgarner, R. E.; Dasgupta, S.; Goddard III, W. A.; Blake, G. A. Science 1992, 257, 942. (19) Maxton, P. M.; Schaeffer, M. W.; Felker, P. M. Chem. Phys. Lett. 1995, 241, 603. (20) Pribble, R. N.; Zwier, T. S. Science 1994, 265, 75. (21) Pribble, R. N.; Zwier, T. S. Faraday Discuss. 1994, 97, 229. (22) Pribble, R. N.; Garret, A. W.; Haber, K.; Zwier, T. S. J. Chem. Phys. 1995, 103, 531. (23) Augspurger, J. D.; Dykstra, C. E.; Zwier, T. S. J. Phys. Chem. 1992, 96, 7252; 1993, 97, 980. (24) Xantheas, S. S.; Dunning Jr., T. H. J. Chem. Phys. 1993, 99, 8774. (25) Fowler, J. E.; Schaefer III, H. F. J. Am. Chem. Soc. 1995, 117, 446. (26) Mhin, B. J.; Kim, J.; Lee, S.; Lee, J. Y.; Kim, K. S. J. Chem. Phys. 1994, 100, 4484. (27) van Duijneveldt-van de Rijdt, J. G. C. M.; van Duijneveldt, F. B. Chem. Phys. 1993, 175, 271. (28) Kim, K.; Jordan, K. D.; Zwier, T. S. J. Am. Chem. Soc. 1994, 116, 11568. (29) Tsai, C. J.; Jordan, K. D. Chem. Phys. Lett. 1993, 213, 181. (30) Feller, D. J. Chem. Phys. 1992, 96, 6104. (31) Kim, J.; Lee, J. Y.; Lee, S.; Mhin, B. J.; Kim, K. S. J. Chem. Phys. 1995, 102, 310. (32) Chakravorty, S. J.; Davidson, E. R. J. Phys. Chem. 1993, 97, 6373. (33) van Duijneveldt-van de Rijdt, J. G. C. M.; van Duijneveldt, F. B. J. Chem. Phys. 1992, 97, 5019. (34) Marsden, C. J.; Smith, B. J.; Pople, J. A.; Schaefer III, H. F.; Radom, L. J. Chem. Phys. 1991, 95, 1825. Frisch, M. J.; Del Bene, J. E.; Binkley, J. S.; Schaefer III, H. F. J. Chem. Phys. 1986, 84, 2279.

Benzene-(H2O)n Clusters (35) Kim, K.; Jordan, K. D. J. Phys. Chem. 1994, 98, 10089. (36) Bu¨rgi, T.; Graf, S.; Leutwyler, S.; Klopper, W. J. Chem. Phys. 1995, 103, 1077. Klopper, W.; Schu¨tz, M.; Lu¨thi, H. P.; Leutwyler, S. J. Chem. Phys. 1995, 103, 1085. (37) Frisch, M. J.; Trucks, G. W.; Schlegal, H. B.; Gill, P. M. W.; Johnson, B. G.; Wong, M. W.; Foresman, J. B.; Robb, M. A.; Head-Gordon, M.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley, J. S.; Gonzalez, C.; Martin, R. L.; Fox, D. J.; Defrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. In Gaussian92, DFT Manual; Gaussian, Inc.: Pittsburgh, PA, 1993. (38) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (39) Vosko, S. H.; Wilk, L.; Nusir, M. Can. J. Phys. 1980, 58, 1200. (40) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. B 1988, 37, 785. (41) Kim, K.; Jordan, K. D. Unpublished results. (42) Del Bene, J. E.; Person, W. B.; Szczepaniak, K. J. Phys. Chem. 1995, 99, 10705. (43) Pople, J. A.; Head-Gordon, M.; Raghavachari, K. J. Chem. Phys. 1987, 87, 5968. (44) Karlstro¨m, G.; Linse, P.; Wallqvist, A.; Jo¨nsson, B. J. Am. Chem. Soc. 1983, 105, 3777. (45) Bre´das, J. L.; Street, G. B. J. Chem. Phys. 1989, 90, 7291. (46) Cheney, B. V.; Schulz, M. W. J. Phys. Chem. 1990, 94, 6268. (47) Clark, T.; Chandrasekhar, J.; Spitznagel, G. W.; Schleyer, P. v. R. J. Comput. Chem. 1983, 4, 294. Hehre, W. J.; Ditchfield, R.; Pople, J. A. J. Chem. Phys. 1972, 56, 2257. Frisch, M. J.; Pople, J. A.; Binkley, J. S. J. Chem. Phys. 1984, 80, 3265. (48) Kendall, R. A.; Dunning, Jr., T. H.; Harrison, R. J. J. Chem. Phys. 1992, 96, 6796.

J. Phys. Chem., Vol. 100, No. 19, 1996 7821 (49) The MP2/6-31+G[2d,p] basis set was originally introduced in ref 28. Although it was previously tested for W1 and W2 (refs 28 and 35), the geometries and frequencies obtained from MP2/6-31+G[2d,p] calculations were not previously reported. (50) Benedict, W. S.; Gailar, N.; Plyler, E. K. J. Chem. Phys. 1956, 24, 1139. (51) Dyke, T. R.; Muenter, J. S. J. Chem. Phys. 1973, 59, 3125. (52) The numbering scheme for the hydroxy H atoms of BW3 is the same as for those of W3 (Figure 3). Flipping an OH group in the higher energy form of BW3 actually gives an isomer with the same energy of the low-energy structure of BW3. (53) Boys, S. F.; Bernardi, F. Mol. Phys. 1970, 19, 553. (54) Lothman, L. S.; Gmache, R. S.; Goldman, A.; Brown, L. R.; Toth, R. A.; Pickett, H. M.; Poynter, R. L.; Flaud, J.-M.; Camy-Peyret, C.; Barbe, A.; Husson, N.; Rinsland, C. P.; Smith, M. A. H. Appl. Opt. 1987, 26, 4058. (55) The asymmetric-to-symmetric stretch intensity ratio in H2O based purely on geometrical considerations would be I(ν3)/I(ν1) ) [2ν33 sin2(52°)/ [ν13 cos2(52°)] ) 3.5, where the factor of 2 arises from the integrated intensity of perpendicular bands relative to parallel bands. See ref. 22 for details. (56) Nelander, B. J. Chem. Phys. 1988, 88, 5254. (57) Forney, D.; Jacox, M. E.; Thompson, W. E. J. Mol. Spectrosc. 1993, 157, 479. (58) Honegger, E.; Leutwyler, S. J. Chem. Phys. 1988, 88, 2582.

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