Infrared spectra of the H 2 O n SO 2 complexes in argon matrices

Transcription

1 THE JOURNAL OF CHEMICAL PHYSICS 125, Infrared spectra of the H 2 O n SO 2 complexes in argon matrices Shinichi Hirabayashi, a Fumiyuki Ito, and Koichi M. T. Yamada National Institute of Advanced Industrial Science and Technology (AIST), EMTech, AIST Tsukuba-West, Tsukuba , Japan Received 10 April 2006; accepted 23 May 2006; published online 20 July 2006 The infrared spectra of the H 2 O n SO 2 complexes trapped in argon matrices have been investigated using Fourier transform infrared spectroscopy. In addition to the 1:1 and 2:1 complexes, the first spectroscopic evidence for the 3:1 complex has been obtained from the spectra of the SO stretching and the OH stretching modes. The observed frequency shifts in the bonded OH stretching region indicate that the hydrogen bonds of the 2:1 and 3:1 complexes are strengthened compared to that of the 1:1 complex, which suggests the cyclic structure of the complexes American Institute of Physics. DOI: / I. INTRODUCTION a Author to whom correspondence should be addressed. Present address: East Tokyo Laboratory, Genesis Research Institute, Inc., Futamata, Ichikawa, Chiba , Japan. Electronic mail: hirabayashi@clusterlab.jp Water H 2 O and sulfur dioxide SO 2 are molecules of interest in atmospheric chemistry. In the atmosphere, SO 2 is oxidized to form SO 3, which produces H 2 SO 4 by a reaction with H 2 O. While the formation of H 2 O SO 3 complex is expected in this process, the H 2 O SO 2 complex is considered to be less important because of its low binding energy. 1 Nevertheless, this complex is of considerable interest for understanding the intermolecular interaction and hydration process. Infrared spectroscopic studies of the H 2 O SO 2 1:1 complex were performed previously in N 2 and Ar matrices. 2,3 The infrared spectrum of the complex was also obtained by the photo-oxidation of H 2 SinO 2 matrices. 4 Because of the small shifts of the H 2 O fundamentals, Nord 2 proposed that H 2 O acts as a lone-pair donor toward SO 2. Schriver et al. 3 also concluded that the 1:1 complex is of charge transfer type with the oxygen atom of H 2 O acting as an electron donor. Shortly after that, Matsumura et al. 5 determined the gas phase geometry of the 1:1 complex by microwave spectroscopy: the double-decker orientation of the H 2 O and SO 2 molecular planes with the oxygen atom of H 2 O close to the sulfur atom of SO 2, which is consistent with the structure proposed by previous matrix studies. The charge transfer interaction of SO 2 with the oxygen atom of H 2 O is likely at the base of the known strong attachment of SO 2 to the ice surface. 6 In addition to the 1:1 complex, Schriver et al. 3 reported the infrared spectra of the H 2 O SO 2 1:2 and 2:1 complexes in Ar and N 2 matrices. For the 2:1 complex, they suggested the cyclic structure with two kinds of hydrogen bonded OH groups. No spectroscopic evidence for the existence of higher hydrates H 2 O n SO 2 n 2 were reported previously. We have reinvestigated the infrared spectra of the H 2 O n SO 2 complexes in Ar matrices with a higher spectral resolution in the present study than those applied in the previous matrix studies and detected the first spectroscopic evidence of the 3:1 complex. The spectral assignments are supported by quantum chemical calculations. II. EXPERIMENT AND CALCULATION The gas mixtures were prepared by standard manometric techniques. Water was distilled and degassed in a vacuum line. Ar Nippon Sanso, % and SO 2 Sumitomo Seika Chemicals, 99.9% were used without further purification. The Ar/H 2 O sample ratio was varied between 1000/2 and 1000/10, and the Ar/SO 2 ratio was varied between 1000/0.2 and 1000/1. The samples were deposited onto a gold-coated copper plate maintained at 25 K using a continuous-flow liquid-helium cryostat Oxford, Ultrastat. The deposition rate was adjusted to 2 mmol/h using a needle valve. Typical deposition time ranged from 30 to 90 min, depending on H 2 O concentration in the sample. Infrared spectra were measured at 25 K in a reflection mode using a JASCO 620 Fourier transform infrared FTIR spectrometer equipped with a liquid-n 2 -cooled mercury cadmium telluride MCT detector at resolutions of 0.25 and 0.5 cm 1, in the cm 1 region. The entire optical path was evacuated to avoid atmospheric absorption of H 2 O and CO 2. We have carried out ab initio calculations with the GAUSSIAN 98 program package. 7 The structures of H 2 O, H 2 O 2, SO 2, and H 2 O n SO 2 complexes with n=1 3 were fully optimized using the second order Møller-Plesset perturbation theory, 8,9 MP2 with the G 2d,2p basis set. The interaction energies were corrected for the basis set superposition error BSSE by the Boys-Bernardi full counterpoise correction. 10 Vibrational frequencies and intensities were predicted both for the monomers and complexes. III. OBSERVED INFRARED SPECTRA The infrared spectra of various Ar/H 2 O/SO 2 samples are shown in Figs The observed frequencies for the H 2 O n SO 2 complexes with n=1 3 are listed in Tables I III /2006/125 3 /034508/6/$ , American Institute of Physics

2 Hirabayashi, Ito, and Yamada J. Chem. Phys. 125, FIG. 1. Infrared absorption spectra recorded with 0.5 cm 1 resolution are reproduced in the OH stretching regions of H 2 O isolated in argon matrices: a Ar/H 2 O=1000/2, b Ar/H 2 O/SO 2 =1000/2/0.2, c Ar/H 2 O =1000/5, and d Ar/H 2 O/SO 2 =1000/10/0.2. The H 2 O SO 2 complex is indicated by 1:1, and the H 2 O n SO 2 complexes are marked by the asterisk. A. OH stretching region FIG. 3. Infrared absorption spectra recorded with 0.5 cm 1 resolution are reproduced in the OH bending region of H 2 O isolated in argon matrices: a Ar/H 2 O=1000/2, b Ar/H 2 O/SO 2 =1000/2/0.2, c Ar/H 2 O=1000/5, and d Ar/H 2 O/SO 2 =1000/10/0.2. The label indicated by 1:1 is assigned to the H 2 O SO 2 complex. In Ar matrices, the rovibrational lines of the H 2 O monomer have been well characterized in recent studies, 11,12 and the bonded OH stretching bands of the water clusters have been identified in our previous study. 13 The observed spectra in the OH stretching region are displayed in Fig. 1. Trace b presents the infrared absorption spectrum measured with the Ar/H 2 O/SO 2 =1000/2/0.2 sample, which should be compared with trace a of the pure water sample: Ar/H 2 O =1000/2. A comparison of the two reveals two additional lines appearing in trace b, at and cm 1. These lines are assigned to the H 2 O SO 2 1:1 complex as reported in literature. 3 By increasing the concentration of H 2 O, the absorptions due to the H 2 O n SO 2 n 1 complexes are expected to appear. In fact, in trace d of the Ar/H 2 O/SO 2 =1000/10/0.2 sample, which may be compared with trace c of the pure water sample, Ar/H 2 O =1000/5, several new features indicated by asterisks appear in addition to the 1:1 complex lines: the sharp lines at and cm 1 and the broad absorptions near 3481, 3443, and 3431 cm 1. In order to make the assignments certain for the absorption peaks of the H 2 O n SO 2 complex, we have inspected the infrared spectra of the Ar/H 2 O/SO 2 samples with higher SO 2 concentration as shown in Fig. 2. In the spectrum of the Ar/H 2 O/SO 2 =1000/2/1 sample see Fig. 2 a, numerous absorption peaks are observed in addition to the H 2 O monomer, dimer, and H 2 O SO 2 1:1 complex lines. Since the most intense band of H 2 O 3 near 3516 cm 1 is very weak in this spectrum, the formation of the H 2 O 3 SO 2 and higher hy- FIG. 2. Infrared absorption spectra recorded with 0.5 cm 1 resolution are reproduced in the OH stretching regions of H 2 O isolated in argon matrices: a Ar/H 2 O/SO 2 =1000/2/1 and b Ar/H 2 O/SO 2 =1000/5/1. The labels indicated by n:1 are assigned to the H 2 O n SO 2 complex. FIG. 4. Infrared absorption spectra recorded with 0.25 cm 1 resolution are reproduced in the SO stretching regions of SO 2 isolated in argon matrices: a Ar/SO 2 =1000/0.2, b Ar/H 2 O/SO 2 =1000/2/0.2, and c Ar/H 2 O/SO 2 =1000/10/0.2. The labels indicate the assignment: M, SO 2 monomer in the stable site; M *,SO 2 monomer in the metastable site; D, SO 2 dimer, m, 34 SO 2 monomer in the stable site; m * ; 34 SO 2 monomer in the metastable site; d, SO 2 34 SO 2 dimer; n:1, H 2 O n SO 2 complex.

3 H 2 O n SO 2 complexes in argon matrices J. Chem. Phys. 125, TABLE I. Observed and calculated frequencies cm 1, frequency shifts cm 1, and calculated intensities km/mol intensities are given in parentheses for the H 2 O SO 2 complex. The values of the monomers are given for comparison. Ar matrix Calc. Mode H 2 O a SO 2 H 2 O SO 2 H 2 O SO 2 H 2 O SO 2 H 2 O 3 OH str OH str HOH bend SO 2 3 SO str SO str SOS bend a Band origin taken from Ref. 12. drates can be safely neglected. Therefore new absorption lines observed in trace a of Fig. 2 are very likely of the H 2 O SO 2 1:n or 2:n complex. Among the five absorptions assigned to the H 2 O n SO 2 complex in Fig. 1 d, the two at and cm 1 clearly observed in Fig. 2 a are, therefore, assigned to the 2:1 complex, which is in good agreement with the previous work. 3 As shown in Fig. 2 b, the higher H 2 O concentration in the sample, Ar/H 2 O/SO 2 =1000/5/1, leads to the increase of the absorption intensity of the n:1 complex. The peak at cm 1 is most likely due to the 3:1 complex. The remaining two bands at 3443 and 3431 cm 1 lines are tentatively assigned to the bonded OH stretching modes of the 3:1 complex. The assignment will be discussed again in Sec. V A by comparison with the results of the ab initio calculation. In contrast to the bonded OH stretching region, the free OH stretching region between 3720 and 3680 cm 1 is obscured by the overlapping of the water cluster bands. The 3715 and 3695 cm 1 absorption lines become stronger with increasing H 2 O concentration, suggesting that they should be assigned to the 2:1 complex. B. OH bending region The observed spectra in the 2 OH bending region are displayed in Fig. 3, where the traces a d correspond to TABLE II. Observed and calculated frequencies cm 1, frequency shifts cm 1 shifts relative to the monomer values; in the case of the free and bonded OH stretching modes, the shifts were measured with respect to the 3 and 1 values respectively, and calculated intensities km/mol intensities are given in parentheses for the H 2 O 2 SO 2 complex. Mode Ar matrix Calc. H 2 -O 2 SO 2 H 2 O 2 SO 2 H 2 O Free OH str Free OH str Bonded OH str Bonded OH str HOH bend HOH bend SO 2 3 SO str SO str SOS bend those in Fig. 1. As shown in Fig. 3 b, a line at cm 1 is assigned to the H 2 O SO 2 1:1 complex. The observed frequency is in good agreement with literature. 3 In contrast to the OH stretching region, no additional absorption line is observed in the spectra of even higher H 2 O concentration, Fig. 3 d, probably due to the overlap of the strong water dimer band at cm 1. C. SO stretching region The infrared spectra of the SO 2 monomer and dimer in Ar matrices have been studied in detail previously In Fig. 4, trace a shows the infrared spectrum of pure SO 2 diluted in Ar. In the 3 antisymmetric stretching region, the absorptions at and cm 1 are assigned to the monomers trapped in the stable and metastable sites, respectively; they are indicated by M and M * for trace a on the left. The 1 symmetric stretching lines of SO 2 monomer are observed at cm 1 for the stable site and at cm 1 for the metastable site as indicated by M and M * for trace a on the right. The absorption lines due to the SO 2 dimer are indicated by D. The 34 SO 2 monomer lines appear on the low frequency side of the 32 SO 2 monomer TABLE III. Observed and calculated frequencies cm 1, frequency shifts cm 1 shifts relative to the monomer values; in the case of the free and bonded OH stretching modes, the shifts were measured with respect to the 3 and 1 values, respectively, and calculated intensities km/mol intensities are given in parentheses for the H 2 O 3 SO 2 complex. Ar matrix Calc. Mode H 2 O 3 SO 2 H 2 O 3 SO 2 H 2 O Free OH str Free OH str Free OH str Bonded OH str Bonded OH str Bonded OH str HOH bend HOH bend HOH bend SO 2 3 SO str SO str SOS bend

4 Hirabayashi, Ito, and Yamada J. Chem. Phys. 125, lines as indicated by m stable and m * metastable. The line indicated by d is assigned to the 32 SO 2 34 SO 2 complex. By adding a small amount of water to the Ar/SO 2 sample, Ar/H 2 O/SO 2 =1000/2/0.2, one new line appears in each SO 2 fundamental region, as shown in trace b of Fig. 4. The and cm 1 lines are assigned to the H 2 O SO 2 1:1 complex, in good agreement with the previous work. 3 For the sample with excess water, Ar/H 2 O/SO 2 =1000/10/0.2, two additional absorption lines are seen in each spectral region, together with the 1:1 complex, as shown by trace c of Fig. 4. These lines at and cm 1 in the 3 region and at and cm 1 in the 1 region are thus assigned to the H 2 O n SO 2 n 1 complexes. For the Ar/H 2 O/SO 2 =1000/2/1 sample not shown in figure, where the absorptions due to the 1:n and 2:n complexes are expected as mentioned in Sec. III A, the cm 1 line is barely observed while the cm 1 line is missing. We therefore assign the former to the 2:1 complex and the latter to the 3:1 complex. The 1 band position for the 2:1 complex is in good agreement with that in literature. 3 On the other hand, the two lines in the 3 region are disturbed by the overlap of the strong absorption lines of SO 2 dimer and 34 SO 2 monomer. The present experiments do not allow us to distinguish the lines of the 2:1 and 3:1 complexes. As will be discussed in Sec. V A, the present quantum chemical calculations indicate that the cm 1 line is assigned to the 2:1 complex and the cm 1 line to the 3:1 complex. We note that the 1339 cm 1 line in the 3 region, which was assigned to the 2:1 complex by Schriver et al., 3 is not observed in our spectrum, even at high H 2 O concentration sample. IV. STRUCTURES OF THE COMPLEXES Figure 5 shows the optimized structures of H 2 O, SO 2, H 2 O 2, and the H 2 O n SO 2 complexes with n=1 3 at the MP2 level with the G 2d,2p basis set, together with the geometrical parameters. The H 2 O SO 2 1:1 complex has a double-decker-type structure with C s symmetry, in which the oxygen atom of H 2 O is bound to the sulfur atom, and both the H 2 O and SO 2 subunits maintain their local C 2v symmetry. The structural parameters of H 2 O and SO 2 essentially remain unchanged upon complex formation. This optimized structure is in good agreement with those obtained by previous microwave spectroscopy 5 and calculations. 1,17,18 The binding energy of the H 2 O SO 2 complex is calculated to be 3.3 kcal/mol which is smaller than that of the H 2 O dimer 4.5 kcal/mol. To our knowledge, the investigations concerning the structure of the H 2 O 2 SO 2 complex are limited to one experimental study 3 and two quantum chemical calculations. 17,18 Schriver et al. 3 concluded that, based on the observed OH stretching frequencies, there are two kinds of bonded OH groups and suggested the cyclic structure. One of the bonded OH stretching bands of the 2:1 complexes is largely redshifted by 90 cm 1 with respect to the corresponding band of the H 2 O dimer, which we have confirmed in the present study. FIG. 5. Optimized structures of H 2 O, H 2 O 2,SO 2,and H 2 O n SO 2 with n=1 3 are shown schematically. The bond lengths and distances between atoms are in angstroms and the bond angles in degrees. We have carried out the structural optimization of the 2:1 complex assuming the cyclic structure in analogy with the water trimer H 2 O The optimal structure obtained in the present calculation is essentially identical to that reported by Li and McKee. 18 The binding energy of the 2:1 complex is calculated to be 11.0 kcal/mol, which is about three times larger than that of the 1:1 complex. This large binding energy is reflected in the geometrical parameters. As shown in Fig. 5, the nuclear distance of the hydrogen bonded O H in the H 2 O 2 subunit is slightly elongated by Å while the O H separation is largely shortened by Å, with respect to the corresponding ones of the H 2 O dimer. As a result, the O O separation between two water molecules is shortened by 0.1 Å, which indicates the strong cooperative effect of the hydrogen bond in the H 2 O 2 subunit upon complex formation. The S O separation between H 2 O and SO 2 molecules is also shorter by Å than the corresponding one in the 1:1 complex. For predicting the structure of the H 2 O 3 SO 2 complex, we limited ourselves to the cyclic structure on the basis of the following experimental facts: 1 three absorptions possibly due to this complex are observed in the bonded OH

5 H 2 O n SO 2 complexes in argon matrices J. Chem. Phys. 125, TABLE IV. Observed and calculated frequency shifts cm 1 for the H 2 O n SO 2 complexes with respect to the frequency of the H 2 O SO 2 1:1 complex. Mode H 2 O 2 SO 2 H 2 O 3 SO 2 Ar matrix Calc. Ar matrix Calc. H 2 O Bonded OH str Bonded OH str Bonded OH str SO 2 3 SO str SO str stretching region and 2 the two lines of these show large redshifts compared to the water trimer and 2:1 complex. As shown in Fig. 5, the optimized structure is similar to that of the water tetramer H 2 O The binding energy of this complex is calculated to be 19.5 kcal/ mol. The nuclear distances of the hydrogen bonded O H are longer than the corresponding ones in the 2:1 complex, which suggests strong cooperative effect. The O O separations between the H 2 O molecules are Å, slightly shorter than that in the 2:1 complex 2.82 Å. In addition, the formation of the cyclic structure results in the shortening of the S O and O O separations between the SO 2 and H 2 O molecules with respect to the corresponding ones in the 2:1 complex. V. DISCUSSION A. Comparison of the experimental results and calculated data The frequencies predicted from the ab initio calculation for the H 2 O n SO 2 n=1 3 complexes are listed in Tables I III. For the SO stretching modes, the present calculations indicate monotonic blueshifts for the 1 lines and monotonic redshifts for the 3 lines, with the increase of the number of water molecules, as listed in Table IV. We have thus assigned the cm 1 line to the 2:1 complex and the cm 1 line to the 3:1 complex, which cannot be distinguished experimentally. As expected, the calculation of the cyclic H 2 O 3 SO 2 complex predicts three strong bands in the bonded OH stretching region see Table III. We assigned first the observed cm 1 band to the highest frequency one of the three. By this correspondence we obtain the frequency scaling factor of The band positions of the two lower frequency bands are then predicted to be 3443 and 3372 cm 1 by multiplying the scaling factor. For the 3443 cm 1 band, we have two candidates in the observed spectra, i.e., 3443 and 3431 cm 1. Only one of them can be assigned to the line. Because of the good agreement with the scaled harmonic frequency we assign tentatively the 3443 cm 1 band to the H 2 O 3 SO 2 complex. To the band predicted at 3372 cm 1, a weak but broad shoulder observed at 3361 cm 1 see Fig. 2 b is assigned. The observed and calculated frequency shifts with respect to the H 2 O and SO 2 monomers are also listed in Tables I III, for the H 2 O n SO 2 complexes with n=1 3. They show a good qualitative agreement for the OH stretching and bending modes of all the complexes, although the calculated frequency shifts are slightly overestimated. The agreements for the H 2 O subunits support the present assignments for the 1:1, 2:1, and 3:1 complexes. On the contrary, the calculated line positions agree only poorly with the observed ones for the SO 2 subunit. In particular, the observed frequencies of the 1:1 complex are redshifted from the monomer values while the calculated frequencies show the blueshifts. As noted in recent studies on the H 2 O 2 SO 2 complex, 20 this discrepancy may be caused by the insufficient inclusion of the electron correlation and incompleteness of the G 2d,2p basis set to describe the SO 2 monomer. In addition, we have to point out that the frequency shifts due to the complex formation cannot be derived correctly from the experimental spectra because SO 2 monomers isolated in Ar matrices show several absorption lines due to the site effect. Nevertheless, if we take the 1:1 complex as the reference, the calculated frequency shifts show good qualitative agreement with the experimental shifts not only for the bonded OH stretching modes but also for the SO stretching modes, as shown in Table IV. The agreements support the assignments and structures of the 2:1 and 3:1 complexes presented here. B. Larger complexes The infrared spectra of the H 2 O n SO 2 n=2 and 3 complexes exhibit the significant redshifts of the bonded OH stretching and SO 2 3 bands and blueshift of SO 2 1 band, with the increase of the number of water molecules in the complex. However, the present matrix spectra show no unambiguous features of the larger complex, H 2 O n SO 2 n 3, even for the samples with high H 2 O concentration, except for the unassigned 3431 cm 1 line. Underlying broad absorption bands are observed in the region of each SO stretching mode; one near 1343 cm 1 in the 3 band region is degraded to red, while another in the 1 band region is nearly symmetric with a peak at 1154 cm 1. These band profiles resemble those in the spectrum of SO 2 trapped in water ice, rather than crystalline SO In addition, the peak positions of the broadbands are closer to those of the SO 2 clathrate hydrate than those of SO 2 in liquid phase, in solid phase, in aqueous solution, and in water ice. 22,23 The absence of the absorption line due to the larger complexes were also reported in the Ar matrix studies of the H 2 O n HNO 3 complexes by McCurdy et al. 24 They interpreted the phenomenon, with the aid of ab initio calculations, as a result of the ionization of HNO 3 in water clusters, which occurs for clusters with n 3. Although we could not find out the previous calculation on the hydrolysis reaction of SO 2 in H 2 O n clusters with n 2, the analogous system, H 2 O n SO 3, is predicted to form the ion-pair structure for n=4 with little or no energy barrier. 25 We thus presume that the infrared features of ions such as HOSO 2 and HSO 3 reported in SO 2 aqueous solutions 22 appear at high H 2 O concentration in matrix environments. However, since the corresponding bands have not been identified in the present Ar

6 Hirabayashi, Ito, and Yamada J. Chem. Phys. 125, matrix, the formation of the ion pair is very unlikely to occur for SO 2 in small water clusters. VI. CONCLUSIONS We have investigated the infrared spectra of the H 2 O n SO 2 complexes trapped in Ar matrices. The concentration dependence confirms the identification for the H 2 O SO 2 1:1 complex, the frequencies of which are in excellent agreement with those reported in the previous study. 3 For the H 2 O 2 SO 2 complex, several bands are reassigned or newly assigned. In addition, the first spectroscopic evidence for the H 2 O 3 SO 2 complex has also been presented in the SO stretching and OH stretching regions. One of the bonded OH stretching bands of the 2:1 complex is significantly redshifted from the corresponding band of the water dimer, suggesting that the hydrogen bond within the H 2 O 2 subunit is strengthened by the formation of the cyclic structure upon complex formation. Similarly, we speculate the cyclic structure for the 3:1 complex on the basis of the experimental spectra. The spectral assignments and structures of the H 2 O n SO 2 complexes with n=1 3 trapped in Ar matrices are supported by ab initio calculations. ACKNOWLEDGMENTS We thank Professor K. Shibuya and Dr. K. Tsuji for supplying us the results of their independent observation of H 2 O SO 2 1:1 complex prior to publication. 1 E. Bishenden and D. J. Donaldson, J. Phys. Chem. A 102, L. J. Nord, J. Mol. Struct. 96, A. Schriver, L. Schriver, and J. P. Perchard, J. Mol. Spectrosc. 127, T.-L. Tso and E. K. C. Lee, J. Phys. Chem. 88, K. Matsumura, F. J. Lovas, and R. D. Suenram, J. Chem. Phys. 91, L. Delzeit, J. P. Devlin, and V. Buch, J. Chem. Phys. 107, M. J. Frisch, G. W. Trucks, H. B. Schlegel et al., GAUSSIAN 98, Revision A.9, Gaussian, Inc., Pittsburgh, PA, C. Møller and M. Plesset, Phys. Rev. 46, J. S. Binkley and J. A. Pople, Int. J. Quantum Chem. 9, S. F. Boys and F. Bernardi, Mol. Phys. 19, J. P. Perchard, Chem. Phys. 273, X. Michaut, A.-M. Vasserot, and L. Abouaf-Marguin, Vib. Spectrosc. 34, S. Hirabayashi and K. M. T. Yamada, J. Chem. Phys. 122, J. W. Hastie, R. Hauge, and J. L. Margrave, J. Inorg. Nucl. Chem. 31, D. Maillard, M. Allavena, and J. P. Perchard, Spectrochim. Acta, Part A 31, L. Schriver-Mazzuoli, A. Schriver, and M. Wierzejewska-Hnat, Chem. Phys. 199, P. L. M. Plummer, J. Mol. Struct.: THEOCHEM 307, W.-K. Li and M. L. McKee, J. Phys. Chem. A 101, S. S. Xantheas and T. H. Dunning, Jr., J. Chem. Phys. 99, S. Pehkonen, J. Lundell, L. Khriachtchev, M. Pettersson, and M. Räsänen, Phys. Chem. Chem. Phys. 6, A. A. Vigasin, L. Schriver-Mazzuoli, and A. Schriver, J. Mol. Struct. 658, Z. Zhang and G. E. Ewing, Spectrochim. Acta, Part A 58, Z. Zhang and G. E. Ewing, J. Phys. Chem. A 108, P. R. McCurdy, W. P. Hess, and S. S. Xantheas, J. Phys. Chem. A 106, L. J. Larson, M. Kuno, and F.-M. Tao, J. Chem. Phys. 112,