The Stability of Rare Gas Clusters by Ionization

The Stability of Rare Gas Clusters by Ionization E. E. Polymeropoulos, S. Löffler, and J. Brickmann Institut für Physikalische Chemie. Technische Hochschule Darmstadt, Darmstadt Z. Naturforsch. 40 a, 516 - 519 (1985); received February 4. 1985 Computer simulations of the dissociation dynamics of argon and xenon neutral and singly charged clusters with 5 — 20 atoms were performed. It is shown that the stability of clusters with 'magic numbers' of atoms (« = 19 for argon, and n = 13,19 for xenon) as found in TOF mass spectra, is more enhanced by ionization than that of their neighbours, indicating the importance of the ionization for the cluster size distribution found in experiments.

I. Introduction An increasing interest in rare gas cluster research is related to the occurence and the n a t u r e of stable clusters with 'magic n u m b e r s ' of atoms. T h e existence of such aggregates has been proposed by H o a r e [1] w h o used sphere packing rules to show that certain clusters are m o r e stable t h a n others. However, the exp e r i m e n t a l difficulties involved in generating and detecting small neutral clusters [2] have lead to a controversy concerning the n a t u r e of rare gas clusters in general, and o f ' m a g i c n u m b e r ' clusters in particular, since in most experiments detection takes place a f t e r neutral clusters have been ionized. T h e controversy is focussed on the question whether ' m a g i c n u m b e r s ' in cluster size distributions are related to properties of the neutral clusters or w h e t h e r the ionization process plays the d o m i n a n t role for the observed stability m a x i m a . T h e available experimental evidence is still non-conclusive [ 2 - 1 0 ] although lately there is a tendency to accept a process that infers f r a g m e n t a t i o n of clusters after ionization which in turn f a v o u r s m o r e stable structures [7—10]. In this work the results of m o l e c u l a r d y n a m i c s simulations on neutral and ionized argon and xenon clusters with 5 - 2 0 a t o m s are presented. T h e calculations were p e r f o r m e d in order to find out the d i f f e r ences in the stability of neutral and c h a r g e d clusters and so to contribute to a solution of the controversy m e n t i o n e d above. S o m e i n f o r m a t i o n concerning the stability of rare gas clusters has already been supplied by c o m p u t e r simulations [ 1 1 - 1 5 ] but most of these calculations were p e r f o r m e d with neutral clusters which were then Reprint requests to Prof. Dr. J. Brickmann, Institut für Physikalische Chemie, Technische Hochschule Darmstadt. Petersenstr. 20. D-6100 Darmstadt.

c o m p a r e d with mass spectra of ionized clusters. T o o u r best knowledge there have been only two simulations on ionic rare gas clusters. In the work of G a y and Berne [14] the c o u l o m b explosion of d o u b l y charged xenon clusters is studied while Soler et al. [15] investigated the stepwise decay of a large singly charged cluster as a function of time.

II. Model Approach In this p a p e r the results of two series of calculations for neutral and ionic clusters are reported. In the first series (series A) neutral clusters with 5 - 2 0 atoms were studied. T h e interatomic interactions were m o d elled by Lennard-Jones (12, 6) potentials with parameters crAr = 3.405 Ä, £ A r = 1 1 9 . 8 K and oo. However, this p r o c e d u r e could not be realized because of the drastic increase of c o m p u t e r time. On the other h a n d such a p r o c e d u r e is not necessary to study the relative stability of neutral and charged clusters of the s a m e size. Since b o t h types of clusters desintegrate in the s a m e m a n n e r (single particle dissociation and r e m a i n i n g c o m p a c t cluster) we assume that the systematic error of the 7^ iss -values is the same for both, the neutral a n d the charged clusters. This ass u m p t i o n is c o n f i r m e d by a few sets of calculations with a slower h e a t i n g rate: T h e dissociation t e m p e r a ture are decreased s m o o t h l y in both cases but the data are insufficient for the limiting p r o c e d u r e m e n t i o n e d above. T h e Tdiss-values for neutral argon and xenon clusters averaged over 20 simulations as a function of the cluster size are s h o w n in F i g u r e 1. T h e average deviation of the Fj iss values does not exceed 3 percent for clusters with m o r e than 14 a t o m s and decreases with increasing cluster size. T h e average fluctuation for the desintegration t i m e Tdiss is higher (7.5 percent for Xei 6 ) as a c o n s e q u e n c e of d i f f e r e n t initial conditions (and t e m p e r a t u r e s ) for the individual runs. T h e FiiSS values of Fig. 1 cannot be related in a simple m a n n e r to the b i n d i n g energy of an atom to the cluster as a c o n s e q u e n c e of the systematic error m e n t i o n e d above. T h i s is clearly seen by considering the average ratio 7^ l i s s (Xe)/7 d i s s (Ar) = 2.03 for clusters with m o r e t h a n ten a t o m s while a ratio of £ x e / £ A r = F 8 5 for the dissociation energies results f r o m the law of c o r r e s p o n d i n g states [1]. A second systematic error is related to the omission of three b o d y interactions in o u r calculations. Additional three b o d y interactions lead to a weak stabilization of a neutral cluster with t h e magic n u m b e r 13 for xenon, as was recently d e m o n s t r a t e d by two of the present a u t h o r s [12, 13], but d o not qualitatively change the results for argon. T h e three b o d y interactions are m u c h w e a k e r t h a n t h e charge-polarizability interactions which are expected in the ionized cluster. In o u r study of the stability e n h a n c e m e n t of neutral clusters by ionization the three b o d y interactions are, therefore, not included in both series of simulations. T h e s i m u l a t i o n s on charged clusters (series B) were p e r f o r m e d following a model a p p r o a c h of H a b e r l a n d

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10 C L U S T E R SIZE

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Fig. 1. Dissociation temperature r diss vs. cluster size for ionic (O xenon, • argon) and neutral (+ xenon, • argon) clusters.

[9], i.e. it was a s s u m e d that directly a f t e r ionization an A r t or a X e 2 complex, respectively, is f o r m e d in the cluster. Again 20 s i m u l a t i o n runs per cluster size were p e r f o r m e d , each one starting with the actual positionand m o m e n t u m coordinates of the c o r r e s p o n d i n g neutral clusters of series A at the s i m u l a t i o n t e m p e r a ture of a b o u t 10 K. T h e pair of n e i g h b o u r i n g a t o m s with the largest distance f r o m the center of m a s s was chosen to build the initial c h a r g e d d i m e r complex. T h e interaction potential for the a t o m s of t h e ionic pair was again m o d e l l e d by a L e n n a r d - J o n e s potential with p a r a m e t e r erAl> = 0.6 • erAr, = 50 • E^, and ^Xe? = 0.7 •