THE PREDICTION OF ISOMERS FOR THE PHOSPHORUS CLUSTERS P7+

M. D. Chen1*, R. B. Huang1, L. S. Zheng1, and C.T. Au2

1 State key Laboratory for Physics Chemistry of Solid Surfaces Department of Chemistry, Xiamen University, Xiamen 361005, China

2 Department of Chemistry, Hong Kong Baptist University, Kowloon Tong, Hong Kong

Abstract In the study of cationic phosphorus cluster produced in direct laser vaporization, it has been

observed P74· shows the highest intensity in the mass spectrum. We acquired twenty-four P74· isomers with molecular graphics and then carried out optimizations with molecular mechanics, PM3 semi-empirical and ADF density functional calculations. In these isomers, the phosphorus atoms could be in two-fold, three-fold, four-fold or six-fold coordination. P7+ which derived from the most stable Ρβ by adding a phosphorus atom against the double bond has the lowest bonding energy. When there is a six-fold atom in the structure, the d orbital is involved in bonding. According to the bonding energies, the models with a planar ring or a six-fold atom are relatively less stable.

1. Introduction A great number of clusters have been generated by laser vaporization techniques or high

energy electron beam. Until now, carbon clusters (e.g. the famous fullerences) have received much attentions. Recently, there has been renewed interest in the studies of phosphorus clusters. Phosphorus has been known to show a wide range of homoatomic clusters. Martin observed large P n

+ clusters (n up to 24) after quenching the vapor of red phosphorus in a helium beam [1], We have reported the generations of phosphorus clusters containing up to 35 and 89 atoms in laser vaporization of red phosphorus [3,4].

Fig. 1 shows a time-of-flight mass spectrum of such an experiment, the numbers next to the peaks denote the atom numbers of phosphorus clusters. After the peak of P25+, relatively high intensities of phosphorus cationic Pn+ clusters were observed with η = 8k+1 (k = 3 -11). Based on the assumption that the high intensity clusters could be built from entities of eight phosphorus atoms, we constructed some structures from P25+ to Pß9+ [7]. To help the interpretation of the mass spectrum of Pn

+ , we have also studied the possible isomers of Pe [8] and Pg+ [9], In the mass spectrum, the signal of P7+ is the most intense, implying that P f + is the most abundant amidst the cationic clusters. It would be revealing to find out the specific configurations of the P7+ clusters.

Theoretical approaches have been performed on phosphorus clusters by means of various methods [2,7-21]. Most studies are devoted to a limited number of neutral phosphorus clusters. Theoretical investigations on cationic clusters are few. Otto et al performed ab initio calculations on two P7+ structures[20]. Based on similar approaches, we predicted the structures of three P7+

isomers [2]. Since phosphorus has a great number of structural varieties, it is of interest to explore the structure variation of the cationic clusters. In this paper, twenty-four P7+ isomers are predicted and the stable configurations are identified by molecular modeling as well as molecular mechanics, semi-empirical PM3 and density functional calculations. The results can be used as guiding factors for future theoretical investigation; they are also helpful information to the understanding of novel cluster materials.

2. Computational Details With a valence configuration of 3s23px3py3pz, each phosphorus atom in the clusters can

coordinate with the other phosphorus atoms in two-fold, three-fold, four-fold or six-fold mode. Three-fold coordination is generally favored in many phosphorus clusters. Two-fold and four-fold coordinations occur in some phosphorus clusters but the most common mode is three-fold [2,10,13]. Six-fold coordination occurs only in some special configurations. According to the description of classical valence bond, we put into consideration the two-fold, three-fold, four-fold and six-fold modes for P7+ investigation.

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Vol. 22, No. 8, 1999 The Prediction of Isomers for the Phosphorus Clusters Ργ+

ρ* •η

35 60 85 110 135 160

Fig. 1 Time-of-flight mass spectrum of phosphorus cluster cations produced by direct laser vaporization of red phosphorus.

We have performed the molecular model design, molecular mechanics and semi-empirical PM3 with HyperChem 5.1 for Windows 95 [22] and Desktop Molecular Modeller 3.0 for Windows [23] on a PC/Pentium II computer. The local density functional calculations reported in this work were done using the Amsterdam Density Functional (ADF) program [24] developed by Baerends and coworkers [25-27]. In this program, the local spin density approximation (LSDA) is invoked with the Vosko-Wilk-Nusair (VWN) local potential [28]. The gradient functional of Becke for exchange [29] and Perdew for correlation [30] were included in all the calculations. We kept the core orbitals up to the 2p level frozen. The triple zeta with a polarization function basis set was used for all atoms. To look for the stable configurations, full geometry optimizations for all phosphorus atoms were done on a DEC alpha 8200 computer. The twenty-four models of Pj+ isomers obtained after geometry optimization are shown in Fig. 2. The corresponding symmetry (C2V. Cs, C3V, Dßh, D3d, D3h. D2d and D2h) and bonding energy of each structure are listed in Table 1.

3. Models of P7+ Isomers Pj + can be formed by adding a phosphorus atom and a positive charge to a P& isomer. The

models of Fig. 2(a-l) are C2v in symmetry. In model 2(a), one two-fold atom is added on the top of a boat-shape Ρβ isomer. Model 2(b) is a structure with a four-fold atom shared between two tetrahedral structures. Containing one double bond, model 2(c) is a planar structure of a four-member ring joining a five-member ring. Model 2(d) is derived from a triangle prism by adding to it a four-fold atom with the breaking of two bonds. Model 2(e) contains five two-fold atoms, four of them forming two double bonds. Model 2(f) is derived from a tetrahedral P4 and a triangle P3; the isomer contains two 3-atom planes vertical to each other. Model 2(g) is derived from the most stable Ρβ (C2v symmetry) by placing a two-fold atom against the double bond. Model 2(h) contains three triangle planes, the middle one is vertical to the other two. Model 2(i) is a planar structure with three double bonds; all atoms are two-fold. Model 2(j) with a five-member ring is formed by adding a triangle P3 to a tetrahedral P4. Model 2(k) is derived from a square-face-capped triangle prism, involving the breaking of two bonds. Model 2(l) contains two triangle P3 connected by a two-fold atom. Model 2(m) of C3V symmetry is a distorted structure of cubic Ps (Oh symmetry), with one atom being taken away. Model 2(n) of C3V symmetry is derived from a triangular-face-capped triangle prism with breaking of three bonds. Models 2(o-s) are Cs in symmetry. Model 2(o) is also derived from a triangular-face-capped triangle prism; only that in this case, two bonds were broken. Model 2(p) contains one four-fold atom and two two-fold atoms forming a double bond. Model 2(q) is

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M.D.Chen et al. Main Group Metal Chemistry

derived from a Ρβ of triangle prism structure (D3h symmetry) by adding to it a two-fold atom close to one of the edges. Model 2(r) is derived from a tetrahedral P4 by adding to it a vertical triangle P3 plane. Model 2(s) is model 2(q) with one bond broken. Model 2(t) of D6h symmetry is a planar structure; a six-fold atom is placed at the center of a six-member ring. Model 2(u) and 2(v) are, respectively, D3d and Dßh in symmetry. They are both sandwich structures with a six-fold atom located between two horizontal three-member rings. Model 2(w) of Ü2d symmetry contains two triangle P3 planes which are vertical to each other and connected by a two-fold atom. Model 2(x) of Ü2h symmetry has a configuration similar to model 2(w) but the whole structure is planar.

u ν w x

Fig.2 Twenty-four models of P7+ isomers

4. Results and Discussion As indicated in Table 1, model 2(o) is the most stable. Otto et al. considered that a structure

similar to that of model 2(s) is stable [20], Our previous calculations suggested that model 2(k) was the most stable whereas the structure similar to model 2(o) was the next stable [2], Jones et al. obtained a neutral P7 structure which resembles model 2(o) by using a density functional method combined with a simulated annealing technique [14]. The most stable P2n+1+ structure is not always derived from the most stable P2n; for example, the most stable P4 is tetrahedral in structure (Td symmetry), but the most P5+ is square pyramidal in structure (C4V symmetry). It is necessary to consider "enough" isomers in order to confirm which is the most stable. In model 2(o), the distance

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Vol. 22, No. 8, 1999 The Prediction of Isomers for the Phosphorus Clusters Ργ+

between the two-fold atom to the upper atom of tetrahedral P4 is 2.78Ä, indicating that there is weak bonding between them; we, however, did not draw this week bonding in the Fig. 2(o). We also consider that model 2(o) is derived from the most stable Ρβ (C2V symmetry) by adding a two-fold atom above the double bond.

Table 1 Symmetries and Bond Energies (kJ/mol) of P7+ isomers illustrated in Fig. 2 Fiaure Svmmetrv BE Fiaure Svmmetrv BE

2(a) C2v -2371.40 2(m) C3v -2531.03 2(b) C2v -2386.79 2(n) C3v -2264.90 2(c) C2v -2398.63 2(o) Cs -2550.14 2(d) C2v -2196.73 2(P) Cs -2448.84 2(e) C2v -2344.34 2(q) Cs -2466.63 2(f) C2v -2516.99 2(r) Cs -2480.35 2(g) C2v -2400.38 2(s) Cs -2465.70 2(h) C2v -2296.53 2(t) Deh -1790.26 2(i) C2v -2213.47 2(u) D3d -2281.63 2(j) C2v -2328.80 2 (v) D3h -1854.13 2(k) C2v -2382.08 2(w) D2d -2221.99 2(1) C2v -2251.88 2(x) D2h -1947.93

So far, there is no report concerning any six-fold coordination mode of phosphorus atom in theoretical studies. The middle atom in the sandwich structures of models 2(u) and 2(v), and the center atom of planar structure in Fig. 2(t) trend to be six-fold. Atomic populations of the three-fold and six-fold atom in model 2(u), 2(v) and 2(t) are listed in Table 2. The d orbital of six-fold atoms is obviously involved in bonding. Compared to the other structures, the models with six-fold atom are energetically unfavorable and indeed structurally unstable. We have investigated other P-/+ models (D3, D4h and Oh symmetry) with six-fold atom; they are with very high bonding energies and are not included in this paper.

Table 2 At omic populations of the threefold and six-fold atom in model 2(u). 2(v) and 2 (t) Model 2(u) Model 2(v) Model 2(t)

Threefold Six-fold Threefold Six-fold Threefold Six-fold S Ρ D

1.8665 1.2349 2.8630 2.1593 0.2387 0.7912

1.8878 1.0215 2.7784 2.6329 0.2160 1.0523

1.7977 1.4079 2.8288 2.3659 0.2891 0.7325

The models of Figs. 2(c), 2(i), 2(t) and 2(x) are all planar isomers. Their bonding energies are rather high, indicating they are unstable. Unlike carbon atoms, a phosphorus atom has a lone pair of electrons, rendering it difficult to from a planar structure. It is clear that the cage structures are generally more stable that the planar ones. Model 2(t) which is planar and with a six-fold atom is the least stable among the twenty-four isomers.

With the enlargement of atom number in a cluster, the number of isomers increases. As the energy surfaces of phosphorus clusters can be very complex, there could be minimums corresponding to geometries that are unexplored. Although a series of P7+ isomers has been constructed and reported in this paper, there could be no guarantee that other isomers do not exist. Theoretical calculations by nature are speculative and it would be of great interest to see more experimental studies being done on these systems.

Acknowledgements The authors are deeply indebted to Professor S. Z. Hu of Xiamen University for his valuable

comments. This work was supported by the National Science Foundation of China (Grant No. 29573117).

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Received: June 5, 1999 - Accepted: June 17, 1999 -Accepted in revised camera-ready format: June 25, 1999

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