J. Phys. Chem. 1984, 88, 1125-1130
Consequently the rather large bandwidths cannot be fully accounted for in terms of the superposition of different cluster sizes. Clusters support a large number of low-frequency intermolecular vibrations and, even at the very low temperatures expected in the molecular beam, many of these modes could be populated. Transitions out of several of these states might also give an inhomogeneous breadth to the absorption bands. This explanation of the observed line widths has been applied successfully to the infrared spectra of (N20)n7 and (H20);S clusters. The final source of inhomogeneous broadening considered here is that due to unresolved rotational structure. This has been shown to be an important component of the line width for (N20), and (C02)2.237326An indication of the importance of this contribution can be obtained from the width of the very weak monomer absorptions seen in the low-pressure propene and isobutene spectra. As the rotational constants for the clusters are smaller than those of the monomer, the associated rotational manifold will be somewhat narrower. However, this contribution is clearly not negligible. As discussed in the Introduction, despite the existence of these sources of inhomogeneous line broadening there is considerable experimental evidence to suggest that the dominant broadening (25) J. R. Reimers and R. 0. Watts, Chem. Phys., submitted for publication. (26) L. S. Bernstein and C. E. Kolb, J . Chem. Phys., 71, 2818 (1979).
1125
mechanism arises from homogeneous effect^."^,^ Perhaps the most surprising result that comes from present and previous studies of infrared predissociation spectra is that in all but the simplest systems the observed bandwidths are not appreciably different. For example, all the values given in Tables I-V lie in the range 4-7 cm-I as do the results of Hoffbauer et aLSfor the OCS-alkane systems. In addition, results for ethene excited either near 950 cm-' 4 ~ 5or in the range 2900-3200 cm-' also give bandwidths close to 5 cm-'. This insensitivity of line width to the system studied and to the mode excited seems to support the suggestion of Hoffbauer et aLs that the major homogeneous broadening mechanism is associated with intramolecular vibrational relaxation rather than with fragmentation. In other words, vibrational relaxation may well proceed through nondissociative channels while dissociation occurs on a much longer time scale. Indeed, as previously indicated, one interpretation of the results summarized in Figure 7 is that the predissociation lifetime of large clusters becomes longer than the molecular flight time. Whether this difference in time scales could also exist for very small clusters, where the number of vibrational degrees of freedom is considerably smaller, is still somewhat unclear. Acknowledgment. We are grateful to Professor R. N. Warrener for the loan of the Grubb and Parsons monochromator. Registry No. Propene, 115-07-1; 1-butene, 106-98-9;isobutene, 11511-7; cis-2-butene, 590-18-1; trans-butene, 624-64-6.
SCF-LCGO Calculations of the Nonrigid Structure of Dioxonium Ion. A Basis for a Structural Analysis of H,O,+ in Crystals A. Potier,*l* J. M. Leclercq,lband M. Allavenalb Laboratoire des Acides MinZraux, US.T.L., 34060 Montpellier CCdex, France, and Centre de MZcanique Ondulatoire Appliquze, 75940 Paris CZdex 19, France (Received: December 3, 1981; In Final Form: April 4, 1983)
The structure of the HS02+cation is determined by ab initio SCF-LCGO calculations using as basis set functions (1 Is, 7p) and (4s) on oxygen and hydrogen, respectively, augmented by d and p polarization functions. A minimization of the total energy is performed with respect to the three angular coordinates and to the O-.-O distance and is followed by a full optimization using the gradient method. As expected from experimental data, the HSO2' system is found to have a rather flexible structure whose symmetry elements reduce to a C, axis. Terminal water molecules may execute large-amplitude motions of rotation and oscillation around the O..O direction at room temperature. These results bring some support to the interpretation of the spatial arrangement of both water molecules in the vicinity of the central proton as depending essentially on the direction of their lone pairs, and to a possible bending of the hydrogen bridge (LOHO 178'). The various structures of H502+ exhibited in solid medium are in the range of the predicted structures.
Introduction The HS02+cation exists in the gas phase either in the D region of the ionosphere, where it is considered as the major component of the positively charged species,* or in flames and discharges as products of reaction^.^ Its short lifetime, due to rapid secondary reactions, prevents use of current detection procedures such as spectroscopy or electron diffraction. This is illustrated by the recent infrared analysis of Schwarz4 which failed to identify HS02+ whereas other ions such as (H,O),H,O+ were effectively detected. The situation is however more favorable in the solid state where first mention of the H502+ion can be found in the pioneering work of Nakahara et aL5 In this work, the crystal structure of [Co(1) (a) Laboratoire des Acides MinCraux; (b) Centre de MBcanique Ondulatoire Appliqute. (2) R. S. Narcisi and A. D. Bailey, J . Geophys. Res., 70, 3687 (1965). (3) W. C. Lineberger and L. J. Puckett, Phys. Rev., 187, 286 (1969). (4) H. A. Schwarz, J . Chem. Phys., 67, 5525 (1977).
0022-3654/84/2088-1125$01.50/0
(en)2C12]HC1.2H20 (where en represents the ethylenediamine group) has been determined by X-ray diffraction. The [H20. -H. -H20]' group was identified and supposed to be located in defects between the layers of [Co(en),Cl,]. Later, Gillard and Wilkinson6 confirmed by infrared spectroscopy the presence of dioxonium ion in the Nakahara salts, though no precise structure could be derived from their exploratory investigation. Since then, more than 13 structures have been proposed7 showing that the cation js a flexible system which may easily adjust itself to its solid environment. This is well illustrated by two recent neutron diffraction experiments which demonstrate that the dioxonium ion
- -
(5) A. Nakahara, Y.Saito, and H. Kuroya, Bull. Chem. SOC.Jpn., 25,331 (1952). (6) R. D. Gillard and G. Wilkinson, J . Chem. Sor., 1640 (1964). (7) J. 0. Lundgren and I. Olovsson in "The Hydrogen Bond", Vol. 11, P. Schuster, G . Zundel, and C. Sandorfy, Eds., North-Holland, Amsterdam, 1976, pp 471-526.
0 1984 American Chemical Society
1126 The Journal of Physical Chemistry, Vol. 88, No. 6,1984 TABLE I: Experimental Data on the Structure of H,O:
host cryst HCI. 2H ,O HC1.3H2O HBr.2H2O
Y H(C,04),~3H,0 Cs(en),Cl,~HC1~2H,O HAuCl ,.4 H,O HAuC1;4HZO (disordered) a
Water 0. $0angle.
meth
temp, K
XI: XP XF N XI: XF XC XC XC N
86 83 83 86 211 83 83 83 RTC RT
XC XC N
RT RT RT
XC N N XC N
RT RT RT RT RT
H bond angle.
Potier et al.
in Various Crystais
d o ...0,.4
2.4 1 2.43 2.4 1 2.40 2.47 2.42 2.43 2.4 1 2.44 2.45 (1.18 1.27) 2.45 2.43 2.44 (1.13 + 1.31) 2.43 2.44 2.43 2.47 (2.57)
+
dihed angle, water angle, deg deg
do^^, A 0.95, 1.07 0.98, 0.96
0.95, 0.98 1.00, 0.99
54.7 109.8 52.1 55.3 170 180 (?) 40.8 94.8 0.5
107, 108
0.5
115, 112
pa
bb
c, 108.5, 108.6
0,41.8
174.7
180
C;
c,
10c
Cj C;
C,,
10d 10e 10f 1og 10h
C,
1og 1Oi
C,
lOj
C,
16 10h 9 101 lorn
c, 176
0.98, 1.00 0.98, 0.99
105.7
107.2, 110.4
45.3, 57.8
175
0.98, 0.99 0.99
136 136.3 180 180
110.7 109.1
42.5 48.6
175.3 180 180 172
109.2
ref 10a 10b 1oc 8
C,
7.9 105.8
(180)
sym C,
C,
ci ci
21m
RT = room temperature.
TABLE 11: Calculated Values of the Equilibrium Structure of H,O,+"
methods SCF-GTO (double 5 ) SCF-GTO SCF-GTO (4-3 1G ) SCP-GTO (double r) SCF-GTO
optimized parameters
R R, r R, a R, r, R, 0
symmetry at equilibrium
R(O. * *O),A
zd zd Dzd cy
Values in parentheses mean adopted data. tion of H,O+.
Id
c*
2.30 2.39 2.36 2.36 2.381
r(0-H), A 0.95 (0.95) 0.966 (0.947),b (0.964)'
Values taken from separate minimization of H,O.
may have either a dissymmetric structure in bromide8 or a symmetric Cistructure (close to D2h)in the Nakahara salts? A review of experimental data8-I0J6 is given in Table I from the work of Lundgren and Olo~sson.~ It is remarkable that only three of these structures belong to the Cisymmetry group whereas four are C2 and the others are nearly C2h.External OH distances also display a variety of bond lengths. Although the experimental results seem to suggest that H502+ is a rather flexible system easily deformed by weak interactions, the theoretical calculations performed to date seem to ignore this property. The system has been assumed to belong to D , synfnfetry type and usually incomplete minimization performed with mnimal (8) R. Attig and J. M. Williams, Angew. Chem., Int. Ed. Engl., 15, 491 (1976). (9) J. RoziQe and J. M. Williams, Inorg. Chem., 15, 1174 (1976). (10) (a) J.-0. Lundgren and I. Olovsson, Acta Crystallogr., 23, 966 (1967); (b) Ibid., 23,971 (1967); (c) J.-0. Lundgren, Acta Crystallogr., Sect. B, 26, 1893 (1973); (d) I. Olovsson, J . Chem. Phys., 49, 1063 (1968); (e) T. Kjlllman and I. Olovsson, Acta Crystallogr., Sect. B, 2& 1962 (1972); ( f ) R. G. Delaplane, J.-0. Lundgren, and I. Olovsson, Ibid., 31, 2208 (1975); (9)
E. Krogh Andersen, 'Experimentelle studier over Strukturen af hydroxyquinoner og deres salte", Molekylstruktur og syrestyrke, Odense Universitetsforlag, Denmark; (h) J. M. Williams and S. W. Peterson, Acta Crystallogr., Sect. A , 25, S113 (1969); (i) J.-0.Lundgren, Acta Crystallogr., Sect. B, 28, 1684 (1972); (j) J.-0. Lundgren and R. Tellgren, Ibid., 30,1937 (1974); (k) C. K. Johnson and G . D. Brunton, "Abstracts of the American Crystallographic Association Meeting, Albuquerque, NM, 1972"; (1) R. A. Pennehn and R. R. Ryan, Acta Crystallogr., Sect. B, 28, 1629 (1972); (m) J. M. , Williams and S. W. Peterson, J . Am. Chem. SOC.,91, 776 (1969). (11) P. A. Kollman and L. C. Allen, J. Am. Chem. SOC.,92,6101 (1970). (12) W. P. Kraemer and G. H. F. Diercksen, Chem. Phys. Lett., 5, 463 (1970). (13) M. D. Newton and S . Ehrenson, J. Am. Chem. Soc., 93,4971 (1971). (14) G. Alagona, R. Cimiraglia, and U.Lamanna, Theor. Chim. Acta, 29, 93 (1973). (15) J. J. Delpuech, G. Serratrice, A. Strich, and A. Veillard, Mol. Phys., 29, 849 (1975). (16) P. A. Kollman and C. F. Bender, Chem. Phys. Lett., 21,271 (1973).
cu(
