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IR spectra of hydrogen bonding of H2S doped in Kr solids
Chemical Physics 285 (2002) 319–326 www.elsevier.com/locate/chemphys
IR spectra of hydrogen bonding of H2S doped in Kr solids Hideji Tsujii, Kenji Takizawa, Seiichiro Koda * Department of Chemical System Engineering, School of Engineering, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-8656, Japan Received 23 April 2002
Abstract Infrared spectra of H2 S doped in Kr solids were obtained by Fourier transform infrared spectroscopy in the region of hydrogen bonding and interpreted on the basis of ab initio density functional theory calculations. Experimentally observed absorption peaks were assigned to a monomer, dimer, and trimer based on the intensity–dilution ratio relationships. The dimer produces a strong absorption at 2575 cm1 and appears to involve at least two weak absorptions in the region of the monomer bands. The ab initio calculation revealed that the dimer has an almost linear form in the gas phase. One H atom is donated from one H2 S molecule and is accepted by the S atom of the other H2 S molecule by hydrogen bonding. A similar structure is expected in Kr solids. The absorption intensity corresponding to the stretching of the hydrogen bond is significantly enhanced and is responsible for the strong peak at 2575 cm1 . An isotope peak was also observed at 2.1 cm1 below this strong peak in accordance with the ab initio calculations. The experimentally observed peak at 2566 cm1 was assigned to the stretching of hydrogen bonds in the trimer. Ó 2002 Elsevier Science B.V. All rights reserved. Keywords: IR spectra; H2 S dimer; Kr solids; Hydrogen bonding; DFT calculation
1. Introduction Analysis of hydrogen bonding in aggregates of small H2 X (X ¼ O, S) molecules is important in understanding phenomena such as solvent effects in the condensed phase. Hydrogen bonding in these aggregates is very strong and the infrared (IR) absorption of vibrations related to the hydrogen bonds sometimes shift markedly and change in
*
Corresponding author. Tel.: +81-3-5841-7327; fax: +81-35841-7255. E-mail address: [email protected] (S. Koda).
intensity. The molecule H2 S aggregates very easily in low-temperature matrices to yield oligomers such as dimers and trimers. The quantitative behavior of the hydrogen bonding of H2 S, however, is not yet fully understood despite extensive work on H2 O trapped in matrices [1]. Indeed, the assignment of IR absorption in the stretching vibration region of H2 S in matrices has remained highly ambiguous [2,3]. The objective of the present work is to determine the mechanism of shift and intensity change attributable to the hydrogen bonding state in oligomers of H2 S in rare gas solids. In the authorsÕ previous report [2,4], the rotational structure of the m3 band of monomer H2 S
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with some contribution of the m1 band was suggested to appear in the range 2640–2600 cm1 when doped in a free-standing Kr crystal and the sharp peak at 2575 cm1 was assigned to the hydrogen bonds of dimer ðH2 SÞ2 . Rotational analysis of the monomer band has not been conclusive [2,3], and there remains some controversy concerning the relative importance of m1 and m3 . The present work does not intend to argue the assignment of the monomer rotational structure, but rather focuses on discussing the hydrogen bonding state in dimer and other oligomer aggregates in Kr free-standing crystals. Although the hydrogen bonding in a dimer ðH2 SÞ2 has been discussed on the basis of ab initio calculations [5,6], the calculation has not been extensive nor have the results been compared with experiments using matrices. In the present study, the authors measured the intensity changes of several representative IR peaks as a function of the dilution ratio of H2 S in solids (1=2000–1=20; 000), from which the relevant number of H2 S units in the oligomer was estimated. Conventional density functional theory (DFT) calculations for H2 S oligomers (in the gas phase and in Kr solids) were performed to obtain IR absorption bands and the corresponding crosssections. By comparing the measurements and calculations, the hydrogen bonding state is found
to affect the position of absorption bands remarkably, as well as the absorption intensity. The effect of the surrounding rare gas atoms in the solid on the IR shifts is also discussed.
2. Experimental and calculations 2.1. Experimental The experimental procedure is based on the method described previously [2]. Briefly, freestanding Kr crystals of cubic structure with a volume of 1 cm3 and an optical length of 1 cm containing small amounts of H2 S (H2 S=Kr ¼ 1= 2000–1=20; 000) were prepared and maintained at 17 K on a copper cryotip. The cryotip was housed in a vacuum chamber with two BaF2 windows on opposite sides of the chamber for spectroscopic access. Commercial gases obtained in cylinders were used as purchased: the nominal purity was 99.5% for H2 S, and 99.995% for Kr. The vacuum chamber containing the freestanding crystal was set in the sample holder of a Fourier transform infrared (FTIR) spectrometer (FTIR System 2000, Perkin–Elmer). IR absorption measurements were performed with a resolution of 0:5–1:0 cm1 .
Fig. 1. Geometry of Kr solid atoms for monomer (a) and dimer (b): the illustration roughly draws the optimized structures.
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2.2. Calculations The monomer H2 S, oligomers of H2 S and H2 Sdoped Kr solid models, were calculated using B3LYP with Gaussian 98. The basis functions employed for H and S were 6-311G(3d,3p) in consideration of previous calculations [6]. Due to a limitation on computational resources, the 3-21G basis function was adopted for Kr. The IR frequency and absorption cross-section were calculated against the obtained structures as shown below. The calculation was performed for monomer H2 S, dimer ðH2 SÞ2 and trimer ðH2 SÞ3 , monomer H2 S surrounded by 12 Kr atoms, and dimer ðH2 SÞ2 surrounded by 18 Kr atoms. In the latter two cases, H2 S and ðH2 SÞ2 are assumed to substitute into the fcc lattice for Kr atoms. The surrounding Kr atoms in the calculation are those in the nearest neighbor positions with respect to the doped molecule. The geometries for the monomer and dimer are illustrated in Fig. 1. The central planes for Kr atoms in Figs. 1(a) and (b) correspond to the (1 1 1) plane, pffiffiffiand the distance d in Fig. 1(b) corresponds to 1= 3 of the lattice constant a. In the case of H2 S, ðH2 SÞ2 and ðH2 SÞ3 , complete optimization of the structure was performed, while in the case of the model Kr solids, the H2 S structure of the monomer and dimer, as well as the size of the lattice cage (represented by d in Fig. 1), were optimized, but the relative geometry of the individual Kr atoms was fixed at that in the initial lattice.
3. Results 3.1. Dimer and oligomer IR bands A typical IR absorption spectrum of H2 S doped in a free-standing Kr crystal at a dilution ratio of 1/6000 at 17 K is shown in Fig. 2. The wavenumbers of several peaks are listed in Table 1. Most of the peaks in the range 2600–2640 cm1 (enlarged in the inset) correspond to the rotational structure of monomer H2 S as previously discussed [2,3], which will not be argued at present. The important point to note is that these peaks are contaminated
Fig. 2. IR spectrum of ðH2 SÞx doped in Kr solids with the dilution ratio of 1/6000 measured at 17 K.
Table 1 Peak positions of IR spectra at 17 K and slope of the intensity vs. dilution ratio curve Peak No.
Frequency (cm1 )
Slope
a b c d e f
2636 2618 2613 2575 2566 2549
0.9 2.5 1.9 1.8 2.6 2.7
by contributions from dimer and/or oligomer peaks as will be discussed later. The peaks between 2500 and 2580 cm1 have been tentatively assigned to oligomers, and in particular, peak d has been assigned to a dimer. The monomer rotational structure peaks broaden and coalesce with increasing temperature as shown in Fig. 3 (25 K). On the contrary, several peaks including b and c in the region 2610–2620 cm1 and strong peaks d, e and f below 2580 cm1 remain largely unchanged with variations in temperature. Eventually, peaks d–f shift slightly to larger wavenumbers with increasing temperature. The small peaks in the neighborhood of 2575 and 2566 cm1 could be isolated more clearly from the stronger peaks when observed at 0.25 cm1 resolution, as shown in Fig. 4. Peak d occurs at 2575.3 cm1 , while d 0 is located at 2573.2 cm1 . The relative intensity of these peaks, 1:0.04 independent of the dilution ratio, strongly suggests that the satellite peak is an isotope peak
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Fig. 3. IR spectrum of ðH2 SÞx doped in Kr solids with the dilution ratio of 1/6000 measured at 25 K.
Fig. 5. The relative IR peak area of a–f peaks vs. dilution ratio measured at 17 K: a (d), b (s), c (M), d (O), e (), and f (}).
Fig. 4. IR spectrum of ðH2 SÞx doped in Kr solids with the dilution ratio of 1/6000 measured at 17 K below 2600 cm1 with the higher resolution of 0.25 cm1 .
due to 34 S. This assignment will be discussed later on the basis of ab initio calculations. The relative peak intensities (i.e. absorbance) of individual peaks changed with the dilution ratio, and the dependence is illustrated in Fig. 5. The approximate value of the slope was measured in the region of dilution ratio below 104 , and the result is given in Table 1. The slope of peak intensity vs. dilution ratio at 2636 cm1 (peak a) is 0.9, which supports the peak assignment as a monomer. Peak d can be assigned to a dimer, while e and f are attributed to a trimer, although the possibility of assignment to other higher oligomers cannot be neglected. The assignment of peak d to a dimer is in accordance with our previous work [2] and work by Isoniemi et al. [3].
The assignment of peak e to a trimer is also in accordance with the tentative assignment by Isoniemi et al. [3]. Peaks b, c and several smaller peaks between 2610 and 2620 cm1 remain as isolated peaks at higher temperature as shown in Fig. 3. This clearly shows that the IR absorptions in this region are not originating from a monomer alone. That is, the peaks can be assigned to dimers, trimers and/or higher oligomers. However, as these peaks are not completely isolated from each other, the estimated slope of intensity vs. dilution ratio for individual peaks in this region is not conclusive. 3.2. DFT calculations for optimum dimer structure The dimer structure optimized in the present work is illustrated in Fig. 6. One H2 S molecule (PD: proton donor) donates a hydrogen bond to the S atom of another H2 S molecule (PA: proton acceptor). The internuclear distance R between the S atoms, and the angles characterizing the dimer structure /1 and /2 , are around the same as those determined by de Oliveira and Dykstra [6]. The optimized structures of the H2 S-Kr solid and ðH2 SÞ2 -Kr solid were shown in Fig. 1. The geometries and characteristic length d of the calculated lattice are listed in Table 2.
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dimer in the gas phase has a symmetry plane containing two S atoms and the two H atoms of the PD, while in the dimer in the Kr solid, the H atom, No. 4 in Fig. 1(b) of the PD is twisted slightly from the plane in order to direct the H4–S2 bond toward the center of the triangle made by Kr1, Kr2 and Kr5 atoms. 3.3. Calculated IR spectra and comparison with experiments Fig. 6. Geometry of ðH2 SÞ2 dimer.
Table 2 Calculated dimer equilibrium geometry
R/nm /1 /deg /2 /deg db
In gas phase
Lit.a
In Kr solids
0.421 95.7 2.3 –
0.411 92.2 5.6 –
0.426 90.2 0.2 0.340
a
Literature value from [6] with the largest basis V/MP2. Lattice distance: for the experimental Kr lattice at 15 K, 0.321 nm, for the calculated lattice containing a monomer H2 S, 0.342 nm. b
The optimum structure of an H2 S unit in the dimer (both in the gas phase and in the Kr solid) is almost unchanged from that of the monomer H2 S in the gas phase (bond length, 0.134 nm; bond angle, 92.4°). The only change is the elongated H– S distance of the PD for the hydrogen bond in the dimer (both in the gas phase and in the Kr solid), by ca. 0.0003 nm from the monomer value. The
As the IR absorption intensity of the bending vibration at 1183 cm1 in the gas phase [7] was very weak in both the experimental and calculated vibrational spectra, this bending motion is not included in the discussion of the structure of H2 S oligomers. Thus, the region of the stretching vibration is examined in detail. The calculated frequency and absorption intensity (relative value) are listed in Table 3. The tabulated frequencies are calculated values that have been corrected by a magnification factor (0.9718) so as to give coincidence between the average gas phase monomer m3 ð2628 cm1 Þ and m1 ð2614 cm1 Þ [8,9] and the calculated value. The dimer vibrations are shown schematically in Fig. 6, with arrows indicating the two normal modes localized in the PD. The vibrations localized in the PA are similar to the normal modes of monomer H2 S. Interestingly, one of the vibrations of the PD, m1 , is shifted remarkably to smaller wavenumbers and IR intensity is significantly enhanced. This enhancement is predicted to occur when H2 S is the donor molecule, presumably a consequence of the very low-infrared intensities in
Table 3 Calculated peak position and relative intensity of IR absorption In gas phase
In Kr solids 1
Position (cm ) Monomer Dimer
PA PD
m3 m1
2628.1 2614.8
m3 m1 m3 m1
2625.1 2611.1 2622.2 2569.9
Intensity 0.025 0.031 0.48 0.16 1.61 82.65
Position (cm1 )
Intensity
2632.9 2616.7
8.96 4.60
2614.2 2600.8 2629.2 2577.0
9.45 8.11 8.51 71.43
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the unperturbed molecule. The other three vibrations of the dimer appear in the region between 2610 and 2630 cm1 . These peaks are weaker than that of PD m1 , although enhanced compared to those for monomer H2 S. When the monomer is surrounded by the model Kr solid atoms, the absorption intensity increases. This is also the case in the three modes of the dimer other than PD m1 . The absorption frequencies are also shifted to some extent from that given by the gas-phase calculation. However, the intensity of the dimer PD m1 is similar to that of the gasphase dimer, probably due to the fact that the hydrogen bonding is concealed inside the dimer structure and does not interact strongly with the Kr solid atoms. The calculated absorption peaks for the gasphase monomer and dimer are illustrated in Fig. 7, and those for the monomer and dimer surrounded by Kr solid atoms are shown in Fig. 8. The strong experimental absorption at 2575 cm1 is reproduced well by the calculated dimer PD m1 band, both in the gas-phase and Kr-solid dimer calculations. The relatively weak dimer bands around 2620 cm1 corresponding to c and/or nearby weaker peaks appear to have been reproduced approximately by the gas-phase and Kr-solid dimer calculations. Unfortunately, the agreement is not satisfactory, and reliable peak-by-peak assignment is not possible due to the difficulty of calculating the dimer in the solid using the present
Fig. 7. Calculated IR spectra of an equimolar mixture of monomer and dimer in the gas phase: monomer peaks (filled bars), and dimer peaks (hatched bars).
Fig. 8. Calculated IR spectra of an equimolar mixture of monomer and dimer in the Kr solids: monomer peaks (filled bars), and dimer peaks (hatched bars).
simplified model of the crystal lattice. The interaction between the surrounding Kr atoms and the guest molecule may therefore not be reasonably described by the present model. However, it is important to note that the solid model peaks are usually at larger wavenumbers compared to the gas-phase peaks. This may imply that the surrounding Kr atoms suppress the free motion of guest molecules. The small increase in the absorption intensity of the S–H stretching vibration may be due to the polar character of Kr atoms. Although the present calculations are limited, we can conclude with confidence that some experimentally observed peaks in the monomer region are attributable to a dimer and/or higher oligomers. The satellite band at 2573.2 cm1 is assignable to the dimer containing 34 S in the PD. The calculated difference between the position of absorption peaks is 2.2 cm1 (2577.0–2574.8 cm1 ), which is in good agreement with the experimental difference of 2.1 cm1 (2575.3–2573.2 cm1 ). The experimental intensity ratio is 1:0.04, which is also in accordance with the isotope abundance ratio of 1:0.044. The optimum structure of the gas-phase trimer ðH2 SÞ3 was also calculated. The structure was found to be an almost planar triangle as shown in Fig. 9, which is the same as derived for the ðH2 OÞ3 trimer in recent calculations [10,11]. The absorption peaks are illustrated in Fig. 10 together with
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Fig. 9. Optimized structure of calculated ðH2 SÞ3 in the gas phase: the three S atoms approximately form an equilateral triangle. The S atoms and the three equatorial H atoms are approximately on one common plane. One of the three axial H atoms directs downwards and the other two, upwards.
ture, and several additional peaks may indeed be present in the range 2550–2570 cm1 . The experimentally observed peaks at 2566 cm1 (e), 2549 cm1 ( f ) and several peaks in the vicinity of 2620 cm1 such as peak b may be reasonably assigned to certain trimers and/or higher oligomers.
4. Discussion
Fig. 10. Calculated IR spectra of an equimolar mixture of monomer, dimer and trimer in the gas phase: monomer peaks (filled bars), dimer peaks (hatched bars), and trimer peaks (cross-hatched bars).
those for H2 S and ðH2 SÞ2 . Calculations for the gas-phase trimer surrounded by Kr atoms were not performed due to the complexity of numerical calculation. The actual structure in the experimental Kr solid may not be limited to one struc-
The IR absorption of hydrogen bonds inside the oligomer structure have been found to be typically very strong and to be located in the lowfrequency region around 2550 cm1 . As previously stated by Amos [5], the quantitative feature exhibited by H2 S and H2 O clusters is that the peak position of acceptor molecules are perturbed only slightly, whereas the positions of stretching vibrations for the donor molecule shift to significantly lower wavenumbers. This trend has been also held true for rare gas matrices. In early research on H2 S spectra in rare gas matrices, the only features commonly observed
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were a broad absorption in the range 2500–2600 cm1 and a trace absorption above 2600 cm1 . It is now understandable why the monomer peaks could not be identified: the monomer peaks were simply too weak compared to the stronger absorption peaks of oligomers or aggregates in the lower-wavenumber region to be detected by early techniques. Moreover, molecules such as H2 S are considered to aggregate readily. In the present work, the analysis of the effect of solid rare gas atoms on the doped H2 S monomer and oligomers was performed using a model in which the solid Kr atoms were fixed to resemble the real fcc Kr lattice, and the center Kr atom was replaced with H2 S. Using this model, only the lattice plane distance was optimized. This type of structure should differ from the isolated clusters in the gas phase. de Oliveira and Dykstra [12] recently showed the minimum-energy structure of Ar16 –H2 S, using rigid body diffusion quantum Monte Carlo calculations, to be a closed structure in which Ar atoms completely surround a central H2 S molecule. This is the case when free boundary conditions are used. It remains uncertain whether such a local minimum structure also occurs in matrices, and at present there are no reports dealing with the vibrational analysis of H2 S inside a local minimum cluster. 5. Conclusion An H2 S dimer doped in a Kr solid produces a strong absorption peak at 2575 cm1 , which is assigned to the PD m1 mode. The dimer is also
responsible for several unassigned peaks in the monomer region. The absorption intensity of the PD m1 mode was found to be significantly enhanced due to intermolecular hydrogen bonding.
Acknowledgements This work was supported by a Grant-in-Aid for Scientific Research (A) from the Ministry of Education, Science, Sports and Culture of Japan (No. 12305051), for which the authors are very grateful.
References [1] J.P. Perchard, Chem. Phys. 273 (2001) 217. [2] K. Koga, A. Takami, S. Koda, Chem. Phys. Lett. 293 (1998) 180. [3] E. Isoniemi, M. Pettersson, L. Khriachtchev, J. Lundell, M. Raesaenen, J. Phys. Chem. 103 (1999) 679. [4] S. Koda, K. Koga, K. Takizawa, Y. Ihara, A. Takami, Chem. Phys. 274 (2001) 283. [5] R.D. Amos, Chem. Phys. 104 (1986) 145. [6] G. de Oliveira, C.E. Dykstra, Chem. Phys. Lett. 243 (1995) 158. [7] O. Ulenikov, G.A. Onopenko, M. Koivusaari, S. Alanko, R. Antila, J. Mol. Spectrosc. 176 (1996) 229. [8] L. Lechuga-Fossat, J.-M. Flaud, C. Camy-Peyret, J.W.C. Johns, Can. J. Phys. 62 (1984) 1889. [9] L.R. Brown, J.A. Crisp, D. Crisp, O.V. Naumenko, M.A. Smirnov, L.N. Sinitsa, A. Perrin, J. Mol. Spectrosc. 188 (1998) 148. [10] T.-L. Tso, E.K.C. Lee, J. Phys. Chem. 89 (1985) 1612. [11] H.M. Lee, S.B. Suh, J.Y. Lee, P. Tarakeshwar, K.S. Kim, J. Chem. Phys. 112 (2000) 9759. [12] G. de Oliveira, C.E. Dykstra, Chem. Phys. Lett. 264 (1997) 85.
IR spectra of hydrogen bonding of H2S doped in Kr solids Hideji Tsujii, Kenji Takizawa, Seiichiro Koda * Department of Chemical System Engineering, School of Engineering, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-8656, Japan Received 23 April 2002
Abstract Infrared spectra of H2 S doped in Kr solids were obtained by Fourier transform infrared spectroscopy in the region of hydrogen bonding and interpreted on the basis of ab initio density functional theory calculations. Experimentally observed absorption peaks were assigned to a monomer, dimer, and trimer based on the intensity–dilution ratio relationships. The dimer produces a strong absorption at 2575 cm1 and appears to involve at least two weak absorptions in the region of the monomer bands. The ab initio calculation revealed that the dimer has an almost linear form in the gas phase. One H atom is donated from one H2 S molecule and is accepted by the S atom of the other H2 S molecule by hydrogen bonding. A similar structure is expected in Kr solids. The absorption intensity corresponding to the stretching of the hydrogen bond is significantly enhanced and is responsible for the strong peak at 2575 cm1 . An isotope peak was also observed at 2.1 cm1 below this strong peak in accordance with the ab initio calculations. The experimentally observed peak at 2566 cm1 was assigned to the stretching of hydrogen bonds in the trimer. Ó 2002 Elsevier Science B.V. All rights reserved. Keywords: IR spectra; H2 S dimer; Kr solids; Hydrogen bonding; DFT calculation
1. Introduction Analysis of hydrogen bonding in aggregates of small H2 X (X ¼ O, S) molecules is important in understanding phenomena such as solvent effects in the condensed phase. Hydrogen bonding in these aggregates is very strong and the infrared (IR) absorption of vibrations related to the hydrogen bonds sometimes shift markedly and change in
*
Corresponding author. Tel.: +81-3-5841-7327; fax: +81-35841-7255. E-mail address: [email protected] (S. Koda).
intensity. The molecule H2 S aggregates very easily in low-temperature matrices to yield oligomers such as dimers and trimers. The quantitative behavior of the hydrogen bonding of H2 S, however, is not yet fully understood despite extensive work on H2 O trapped in matrices [1]. Indeed, the assignment of IR absorption in the stretching vibration region of H2 S in matrices has remained highly ambiguous [2,3]. The objective of the present work is to determine the mechanism of shift and intensity change attributable to the hydrogen bonding state in oligomers of H2 S in rare gas solids. In the authorsÕ previous report [2,4], the rotational structure of the m3 band of monomer H2 S
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with some contribution of the m1 band was suggested to appear in the range 2640–2600 cm1 when doped in a free-standing Kr crystal and the sharp peak at 2575 cm1 was assigned to the hydrogen bonds of dimer ðH2 SÞ2 . Rotational analysis of the monomer band has not been conclusive [2,3], and there remains some controversy concerning the relative importance of m1 and m3 . The present work does not intend to argue the assignment of the monomer rotational structure, but rather focuses on discussing the hydrogen bonding state in dimer and other oligomer aggregates in Kr free-standing crystals. Although the hydrogen bonding in a dimer ðH2 SÞ2 has been discussed on the basis of ab initio calculations [5,6], the calculation has not been extensive nor have the results been compared with experiments using matrices. In the present study, the authors measured the intensity changes of several representative IR peaks as a function of the dilution ratio of H2 S in solids (1=2000–1=20; 000), from which the relevant number of H2 S units in the oligomer was estimated. Conventional density functional theory (DFT) calculations for H2 S oligomers (in the gas phase and in Kr solids) were performed to obtain IR absorption bands and the corresponding crosssections. By comparing the measurements and calculations, the hydrogen bonding state is found
to affect the position of absorption bands remarkably, as well as the absorption intensity. The effect of the surrounding rare gas atoms in the solid on the IR shifts is also discussed.
2. Experimental and calculations 2.1. Experimental The experimental procedure is based on the method described previously [2]. Briefly, freestanding Kr crystals of cubic structure with a volume of 1 cm3 and an optical length of 1 cm containing small amounts of H2 S (H2 S=Kr ¼ 1= 2000–1=20; 000) were prepared and maintained at 17 K on a copper cryotip. The cryotip was housed in a vacuum chamber with two BaF2 windows on opposite sides of the chamber for spectroscopic access. Commercial gases obtained in cylinders were used as purchased: the nominal purity was 99.5% for H2 S, and 99.995% for Kr. The vacuum chamber containing the freestanding crystal was set in the sample holder of a Fourier transform infrared (FTIR) spectrometer (FTIR System 2000, Perkin–Elmer). IR absorption measurements were performed with a resolution of 0:5–1:0 cm1 .
Fig. 1. Geometry of Kr solid atoms for monomer (a) and dimer (b): the illustration roughly draws the optimized structures.
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2.2. Calculations The monomer H2 S, oligomers of H2 S and H2 Sdoped Kr solid models, were calculated using B3LYP with Gaussian 98. The basis functions employed for H and S were 6-311G(3d,3p) in consideration of previous calculations [6]. Due to a limitation on computational resources, the 3-21G basis function was adopted for Kr. The IR frequency and absorption cross-section were calculated against the obtained structures as shown below. The calculation was performed for monomer H2 S, dimer ðH2 SÞ2 and trimer ðH2 SÞ3 , monomer H2 S surrounded by 12 Kr atoms, and dimer ðH2 SÞ2 surrounded by 18 Kr atoms. In the latter two cases, H2 S and ðH2 SÞ2 are assumed to substitute into the fcc lattice for Kr atoms. The surrounding Kr atoms in the calculation are those in the nearest neighbor positions with respect to the doped molecule. The geometries for the monomer and dimer are illustrated in Fig. 1. The central planes for Kr atoms in Figs. 1(a) and (b) correspond to the (1 1 1) plane, pffiffiffiand the distance d in Fig. 1(b) corresponds to 1= 3 of the lattice constant a. In the case of H2 S, ðH2 SÞ2 and ðH2 SÞ3 , complete optimization of the structure was performed, while in the case of the model Kr solids, the H2 S structure of the monomer and dimer, as well as the size of the lattice cage (represented by d in Fig. 1), were optimized, but the relative geometry of the individual Kr atoms was fixed at that in the initial lattice.
3. Results 3.1. Dimer and oligomer IR bands A typical IR absorption spectrum of H2 S doped in a free-standing Kr crystal at a dilution ratio of 1/6000 at 17 K is shown in Fig. 2. The wavenumbers of several peaks are listed in Table 1. Most of the peaks in the range 2600–2640 cm1 (enlarged in the inset) correspond to the rotational structure of monomer H2 S as previously discussed [2,3], which will not be argued at present. The important point to note is that these peaks are contaminated
Fig. 2. IR spectrum of ðH2 SÞx doped in Kr solids with the dilution ratio of 1/6000 measured at 17 K.
Table 1 Peak positions of IR spectra at 17 K and slope of the intensity vs. dilution ratio curve Peak No.
Frequency (cm1 )
Slope
a b c d e f
2636 2618 2613 2575 2566 2549
0.9 2.5 1.9 1.8 2.6 2.7
by contributions from dimer and/or oligomer peaks as will be discussed later. The peaks between 2500 and 2580 cm1 have been tentatively assigned to oligomers, and in particular, peak d has been assigned to a dimer. The monomer rotational structure peaks broaden and coalesce with increasing temperature as shown in Fig. 3 (25 K). On the contrary, several peaks including b and c in the region 2610–2620 cm1 and strong peaks d, e and f below 2580 cm1 remain largely unchanged with variations in temperature. Eventually, peaks d–f shift slightly to larger wavenumbers with increasing temperature. The small peaks in the neighborhood of 2575 and 2566 cm1 could be isolated more clearly from the stronger peaks when observed at 0.25 cm1 resolution, as shown in Fig. 4. Peak d occurs at 2575.3 cm1 , while d 0 is located at 2573.2 cm1 . The relative intensity of these peaks, 1:0.04 independent of the dilution ratio, strongly suggests that the satellite peak is an isotope peak
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Fig. 3. IR spectrum of ðH2 SÞx doped in Kr solids with the dilution ratio of 1/6000 measured at 25 K.
Fig. 5. The relative IR peak area of a–f peaks vs. dilution ratio measured at 17 K: a (d), b (s), c (M), d (O), e (), and f (}).
Fig. 4. IR spectrum of ðH2 SÞx doped in Kr solids with the dilution ratio of 1/6000 measured at 17 K below 2600 cm1 with the higher resolution of 0.25 cm1 .
due to 34 S. This assignment will be discussed later on the basis of ab initio calculations. The relative peak intensities (i.e. absorbance) of individual peaks changed with the dilution ratio, and the dependence is illustrated in Fig. 5. The approximate value of the slope was measured in the region of dilution ratio below 104 , and the result is given in Table 1. The slope of peak intensity vs. dilution ratio at 2636 cm1 (peak a) is 0.9, which supports the peak assignment as a monomer. Peak d can be assigned to a dimer, while e and f are attributed to a trimer, although the possibility of assignment to other higher oligomers cannot be neglected. The assignment of peak d to a dimer is in accordance with our previous work [2] and work by Isoniemi et al. [3].
The assignment of peak e to a trimer is also in accordance with the tentative assignment by Isoniemi et al. [3]. Peaks b, c and several smaller peaks between 2610 and 2620 cm1 remain as isolated peaks at higher temperature as shown in Fig. 3. This clearly shows that the IR absorptions in this region are not originating from a monomer alone. That is, the peaks can be assigned to dimers, trimers and/or higher oligomers. However, as these peaks are not completely isolated from each other, the estimated slope of intensity vs. dilution ratio for individual peaks in this region is not conclusive. 3.2. DFT calculations for optimum dimer structure The dimer structure optimized in the present work is illustrated in Fig. 6. One H2 S molecule (PD: proton donor) donates a hydrogen bond to the S atom of another H2 S molecule (PA: proton acceptor). The internuclear distance R between the S atoms, and the angles characterizing the dimer structure /1 and /2 , are around the same as those determined by de Oliveira and Dykstra [6]. The optimized structures of the H2 S-Kr solid and ðH2 SÞ2 -Kr solid were shown in Fig. 1. The geometries and characteristic length d of the calculated lattice are listed in Table 2.
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dimer in the gas phase has a symmetry plane containing two S atoms and the two H atoms of the PD, while in the dimer in the Kr solid, the H atom, No. 4 in Fig. 1(b) of the PD is twisted slightly from the plane in order to direct the H4–S2 bond toward the center of the triangle made by Kr1, Kr2 and Kr5 atoms. 3.3. Calculated IR spectra and comparison with experiments Fig. 6. Geometry of ðH2 SÞ2 dimer.
Table 2 Calculated dimer equilibrium geometry
R/nm /1 /deg /2 /deg db
In gas phase
Lit.a
In Kr solids
0.421 95.7 2.3 –
0.411 92.2 5.6 –
0.426 90.2 0.2 0.340
a
Literature value from [6] with the largest basis V/MP2. Lattice distance: for the experimental Kr lattice at 15 K, 0.321 nm, for the calculated lattice containing a monomer H2 S, 0.342 nm. b
The optimum structure of an H2 S unit in the dimer (both in the gas phase and in the Kr solid) is almost unchanged from that of the monomer H2 S in the gas phase (bond length, 0.134 nm; bond angle, 92.4°). The only change is the elongated H– S distance of the PD for the hydrogen bond in the dimer (both in the gas phase and in the Kr solid), by ca. 0.0003 nm from the monomer value. The
As the IR absorption intensity of the bending vibration at 1183 cm1 in the gas phase [7] was very weak in both the experimental and calculated vibrational spectra, this bending motion is not included in the discussion of the structure of H2 S oligomers. Thus, the region of the stretching vibration is examined in detail. The calculated frequency and absorption intensity (relative value) are listed in Table 3. The tabulated frequencies are calculated values that have been corrected by a magnification factor (0.9718) so as to give coincidence between the average gas phase monomer m3 ð2628 cm1 Þ and m1 ð2614 cm1 Þ [8,9] and the calculated value. The dimer vibrations are shown schematically in Fig. 6, with arrows indicating the two normal modes localized in the PD. The vibrations localized in the PA are similar to the normal modes of monomer H2 S. Interestingly, one of the vibrations of the PD, m1 , is shifted remarkably to smaller wavenumbers and IR intensity is significantly enhanced. This enhancement is predicted to occur when H2 S is the donor molecule, presumably a consequence of the very low-infrared intensities in
Table 3 Calculated peak position and relative intensity of IR absorption In gas phase
In Kr solids 1
Position (cm ) Monomer Dimer
PA PD
m3 m1
2628.1 2614.8
m3 m1 m3 m1
2625.1 2611.1 2622.2 2569.9
Intensity 0.025 0.031 0.48 0.16 1.61 82.65
Position (cm1 )
Intensity
2632.9 2616.7
8.96 4.60
2614.2 2600.8 2629.2 2577.0
9.45 8.11 8.51 71.43
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the unperturbed molecule. The other three vibrations of the dimer appear in the region between 2610 and 2630 cm1 . These peaks are weaker than that of PD m1 , although enhanced compared to those for monomer H2 S. When the monomer is surrounded by the model Kr solid atoms, the absorption intensity increases. This is also the case in the three modes of the dimer other than PD m1 . The absorption frequencies are also shifted to some extent from that given by the gas-phase calculation. However, the intensity of the dimer PD m1 is similar to that of the gasphase dimer, probably due to the fact that the hydrogen bonding is concealed inside the dimer structure and does not interact strongly with the Kr solid atoms. The calculated absorption peaks for the gasphase monomer and dimer are illustrated in Fig. 7, and those for the monomer and dimer surrounded by Kr solid atoms are shown in Fig. 8. The strong experimental absorption at 2575 cm1 is reproduced well by the calculated dimer PD m1 band, both in the gas-phase and Kr-solid dimer calculations. The relatively weak dimer bands around 2620 cm1 corresponding to c and/or nearby weaker peaks appear to have been reproduced approximately by the gas-phase and Kr-solid dimer calculations. Unfortunately, the agreement is not satisfactory, and reliable peak-by-peak assignment is not possible due to the difficulty of calculating the dimer in the solid using the present
Fig. 7. Calculated IR spectra of an equimolar mixture of monomer and dimer in the gas phase: monomer peaks (filled bars), and dimer peaks (hatched bars).
Fig. 8. Calculated IR spectra of an equimolar mixture of monomer and dimer in the Kr solids: monomer peaks (filled bars), and dimer peaks (hatched bars).
simplified model of the crystal lattice. The interaction between the surrounding Kr atoms and the guest molecule may therefore not be reasonably described by the present model. However, it is important to note that the solid model peaks are usually at larger wavenumbers compared to the gas-phase peaks. This may imply that the surrounding Kr atoms suppress the free motion of guest molecules. The small increase in the absorption intensity of the S–H stretching vibration may be due to the polar character of Kr atoms. Although the present calculations are limited, we can conclude with confidence that some experimentally observed peaks in the monomer region are attributable to a dimer and/or higher oligomers. The satellite band at 2573.2 cm1 is assignable to the dimer containing 34 S in the PD. The calculated difference between the position of absorption peaks is 2.2 cm1 (2577.0–2574.8 cm1 ), which is in good agreement with the experimental difference of 2.1 cm1 (2575.3–2573.2 cm1 ). The experimental intensity ratio is 1:0.04, which is also in accordance with the isotope abundance ratio of 1:0.044. The optimum structure of the gas-phase trimer ðH2 SÞ3 was also calculated. The structure was found to be an almost planar triangle as shown in Fig. 9, which is the same as derived for the ðH2 OÞ3 trimer in recent calculations [10,11]. The absorption peaks are illustrated in Fig. 10 together with
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Fig. 9. Optimized structure of calculated ðH2 SÞ3 in the gas phase: the three S atoms approximately form an equilateral triangle. The S atoms and the three equatorial H atoms are approximately on one common plane. One of the three axial H atoms directs downwards and the other two, upwards.
ture, and several additional peaks may indeed be present in the range 2550–2570 cm1 . The experimentally observed peaks at 2566 cm1 (e), 2549 cm1 ( f ) and several peaks in the vicinity of 2620 cm1 such as peak b may be reasonably assigned to certain trimers and/or higher oligomers.
4. Discussion
Fig. 10. Calculated IR spectra of an equimolar mixture of monomer, dimer and trimer in the gas phase: monomer peaks (filled bars), dimer peaks (hatched bars), and trimer peaks (cross-hatched bars).
those for H2 S and ðH2 SÞ2 . Calculations for the gas-phase trimer surrounded by Kr atoms were not performed due to the complexity of numerical calculation. The actual structure in the experimental Kr solid may not be limited to one struc-
The IR absorption of hydrogen bonds inside the oligomer structure have been found to be typically very strong and to be located in the lowfrequency region around 2550 cm1 . As previously stated by Amos [5], the quantitative feature exhibited by H2 S and H2 O clusters is that the peak position of acceptor molecules are perturbed only slightly, whereas the positions of stretching vibrations for the donor molecule shift to significantly lower wavenumbers. This trend has been also held true for rare gas matrices. In early research on H2 S spectra in rare gas matrices, the only features commonly observed
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were a broad absorption in the range 2500–2600 cm1 and a trace absorption above 2600 cm1 . It is now understandable why the monomer peaks could not be identified: the monomer peaks were simply too weak compared to the stronger absorption peaks of oligomers or aggregates in the lower-wavenumber region to be detected by early techniques. Moreover, molecules such as H2 S are considered to aggregate readily. In the present work, the analysis of the effect of solid rare gas atoms on the doped H2 S monomer and oligomers was performed using a model in which the solid Kr atoms were fixed to resemble the real fcc Kr lattice, and the center Kr atom was replaced with H2 S. Using this model, only the lattice plane distance was optimized. This type of structure should differ from the isolated clusters in the gas phase. de Oliveira and Dykstra [12] recently showed the minimum-energy structure of Ar16 –H2 S, using rigid body diffusion quantum Monte Carlo calculations, to be a closed structure in which Ar atoms completely surround a central H2 S molecule. This is the case when free boundary conditions are used. It remains uncertain whether such a local minimum structure also occurs in matrices, and at present there are no reports dealing with the vibrational analysis of H2 S inside a local minimum cluster. 5. Conclusion An H2 S dimer doped in a Kr solid produces a strong absorption peak at 2575 cm1 , which is assigned to the PD m1 mode. The dimer is also
responsible for several unassigned peaks in the monomer region. The absorption intensity of the PD m1 mode was found to be significantly enhanced due to intermolecular hydrogen bonding.
Acknowledgements This work was supported by a Grant-in-Aid for Scientific Research (A) from the Ministry of Education, Science, Sports and Culture of Japan (No. 12305051), for which the authors are very grateful.
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