Matrix Isolation Studies of C02 Clusters Emerging from Adiabatic

J. Phys. Chem. 1995, 99, 4906-4911

4906

Matrix Isolation Studies of C02 Clusters Emerging from Adiabatic Expansion7 Erich Kniizinger" and Peter Beichert' Institut f i r Physikulische Chemie, TU Wien, Getreidemarkt 9, A-I 060 Wien, Austria Received: August 15, 1994; In Final Form: November 30, 1994@

FT-IR spectroscopic studies of the relaxation of binary solid nonequilibrium mixtures of COZ and Ar or Kr (1:1000 molar ratio) are reported. The samples were prepared by embedding carbon dioxide in solid rare gas, either after thermal effusion or after adiabatic expansion. The resulting matrices then contained exclusively isolated monomer COZ or both monomer and aggregate species, respectively. These two nonequilibrium systems were subjected to appropriate thermal treatment, which initiated a stepwise transition to the same final state, namely, the equilibrium solid. The relaxation paths traced by monitoring the asymmetric stretching vibration of l3CO2in natural abundance are, however, fundamentally different. They include an intermediate amorphous and a COZcluster phase, respectively. The studies were preferentially carried out in Kr matrix, since the initial spectrum indicates the presence of only one substitutional site for the COz monomer, whereas in Ar there are four sites. To facilitate the interpretation of the IR spectra, ab initio calculations were performed on small C02 clusters.

Introduction Solid phases and aggregate species of carbon dioxide have attracted considerable interest from both theoreticians and experimentalists. Crystalline and amorphous CO:! were studied intensively with the aid of vibrational and although a relatively large number of s p e c t r o s ~ o p i c ~and -~~ theoretical14-16 studies were exclusively dedicated to the COz dimer, the question related to its structure remained unresolved for a considerable period of time. Initially, the global potential minimum was attributed by experimentalists to the T-shaped dimer. This highly speculative model was based on the quadrupole properties of the C02 molecule. More recent calculation^^^^^^ incorporating large basis sets and correlated wave functions clearly showed that the offset parallel dimer is more stable than the T-shaped structure. The experimental evidence for this prediction was provided by the laser spectroscopic studies of Jucks et al.,1° in which both species were observed. From tunneling modes, these researchers derived interesting dynamic properties. Besides the dimer, large COz clusters of more than 100 molecules were the subject of frequent t h e o r e t i ~ a l ' ~and ~ ' ~e ~ p e r i m e n t a l ~investigations. ~'~-~~ However, there is an evident lack of experimental and theoretical data related to C02 clusters of intermediate size ((COz),,with 2 < n < 100). To the best of our knowledge, only one study so far has been carried out that provided the rotationally resolved IR spectrum of a C02 trimer emerging under supersonic beam

condition^.^^ The theoretical treatment of small C02 clusters is extremely difficult. Classical calculations based on empirical potentials may be applied successfully only to the solid and to large clusters. On the other hand, even small C02 clusters generally are too large for ab initio calculations aiming at an accurate description of weak intermolecular forces. The unavoidable use of large basis sets and correlated wave functions would raise the required memory capacity and CPU time to prohibitive numbers.

* Author to whom correspondence

should be addressed. Dedicated to Prof. Dr.H. D. Lutz, Fachbereich Chemie, Universititt-GH Siegen, Germany, on the occasion of his 60th birthday. Current address: Department of Chemistry, University of California at Irvine, Irvine, CA 92717-2025. Abstract published in Advance ACS Abstracts, March 15, 1995.

*

@

The experimental investigation of C02 clusters is not free from serious drawbacks either. So far, no size-selective technique of C02 cluster production is available. Hence, the experimentalist has to cope with a more or less broad size distribution of COz clusters. This makes it difficult or even impossible to isolate the data on just one species out of the whole spectrum of information of the size distribution. The present paper reports a detailed investigation of CO:! clusters produced in the course of an adiabatic expansion in a pulsed supersonic nozzle. The aim was not to be size-selective, but rather to be able to influence the resulting COz cluster size distribution, which is intimately related to the expansion conditions. The size distribution and associated changes triggered by variation of the expansion conditions may then be monitored in two different ways: (1) by in-flight mass spectroscopy in the beam and (2) by FT-IR spectroscopy applied to the clusters after their immobilization and isolation in a cryogenic matrix. Ab initio calculations were performed in order to obtain support for the interpretation of experimental data. The objective of the theoretical studies was to resolve trends in certain properties (e.g., stability, harmonic frequencies) within a series of clusters, rather than to obtain an accurate description of the properties of each species.

Experimental Section The combined molecular b e d m a t r i x apparatus has been previously described in The clusters are formed by an expansion of mixtures of COZ with noble gases (Messer Griesheim; purity '99.999% for CO2, Kr, and Ar and >99.998% for Ne) through a pulsed nozzle of 0.1 mm diameter from a reservoir at 293 K. The stagnation pressure is variable up to 10 bar. The duration of each pulse is 150 ps, and the pulse frequency equals 6 Hz. The cluster beam passes through a skimmer with 0.5 mm diameter and then enters the mass spectrometer chamber, which is pumped separately. The mass distribution in the cluster beam is determined by a quadrupole mass spectrometer (SXP 400, VG instruments) with electron impact ionization. Its ion source is of the open crossed beam type. Finally, the clusters are trapped on a gold-plated aluminum mirror, which is mounted at the cold end of a closed-cycle helium refrigerator (ROK 10, Leybold). The temperature (12

0022-3654/95/2099-4906$09.00/0 0 1995 American Chemical Society

J. Phys. Chem., Vol. 99, No. 14, 1995 4907

Matrix Isolation Studies of COz Clusters

K) of the mirror where the COZclusters are deposited does not permit the condensation of the seed gas Ne, which has to be pumped off efficiently. In order to isolate the clusters, a thermal effusive stream of argon or krypton acting as matrix gas is directed from a separate inlet onto the mirror. The outer shroud of the cryostat is equipped with a KBr window to allow the IR beam to propagate through the cryogenic sample. A reflectance unit mounted in the sample compartment of the interferometer is used to reflect the beam of the light source to the cold mirror coated with the matrix. It then returns the reflected light to the spectrometer optical path. There is practically no mechanical contact between the vacuum shroud of the vibrating cryostat and the interferometersz6 It should be noted that the space between the windows in the front plate of the sample compartment and in the shroud of the cryostat has to be purged with dry air or N2 to remove traces of atmospheric water and carbon dioxide in the optical path. The IR spectra were recorded with a Fourier transform infrared spectrometer (IFS 113v, Bruker Analwsche Messtechnik GmbH) equipped with a liquid nitrogencooled MCT detector. A total of 100 scans was accumulated for each spectrum at a resolution of 0.2 cm-’. Method of Calculation. All calculations reported in this study have been performed at the SCF or MP2 level using the Gaussian 90192 program.*’ The geometry of the clusters was obtained by a full gradient optimization of the intermolecular and intramolecular degrees of freedom. The basis sets we used were 4-31G (split valence) and D95* (double zeta with one set of d functions). In order to eliminate the basis set superposition error (BSSE), all calculations were performed with the counterpoise correction. For each stable cluster, an analysis of the harmonic vibrational frequencies was carried out by computing the second derivatives of the energy. Results Mass Spectra. The objective of mass spectroscopy in the present investigation is to monitor the efficiency of cluster production for a given set of experimental conditions defining the adiabatic expansion. In spite of the distinct differences in the molar masses of Ne, Ar, and Kr, and hence of the momentum transfer between C02 and the rare gas, the mass spectra do not exhibit any significant dependence on the type of seed gas (8,if large COz (A) concentrations are applied (e.g., A:S = l:lO, Figure la). Under these conditions, the relaxation of vibrationally and rotationally excited C02 molecules is not complete at the end of the expansion. Therefore, the resulting clusters are relatively hot irrespective of which type of seed gas had been used. This explains both the absence of mixed cluster species (e.g., Krm(C02),) and the similarity of the mass spectra for CO2 in Ne, Ar, and Kr as seed gases (Figure la). For smaller molar ratios (e.g., A:S = 1:100, Figure lb), the respective mass spectra exhibit significant differences. In Ne only pure COz clusters are formed. However, the efficiency is low compared to Ar. This may be understood in terms of the larger mass of Ar, which facilitates the momentum transfer between Ar and COz. Therefore, far fewer collisions are needed to transfer the vibrational and rotational energy from COz to Ar. In addition, the similarity of the molar masses of COz and Ar results in an effectively negligible velocity slip.28 This means that, in Ar as seed gas, less kinetic energy has to be transferred to the COz molecules in order to accelerate them to the final speed (mls 780 for Ne and mls 5 5 1 for Ar after an expansion at 293 K). On the other hand, Ar itself undergoes aggregation, giving rise to the appearance of both pure rare gas and mixed clusters. This is also true for Kr. The only pure COz cluster

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Figure 1. Mass spectra after the expansion of COz with different rare gases (stagnation pressure: 5 bar): (a) molar ratio A:S = 1:lO; (b) A:S = 1:loo.

to be observed is the dimer. The broad isotopic distribution of natural Kr additionally complicates the mass spectra. Furthermore, intermolecular fragmentation is observed for the expansion of the C O D mixture (fragments: KrO+, KrC+, and KrCO+; Figure 1b, top). Evidently, fragmentation always occurs to a limited extent when electron impact ionization is applied. There is, however, no experimental evidence for intramolecular fragmentation when Ne or Ar is used in the expansion. In spite of the relatively low efficiency of COz cluster formation, Ne appears to be the more appropriate seed gas than Ar, since the respective mass spectra are free from rare gas and mixed clusters (Figure lb, bottom). It must be emphasized that the observed mass spectra do not reflect the true size distribution in the beam. Ion impact ionization may destroy clusters of a certain size by intermolecular fragmentation. It may, however, at the same time produce clusters of this particular size by initiating the fragmentation of larger ones. Hence, we have to refrain from interpreting the size distribution provided by mass spectroscopy. Nonetheless, the mass spectra do have considerable diagnostic importance. They reveal whether and to which extent the applied expansion conditions permit aggregation. This information greatly facilitates the evaluation of IR matrix spectra obtained on COz species emerging from the adiabatic expansion in question. FT-IR Spectra. The CO2 species emerging from an adiabatic expansion are codeposited with an excess of Ar or Kr, such that the molar ratio A:M of COz (A) in the matrix (M) is kept nearly constant for all experiments (on the order of 1:lOOO). The trapped CO2 species-monomers and aggregates-are then subjected to an FT-IR spectroscopic analysis. The asymmetric stretching region of COz exhibits the highest signal-to-noise ratio and the most significant changes upon varying the stagnation pressure or the molar ratio A S of COz in the seed gas. This spectral region is, therefore, considered here exclusively.

4908 J. Phys. Chem., Vol. 99, No. 14, 1995 4

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Figure 2. IR spectra of COz in Ar after expansion at different molar ratios A:S (the molar ratio of the matrix A:M is, in all cases, 1:1000). Stagnation pressure during the expansion: 5 bar. Small inset: Spectra

2290

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Figure 4. "COz stretching region of COZin Kr (A:M = 1:lOOO) after isolation from a thermal effusive stream (a) and after supersonic expansion with Kr (b) and Ne (c), followed by matrix deposition in Kr (A:M = 1:lOOO; expansion conditions prior to matrix deposition, A:S = 1:100; stagnation pressure, 5 bar).

of l3Co2.

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2350 2340 2330 Wavenumber I cm-' Figure 3. R spectra of COZin Ar (A:M = 1:1000) after an expansion with Ne (A:S = 1:lOOO) at different stagnation pressures.

The spectrum obtained after expansion in Ar (A:S = 1:lOOO) and subsequent isolation in an Ar matrix (A:M= 1:lOOO; Figure 2) is nearly identical to that resulting after normal matrix deposition (codeposition of CO2 and Ar after the thermal effusive expansion of a gas mixture with A:M = 1:1000). The four bands (Figure 2) were previously interpreted in terms of two monomer and two dimer species at different The increase in the molar ratio A:S from 1:lOOO to 1:lOO induces the appearance of a broad band that overlaps the abovementioned pattern. This is indicated in Figure 2 by the broken line, which results from a band fitting procedure. Comparable spectral changes are observed upon varying the stagnation pressure from 1 to 6 bar. The natural abundance of 13C02, which amounts to 1%, gives rise to a second pattern for the asymmetric CO?;stretching vibration around 2277 cm-' (Figure 2, inset). Its contour is nearly identical to that observed for the 12C02stretching region. If we expand COz with Ne and isolate the clusters in Ar, we observe an additional band at 2342.6 cm-' (Figure 3). The strong dependence of the intensity of this band on the stagnation pressure (Figure 3) clearly shows that it must originate from a cluster species that is formed in the course of the adiabatic expansion prior to the deposition. For I3CO2,the band is shifted to 2277.2 cm-'. After the isolation of 13C02monomers in a Kr matrix (Figure

4a), only one sharp band appears at 2275.1 cm-' (the I2C02 counterpart is located at 2340.5 cm-'). The adiabatic expansion of a C02K.r mixture and subsequent isolation in a Kr matrix give rise to an additional broad band on the high-frequency side (Figure 4b). After expansion with Ne and isolation of the resulting clusters in Kr, a Ne-specific band again is observed (Figure 4c). It is red shifted with respect to the monomer band at 2275.1 cm-'. It is well-known that appropriate thermal treatment initiates the aggregation of matrix-isolated species. In fact, the monomer band of COz in Kr irreversibly loses intensity upon raising the annealing temperature. This is shown for the asymmetric CO2 stretching band of I3CO2 available from carbon dioxide containing 13Cin natural abundance (Figure 5a: the two bottom traces in Figures 4 and 5a are identical). After annealing at 55 K the band has completely vanished. On the other hand, there is no equivalent increase in intensity that could be attributed to welldefined structures of dimers, trimers, etc., incorporating 13C02. Furthermore, annealing at 70 K causes the evaporation of Kr and leaves 13C02 isolated in a 12C02matrix. Under these conditions, 13C02exhibits a relatively prominent band at 2283.1 cm-'. Due to dynamic coupling, the corresponding band of the pure 12C02solid is broad and unspecific. By starting the annealing procedure from a Kr matrix containing aggregate species of COz emerging from an adiabatic expansion (e.g., Figure 4c), the resulting IR spectra (Figure 5b) differ considerably from those previously described (Figure 5a). The loss of band intensity for the monomer is balanced by the increase in intensity of a broad band on the high-frequency side of the monomer feature around 2275.1 cm-'. The band center is continuously shifted to higher wavenumbers upon increasing the annealing temperature, and at 55 K it abruptly transforms into the solid state band at 2283.1 cm-' (see above). It is obvious from Figures 4 (trace b) and 5b that FT-IR spectroscopy does not provide size-selective structural information on aggregates and clusters of C02 in cryogenic matrices. There are, however, substantial spectral changes originating from the adiabatic expansion of the matrix gas mixture prior to its deposition (Figures 4 and 5). In order to aid in the interpretation of these phenomena, ab initio calculations were performed. Theoretical Calculations. Figure 6 shows the geometries of the dimers, trimers, and tetramers of COz, which correspond to potential minima. The number of stable configurations rapidly increases with the number of constituents in a cluster. Table 1 gives insight into the relative stability of the resulting conformers. As a rough rule, species may by considered

J. Phys. Chem., Val. 99, No. 14, 1995 4909

Matrix Isolation Studies of C02 Clusters 1

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Figure 6. Calculated geometries of C02 clusters. All of the geometries have a potential minimum in SCF (with 4-31G and D95* basis sets) calculations. The dimers and trimers are also calculated at the MP2 level (D95* basis set).

Discussion

TABLE 1: Calculated Stablization Energies of COz Clusters from Firmre 7 (after Countemoise Correction) stabilization energy (kT mol-') code of cluster Figure 7 HF 4-31G HF 6-31G* MP2 D95* offset parallel dimer 2- 1 -5.3 -2.5 -2.5 2-2 -5.7 -2.4 -2.2 T-shaped dimer 3-1 -18.2 -7.7 -7.3 trimer 1 3-2 -10.4 -4.9 trimer 2 trimer 3 3-3 -10.5 -5.0 3-4 -10.7 -5.1 trimer 4 trimer 5 3-5 -10.6 -5.0 4- 1 -26.1 -11.1 tetramer 1 tetramer 2 4-2 -15.3 -7.0 tetramer 3 4-3 -15.7 -7.2 4-4 -24.0 -10.2 tetramer 4 tetramer 5 4-5 -23.9 -10.1 tetramer 6 4-6 -23.5 -10.3 4-7 -24.7 -10.5 tetramer 7 4-8 -15.0 -6.9 tetramer 8 4-9 -25.3 -11.1 tetramer 9

In general, cryogenic matrices containing isolated species are nonequilibrium systems exhibiting a miscibility gap under the experimental conditions normally applied in matrix isolation spectroscopy. The thermodynamically unstable solid mixture is produced by freezing the gaseous mixture as abruptly as possible. A matrix containing exclusively monomer species should provide an ideal system to start a time- and temperaturecontrolled relaxation toward thermodynamic equilibrium. The stepwise transition from the isolated monomer to the extended condensed phase includes the formation of aggregates and clusters as intermediates. The respective changes within the

matrix are reflected by the intramolecular vibrational behavior of the guest molecules and may, therefore, be monitored by IR spectroscopy. The feasibility of such experiments necessarily implies an accurate description of the initial stage of the matrix before the annealing procedure is applied to start relaxation. This may be an extremely difficult task. An example is C02 suspended in an Ar matrix. It has previously been studied by IR s p e c t r o ~ c o p yAfter . ~ ~ ~ thermal effusive expansion, four sharp bands were found in the asymmetric stretching region around 2340 cm-'. They were interpreted in terms of monomer (2339.0

energetically favorable when exhibiting a maximum number of nearly T-shaped substructures. This rule agrees with the most stable crystalline structure of C02 ( ~ C C )An . ~exception ~ is the T-shaped dimer, which is less stable than the offset parallel one. Figure 7 presents the corresponding calculated harmonic frequencies of the asymmetric stretching vibration. Although the agreement of calculated frequencies with those obtained by IR spectroscopy is not satisfactory, reliable trends may, nonetheless, be observed: (1) Cluster formation of C02 is related to a large variety of separate frequencies (both the number of conformers and the number of normal modes increase with the size of the cluster) within an extremely narrow interval of 20 cm-' (the intermolecular interactions that govern cluster formation are weak). (2) With increasing cluster size, the center of the frequency interval in question is shifted to higher values.

Knozinger and Beichert

4910 J. Phys. Chem., Vol. 99, No. 14, 1995

-I

I

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and 2345.0 cm-') and dimer (2340.5 and 2346.7 cm-') absorption originating from species in different substitutional sites. This assignment contradicts recent t h e ~ r e t i c a l ' ~and , ' ~ expenmentallo studies, which provide unambiguous evidence that the potential energy for the dimer has two nearly equivalent minima that correspond to the T-shaped (CzV)and the offset parallel (C2h) structures. Both species should be present in the matrix and should exhibit at least two plus one IR-active bands, respectively. If the monomer and dimer species mentioned earlier have contributed to the spectrum, the relative band intensities should sensitively react upon variations in the experimental conditions applied during the production of the matrix. Therefore, the thermal effusive expansion generally applied to the gas mixture prior to deposition was replaced by an adiabatic expansion. For small molar ratios of COz and Ar, the absorption pattern (Figure 2, bottom) is very similar to that reported p r e v i o ~ s l y(thermal ~ ~ ~ effusive expansion). Upon an increase in the molar ratio from 1:lOOO to 1:lOO (Figure 2, top) or the stagnation pressure from 1 to 6 bar, the major spectral change to be observed is the growth of an unspecific broad absorption centered around 2347 cm-' (Figure 2), which will be discussed further in the following. It superimposes the above-mentioned pattern of four bands, which as a whole loses intensity at the same time. The changes in the relative intensity within the pattern certainly are not as dramatic as expected given the considerable variations in the respective experimental conditions. The key result that permits a reliable assignment stems from the asymmetric stretching vibration of 13C02. The natural abundance of 13Cis ca. 1%. Hence, dimers containing two 13C02 molecules are 2 orders of magnitude less likely than those that consist of two different isotopic species. If the 1 2 C Oabsorption ~ pattern between 2338 and 2348 cm-' had to be attributed to two monomer and two dimer species, then the 13C02 pattern between 2273 and 2281 cm-' should-because of reduced dynamic coupling-exhibit a completely different shape. In fact, the two isotopic species give rise to the same fine structure of the vibrational transition in question (Figure 2). Therefore, the four sharp CO2 bands have to be assigned to four monomer species in different substitutional sites of the Ar matrix. The additional feature observed at 2342.6 cm-' upon replacing the seed gas Ar by Ne grows much faster with the stagnation pressure than the other bands (Figure 3). This indicates that the corresponding species are created during the adiabatic expansion and require a particularly high cooling efficiency for their formation. Hence, the band at 2342.6 cm-' is attributed to a hitherto unspecified heterocluster incorporating at least one Ne atom. Such weakly bound species were not revealed by

mass spectroscopy in the molecular beam (Figure 1),since these species tend to dissociate into charged and/or neutral fragments during the ionization. In fact, it has been shown that large and weakly bound species preferentially undergo fragmentation into neutral component^.^^ Figure 2 clearly demonstrates that the integral absorbance of the broad band increases upon increasing the molar ratio of CO2 in Ar. An increase in stagnation pressure during the adiabatic expansion provokes the same spectral change. These variations in experimental parameters undoubtedly favor aggregation and cluster formation of COz. The broad band rather than the sharp features (Figure 2) should, therefore, be attributed to dimers, trimers, and larger units. This assignment is supported by calculated harmonic frequencies (Figure 7) of stable configurations of dimers, trimers, and tetramers (Figure 6). The absolute values are not of interest here. What is important, however, is the spectral interval in which the frequencies of the asymmetric stretching vibration are spread. It comprises approximately 15 cm-' and includes more than 50 different-not necessarily IRactive-frequencies for the three types of aggregates mentioned previously. Under the assumption that the minimum FWHM of the respective vibrational transitions is 0.5 cm-', the presence of dimers, trimers, and tetramers already suffices to explain the 15 cm-' broad feature. Both the simultaneous appearance of monomer bands of COz in the IR spectrum of the matrix (Figure 2) and the observation of relatively intense peaks for (COZ)~ with x = 2-4 in the mass spectrum of the molecular beam (Figure 1) additionally support this assignment. Obviously the experimental conditions applied during matrix production favor the presence of small species in the matrix. A possible reason for the complicated monomer spectrum of COz in Ar relates to sterical considerations. Carbon dioxide is too large to fit properly into a substitutional site of Ar. The matrix environment becomes distorted, and four different types of short range order are created (Figure 2). In Kr the situation is fundamentally different. Due to the larger substitutional site, the guest COz induces less distortion in the host Kr than in Ar. Accordingly, C02 molecules isolated in the Kr matrix exhibit only one sharp asymmetric stretching band (Figure 4, curve a). Aggregation and cluster formation are avoided by low deposition temperature (14 K) and low COz concentration ( A M = 1:1000) after thermal effusive expansion. The effect of aggregation initiated by adiabatic expansion in Kr and Ne becomes evident from the curves of Figures 5 and 4b,c, respectively: an additional broad band appears on the high-frequency side of the monomer feature. The band on the low-frequency side corresponds to an unspecific mixed species consisting of COz and Ne (compare Figure 3 and related text). Both the position and width of the COz cluster band are in qualitative agreement with the predictions of the theoretical calculations (Figure 7). The frequencies related to the aggregates lie preferentially above that of the monomer. The interval in which they are spread is obviously smaller than the value estimated from the theoretical calculations (Figure 7). This has to be expected since dynamic coupling is considerably reduced for vibrations of 13C02attached to 12COzmolecules. Upon comparison of Figure 4b with Figure 2, it becomes evident that the Kr matrix is much better suited for the study of aggregate formation of COz than the Ar matrix. In Kr the monomer spectrum is less complicated and it exhibits less overlap with the aggregate band. In fact, careful annealing (e50 K) of the Kr matrix containing exclusively monomer CO:! gives rise to the appearance of a sequence of weak cluster bands (Figure 5a). There is, however, considerable mismatch between the loss of monomer intensity and the gain of aggregate intensity.

Matrix Isolation Studies of C02 Clusters The explanation is intimately related to the mechanism of aggregate formation. From our own diffraction studies, it is known that recrystallization in Kr matrices is extremely unlikely at temperatures below 50 K. The question then arises: how is it possible that CO2 monomers suspended in a Kr matrix form stable aggregates? This, in principle, arises from diffusion on surfaces and grain boundaries, and perhaps to some extent also from local ordering effects associated with accidentally neighboring C02 molecules. At the onset of substantial evaporation of Kr, isolated C02 molecules and aggregates are forced from a random orientation into a quasi-amorphous C02 solid. This is evidenced by the very flat and broad absorption observed after annealing at 55 K (Figure 5a). The transition into a crystalline structure is then indicated after annealing at 70 K by the appearance of a relatively sharp band at 2283.1 cm-' with little structure in its wings. This band represents the asymmetric stretching vibration of a dynamically decoupled 13C02 monomer in an essentially uniform crystal field made up of l2C02 molecules. Figure 5b shows a second series of annealing experiments starting with a Kr matrix, which was deposited after adiabatic expansion of a properly selected COd Ne mixture and, therefore, incorporates both monomer and aggregate species of COz. Qualitatively, the spectra reveal the same trend as that demonstrated earlier (Figure 5a). There are, however, two fundamental quantitative differences: (1) The aggregation process at temperatures of about 40 K is much more efficient, if aggregated species are available as nucleation centers from the beginning. (2) At 45 K the monomers are nearly completely transformed into aggregates and clusters. The evaporation of Kr at temperatures above 45 K then gives rise to a continuous transition from the cluster phase of COZto the crystalline phase.

Conclusion COz clusters available under the collision-free conditions of a supersonic molecular beam can be isolated in cryogenic matrices. Major problems come up during the FT-IR spectroscopic analysis, which has to cope with limited specificity with respect to the COz cluster size distribution. Theoretical calculations (ab initio, frequency analysis) help to interpret spectral trends induced by properly changing the experimental conditions of expansion, matrix production, and subsequent annealing. As in the case of a~etonitrile,~~ the stepwise transition from dimer to larger units cannot be manifested explicitly due to the weak intermolecular interactions (dipole-dipole for CH3CN, quadrupole-quadrupole for C02). The situation changes drastically when comparatively strong interactions such as hydrogen bonds become effective. Then individual clusters may be traced during the transition from the monomer to the solid phase. This has been shown only recently for hydrogen cyanide.31

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Acknowledgment. This research was funded by the Deutsche Forschungsgemeinschaft, the Fond der Chemischen Industrie, and the Kanzler der Universittit-GH Siegen. We are grateful for their considerable financial support. Thanks are also due to Dr. Doris Pfeiler and Dr. Osman El-Dusouqui for revising the manuscript and helpful discussions. References and Notes (1) Cardini, G.; Rocacci, P.; Righini, R. Chem. Phys. 1987, 117, 355. (2) Dows, D. A.; Schettino, V. J. Chem. Phys. 1973, 58, 5009. (3) Falk, M. J. Chem. Phys. 1987, 86, 560. (4) Bini, R.; Salvi, P. R.; Schettino, V.; Jodl, H. J.; Orlic, N. J. Mol. Struct. 1992, 266, 165. (5) Olijnyk, H.; Dhufer, H.; Jodl, H. J.; Hochheimer, H. D. J. Chem. Phys. 1988, 88,4204. (6) Fredin, L; Nelander, B.; Ribbegard, G. J. Mol. Spectrosc. 1974, 53, 410. (7) Guasti, R.; Schettino, V.; Brigot, N. Chem. Phys. 1978, 34, 391. (8) Pubanz, G. A.; Maroncelli, M.; Nibler, J. W. Chem. Phys. Lett. 1985, 120, 313. (9) Barnes, J. A.; Gough, T. E. J. Chem. Phys. 1987, 86, 6012. (10) Jucks, K. W.; Huang, Z. S.;Dayton, D.; Miller, R. E.; Lafferty, W. J. J. Chem. Phys. 1984, 86, 4341. (11) Barton, A. E.; Chablo, A.; Howard, B. J. Chem. Phys. Lett. 1979, 60, 414. (12) Miller, R. E.; Watts, R. 0. Chem. Phys. Lett. 1984, 105, 409. (13) Mannik, L.; Stryland, J. C.; Welsh, H. L. Can. J. Phys. 1971, 49, 3056. (14) Brigot, N.; Odiot, S.; Walmsley, S. H.; Whitten, J. L. Chem. Phys. Lett. 1977, 49, 157. (15) Illies, A. J.; McKee, M. L.; Schlegel, H. B. J. Chem. Phys. 1987, 91, 3489. (16) Bone, R. G. A.; Handy, N. C. Theor. Chim. Acta 1990, 78, 133. (17) Cardini, G.; Schettino, V.; Klein, M. L. J. Chem. Phys. 1989, 90, 4441. (18) Disselkamp, R.; Ewing, G. E. J. Chem. Soc., Faraday Trans. 1990, 86, 2369. (19) Torchet, G.; Bouchier, H.; Farges, J.; Feraudy, de M. F.; Raoult, B. J. Chem. Phys. 1984, 81, 2137. (20) Fleyfel, F.; Devlin, J. P. J. Phys. Chem. 1989, 93, 7292. (21) Barth, H. D.; Huisken, F. Chem. Phys. Lett. 1990, 169, 198. (22) Barnes, J. A.; Gough, T. E.; Stoer, M. J. Chem. Phys. 1991, 95, 4840. (23) Gough, T. E.; Miller, R. E.; Scoles, G. J. Phys. Chem. 1981, 85, 4041. (24) Fraser, G. T.; Pine, A. S.; Lafferty, W. J.; Miller, R. E. J. Chem. Phys. 1987, 87, 1502. (25) Knozinger, E.; Beichert, P.; Hermeling, J.; Schrems, 0. J. Phys. Chem. 1993, 97, 1324. (26) Knozinger, E.; Schrems, 0. In Vibrational Spectra and Structure; Elsevier: Amsterdam, 1987; Vol. 16. (27) Frisch, M. J.; et al. Gaussian 90/92; Gaussian Inc.: Pittsburgh, PA, 1990/1992. (28) Kappes, M.; Kunz, R. W.; Schumacher, E. Chem. Phys. Lett. 1982, 91, 413. (29) Krupskil, I. N.; Prokhvatilov, A. I.; Ehrenburg, A. I.; Barylnik, A. S. Sov. J. Low Temp. Phys. 1982, 8, 263. (30) Schlag, E. W.; Grotemeyer, J.; Levine, R. D. Chem. Phys. Lett. 1992, 190, 521. (31) P. Beichert, and E. Knozinger, manuscript in preparation. JP9421747