J. Phys. Chem. 1994, 98, 13443-13446
13443
Molecular Solvation in van der Waals Heteroclusters. Magic Numbers in the Mass Spectra: A Dynamical Signature of Solvent Shell Saturation in the Ion C. Guillaume, J. Le CalvC, I. Dimicoli, and M. Mons* CEA, Centre d'Etudes de Saclay, Biit 522, Service des Photons, Atomes et Moltcules, 91191 Gif-sur-Yvette Cedex, France Received: July 14, 1994@
The systematic existence of magic numbers in the mass spectra of van der Waals heteroclusters is illustrated in the case of two solute molecules (benzene and aniline) solvated by a series of five nonpolar solvents (argon, krypton, xenon, nitrogen, and methane). For each solute-solvent pair, the microsecond time scale evaporation kinetics of the laser-ionized clusters is found to exhibit anomalies for these magic sizes, showing that the ionic evaporation is responsible for the magic numbers of the mass spectra. The comparative study within the series of solvent entities of various size allows us to assign the magic numbers to the closure of the first solvation shell around the solute cation, demonstrating the wetting character of the solvent in these cluster ions.
Introduction
In the past decade, molecular heteroclusters have been considered as informative model systems for the study of solvation on the microscopic scale.'-3 In particular, solvation by nonpolar solvents has been widely investigated both experimentally and theoretically using this original approach.'-14 Experiments based on spectroscopic measurements on clusters (electronic transition shifts,'-l0 vibrational energy shifts of the solutell and of the solvent molecule,12 and ionization potent i a l ~ ~ , have ~ , ~ been , ~ ) shown to provide useful geometrical and dynamical information. Although the geometry of small complexes can be obtained with reliabilit~,~ clear conclusions on the structure of larger clusters are, however, seldom derived. In particular, the signature of the closure of the first solvent shell in electronic spectra is not clearly established often because of the intricacy of both geometrical and dynamical influences upon the spectral features like, for instance, the simultaneous presence of numerous isomers. Thus, a question as simple as the solute location in the large benzene-argon clusters is still contro~ersial.~-~J 1-14 Confronted with this obstacle, we have chosen an altemative approach in order to study and characterize the first solvation shell around a molecular system. This approach, of dynamical nature, is based on the fact that the evaporation energy of a solvent particle from a given cluster is expected to be larger in the first shell than in the outer shells, provided that the solvent is of wetting nature, Le., provided that the solute-solvent binding energy is larger than the solvent-solvent interaction. The consequence of such a stability difference is currently observed as "magic numbers" in the mass spectra of rare gas homogeneous ~ 1 u s t e r s ~and ~ Jof ~ related species (mixed rare gas ~ 1 u s t e r s ' ~or J ~molecular cluster^^^^^^). Because of the successive evaporation events undergone by the aggregates following ionization, particular cluster species having larger evaporation energies exhibit a positive population balance: the population of those species is indeed increased by fragmentation from the less bound species above them and is less decreased than other sizes because of their large evaporation energy. They consequently appear as more intense peaks in the mass spectra, giving rise to magic numbers. Such effects have been rarely @
Abstract published in Advance ACS Abstracts, December 1, 1994.
0022-3654/94/2098- 13443$04.50/0
reported for the van der Waals h e t e r o c l ~ s t e r s , ~despite ~ ~ J ~ *the ~~ numerous studies devoted to these species, partly because the intensity anomaly is less prominent there than in the case of the shell closure in the rare gas cluster^'^*^^ and also partly because experimentalists have been much more active on the size dependence of the cluster spectroscopy rather than on the size distribution in the mass spectra. In the present paper, the systematic existence of magic numbers is demonstrated for the aggregates of one aromatic molecule (benzene or aniline) with rare gas atoms (Ar, Kr, and Xe) and nonpolar (nitrogen and methane) molecules. Microsecond time scale evaporation rates of the cluster ions are reported for each solute-solvent pair studied. The results clearly show that the magic numbers have to be assigned to the dynamics of the cluster ions since the evaporation efficiency exhibits a prominent drop at the same size. Arguments for the observation of the the first solvent shell closure are given from the evolution of the magic numbers with the solvent size as well as from theoretical considerations. Experimental Setup In the present experiment, neutral clusters are formed in a pulsed supersonic expansion and are laser ionized and the corresponding isolated cluster ions are detected and analyzed in a time-of-flight mass spectrometer. Details of the setup are given e l s e ~ h e r e .The ~ ~ solute ~ * ~ ~molecules (benzene and aniline) have been chosen for their ability to be laser ionized through a one-color resonant two-photon ionization process. The laser wavelength has been taken in the vicinity of a strong W absorption transition of the solute molecule, in order to optimize the cluster excitation, in accordance with cluster absorption spectra when available.6-10The solvents chosen are nonpolar, gaseous, and easily mixed with the room temperature vapor pressure of the solute molecules. The mass spectra of aniline (An) or benzene (Bz) aggregates with various nonpolar solvents have been recorded using a reflectron-type mass spectrometer in a linear detection mode, Le., using a dectector located behind the electrostatic mirror? The microsecond time scale evaporation rates of the ionic clusters of Bz and An have been investigated using a kinetic energy analysis (KEA) technique described in detail elsewhere.*' Briefly, just before detection, ions have to cross an electrostatic barrier (the mirror of the reflectron mass spectrometer ap0 1994 American Chemical Society
Letters
13444 J. Phys. Chem., Vol. 98, No. 51, 1994 TOF
'
m
=ii +. -
number of N, molecules Figure 1. Mass spectrometry and microsecond time scale dynamics: (a) part of the mass spectrum (linear detection mode) of the laser ionized Bz-(Nz)" species showing a marked intensity anomaly between n = 20 and 21; (b) part of the KEA mass spectrum (see text) of the same species, showing a doublet series; the early component corresponds to those ions which did not evaporate in the field-free region of the mass spectrometer; the late component is composed of clusters having lost one nitrogen molecule during the same time window (2-35 ,us); the KEA spectrum has been rescaled to make the comparison with spectrum a easier; (c) size dependence of the cluster ion survival probability as obtained from the KEA spectrum of b; (d) size dependence of the relative evaporation energies E,,/En+las obtained from the deconvolution procedure of Klotsz2(Gspann parameter, 23.5; C,(n) = (3.94 n - 6 ) k ) .
propriately biased) which delays the ions according to their kinetic energy. Daughter ions originating from the field-free region have the same velocity as their parents and consequently a smaller kinetic energy due to their smaller mass. Those ions are thus more delayed than their parents by the electrostatic barrier and are detected some hundreds of nanoseconds later. This delay is experimentally sufficient to measure the parent survival probability during their flight in the field-free region (typical time window 2-35 ,us).
Results and Discussion A typical mass spectrum obtained for the Bz+-(N*), species in the linear detection mode is reproduced in Figure la. It clearly exhibits a significant intensity drop at n = 20. In each solute-solvent pair presently studied, such an intensity drop was observed in the 15-22 size range, with a more or less pronounced character. These intensity distributions of cluster ions actually depend upon three parameters, namely, the neutral distribution, the excitation efficiency, and the evaporation dynamics of the ionized clusters. This latter process deserves special attention since in the laser ionization scheme used, the excess energy in the ion is indeed significant (up to ca. 1 eV in the case of aniline clusters). In some respects laser ionization produces an annealing of the clusters. Indeed, clusters are left more or less hot following ionizationz1and cooling takes place via successive evaporations of solvent moieties, down to a temperature which depends essentially upon the evaporation energy and the time scale of the experiment.22 Simple statistical RRK models predict final temperatures of 40-30 K for argon clusters as well as typical 105-io6 s-' rates for the evaporations occumng some
microseconds after the ionization event. These long time scale evaporations, which are actually the last step of the cooling process, i.e., the last evaporations undergone by the clusters in the experiment, take place in the field-free region of the mass spectrometer and can thus be detected using the spectrometer in the KEA mode. The effect of evaporation in the field-free region is shown in Figure l b for the Bz+-(Nz), clusters. The KEA spectrum is composed of two slightly shifted peak series: the first one corresponds to parent ions which did not evaporate in the fieldfree region; the second one consists of daughter ions, Le., parent ions having lost one solvent atom in the field-free region. From these observations, it appears that the Bzf-(N2), clusters with n I 21 present a much larger probability to evaporate one solvent molecule than the smaller species. The measurement of the parent and daughter intensity for each mass allows us to extract the fiist quantitative information, i.e., the parent ion survival probability during its flight in the field-free region (Figure IC). The sudden drop in the cluster ion survival probability shows that the evaporation dynamics in the ion is a strongly size-dependent process. The exact correspondence between the magic number n = 20 in the mass spectrum (Figure la) and the survival probability drop (Figure IC) shows that the major process responsible for the occurrence of magic numbers in mass spectra is the evaporation process in the ionic cluster; the role of the neutral size distribution and of an eventual size selectivity of the R2PI process appears here negligible. The deconvolution procedure for the evaporation rates proposed by has been used to quantify the difference in stability responsible for the observed decrease of the survival probability. This procedure allows us to estimate the size dependence of the relative evaporation energies E,IE,+1, provided that some data are available (survival probabilities, time window of the experiment, Gspann parameter, and cluster caloric capacities) and that each cluster observed has undergone at least one evaporation. The values obtained for the Bz-Nz system are given in Figure Id; they show that the experimental evaporation data are accounted for by a sudden discontinuity of the evaporation energy between n = 20 and n = 21. Reminding us that the evaporation rate is a steep function of the evaporation energy, we see that, during the cascading evaporative process, an accumulation of cluster population will take place at the sizes where the EJE,+I curve presents anomalies. KEA spectra have been carried out for each solute-solvent pair studied. The survival probabilities derived (Figure 2) exhibit in each case a sudden and marked drop: the magic numbers observed in the mass spectra (Figure 1) are confirmed as magic numbers by the KEA spectra and the size dependence of the survival probability (Figure 2). It should be noticed that even when the intensity drop was not very marked in the mass spectrum, for example, because the cluster population could not be fully optimized in the region of the considered magic number, identification and characterization of the magic number appear much safer from the KEA spectra. The coincidence of the magic sizes with the anomalies in the evaporation rates measurement thus appears a general behavior indicating that the magic numbers are actually the dynamical signature of a size-specific evaporation process occurring in the ionic state. The assignment of the magic sizes and of the evaporation anomalies to a solvent shell closure around the ionized molecule is supported by the following observations derived from Figure 2. First, the magic size observed varies with the solute-solvent pair considered. This clearly shows that magic numbers do not
Letters
J. Phys. Chem., Vol. 98, No. 51, 1994 13445 SOLVATED BENZENE 15 20
SOLVATED ANILINE 20 25
15
35*
i
Solvated benzene O
3.7 3.0 3.9 4.0
4.1 4.2
4.3 4.4
van der Waals diameter of the solvent
M
(A)
Figure 3. Comparison of the observed with the predicted magic numbers for benzene solvated by spherical solvents. The hollow square corresponds to the 0 K molecular dynamics simulation of the shell closure in the benzene-argon s y ~ t e m . ~ ~ , * ~
Figure 2. Survival probability of the cluster ions of benzene and aniline with several nonpolar solvents of different van der Waals radius: argon, nitrogen, krypton, methane, and xenon. For the clusters of Bz,the laser was tuned in the vicinity of the SI- S06; transition (-37, -67, -86, and -93 cm-l relative to the monomer, respectively); with xenon, the mass distribution could not be experimentally optimized for clusters larger than n = 10. For the clusters of An the laser was tuned in the vicinity of the origin of the S1 SO origin transition (-95, -313, -200, -256, and -200 cm-' relative to the monomer, respectively). The magic numbers, i.e., sizes at which the peak intensity drops significantly, are indicated by arrows.
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correspond to specific structural arrangements of the solvent cluster itself, like those observed for rare gas cluster ion^'^^'^ or for solvated molecular ions at the surface of a large solvent cluster.18 Second, for a given solvent the magic numbers observed are always larger for the larger solute molecule (for instance, n, = 22 for aniline with Ar and NZ vs 20 for benzene). Third, with solvents of comparable size and shape,23 like xenon and methane, similar magic numbers are found around a given solute (n, = 18 for Xe and CH4 around aniline; see Figure 2). Fourth, for each solute molecule, a monotonic decrease of the magic number is observed as the solvent sizez3 increases (Figures 2 and 3). These four points together suggest that, in these cluster ions, the solvent exhibits a wetting behavior, Le., it covers the surface of the solute molecule, and the discontinuity observed in the size-dependence of the evaporation energies corresponds very likely to the saturation of the first solvent shell around the molecule. In order to strengthen this conclusion, the observed magic numbers have been compared to predicted magic numbers. These values have been estimated on a simple geometrical basis, Le., by dividing the surface of the solute molecule (Ssolute) by the surface covered by each solvent molecule, which is supposed to be in contact with the solute and its nearest solvent molecule neighbors. The surface of the solute, Le., the surface on which the solvent nuclei are supposed to evolve, was estimated within the frame of an interaction model based upon a sum of pairwise
atom-atom Lennard-Jones interactions; such a surface is obtained from the molecular skeleton of the solute dressed by spheres centered on each solute atom Ai and having a radius corresponding to the equilibrium distance Ai-solvent. These distances have been derived from experimental data on gases23 and semiempirical combination rules.% In the case of benzene, taking advantage of the resemblance of this surface with a revolution ellipsoid, SsOlute has been estimated from the calculation of the volume inside the surface. The surface covered by one solvent molecule has been taken as a z h2, where h is the van der Waals radius of the solvent which is assumed to be sphericalz3and a is a coefficient which takes into account the interstitial surface between projected spheres in a bidimensional close-compact arrangement (a = 2&/z). Figure 3 summarizes the results of this estimation for the benzene clusters. One observes that the calculated magic size decreases monotonically with the van der Waals radius of the solvent within the solvent set considered. This trend corresponds well to the experiment, which supports our assignment in terms of solvent shell closure. The discrepancy in terms of absolute values deserves, however, some comments. First, the crudeness of the present model makes its use difficult for a comparison other than qualitative. Molecular dynamics (MD) simulations appear to be much more pertinent here. Calculations on neutral Bz-Ar, clusters at 0 K thus predict the first shell completion to occur for n = 2525J-6(hollow square in Figure 3). The significant discrepancy which still exists between the MD simulations and experimental magic numbers may have two possible origins: (i) the MD calculation pertains to neutral aggregates while the experiment is performed on cluster ions and (ii) the MD calculations only concem classical minimum energy (0 K) conformations. Concerning the former point, the solvent shell can intuitively be smaller in the ion because of the increased solute-solvent interaction relative to neutral. It appears nevertheless unlikely that the resulting difference would reach five solvent units. More probably, the difference between experiment and MD simulations might be accounted for by an enlarged effective radius of the solvent due to the cumulative effects of zero-point quantum energy and thermal vibrational motion existing in the clusters, since, although being in the last stage of their cooling, the temperature should not be less than 30 K.z7 Thus these results would also illustrate the temperature dependence of the concept of solvent shell closure. In connection with this point, it should be noticed that the observation
13446 J. Phys. Chem., Vol. 98, No. 51, 1994 of a unique magic number for each solute-solvent pair suggests that the density of the solvent shell is pretty well defined and consequently that the cluster temperature is fixed unambiguously by the evaporation process, in agreement with the evaporative ensemble model of Klots.22 In the present comparative study, the linear N2 molecule is a special case because of its nonspherical shape. Dispersion interaction should a priori favor a tangential solvent confoxmation relative to the ionic solute whereas radial orientations should optimize both charge-induded dipole and solvent-solvent interactions. The systematic coincidence between the magic numbers obtained with argon and nitrogen around benzene and aniline cations as well as around toluene and fluorobenzene26 suggests that each argon and nitrogen molecule occupies a similar surface around the ionic solute. Considering that the commonly admitted van der Waals “diameter” of nitrogen (4.15 A231 is larger than that of argon, the experimental results suggest that N2 molecules are rather radially aligned relative to the ion. This conclusion finds support in recent calculated structures of the N2 dimer for which an intermolecular distance of 3.65 8, is reported for a parallel dimer geometry.30
Conclusion The present experiment demonstrates the ability of molecular clusters composed of a molecule embedded in a nonpolar solvent environment to give rise to magic numbers in their mass distribution. The magic numbers appear as a consequence of evaporation in the cluster ion, which is revealed to be strongly size dependent, with a steep efficiency change in the n = 1522 range. The study of solvation by a series of solvents allows us to assign the magic numbers to the closure of the f i s t solvent shell in the ionic clusters, illustrating the two-dimensional character of these van der Waals bound clusters. The present result shows that magic numbers can appear in molecular clusters for reasons other than purely geometrical, like in the icosahedral rare gas clusters,15-18 or chemical, like for the hydrogen bounded cluster^.^^^^^ The observation of magic numbers due to solvent shell closure is very likely a general phenomenon which can be encountered in the mass spectra of aggregates of similiarly loosely-bound nature, i.e., ionized complexes composed of a molecular solute in a nonpolar environment with comparable solute-solvent and solventsolvent interaction strengths. The measurement of the microsecond time scale evaporation rate thus appears to be a pertinent method to quantify directly the number of molecules in the first solvent shell, which is information often difficult to obtain from purely spectroscopic diagnostics.
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