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Lowest-energy structures of AlnPn (n = 1–9) clusters from density functional theory
Chemical Physics Letters 443 (2007) 29–33 www.elsevier.com/locate/cplett
Lowest-energy structures of AlnPn (n = 1–9) clusters from density functional theory Jijun Zhao
a,b,c,*
, Lu Wang b, Jianming Jia a, Xiaoshuang Chen
c,* ,
Xiaolan Zhou c, Wei Lu
c
a
Jiangsu Key Laboratory for Chemistry of Low-Dimensional Materials, Huaiyin Teachers College, Huaian 223300, China State Key Laboratory of Materials Modification by Laser, Electron, and Ion Beams, School of Physics and Optoelectronic Technology and College of Advanced Science and Technology, Dalian University of Technology, Dalian 116024, China National Laboratory for Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 224502, China b
c
Received 1 February 2007; in final form 11 June 2007 Available online 17 June 2007
Abstract The lowest-energy structures of AlnPn clusters up to n = 9 have been explored using all-electron density functional calculations with a gradient correction. For smaller AlnPn clusters with n = 1–4, we successfully reproduced the previously reported lowest-energy structures. Novel cage structures with Al–P alternating arrangement were observed for n P 5. The comparison of the lowest-energy structures of AlnPn clusters with those of Si2n, BnNn, and GanAsn clusters has been made. Size-dependent cluster properties such as binding energy, HOMO–LUMO gaps, electron affinities, and photoelectron spectra have been computed and compared with experiments. Ó 2007 Elsevier B.V. All rights reserved.
As the bridge between atoms and matters, clusters have been subjects of intensive studies due to their novel structural, electronic, optical, and chemical properties [1,2]. The semiconductor clusters have attracted significant attention because of the desire to understand the growth mechanism of bulk semiconductor materials and to reveal the novel semiconductor nanostructures that are technologically promising. Considerable amount of attentions have been paid to silicon clusters [3–8] due to the importance of silicon-based materials in modern microelectronics industry as well as the relatively simple nature of the Si–Si interatomic bonding. On the contrary, much less is known about their isoelectronic counterpart, aluminum phosphide clusters. It would be interesting to explore the isoelectronic systems, i.e. AlnPn and Si2n clusters, and to compare AlnPn clusters with other III–V compound clusters by lighter or
* Corresponding authors. Address: State Key Laboratory of Materials Modification by Laser, Electron, and Ion Beams, School of Physics and Optoelectronic Technology and College of Advanced Science and Technology, Dalian University of Technology, Dalian 116024, China. E-mail addresses: [email protected] (J. Zhao), [email protected]. ac.cn (X. Chen).
0009-2614/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2007.06.055
heavier elements like BnNn [9,10] and GanAsn [11]. Such kinds of studies would enrich our understanding of the structure and bonding characteristics of small semiconductor clusters and might provide us some implications to develop novel semiconductor nanostructures. Previously, there have been few experimental works on the small AlP clusters. Liu et al. [12] synthesized gas-phase aluminum phosphide clusters by laser ablation and recorded mass distribution of anion Aln Pm . Gomez et al. [13,14] investigated photoelectron spectra for anionic Alx Py (x, y 6 4) clusters and obtained the adiabatic electron affinities (AEA) and vertical detachment energies (VDE) of these negative clusters. On the theoretical side, Al-Laham et al. [15,16] determined the lowest-energy structures for (AlP)n (n = 1–4) using Hatree–Fock (HF) and second-order Mø´ller–Plesset (MP2) perturbation theory. Using density functional theory (DFT), Tomasulo and Ramakrishna [17] explored (AlP)n clusters up to n = 6 and obtained structures that are significantly different from the isoelectronic Si2n clusters. Feng and Balasubramanian performed accurate quantum chemistry calculations at levels of CASSCF and MRSDCI on neutral and charged AlnPm clusters with five or fewer atoms [18,19]. Archibong
30
J. Zhao et al. / Chemical Physics Letters 443 (2007) 29–33
et al. [20,21] calculated atomic structures and electron detachment energies for AlP2 , Al2 P2 , Al3P , Al3 P3 and their neutral counterparts at DFT and CCSD(T) levels of theory. Using DFT calculations, Costales et al. [22] investigated the structure and vibration frequencies of (AlP)n with n = 1–3, while Qu and Bian [23] did similar calculations within size range up to n = 4. Wu and co-authors investigated the structures, electronic states, and stability of neutral and charged AlnPm clusters at B3LYP/6311+G(d) level [24,25]. Since previous calculations were limited to small clusters with less than eight atoms, it is difficult to draw a clear picture on the size-evolution behavior of the structures and properties of the clusters. In this Letter, we consider the AlnPm clusters in a broader size range up to totally eighteen atoms (n + m = 18). For simplicity and to a focus on the size-dependent evolution towards bulk limit, we limited the stoichiometric composition 1:1 (n = m), which leads to closed-shell electron structures of the clusters. First-principle calculations were performed using an allelectron density functional theory DMol package [26]. The exchange–correlation interaction was treated by the generalized gradient approximation with BLYP parameterization [27,28]. To search for the lowest-energy configuration of AlP clusters, we generated a number of possible structural isomers (typically 10–20 isomers for each cluster size). These candidate structures were adopted from those previously proposed for other III–V and II–V compound clusters such as BN [9,10], GaAs [11], and ZnO [29], and from hand-made construction following chemical intuition. Full geometry optimizations were then performed using the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm. Double numerical plus d-polarization (DND) basis set [26] was adopted. For the lowest-energy structures of each cluster size, we performed normal mode analysis to ensure that they are true minima on the potential energy surface. In Table 1, our theoretical results at BLYP/DND level are compared with experimental data for diatomic AlP molecule. For both neutral AlP and anionic AlP , the theoretical binding energy, bond length, and vibration frequency compare well with the measured data [13,14,30,31]. The lowest-energy structures obtained for the AlnPn clusters with n = 2–9 are shown in Fig. 1. To compute the electronic affinities of the AlnPn clusters, we have also determined the lowest-energy configurations for the anionic clusters by considering different isomer structures. For most cluster sizes, same atomic structures were found
for the neutral and anionic ones, except at n = 2, 5, 7. Hence the lowest-energy structures of anionic Al2 P2 , Al5 P5 , and Al7 P7 clusters are also shown in Fig. 1 for comparison. The most stable structure found for Al2P2 is a planar rhombus (D2h symmetry) with P–P bond in the short diag˚ , Al–P bond of 2.568 A ˚ , and Al–P–Al onal of 2.091 A angle of 131.9°, in agreement with previous results [15,17,18,20–25]. Compared to the lowest-energy structure, the energy for Y-shaped structure with P atom on top site is 0.875 eV higher, and the planar rhombus with Al–Al bond in short diagonal is 0.909 eV higher. Other structures such as linear chain were found to be rather energetically unfavorable. Previously, planar rhombus was also found as the lowest-energy configuration for Si4 [3], B2N2 [10], and Ga2As2 cluster [11]. From our calculation, the lowest-energy structure for the anionic Al2 P2 cluster is a planar rhombus (D2h symmetry) with Al–Al bond in the short diagonal, different from the neutral one (see Fig. 1). The lowest-energy configuration of Al3P3 is a hexagonal planar structure (D3h symmetry), in which three P atoms edge-cap the central Al3 triangle (Al–Al bond length: ˚ ). The Al–P bond length 2.237 A ˚ from our calcula2.744 A ˚ ) [22]. Same configtion agree with Costales’ result (2.24 A uration was reported by Al-Laham et al. [15], Archibong et al. [20], Qu et al. [23], and Guo et al. [24]. Tomasulo et al. predicted a trigonal bipyramid face-capped with one Al atom as the lowest-energy structure of Al3P3 [17], which was also found for Ga3As3 cluster [11]. From our calculation, it is a metastable isomer with 0.301 eV higher. A trigonal bipyramid with one Al atom capped on the equatorial edge lies 0.346 eV higher in energy. The energy for the isomer of trigonal prism is energetically less favorable by 0.513 eV. The present lowest-energy structure of Al3P3 is significantly different from Si6 [3,5] but similar to B3N3 [10]. The lowest-energy structure of Al4P4 adopts Td form consisting of two interpenetrating Al4 and P4 tetrahedrons, consistent with previous works [16,17,23]. In this structure, the Al and P atoms are alternatively placed, with Al–P ˚ and Al–Al bond of 2.71 A ˚ . In a previous bond of 2.382 A study [16], natural bonding analysis indicated that there is no significant bonding between the nearby Al atoms. Meanwhile, P atoms locate relatively far from each other ˚ ) due to the repulsion between (P–P distance of 3.837 A the lone-pair electrons on each P. As for the other isomer structures, a tetra-capped square with D2d symmetry is a
Table 1 Equilibrium bond length R0, vibration frequency x, and binding energy Eb of neutral Al1P1 and anionic AlP clusters from experiments [13,14,29,30] and present BLYP/DND calculation AlP
Experiments This work
AlP
˚) R0 (A
x (cm 1)
Eb (eV/atom)
EA (eV)
˚) R0 (A
x (cm 1)
2.40 2.223
379 372
2.20 2.106
2.043 1.975
2.163 2.165
516 496
J. Zhao et al. / Chemical Physics Letters 443 (2007) 29–33
31
Fig. 1. The lowest-energy structures of neutral and anionic Aln Pn (n = 2–9) clusters.
metastable isomer which only 0.2 eV higher in energy. A distorted bi-capped trigonal antiprism with Ci symmetry, which was predicted as the most stable configuration for Ga4As4 [11], lies 0.822 eV higher than the lowest-energy one. It is noteworthy that AlnPn clusters start to adopt cage-like configuration from n = 4. The present Td structure for Al4P4 was proposed as a locally stable isomer for B4N4 [10], while it is also different from the lowest-energy structure predicted for Si8 [3,5]. The most stable configuration of neutral Al5P5 cluster is a twisted pentagonal prism, which can be viewed as two staggered five-membered-rings (5MR). Its energy is 0.67 eV lower than that of the tricapped pentagonal bipyramid found by Tomasulo [17]. In contrast, both Si10 [3] and Ga5As5 [11] adopt tetra-capped trigonal prism, while B5N5 prefer a pentagonal ring configuration [10]. With one extra electron, the lowest-energy configuration of the anionic Al5 P5 cluster transform into a prolate cage with no symmetry (see Fig. 1). Similar to Al5P5, the lowest-energy structure found for Al6P6 is a hexagonal prism (D3h) with alternating aluminum and phosphorus atoms, in agreement with Tomasulo’s finding [17]. It can also be viewed as two Al3P3 hexagonal rings. The present structure resembles none of the lowestenergy configuration found for Si12 (pentacapped trigonal prism) [5], B6N6 (hexagonal ring) [10], and Ga6As6 (basket-like cage) [11].
There was no previous calculations on the AlnPn clusters with n > 6. For Al7P7, we found an unsymmetric cage consisting of one hexagonal face, four pentagonal faces, and four tetragonal faces. Most Al and P atoms arrange in an alternating way, while there are one Al–Al and one P–P bonds. The same cage configuration was predicted as the most stable one for Ga7As7 [11], while the structure of Si14 is rather different, i.e. a prolate multi-cage configuration [6]. For the anionic Al7 P7 cluster, our calculations revealed that its most stable structure is a C3v cage consisting of four hexagonal faces and six tetragonal faces (see Fig. 1). The most stable structure of Al8P8 is a S4 cage including four hexagonal faces and six tetragonal faces in an exactly Al–P alternating arrangement. It can also be viewed as one Al6P6 hexagonal prism added by an Al2P2 square. The same S4 cage was proposed for B8N8 but it is less energetically favorable than the ring configuration [9,10]. Meanwhile, Ga8As8 adopts an unsymmetric cage as its lowestenergy configuration. The structure of Si16 is prolate [8], far from Al6P6. A highly symmetric C3h cage was found for Al9P9, which contains five hexagonal faces and six tetragonal faces in an Al–P alternating way. Similar cage structures were predicted as the lowest-energy configuration for Ga9As9 and locally stable isomer for B9N9 [9], whereas Si18 still follows the prolate structural motif [8].
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J. Zhao et al. / Chemical Physics Letters 443 (2007) 29–33
We further computed the electronic properties such as binding energies, HOMO–LUMO gaps, adiabatic electron affinities (AEA) of the neutral AlnPn clusters , the vertical detachment energy (VDE) of the negative Aln Pn clusters, and the theoretical results are summarized in Table 2. The binding energy generally increases with cluster size. Thus, the clusters continue to gain energy during the growth process. Within the size range studied (n = 1–9), Al9P9 possesses the largest HOMO–LUMO gap. The AEA and VDE computed for small AlnPn clusters (n = 1–3) are comparable to experimental data and highlevel quantum chemistry calculations. For example, experiment gave AEA = 2.15 ± 0.10 eV, VDE = 2.33 eV for Al2P2 and AEA = 2.45 ± 0.02 eV, VDE = 2.63 eV for Al3P3 [13]. Meanwhile, previous quantum chemistry calculation at CCSD level [20,21] predicted 1.83 eV and 2.46 eV of the AEA for Al2P2 and Al3P3, respectively. To further compare with experimental results [13], we computed the photoelectron spectra (PES) of the anionic clusters from their electron density of states using the approach described in Ref.[33]. The simulated spectra of Aln Pn for n = 2–9 are shown in Fig. 2, along with the experimental ones for n = 2–4 [13]. Good agreement between theoretical and experimental spectra can be seen for AlP and Al2 P2 , while there is some discrepancy for Al3 P3 . For larger Aln Pn clusters with n > 3, there was no experimental PES available and our present theoretical predictions need future experimental validation. To summarize, the lowest-energy configurations of AlnPn clusters up to n = 9 were determined from a number of candidate structures. The nature of partial ionic bonding lead to distinctly different atomic structures between AlnPn
Table 2 Lowest-energy structures, binding energies per atom (BE), HOMO– LUMO gaps, and adiabatic electron affinities (AEA) of the AlnPn clusters, and vertical detachment energies (VDE) of the Aln Pn clusters from our BLYP/DND calculations n
Structure
BE (eV)
Gap (eV)
AEA (eV)
VDE (eV)
1 2 3 4 5
Linear Rhombus Hexagonal ring Cage Twisted pentagonal prism Hexagonal prism Cage Cage Cage
1.05 2.39 2.63 2.79 2.90
0.04 1.08 0.98 0.73 1.43
1.98 2.34 2.16 2.71 1.96
1.99 2.44 2.28 2.75 2.34
3.04 3.05 3.13 3.18
1.21 1.52 1.55 1.75
2.47 2.60 2.37 2.30
2.51 2.71 2.41 2.33
6 7 8 9
From the above results, it is interesting to find that the lowest-energy configurations of AlnPn clusters are rather different from those of Si2n except at n = 2. Compared to the other III–V compound clusters, the structures of AlnPn clusters resemble those of BN cluster at smallest sizes (n = 2, 3). From n = 7, AlnPn clusters adopt cage-like configurations that are similar to GanAsn. The present observation can be partially understood by the difference of electronegativity [32] between these elements, which is 1.0 for B–N, 0.58 for Al–P, and 0.37 for Ga–As, respectively. Thus, the chemical bonding in AlP clusters is more covalent than BN and more ionic than GaAs. For example, Ga5As5 has the same lowest-energy structure with Ge10, while the structures of Al5P5 and Si10 are different. The ring-to-cage transition in BnNn clusters occur at n = 11 [9] while it occur as early as at n = 4 in AlnPn clusters.
−
−
Intensity (arb. unit)
Al3P3 (Expt.)
Al2P2 (Expt.)
Al3P3
Al2P2
AlP
−
Al6P6
Al5P5
−
Al8P8
Al7P7
2
3
4 1
−
−
−
Al4P4
1
−
−
−
AlP (Expt.)
−
−
Al9P9
2
3
4 1
2
3
4
Electron Binding Energy (eV) Fig. 2. The photoelectron spectra of anionic Aln Pn (n = 2–9) clusters from theoretical simulations (the lower nine plots) as well as from experiment (the upper three plots labeled by Expt.).
J. Zhao et al. / Chemical Physics Letters 443 (2007) 29–33
and Si2n clusters, although they are isoelectronic. The compromise between covalent and ionic bonding in the AlnPn clusters lead to Al–P alternating cage-like configuration from n = 4. The electronic properties such as HOMO– LUMO gap, electron affinity, and photoelectron spectra of the AlnPn clusters were computed. Acknowledgements This work was supported by Program for New Century Excellent Talents in University of China (NCET06-0281), Chinese National Key Basic Research Special Fund (60221502), and Chinese National Science Foundation (60476040). References [1] H. Haberland (Ed.), Clusters of Atoms and Molecules I, Springer, Berlin, 1995. [2] R.L. Johnston, Atomic and Molecular Clusters, Tylor & Francis, London, 2002. [3] K. Raghavachari, C.M. Rohlfing, J. Chem. Phys. 89 (1988) 2219. [4] K.M. Ho et al., Nature 392 (1998) 582. [5] Z.Y. Lu, C.Z. Wang, K.M. Ho, Phys. Rev. B 61 (2000) 2329. [6] J.L. Wang, G.H. Wang, F. Ding, H. Lee, W.F. Shen, J.J. Zhao, Chem. Phys. Lett. 341 (2001) 529. [7] S. Yoo, J.J. Zhao, J.L. Wang, X.C. Zeng, J. Am. Chem. Soc. 126 (2004) 13845. [8] S. Yoo, X.C. Zeng, J. Chem. Phys. 123 (2005) 164303. [9] D.L. Strout, J. Phys. Chem. A 105 (2001) 261. [10] J.M. Matxain, J.M. Ugalde, M.D. Towler, R.J. Needs, J. Phys. Chem. A 107 (2003) 10004.
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[11] J.J. Zhao, J.R.H. Xie, X.L. Zhou, X.S. Chen, W. Lu, Phys. Rev. B 74 (2006) 035319, and references therein. [12] Z.Y. Liu, C. Wang, R. Huang, L. Zheng, Int. J. Mass. Spect. Ion. Process. 141 (1995) 201. [13] H. Gomez, T.R. Taylor, D.M. Neumark, J. Phys. Chem. A 105 (2001) 6886. [14] H. Gomez, T.R. Taylor, Y. Zhao, D.M. Neumark, J. Chem. Phys. 117 (2002) 8644. [15] M.A. Al-Laham, G.W. Trucks, K. Raghavachari, J. Chem. Phys. 96 (1992) 1137. [16] M.A. Al-Laham, G.W. Trucks, K. Raghavachari, J. Chem. Phys. 98 (1993) 8770. [17] A. Tomasulo, M.V. Ramakrishna, J. Chem. Phys. 105 (1996) 10449. [18] P.Y. Feng, K. Balasubramanian, J. Phys. Chem. A 103 (1999) 9093. [19] P.Y. Feng, K. Balasubramanian, Chem. Phys. Lett. 318 (2000) 417. [20] E.F. Archibong, R.M. Gregorius, S.A. Alexander, Chem. Phys. Lett. 321 (2000) 253. [21] E.F. Archibong, A. St-Amant, S.K. Goh, D. Marynick, J. Phys. Chem. A 106 (2002) 5932. [22] A. Costales, X.K. Kandalam, R. Franco, R. Pandey, J. Phys. Chem. B 106 (2002) 1940. [23] Y. Qu, X. Bian, J. Comp. Chem. 26 (2004) 226. [24] L. Guo, H.S. Wu, Z.H. Jin, J. Mol. Str. (Theochem) 648 (2004) 67. [25] L. Guo, H.S. Wu, Z.H. Jin, Int. J. Mass Spect. 240 (2005) 149. [26] B. Delley, J. Chem. Phys. 92 (1990) 508. [27] A.D. Becke, J. Chem. Phys. 88 (1988) 2547. [28] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 786. [29] B.L. Wang, S. Nagase, J.J. Zhao, G.H. Wang, J. Phys. Chem. C 111 (2007) 4956. [30] K.P. Huber, G. Herzberg, Molecular Spectra and Molecular Structure, vol. 4, Van Nostrand-Reinhold, New York, 1979. [31] P.J. Bruna, F. Grein, J. Phys. B 22 (1989) 1913. [32] A.L. Allred, J. Inorg. Nucl. Chem. 17 (1961) 215. [33] J. Akola, M. Manninen, H. Hakkinen, U. Landman, X. Li, L.S. Wang, Phys. Rev. B 60 (1999) 11297.
Lowest-energy structures of AlnPn (n = 1–9) clusters from density functional theory Jijun Zhao
a,b,c,*
, Lu Wang b, Jianming Jia a, Xiaoshuang Chen
c,* ,
Xiaolan Zhou c, Wei Lu
c
a
Jiangsu Key Laboratory for Chemistry of Low-Dimensional Materials, Huaiyin Teachers College, Huaian 223300, China State Key Laboratory of Materials Modification by Laser, Electron, and Ion Beams, School of Physics and Optoelectronic Technology and College of Advanced Science and Technology, Dalian University of Technology, Dalian 116024, China National Laboratory for Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 224502, China b
c
Received 1 February 2007; in final form 11 June 2007 Available online 17 June 2007
Abstract The lowest-energy structures of AlnPn clusters up to n = 9 have been explored using all-electron density functional calculations with a gradient correction. For smaller AlnPn clusters with n = 1–4, we successfully reproduced the previously reported lowest-energy structures. Novel cage structures with Al–P alternating arrangement were observed for n P 5. The comparison of the lowest-energy structures of AlnPn clusters with those of Si2n, BnNn, and GanAsn clusters has been made. Size-dependent cluster properties such as binding energy, HOMO–LUMO gaps, electron affinities, and photoelectron spectra have been computed and compared with experiments. Ó 2007 Elsevier B.V. All rights reserved.
As the bridge between atoms and matters, clusters have been subjects of intensive studies due to their novel structural, electronic, optical, and chemical properties [1,2]. The semiconductor clusters have attracted significant attention because of the desire to understand the growth mechanism of bulk semiconductor materials and to reveal the novel semiconductor nanostructures that are technologically promising. Considerable amount of attentions have been paid to silicon clusters [3–8] due to the importance of silicon-based materials in modern microelectronics industry as well as the relatively simple nature of the Si–Si interatomic bonding. On the contrary, much less is known about their isoelectronic counterpart, aluminum phosphide clusters. It would be interesting to explore the isoelectronic systems, i.e. AlnPn and Si2n clusters, and to compare AlnPn clusters with other III–V compound clusters by lighter or
* Corresponding authors. Address: State Key Laboratory of Materials Modification by Laser, Electron, and Ion Beams, School of Physics and Optoelectronic Technology and College of Advanced Science and Technology, Dalian University of Technology, Dalian 116024, China. E-mail addresses: [email protected] (J. Zhao), [email protected]. ac.cn (X. Chen).
0009-2614/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2007.06.055
heavier elements like BnNn [9,10] and GanAsn [11]. Such kinds of studies would enrich our understanding of the structure and bonding characteristics of small semiconductor clusters and might provide us some implications to develop novel semiconductor nanostructures. Previously, there have been few experimental works on the small AlP clusters. Liu et al. [12] synthesized gas-phase aluminum phosphide clusters by laser ablation and recorded mass distribution of anion Aln Pm . Gomez et al. [13,14] investigated photoelectron spectra for anionic Alx Py (x, y 6 4) clusters and obtained the adiabatic electron affinities (AEA) and vertical detachment energies (VDE) of these negative clusters. On the theoretical side, Al-Laham et al. [15,16] determined the lowest-energy structures for (AlP)n (n = 1–4) using Hatree–Fock (HF) and second-order Mø´ller–Plesset (MP2) perturbation theory. Using density functional theory (DFT), Tomasulo and Ramakrishna [17] explored (AlP)n clusters up to n = 6 and obtained structures that are significantly different from the isoelectronic Si2n clusters. Feng and Balasubramanian performed accurate quantum chemistry calculations at levels of CASSCF and MRSDCI on neutral and charged AlnPm clusters with five or fewer atoms [18,19]. Archibong
30
J. Zhao et al. / Chemical Physics Letters 443 (2007) 29–33
et al. [20,21] calculated atomic structures and electron detachment energies for AlP2 , Al2 P2 , Al3P , Al3 P3 and their neutral counterparts at DFT and CCSD(T) levels of theory. Using DFT calculations, Costales et al. [22] investigated the structure and vibration frequencies of (AlP)n with n = 1–3, while Qu and Bian [23] did similar calculations within size range up to n = 4. Wu and co-authors investigated the structures, electronic states, and stability of neutral and charged AlnPm clusters at B3LYP/6311+G(d) level [24,25]. Since previous calculations were limited to small clusters with less than eight atoms, it is difficult to draw a clear picture on the size-evolution behavior of the structures and properties of the clusters. In this Letter, we consider the AlnPm clusters in a broader size range up to totally eighteen atoms (n + m = 18). For simplicity and to a focus on the size-dependent evolution towards bulk limit, we limited the stoichiometric composition 1:1 (n = m), which leads to closed-shell electron structures of the clusters. First-principle calculations were performed using an allelectron density functional theory DMol package [26]. The exchange–correlation interaction was treated by the generalized gradient approximation with BLYP parameterization [27,28]. To search for the lowest-energy configuration of AlP clusters, we generated a number of possible structural isomers (typically 10–20 isomers for each cluster size). These candidate structures were adopted from those previously proposed for other III–V and II–V compound clusters such as BN [9,10], GaAs [11], and ZnO [29], and from hand-made construction following chemical intuition. Full geometry optimizations were then performed using the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm. Double numerical plus d-polarization (DND) basis set [26] was adopted. For the lowest-energy structures of each cluster size, we performed normal mode analysis to ensure that they are true minima on the potential energy surface. In Table 1, our theoretical results at BLYP/DND level are compared with experimental data for diatomic AlP molecule. For both neutral AlP and anionic AlP , the theoretical binding energy, bond length, and vibration frequency compare well with the measured data [13,14,30,31]. The lowest-energy structures obtained for the AlnPn clusters with n = 2–9 are shown in Fig. 1. To compute the electronic affinities of the AlnPn clusters, we have also determined the lowest-energy configurations for the anionic clusters by considering different isomer structures. For most cluster sizes, same atomic structures were found
for the neutral and anionic ones, except at n = 2, 5, 7. Hence the lowest-energy structures of anionic Al2 P2 , Al5 P5 , and Al7 P7 clusters are also shown in Fig. 1 for comparison. The most stable structure found for Al2P2 is a planar rhombus (D2h symmetry) with P–P bond in the short diag˚ , Al–P bond of 2.568 A ˚ , and Al–P–Al onal of 2.091 A angle of 131.9°, in agreement with previous results [15,17,18,20–25]. Compared to the lowest-energy structure, the energy for Y-shaped structure with P atom on top site is 0.875 eV higher, and the planar rhombus with Al–Al bond in short diagonal is 0.909 eV higher. Other structures such as linear chain were found to be rather energetically unfavorable. Previously, planar rhombus was also found as the lowest-energy configuration for Si4 [3], B2N2 [10], and Ga2As2 cluster [11]. From our calculation, the lowest-energy structure for the anionic Al2 P2 cluster is a planar rhombus (D2h symmetry) with Al–Al bond in the short diagonal, different from the neutral one (see Fig. 1). The lowest-energy configuration of Al3P3 is a hexagonal planar structure (D3h symmetry), in which three P atoms edge-cap the central Al3 triangle (Al–Al bond length: ˚ ). The Al–P bond length 2.237 A ˚ from our calcula2.744 A ˚ ) [22]. Same configtion agree with Costales’ result (2.24 A uration was reported by Al-Laham et al. [15], Archibong et al. [20], Qu et al. [23], and Guo et al. [24]. Tomasulo et al. predicted a trigonal bipyramid face-capped with one Al atom as the lowest-energy structure of Al3P3 [17], which was also found for Ga3As3 cluster [11]. From our calculation, it is a metastable isomer with 0.301 eV higher. A trigonal bipyramid with one Al atom capped on the equatorial edge lies 0.346 eV higher in energy. The energy for the isomer of trigonal prism is energetically less favorable by 0.513 eV. The present lowest-energy structure of Al3P3 is significantly different from Si6 [3,5] but similar to B3N3 [10]. The lowest-energy structure of Al4P4 adopts Td form consisting of two interpenetrating Al4 and P4 tetrahedrons, consistent with previous works [16,17,23]. In this structure, the Al and P atoms are alternatively placed, with Al–P ˚ and Al–Al bond of 2.71 A ˚ . In a previous bond of 2.382 A study [16], natural bonding analysis indicated that there is no significant bonding between the nearby Al atoms. Meanwhile, P atoms locate relatively far from each other ˚ ) due to the repulsion between (P–P distance of 3.837 A the lone-pair electrons on each P. As for the other isomer structures, a tetra-capped square with D2d symmetry is a
Table 1 Equilibrium bond length R0, vibration frequency x, and binding energy Eb of neutral Al1P1 and anionic AlP clusters from experiments [13,14,29,30] and present BLYP/DND calculation AlP
Experiments This work
AlP
˚) R0 (A
x (cm 1)
Eb (eV/atom)
EA (eV)
˚) R0 (A
x (cm 1)
2.40 2.223
379 372
2.20 2.106
2.043 1.975
2.163 2.165
516 496
J. Zhao et al. / Chemical Physics Letters 443 (2007) 29–33
31
Fig. 1. The lowest-energy structures of neutral and anionic Aln Pn (n = 2–9) clusters.
metastable isomer which only 0.2 eV higher in energy. A distorted bi-capped trigonal antiprism with Ci symmetry, which was predicted as the most stable configuration for Ga4As4 [11], lies 0.822 eV higher than the lowest-energy one. It is noteworthy that AlnPn clusters start to adopt cage-like configuration from n = 4. The present Td structure for Al4P4 was proposed as a locally stable isomer for B4N4 [10], while it is also different from the lowest-energy structure predicted for Si8 [3,5]. The most stable configuration of neutral Al5P5 cluster is a twisted pentagonal prism, which can be viewed as two staggered five-membered-rings (5MR). Its energy is 0.67 eV lower than that of the tricapped pentagonal bipyramid found by Tomasulo [17]. In contrast, both Si10 [3] and Ga5As5 [11] adopt tetra-capped trigonal prism, while B5N5 prefer a pentagonal ring configuration [10]. With one extra electron, the lowest-energy configuration of the anionic Al5 P5 cluster transform into a prolate cage with no symmetry (see Fig. 1). Similar to Al5P5, the lowest-energy structure found for Al6P6 is a hexagonal prism (D3h) with alternating aluminum and phosphorus atoms, in agreement with Tomasulo’s finding [17]. It can also be viewed as two Al3P3 hexagonal rings. The present structure resembles none of the lowestenergy configuration found for Si12 (pentacapped trigonal prism) [5], B6N6 (hexagonal ring) [10], and Ga6As6 (basket-like cage) [11].
There was no previous calculations on the AlnPn clusters with n > 6. For Al7P7, we found an unsymmetric cage consisting of one hexagonal face, four pentagonal faces, and four tetragonal faces. Most Al and P atoms arrange in an alternating way, while there are one Al–Al and one P–P bonds. The same cage configuration was predicted as the most stable one for Ga7As7 [11], while the structure of Si14 is rather different, i.e. a prolate multi-cage configuration [6]. For the anionic Al7 P7 cluster, our calculations revealed that its most stable structure is a C3v cage consisting of four hexagonal faces and six tetragonal faces (see Fig. 1). The most stable structure of Al8P8 is a S4 cage including four hexagonal faces and six tetragonal faces in an exactly Al–P alternating arrangement. It can also be viewed as one Al6P6 hexagonal prism added by an Al2P2 square. The same S4 cage was proposed for B8N8 but it is less energetically favorable than the ring configuration [9,10]. Meanwhile, Ga8As8 adopts an unsymmetric cage as its lowestenergy configuration. The structure of Si16 is prolate [8], far from Al6P6. A highly symmetric C3h cage was found for Al9P9, which contains five hexagonal faces and six tetragonal faces in an Al–P alternating way. Similar cage structures were predicted as the lowest-energy configuration for Ga9As9 and locally stable isomer for B9N9 [9], whereas Si18 still follows the prolate structural motif [8].
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J. Zhao et al. / Chemical Physics Letters 443 (2007) 29–33
We further computed the electronic properties such as binding energies, HOMO–LUMO gaps, adiabatic electron affinities (AEA) of the neutral AlnPn clusters , the vertical detachment energy (VDE) of the negative Aln Pn clusters, and the theoretical results are summarized in Table 2. The binding energy generally increases with cluster size. Thus, the clusters continue to gain energy during the growth process. Within the size range studied (n = 1–9), Al9P9 possesses the largest HOMO–LUMO gap. The AEA and VDE computed for small AlnPn clusters (n = 1–3) are comparable to experimental data and highlevel quantum chemistry calculations. For example, experiment gave AEA = 2.15 ± 0.10 eV, VDE = 2.33 eV for Al2P2 and AEA = 2.45 ± 0.02 eV, VDE = 2.63 eV for Al3P3 [13]. Meanwhile, previous quantum chemistry calculation at CCSD level [20,21] predicted 1.83 eV and 2.46 eV of the AEA for Al2P2 and Al3P3, respectively. To further compare with experimental results [13], we computed the photoelectron spectra (PES) of the anionic clusters from their electron density of states using the approach described in Ref.[33]. The simulated spectra of Aln Pn for n = 2–9 are shown in Fig. 2, along with the experimental ones for n = 2–4 [13]. Good agreement between theoretical and experimental spectra can be seen for AlP and Al2 P2 , while there is some discrepancy for Al3 P3 . For larger Aln Pn clusters with n > 3, there was no experimental PES available and our present theoretical predictions need future experimental validation. To summarize, the lowest-energy configurations of AlnPn clusters up to n = 9 were determined from a number of candidate structures. The nature of partial ionic bonding lead to distinctly different atomic structures between AlnPn
Table 2 Lowest-energy structures, binding energies per atom (BE), HOMO– LUMO gaps, and adiabatic electron affinities (AEA) of the AlnPn clusters, and vertical detachment energies (VDE) of the Aln Pn clusters from our BLYP/DND calculations n
Structure
BE (eV)
Gap (eV)
AEA (eV)
VDE (eV)
1 2 3 4 5
Linear Rhombus Hexagonal ring Cage Twisted pentagonal prism Hexagonal prism Cage Cage Cage
1.05 2.39 2.63 2.79 2.90
0.04 1.08 0.98 0.73 1.43
1.98 2.34 2.16 2.71 1.96
1.99 2.44 2.28 2.75 2.34
3.04 3.05 3.13 3.18
1.21 1.52 1.55 1.75
2.47 2.60 2.37 2.30
2.51 2.71 2.41 2.33
6 7 8 9
From the above results, it is interesting to find that the lowest-energy configurations of AlnPn clusters are rather different from those of Si2n except at n = 2. Compared to the other III–V compound clusters, the structures of AlnPn clusters resemble those of BN cluster at smallest sizes (n = 2, 3). From n = 7, AlnPn clusters adopt cage-like configurations that are similar to GanAsn. The present observation can be partially understood by the difference of electronegativity [32] between these elements, which is 1.0 for B–N, 0.58 for Al–P, and 0.37 for Ga–As, respectively. Thus, the chemical bonding in AlP clusters is more covalent than BN and more ionic than GaAs. For example, Ga5As5 has the same lowest-energy structure with Ge10, while the structures of Al5P5 and Si10 are different. The ring-to-cage transition in BnNn clusters occur at n = 11 [9] while it occur as early as at n = 4 in AlnPn clusters.
−
−
Intensity (arb. unit)
Al3P3 (Expt.)
Al2P2 (Expt.)
Al3P3
Al2P2
AlP
−
Al6P6
Al5P5
−
Al8P8
Al7P7
2
3
4 1
−
−
−
Al4P4
1
−
−
−
AlP (Expt.)
−
−
Al9P9
2
3
4 1
2
3
4
Electron Binding Energy (eV) Fig. 2. The photoelectron spectra of anionic Aln Pn (n = 2–9) clusters from theoretical simulations (the lower nine plots) as well as from experiment (the upper three plots labeled by Expt.).
J. Zhao et al. / Chemical Physics Letters 443 (2007) 29–33
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