J. Phys. Chem. 1992, 96, 1040-1045
1040
used in the calculation of dynamics in three dimensioos for chemically bound systems.2'.22 The collocation method has the considerable advantage that it can incorporate nondirect product basis functions such as the spherical harmonics. This aspect of the method is exploited in our recent analysis of the Ar-H20 cluster which exhibitsvan der Waals dynamics in threedimensions (Ref 90 and 91). These computational methods, and perhaps others, may permit extraction of many-dimensional IPS'S from experimental data when further algorithmic improvements are made or faster supercomputers become available. Detailed as(185) Schliepen, J.; Nema, L.; Heinge, J.; ter Meulen, J. J. Chem. Phys.
Le??.1990, 175, 561.
sessments of the various contributions to both pairwise and many-body intermolecular forces will then become possible, perhaps finally leading to the capability to accurately represent the structures and dynamics of both isolated clusters and condensed phases from first principles computer simulations, employing accurate and physically meaningful intermolecular potentials as the input. Acknowledgment. This work was supported by the National Science Foundation (Grant CHE-8612296). R.C.C. was sup ported by the Director, Office of Energy Research, o f f i c e of Basic Energy Sciences, Chemical Sciences Division of the US.Department of Energy, under Contract DE-AC03-76SF000098.
ARTICLES Spectroscopic and ab Inltlo Study of the Interactlon of Molecular Hydrogen with the Isolated Slllca Hydroxyls and Related Systems E. Garrone,**+V. B. Kazansky,* L. M. Kustov,* J. Sauer,f I. N. Senchenya,* and P. Ugliengot Dipartimento di Chimica Inorganica. Chimica Fisica e Chimica dei Materiali, Universitb di Torino, Via P. Giuria 7, 1-10125 Torino, Italy, N. D. Zelinsky Institute of Organic Chemistry, Academy of Sciences USSR, Leninsky Prospect 47, Moscow B-334. USSR,and Institut far Physikalische Chemie der Akademie der Wissenschaften, Rudower Chaussee 5, Berlin, FRG (Received: January 29, 1991)
Experimental vibrational data concerning the interaction of dihydrogen with the isolated hydroxyl of amorphous silica are compared with the results of ab initio calculations, both HartreeFock and correlated through perturbative technique (MP2). Si01(H8iOH) is chosen to mimic the silica free hydroxyl. Two modes of interaction are considered,one envisaging dihydrogen as a proton donor to the oxygen atom in SiOH (structure F), the other as a proton acceptor in a T-shaped structure (structure T). Calculated properties are the binding energy, frequencies of vibrational motions in the harmonic approximation, and H-H infrared intensity in the doubleharmonicapproximation. Both structures are stable. Structure T is more weakly bound and has less IR active H-H stretch than structure F, whose calculated features are in better agreement with the experiment. Experimental results concerning the bridging hydroxyl of H-mordeniteare also reported. Structures F and T are compared with the known gas-phase complexes of molecular hydrogen.
Introduction In recent years, Kazansky and co-workers have shown that dihydrogen can be efficiently employed in low-temperature IR surface studies to reveal pairs of acid-base Lewis sites in aluminas and The perturbation suffered by the H2 molecule breaks the local symmetry, so rendering its stretching mode IR active (the more so the stronger the interaction), and causes a red shift of the frequency, which is also a measure of the strength of the interaction. In the presence of very strong acid-base pairs dihydrogen may break up heterolytically.2 Dihydrogen also interacts with surface hydroxyls.' Detailed studies4 of the interaction of H2 with the free hydroxyl of amorphous silica and zeolites, inclusive of the H-H modes, have shown that at low coverages a definite adduct is formed. Two other cases are known where the interaction of molecular hydrogen and silica is instead nonspecific: (i) the perturbation of hydroxyls in Vycor glass brought about by hydrogen physisorption, very recently studied in the near IR,S which takes place at higher coverages than in the previous case;(ii) the trapping of molecular UniversitH di Torino. $Academy of Sciences USSR. Akademie der Wissenschaften.
0022-3654/92/2096-1040$03.00/0
hydrogen by Si02-based fibers, which interferes with their optical performances.6 As silica notoriously exhibits acidic properties only, the interaction mechanism is probably different from that observed in the case of acid-base pairs and is basically still to be understood: this is the theme of the present paper. To this purpose, we report and discuss both spectroscopicmeasurements and computational results. The systems investigated on the experimental side are again the isolated hydroxyl of amorphous silica (denoted hereafter S O H ) and the closely related bridged hydroxyl in H-mordenite [denoted hereafter Si(Al)OH]. The study has been carried out at relatively high temperatures (77 K) and low pressures, to avoid (1) Kazansky, V. B.; Borovkov, V. Yu.;Kustov, L. M. Proc.-Zn?. Congr. Caral. [Proc.],8rh 1984. 3. ( 2 ) Kazansky, V. B.; Borovkov, V. Yu.;Zaitsev, A. V. In Catalysis: from theory to practice. Proc.-In?. Congr. Catal., 9th 1988, 1426. (3) Kazansky, V. B. Caral. Today 1988, 3, 367. (4) Kustov, L. M.; Borovkov, V. Yu.;Kazansky, V. B. J. Catal. 1981. 72, 149. Kustov, L. M.; Alexeev, A. A,; Borovkov, V. Yu.;Kazansky, V. B. Bull. Acad. Sci. USSR 1981, 261, 1374 (Russ.) (5) Huber, T. E.;Huber, C. A. J . Phys. Chem. 1990.94.2505, (6) Welsh, H. L.; Kriegler, R. T. J . Chem. Phys. 1%9,50, 1043. Cocito, G.; Cognolato, L.; Modone, E.;Sordo, B. J. Opt. Commun. 1988, 9, 1 , and references cited therein.
0 1992 American Chemical Society
Interaction of Molecular Hydrogen with Silica Hydroxyls
The Journal of Physical Chemistry, Vol. 96, No. 3, 1992 1041
7983
I
b
t
e1 Figure 2. IR spectra concerning the 77 K adsorption of dihydrogen on synthetic H-mordenite (Si02/A1203= 10) outgassed at 770 K. Hydrogen pressure was 60 Torr. (a) H-H modes; (b) Si(A1)O-H modes. Figure 1. IR spectra concerning the 77 K adsorption of dihydrogen on silica gel (Davieon grade 12) outgassed at 770 K. Hydrogen prarsure was 300 Torr. (a) H-H modes; (b) SiO-H modes.
physical effects. On the theoretical side, the effort has been concentrated on high-level computations performed on a model system comprising dihydrogen and silanol (H3SiOH), which mimics the isolated silica hydroxyl. The work described bears similarities with the much studied van der Waals complexes of dihydrogen HF/H2 and (H&. Indeed, such complexes represent the only reference available: for the former, both computational' and experimental (matrix isolation; ref 8) studies have been conducted. The latter has been initially characterized theoretically9and very recently also from the experimental point of viewelo In both cases a T-shaped structure has been found. ExperimeaW Section ExperimcnblDedgn. Samples of both silica gel (Davison, grade
12) and synthetic H-mordenite with Si02/A1,03 = 10 were pretreated in vacuum at 770 K for 8 h. Silica was also deuterated via repeated treatments in 30 Torr of D2 (1 Torr = 133 Nm-2) at 770 K for 30 min. All pretreatments were performed in situ by means of a cell thoroughly described el~ewhere;~ at no stage was the sample exposed to air. Normal hydrogen was used; i.e., no enrichment in either ortho or para form was performed. IR spectra were measured in the regions 3000-4000 and 400&9000 cm-' using Perkin-Elmer 580 B and Beckman Acta M-VI1 spectrophotometers, respectively, supplied with homemade Muse reflectance attachment^.^ Uncertainty on the peak position is evaluated to be f l cm-'for peaks around 3700 ax-'and f 3 cm-' for peaks around 8000 cm-'.Hydrogen pressure ranged between 60 and 300 Torr; the nominal temperature of measure was 77 K. Results and P r e h h r y Discdon. Figure 1 illustrates the IR spectra due to the adsorption of H2 at 300 Torr and 77 K on (7) Bemholdt, D. E.;Liu, Shi-yi; Dyhtra, C. E.J. Chem. Phys. 1986,85, 5120. (8) Hunt, R.D.; Andrews, L. J. Chem. Phys. 1987,86, 3781. (9) Hobza, P.;Schneider, B.;Sauer, J.; Carsky, P.; Zahradnik, R. Chem. Phys. Lcrr. 1987, 134, 418. (10) McKellar, A. R. W.J. Chem. Phys. 1990, 92, 3261.
NO2. Figure l a refers to the H-H stretching modes, both fundamental and first overtone, and Figure l b to the SiO-H stretching modes, again for the same transitions. Because the experiments have been conducted at coverages well below the monolayer (although the exact values have not been evaluated), the band Ql+S observed,e%., at 4695-4735 cm-'on porous Vycor, is always absent here. The fundamental stretch (hereafter wol) of adsorbed dihydrogen gives rise to a high intensity band at 4129 cm-'. In the overtone region, around 8000 cm-' a triplet is observed. Comparison, however, with the spectra recorded on the deuterated sample (broken curve) shows that the component at 8015 cm-' is that due to the 0 2 vibrational transition of H2 (hereafter wO2),whereas the two components at 8110 and 8165 cm-' are ascribable to combination modes of S O H , actually v(0H) + 6(OH) and v(0H) v(Si-OH), respecti~ely.~The fundamental and first overtone in gaseous H2 (obviously only Raman active) fall at 4162.1 and 8088.8 cm-I, respectively." It is well-known that all stretching modes involving a hydrogen atom show anharmonicity, which is obviously largest for dihydrogen itself. A rough measure of anharmonicity consists in the difference between w m and twice wol. If a Morseliie potential is assumed for H-H motion, it results12 wol = we - 2w&,; wo2 = 2we - 6w$, or (1)
-
+
= Wol - 1/2 W O ~ ; We = 3Wol - Wo, where we is the frequency in the harmonic approximation and xe is the anharmonicity parameter. Under this assumption, the energy of higher order transitions 0 n is given by won = n[we - (n + 1 ) w e ~ e l Even though the H-H potential is not strictly Morse-like,ll one can use eq 1 to compute wg, and we from the fundamental and first overtone transitions. The results are 117.7 and 4397.5 cm-' for the free dihydrogen, respectively, and 122 and 4374 cm-' for dihydrogen interacting with S O H , respectively. Interaction has W$,
-
(1 1) Herzberg, G. Molecular Specrra and Molecular Srrucrure I, Spectra of Diaromic Molecules, 2nd 4.Van ; Nostrand: Princeton, NJ, 1950. (12) KazansLy, V. B.;Gritcov, A. M.;Andrew, V. M.; Zhidomorov, G. M. J. Mol. Caral. 1984, 4, 135.
1042 The Journal of Physical Chemistry, Vol. 96, No. 3, 19'92 TABLE I: Comparison between Experimental IR Frequencies of the Dihydrogen Complex with the Silica Hydroxyl and Those of the Constituent Mokules (cm-I) free complex Av H-H stretch 4162.1 4129 -3 3 0+1 8088.8 8015 -74 0-2 4373 -24 WC 4397.5 117.7 122 +4 we& 0-H stretch 3748 3742 -6 0-1 7325 7312 -1 5 0-2 3913 -6 WC 3919 85.5 85.5 0 wr%
brought about a small decrease in frequency and a slight increase in anharmonicity. The fundamental SiO-H stretch moves slightly because of the hydrogen interaction from 3748 to 3743 cm-I and the first overtone from 7325 to 7310 cm-I. Hydrogen interaction with Si(Al)OH is described in Figure 2. As before, Figure 2a describes the IR features due to H2 molecules and Figure 2b those due to the hydroxyl groups. A high-intensity fundamental is seen at 4108 cm-l, whose first overtone is at 7983 cm-I. Low-intensity bands at frequency lower than 4100 cm-I, with overtone partners at frequency lower than 7900 cm-I, are attributed to H2 complexes with Lewis acidic sites present on mordenite even after moderate thermal treatments, not considered in detail here. Through eq 1, it results that w g e is 116.5 cm-' and we is 4341 cm-'. The anharmonicity parameter in this case practically coincides with the free molecule value, whereas the harmonic frequency is definitely decreased (AYH-H = -57 cm-I as opposed to -24 cm-' in the SiOH case). The effect of hydrogen interaction with Si(A1)OH is to shift the fundamental 0-H stretch from 3620 to 3580 cm-' and the first overtone from 7090 to 7010 cm-I. Other features in Figure 2b, namely the shoulder at -3740 cm-I and the band at 7320 an-', are due to hydroxyls sitting on Si atoms also present in zeolites, absorbing at slightly lower frequencies. The interaction of hydrogen with Si(A1)OH is stronger than that with SiOH, and indeed a lower H2 pressure is sufficient to bring about extensive spectral changes, whereas SiOH species are unperturbed. Kazansky and co-workersI2have shown that the potential for the 0-H stretching mode of both SiOH and Si(Al)OH is given, to a good approximation,by a Morse function. Again, a simple calculation using eq 1 gives the anharmonicity constant and the harmonic frequency. For the free SiOH group the results are w p c = 85.5 cm-' and we = 3919 cm-I; for free Si(A1)OH the values are 80 and 3770 cm-I, respectively. When interacting with H2, SiOH has w g c = 88 cm-' and we = 3919 cm-' and Si(A1)OH has w g , = 75 cm-' and we = 3730 cm-I. The two cases seem to behave differently: with Si(Al)OH, the interaction with H2 does not cause any increase in anharmonicity in the 0-H motion, whereas it causes a decrease in the harmonic stretching frequency of 40 cm-I; with SiOH, no red shift is observed in the harmonic frequency, and the slight shifts in both wol and wO2are amenable to an increase in anharmonicity of the O-H motion. This could be an indication that the interaction between hydroxyl and hydrogen is different in the two cases. It has, however, to be noted that it is sufficient to assume wol = 3142 cm-' and woz = 7313 cm-', i.e., to alter the values within the experimental uncertainty, to obtain we = 3913 cm-' and wse= 85.5 cm-l. This pair of values would suggest that no change in anharmonicity is taking place and that the shifts are entirely due to a change in we. Kazansky and co-workersI2have shown that an increase in anharmonicity in the OH stretch is only observed for rather strong interactions, both for SiOH and Si(A1)OH: the extreme weakness of the H2/SiOH interaction lead us to assume that changes in anharmonicity are unlikely and to choose for we and w g e the values 3913 and 85.5 cm-I, as reported in Table I. Computational Section Methods. Due to the covalent nature of the solid, the isolated surface hydroxyl is particularly suitable to be dealt with in a cluster
Garrone et al. TABLE II: Band Zero-Point Energies of the Hydrogen/Sulaol Complex at Various Levels of Approach in cm-l (Values in Parentheses Are Corrected for BSSE)"
MP2 102 (76) 295 (129) 168 (139)
AZPE
65 (53) 102 (59) 75 (65) 186 ( 5 8 ) 183 (62) 101 (82)
336 (116) 393 (156) 202 (157)
347
SCF T-shaped
A
B C F-shaped
A
B C
189
"Standard Pople 6-31G(d,p). d on 0 and Si, exponent = 0.8/0.45; p on H, exponent = 1.1; d consists of five functions only. B, Dunning contraction valence double-zeta set of type (1 1,7/9,5/4)/[6,4/3,2/2] of Huzinaga's set. The contraction schemes were [5,2,1,1,1,1/4,1,1,1] for Si, [7,1,1/4,1]for 0, and [3,1]for H. The standard set is supplemented with a set of diffuse functions (s on H, exponent = 0.06;p on 0 and Si, exponents 0.06 and 0.0027,respectively) and a double set of polarization functions (p on H, exponents = 0.12/1.9;d on 0 and Si, exponents = 0.15/0.9and 0.25/0.9,respectively). d sets consists of six functions. C, valence sets of triple-zeta quality. For Si the McLean and Taylor scheme (12,9)/[6,5]is adopted, where the contraction follows the pattern [6,2,1,1,1,1/4,2,1,1,1]; for 0 the (10,6)/[5,3]contraction of Huzinaga's set, according to the scheme [6,1,1,1,1/4,1,1]; for H the scheme (5)/[3]. Two sets of polarization functions: exponents for 0 = 0.69/2.08;for Si 0.23/0.69;for H adjacent to 0 = 0.46/1.39;for H adjacent to Si = 0.25/0.75. d sets consists of five functions only.
a p p r ~ a c h , 'involving ~ as a model either silanol (H3SiOH) or orthosilicic acid (H303SiOH).14-'7To calculate reliably minute energies of interaction, it is vital to use a suitably large basis set and introduce electron correlation techniques. All of this compulsorily leads us to assume as a model for SiOH the simplest one, silanol (H3SiOH). The anharmonic OH stretching modes including overtones, the Si-O-H bending, and torsion modes computed at ab inito level are in satisfactory agreement with experiment.'*.19 As far as the interaction with molecules is concerned, silanol quite satisfactorily models SiOH in rather different interactions with CO, H20, NH3, and H2C0,Malthough silanol (H3SiOH) is probably somewhat less acidic than the real silica hydroxyl. Because we are dealing with a molecular complex, the calculations consist of the comparison of energy, geometry, and vibrational features of the molecules in interaction and, when separated, at various levels of approximations. All of the calculations have been performed at ab initio level, using GAUSSIAN82.21 Three bash Sets have been used throughout: basis set A is the standard Pople 6-31(d,p) set.228 Basis set B consists of a Dunning valence double-zeta set22bplus the same (13) Zhidomirov, G. M.; Kazansky, V. B. Adu. Catal. 1986,34,131,and references cited therein. Sauer, J. Chem. Rev. 1989,89,199,and references cited therein. (14)Hobza, P.; Sauer, J.; Morgeneyer, C.; Hurych, J.; Zahradnik, R. J . Phys. Chem. 1981,85,406!. (15)Sauer, J.; Zahradnik, R. Int. J . Quantum Chem. 1984, 26, 793. (16)Mix, H.;Sauer, J.; SchrMer, K. P.; Merkel, A. Collect. Czech. Chem. Commun. 1988,53,2191. (17) Geerlings, P.; Tariel, N.; Botrel, A.; Lissillour, R.; Mortier, W. J. J . Phys. Chem. 1984,88, 5752. (18) Garrone, E.; Ugliengo, P. Structure and Reactiuify of Surfaces, Proceedingsof the European Conference, Tricste Sept 13-20.1988;Zecchima, A., Costa, G., Morterra, C.,Eds.; Studies in Surface Science and Catalysis; Elsevier: Amsterdam, 1988;p 405. (19)Ugliengo, P.; Garrone, E. J . Mol. Carol. 1989,54,439. (20)Ugliengo, P.; Saunders, V. R.; Garrone, E . J. Phys. Chem. 1989,93, 5210. Ugliengo, P.; Saunders, V. R.; Garrone, E. Surf. Sci. 1989,224,498. Ugliengo, P.; Saunders, V. R.; Garrone, E. J . Phys. Chem. 1990,94,2260. Ugliengo, P.; Saunders, V. R.; Garrone, E. Chem. Phys. Lett. 1990,169,501. (21)Binkley, J. S.; Frisch, M. J.; Defrees, D. J.; Rahgavachari, K.; Whiteside, R. A.; Schlegel, H.B.; Flufer, E. M.; Pople, J. A. GAUSSIAN~~, Department of Chemistry, CamegieMeUon University, Pittsburgh, PA, 1982. (22) (a) Hehre, W. J.; Radom, L.; Schleyer, P. V. R.; Pople, J. A. Abinitio Molecular Orbital Theory; Wiley: New York, 1986. (b) Dunning, T. H., Jr.; Hay, P. J. In Modern Theoretical Chemistry; Schaefer, H.F., 111, Ed.; Jr.; J . Chem. Plenum Res: New York,1977;Vol. 3, p 1. (c) Dunning, T. H., Phys. 1970,53,2823.(d) Dunning, T. H.,Jr.; J. Chem. Phys. 1971,55,716. ( e ) McLean, A. D.; Chandler, G. S. J . Chem. Phys. 1980,7 2 , 5639. (0 Ahlrichs, R.;Taylor, P. R. J . Chim. Phys. 1981,78, 315.
The Journal of Physical Chemistry, Vol. 96, No. 3, 1992 1043
Interaction of Molecular Hydrogen with Silica Hydroxyls
-5
-8
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IY F w e 3. Conformation of two types of hydrogen/silanol adducts: structure I or T, hydrogen as H-acceptor; structure I1 or F, hydrogen as H-donor, calculated at HF//A (bare numbers) HF//B (numbers in parentheses) HF//C (numbers in braces). The geometries of free silanol and hydrogen calculated at the same level are shown as structures 111and IV, respectively. Angles are in degrees and lengths in angstroms.
set of polarization and diffuse functions used by Dykstra for studying FH/H2.7 Basis set C has a triple-zeta quality valence set as well as different sets of polarization and diffuse functions. These latter coincide with those used by one of us in a separate study on proton affinity of silanol and related sy~tems.2~Details of the three basis sets are reported in Table 11. Full geometry optimization has been carried out at HartreeFock (HF) level, with basis sets A and B only, using analytical gradient techniques and constraining the system to have a symmetry plane, by locating the H2 molecule either in or perpendicular to the H - S i U H plane. Because the changes in internal coordinates upon complex formation turn out to be small, only the intermolecular coordinates were optimized when basis set C was used. Basis set superposition error (BSSE) has been evaluated using the full counterpoise method24 for both H F and MP2 calculations and for all basis sets. Harmonic normal-mode frequencies have been computed by adopting analytical second-energy derivatives and solving the equations of nuclear motion by standard methods.2* The IR intensity of the H-H stretch has been evaluated in the doubly harmonic approximation through the change in the overall dipole moment brought about by a AO.01-A variation in the H-H equilibrium distance. Electronic correlation has been evaluated using perturbative truncated at second order (MP2). Mdler-Plesset Hereafter, any calculation is indicated by either H F or MP2 followed by the letter labeling the basis set, e.g., HF-A or MP2-B. A double slash (//) indicates the basis set at which the geometry has been optimized. The calculations have been carried out on the IBM 3090 mainframe at the CSI Piemonte computer center. Models for the Interaction. The ab initio characterization of the silanol molecule at HF-A'* and at MP2-A level19 has been already published by two of us; the geometries at HF-A and HF-B levels are illustrated in structure I11 of Figure 3, while structure IV shows the hydrogen molecule optimized at HF-A and -B. Figure 4 reports the molecular electrostatic potential of both H2 and silanol computed at the H F level with basis set A. It is evident that, from an electrostatic viewpoint, binding can occur by matching positive and negative ends with corresponding counterparts. Two modes of interaction are so possible, illustrated in structures I and I1 of Figure 3, denoted hereafter T (T-shaped) ~~~
~
(23) Sauer, J.; Ahlrichs, R. J. Chem. Phys. 1990, 93, 2575. (24) Boys, S.F.; Bernardi, F. Mol. Phys. 1970, 19, 553. (25) Wilson, E. B., Jr.; Decius, J. C.; Cross,P. C. Molecular Vibrations; McGraw-Hill: New York, 1955. (26) Msllcr, C.; Plcsset, M. S.Phys. Reo. 1934, 46, 618. Binklcy, J. S.; Pople, J. A. Int. J. Quantum Chem. 1975, 9, 229.
-7
-6
-5
-4
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2
1
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6
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1 2
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-7
-6
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1
2
3
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Figure 4. Maps of the Hartree-Fock molecular electrostatic potential
(kcal mol-') of H2 (a) and H3SiOH (b) computed with basis set A. For H3SiOH the map is relative to the symmetry plane. Grid unit is in angstroms.
and F (faced), respectively, by reference to the spatial location of H2 with respect to silanol. Making reference to H-bonding, H2 appears as H-donor and as H-acceptor, respectively. Structure T is close to the spatial arrangement of HF/H2 and H2/H2 complexes.7-1 O Configurations obtained by rotation of the H2 moiety around the 0-H axis are not equivalent in principle. We have thus studied, besides structure I where the H2 molecule lies in the symmetry plane, the conformation in which the H2 molecule is orthogonal to it. We have found, however, that the two structures are energetically indistinguishable, so that in the following only structure I is considered. In H-bonded van der Waals complexes the H atom of the donor molecule often orients so as to maximize the interaction with the H-acceptor lone pair.27 This means that a skew configuration of structure F, allowing a larger interaction between the hydrogen H atom and one of the 0 lone pairs, could be preferable. For example, in the case of SiOH/H20 interaction, a stable skew configuration of the water molecule when acting as H-donor has been found.20 We have thus also studied one feasible skew configuration of structure F, shown as structure 11' in Figure 3, the geometry of which has been determined by HF-A only. Its energetic and geometrical features turn out to be very close to those of structure II; no further investigation was thus carried out, one reason being the large cost of the calculations on such nonsymmetric structure. Results and Discussion. For both structures F and T stable minima result upon geometry optimization, although very weakly bound. Table I1 reports binding energies for both H F and MP2 levels of treatment, for all basis sets, both as such and corrected (27) Legon, A. C.; Millen, D. J. J. Chem. Reu. 1986,86, 635. Legon, A. C.; Millen, D. J. Acc. Chem. Res. 1987, 20, 39.
Garrone et al.
1044 The Journal of Physical Chemistry, Vol. 96, No. 3, 1992
CT 1-53 (-2.61
Figure 5. Mulliken net charges for dihydrogen moiety in structures F and T after BSSE correction. Bare numbers, basis set A,numbers in braces, basis set C; CT, total charge transfer. Unit = lo-' electron.
for BSSE. The ratios F/T between the HF uncorrected binding energies are 2.86, 1.79, and 1.35 for basis sets A, B, and C, respectively, whereas the corresponding uncorrected MP2 values are 3.29, 1.33, and 1.20, thus showing that the dispersive forces and corrections to the monomer electrostatic properties introduced by correlation do not alter the order of stability found at H F level. Larger basis sets rather than higher level in the perturbative MP series are expected to give a further increase in the binding energy, as it happens with the H2 dimer? No comparison with experiment is available; it is, however, probable that the computed values are definitely underestimated, because their extent is only a few kT at the temperature of experiment (77 K kT = 50 cm-I). Indeed, correction for zero-point energy calculated on the basis of vibrational data (vide infra) is of the order of the whole binding energy, so that the complexes are actually unbound. Another piece of evidence pointing to the great delicacy of these calculations is the large extent of BSSE, which is some 50% of the whole bmding energy for basis sets A and B. Basis set C shows a more reasonable BSSE than the comparable case of basis set B; this is evidence that the diffuse and polarization functions are in this case more suitable than those of basis sets A and B. Features of optimized geometries are reported in Figure 4 as far as the intermolecular degrees of freedom are concemed. The changes in geometry within the two moieties are very small, and the only noteworthy one is some lengthening of the H-H distance of the order of lr3 A in both structures F and T. As to the relative location of the two moieties, in structure T the two H atoms are almost equally distant from the hydrogen atom in SiOH (basis set A, 2.755,2.812 A; basis set B, 2.61,2.70 A; basis set C, same as for B). In structure F, the H atom interacting with the oxygen atom in S O H has a distance from this latter of 2.80,2.96, and 2.98 A with basis sets A, B, and C, respectively. It is noteworthy that basis sets B and C, which give rise to quite different BSSE, lead to the same geometric features. The angle H-H--0 is close to 180' in all three cases. It is well-known that in H-bonding a flow of charge takes place from the proton-acceptor molecule to the proton-donor one, the extent and importance of which has been long debated. To characterize such a flow, a simple tool like Mulliken population analysis can be used by comparing the electronic charges before and after complex formation," although the absolute values of charges have no precise physical meanining and are base-dependent. Moreover, in the present case of extremely weak interactions, precaution has to be exercised, because the changes are tiny and biased by the superposition of basis sets of the individual molecules. In the case of basis set B, which contains very diffuse functions, the changes in electronic populations are overwhelmed by the BSSE and thus not further considered. For both structures with basis set A and for complex T with basis set C the uncertainty on electronic charges brought about by basis set superposition is an order of magnitude smaller than the actual values. The case of structure F with basis set C is intermediate, in that the correction for BSSE is of the order of magnitude of the actual values. Figure 5 reports electronic charges for the hydrogen moiety only for basiis sets A and C and structures F and T after correction for BSSE. The overall charge transfer between H2 and silanol upon complex formation is -5.3/-2.6 (basis A/basis
TABLEm. CalmhtedHuwMIc ' Frequeaciea ( c d ) of the HJHSiOH T .ad F Addacts d of the Comtitwnt Molecuka mode H'SiOH Hz T complex F complex l4O-H) 4231 4231 4229 v(Si-0) 951 954 951 Q(Si-0-H) 904 906 906 T(H-Si-OH) 201 238 291 v(H-H) 4633 4621 4623
TABLE Iv: C o m q " between cllcplrted md Experhentd Shifts in H " i c Froqwacks (em-') Av(0-H) Av(H-H) Ab(HSi0H)
T complex
F complex
0 -12 +39
-2
exut -6
-10
-24
+9 1
?
+
C) and 1.9/+ 1.8 (basis A/basis C) millielectrons for complexes F and T, respectively (signs refer to the H2 molecule). The two basis sets yield comparable results, indicating that the extent of charge transfer in complex F is about 1.5 times larger than that computed for the T complex. It is noteworthy that both the sign and the extent of the charge transfer are in agreement with that calculated for the interaction of silanol with other molecules capable of acting as proton donors as well as proton acceptors, namely water and In the case of proton donation, the electron transfer is -5 (ammonia) and -9 (water) millielectrons, in agreement with the known fact that ammonia is less acid than water; in structure F (basis set C), where Hz acts as proton donor, a negative flux is observed as in the other two cam, although of lesser extent. With structure T, where Hz acts as a proton acceptor, a positive variation around 2 millielectrons is observed, as in the other two cases (+11 and +13 millielectrons for ammonia and water, respectively). All of this seems to suggest that the Hz molecule is a poorer H-acceptor than it is a H-donor. Interestingly, the small electron transfer is accompanied by a more substantial internal polarization within the Hz molecule, in both structures F and T, which seems to be larger in structure F. This suggests that also the IR intensity of the H-H stretch should be more intense with structure F than with structure T. Indeed, the evaluation of the change in dipolar moment brought about by a change (fO.O1 A) in the H-H equilibrium distance leads to an absolute intensity of the H-H stretch of 1.2 and 8.7 (Wi set A) and of 2 and 5.9 km mol-' (basis set B) for structum T and F, respectively; Le., the H-H stretch turns out to be from 3 to 7 times more intense in structure F than in structure T. The main vibrational features of adducts T and F calculated at the H F level with basis set A in the harmonic approximation are reported in Table 111, together with those of the constituent molecules, whereas Table IV compares the harmonic experimental shifts reported above with calculated values. As is well-known, IR frequencies calculated with a proper basis set at H F level are some 10% larger than the experimental values; data in Table I11 are no exception when a direct comparison is possible, e.g., the H-H stretch in molecular H2. Consequently, a scaling factor of 0.9 has been used when absolute frequency values were needed, e.g., in the calculation of zero-point energies: no correction was applied to shifts. Both structures show comparable shifts of the H-H harmonic stretch and cannot thus be discriminated on this basis. The calculated shifts are about half of the experimental value. In calculations concerning similar systems, e.g., in the interaction of silanol with ammonia or CO," it has been observed that the red shift of the W H involved in the H-bonding was also about half of the experimental value. Inclusion of electron correlation, however, and, to a l e s a extent, anhannonicity markedly improved the agreement;" it is probable that the same holds here, although explicit calculations have not been carried out. The two structures may be discriminated on the basis of the 0-H stretch, which is vanishingly small for structure T and -2 (28) Gamone, E.; Ugliengo, P. Unpublished results.
J. Phys. Chem. 1992,96, 1045-1051
cm-l for structure F. As above, it is probable that twice as much yields a more realistic value: this renders the shift in wolquite satisfactorily accounted for by structure F. The absence of any shift of the 0-H stretch in structure T together with the presence of a small but defhte shift in structure F requires some comment. In H-bonded complexes it is usual to observe a definite shift in the stretching mode of the H-donor molecule (here silanol), which is a measure of the strength of interaction. When the partner in the interaction can act as both H-donor and H-acceptor, e.&, in the previously mentioned complexes of silanol with water and ammonia,z0the perturbation of the 0-H stretch is much higher when ammonia (or water) acts as H-acceptor than in the opposite case. Similarly, the stretching modes of a vicinal pair of interacting silica hydroxyls (one Hacceptor, the other H-donor) fall at 3520 and 3720 cm-I, re~pectively;~~ the shifts from the unperturbed value of 3748 cm-' differ by an order of magnitude. All of this seems to suggest that structure T has little to do with H-bonding and that the structure is held together by electrostatic interactions only, as suggested by Dykstra as it concerns the Hz/HF complex.' Structure F shows instead the vibrational features expected for H-bonded complexes. Lastly, the two structures show distinct shifts of the torsion mode also reported in Table IV, which are unfortunately unaccessible to measure.
General Discussion and Conclusions The van der Waals complex Hz/HF constitutes the closest system to that under investigation. Both the experimental*and published ab initio calculations7show that a T-shaped geometry is found, whereas no evidence of a F structure has been produced. Unpublished calculations by two of uszs show that also in this case an F structure is possible, although less stable than structure T: BSSE-corrected binding energies calculated with basis set B at MP2 level are -89 and -178 cm-' for F and T conformers, respectively. In the present case, the order of stability between the two structures is reversed at any level of computation. By generalizing these results, one may assume that the interaction of molecular hydrogen with a group X-H (where X is a highly electronegative element like fluorine or oxygen) can be twofold: Hz acts as either acceptor of acidic hydrogen atom of X-H or (29)
1045
as donor of one of its hydrogen atoms to the basic atom X. This latter interaction brings about an internal polarization of the H2 molecule and has the features of a true hydrogen bond. The former interaction seems more to be due to electrostatic interactions only, mainly between the dipole of X-H and the quadrupole of Hz.The cases known so far of FH/Hz and (HJ2 are only of the former type; the interactions studied in the present paper seem relatable, as discussed below, to the latter type. Preliminary calculations on the interaction of molecular hydrogen with the water molecule30also seem to be of the latter type. Another aspect of the H2/HF complex which is relevant to the present problem is the extent of the interaction energy. Dykstra7 has calculated -306 cm-I with a triplezeta quality basis set,difTuse and polarization functions identical to those of basis set B, taking into account electron correlation with an approximate coupled cluster approach. No evaluation of BSSE was carried out, nor was the zero-point energy taken into account. If this latter is done," it turns out that the complex is unbound, just as it happens with the cases under study here: we consider this fact as evidence that even rather sophisticated computations seriously underestimate such weak interactions and that we are not facing a failure of silanol as a model for the silica hydroxyl. This does not rule out, however, that relative values of interaction energies may be meaningful, as well as other computable features, like net charges or vibrational data. Indeed, the work by Dykstra' shows that the experimental shifts in both the H-H and H-F stretch can be reproduced satisfactorily by calculus. For these reasons, we assume the calculated spectroscopic features to be reliable. The choice of structure T or F as that representative for the interaction of H2 with the isolated hydroxyl of silica is not clear-cut, because neither the binding energies, nor the frequency shifts, nor the intensities of the H-H made are much different in the two cases. However, all three of these features concur in suggesting that structure F is the more probable, being the stronger, having a more intense H-H stretch, and leading to frequency shift in better agreement with the experiment. Acknowledgment. We are grateful to CSI Piemonte for generous allowance of computer resources. Registry No. Hz, 1333-74-0; OH, 3352-57-6; SOz, 7631-86-9; H3SiOH, 14475-38-8; mordenite, 12173-98-7.
Morrow, B. A.; Cody, I. A,; Lee, Lydia S. M. J . Phys. Chem. 1976,
~~
(30) Kazansky, V. B.; Senchenya, I. N.; Sauer, J. Unpublished results.
80, 2761.
Low-Temperature Vlbrational Relaxation in Crystalline CS2 at High Pressure Robert A. Crowell and Eric L. Chronister* Department of Chemistry, University of California. Riverside, California 92521 (Received: May 2, 1991; In Final Form: August 22, 1991)
Picosecond coherent Raman measurements are made on crystalline CS, in a high-pressurediamond anvil cell at low temperature as a sensitive probe of the intermolecular interactions which give rise to relaxation phenomena. We observe density-dependent changes in the low-temperature vibrational relaxation rate of the v 1 and 2vz vibrational modes and analyze these results in terms of pressure-induced changes in intermolecular anharmonicitiesand pressure-induced shifts in the phonon density of states.
Introduction Raman spectroscopy under high-pressure conditions has proven to be a useful probe of the structure of a wide variety of molecular solids.' More recently, timeresolved coherent Raman experiments have been used to probe pressure-induced vibrational dephasing ( 1) Ferraro, J. Vibrational Spectroscopy at High External Pressures; Academic Press: Orlando, FL, 1984.
in solid benzene2J and nitromethane4at room temperature. Thw pressure-induced dephasing measurements have been performed at relatively high temperatures and are therefore complicated by thermally induced dephasing and relaxation processes such as (2) Baggen, M.; van Exter, M.; Lagendijk, A. J. Chem. Phys. 1987,86, 2423. (3) Della Valle, R. G.; Righini, R. Chem. Phys. Lett. 1988, 148, 45. (4) Rice, S.; Costantino, M. J. Phys. Chem. 1989, 93, 536.
0022-365419212096-1045$03.00/0 0 1992 American Chemical Society
