Available online at www.sciencedirect.com Chemical Physics 342 (2007) 253–259 www.elsevier.com/locate/chemphys The growth behaviors of the Zn-doped different sized germanium clusters: A density functional investigation Jin Wang b a,1 , Ju-Guang Han b,* a Department of Chemistry, University of Guelph, Guelph, Ontario, Canada N1G 2W1 National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei 230026, People’s Republic of China Received 11 July 2007; accepted 17 October 2007 Available online 22 October 2007 Abstract Growth behaviors of the Zinc doped germanium clusters are systematically investigated by using density functional method The growth-patterns, relative stabilities, charge-transfers, highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO–LUMO) gaps and polarities of these clusters are discussed in detail The threshold size of the Zn-encapsulated germanium clusters emerges as n = 10 while the icosahedral ZnGe12 cluster has stronger relative stability as compared to other sized clusters, which differs from the first-row unfilled d orbitals transition metal doped germanium clusters The calculated fragmentation energies manifest that the magic numbers of relative stabilities for the Zn-doped germanium clusters are 5, 9, and 12 Natural population analyses show that charges transfer from the Zn to the germanium framework It is worth pointing out that the HOMO–LUMO gap of the icosahedral ZnGe12 is remarkably large (3.159 eV) in comparison with other sized caged ZnGen (n = 1–11, 13) clusters Ó 2007 Elsevier B.V All rights reserved Keywords: Clusters; Geometry; Electronic structure; Computational investigation Introduction Currently, theoretical and experimental investigations on the transition metal (TM) doped silicon and/or germanium clusters reveal a novel way contributing to strengthening clustered stability [1–8] As for the semiconductor germanium clusters, the TM-doped large-sized caged germanium clusters (n = 14–16) have been investigated by using ab initio pesudopotential plane wave methods with spin-polarized generalized gradient approximation [9] indicating that the growth behaviors of metal encapsulated germanium clusters are different from those of metal * Corresponding author Fax: +86 551 514107 E-mail address: jghan@ustc.edu.cn (J.-G Han) On leaving from National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei 230026, People’s Republic of China 0301-0104/$ - see front matter Ó 2007 Elsevier B.V All rights reserved doi:10.1016/j.chemphys.2007.10.008 encapsulated silicon clusters The larger HOMO–LUMO gaps and the weaker interactions between the clusters make these species attractive for germanium clustered assembled materials In addition, the anion binary CoGeÀ 10 cluster with high abundance in mass spectrum has been produced by laser ablation and the bicapped tetragonal antiprism is assigned as the most stable structure for these cluster series [10] Our previous investigations [11,12] on the first-row TM (TM = Ni and Cu) with unfilled d subshell doped germanium clusters indicate the threshold number at which the endohedral coordination is favored at n = 10, which is different from many TM-doped silicon clusters However, to our knowledge, there is no detailed investigation on the growth behaviors of the TM (with filled d orbitals) doped germanium clusters, e.g., the growth pattern, the sized selectivity, the charge-transfer, etc In this paper, transition metal zinc doped germanium clusters with size varying from the small-size clusters to the relative large-size clusters are investigated 254 J Wang, J.-G Han / Chemical Physics 342 (2007) 253–259 Computational details The geometry optimizations of the ZnGen (n = 1–13) clusters are carried out by using density functional theory (DFT) with the (U)B3LYP exchange-correlation potential [13,14] and standard 6-31G basis sets The polarization basis sets are not considered in this work because our previous work showed that they are insignificant to our results [6] In order to test the reliability of our calculations, the Zn2 dimer is calculated and Zn–Zn bond distance of ˚ , which is in good agreement with ground state is 2.77 A ˚ [15,16] and some ideal Zn–Zn bond distance of 2.70 A ˚ experimental values of 2.3–2.94 A in solid crystal structures [17–20] One can find that the calculated results of the Ge2 and Zn2 clusters are in good agreement with the reported theoretical or experimental results that are available [11,12,17–20] It can be concluded that the calculated results at the UB3LYP/6-31G level are accurate and reliable in the present work Equilibrium geometries of the Gen clusters were optimized previously [12] On the basis of the previous optimized Gen geometries, different evolution patterns for determining the different sized ZnGen isomers, i.e., Zn capped, Zn substituted and Zn concaved patterns as well as Ge-capped pattern, are taken into accounts Furthermore, different spin states of ZnGen clusters are considered and calculated by using the Gaussian-03 program package [21] and the calculated results indicate that the ground states of the ZnGen (n = 1–2) correspond to spin triplet state; however, spin singlet state for each isomer is the lowest-energy state as compared to other spin states of this unit when the size of the ZnGen clusters exceeds The detailed calculated results and discussions are followed Results and discussions 3.1 The Zn exohedral doped ZnGen (n = 1–9) clusters As seen from the optimized small-sized ZnGen (n = 1–3) geometries, the symmetric triangular ZnGe2 structure is slightly weaker in stability than the non-symmetric triangular structure in that total energy of the former is higher than that of the latter by 0.08 eV Moreover, their triplet states of the ZnGen (n = 1–2) clusters are obviously lower in total energies than the singlet states, indicating that the ground states for the ZnGe and ZnGe2 clusters are the triplet spin states, the correspondingPelectronic states for the ZnGe and ZnGe2 clusters are and 3A00 , respectively The singlet state of the rhombus Cs ZnGe3 3a isomer is optimized to be a stable structure while the spin triplet state of the bent rhombus 3b structure is a stable state; furthermore, the singlet spin state is the ground state and the corresponding electronic state is 1A Consequently, beginning from the ZnGe3 clusters, the electronic spin state of the lowest-energy structure varies from spin triplet state to spin singlet state As the size of clusters grows up to 4, the Zn exohedral Gen clusters are formed Two different ZnGe4 geometries are found as the stable structures; the 4a structure is described as the Zn atom being only bonded with the planar rhombus Ge4 frame, and the 4b isomer is shown as the Zn atom being face-capped on bent rhombus Ge4 framework and interacting with two germanium atoms directly Furthermore, on the basis of the calculated total energy, the lowest-energy ZnGe4 structure is confirmed to be the 4b isomer which is similar to those of the NiGe4 and CuGe4 molecules [11,12] Two kinds of bi-pyramidal ZnGe5 geometries are found as the stable structures As seen from Fig 1, difference between 5a and 5b geometries lies in the Zn position in the bi-pyramidal frames It should be pointed out that the 5a and 5b isomers are generated from different lowsized molecules That is: the 5a is generated from rhombus ZnGe3 3a structure when the two germanium atoms are capped on top and bottom of the planar rhombus; for the 5b isomer, it is obtained from the ZnGe4 4b above As illustrated in Table 1, the 5a is more stable than the 5b, reflecting that the 5a is the lowest-energy structure, which is different from those of the CuGe5 and NiGe5 isomers [11,12] However, the most stable 4b and 5a clusters are depicted as the Zn atom being face-capped on the most stable Gen (n = and 5) clusters [11] (Table 2) On the base of the multi-rhombus Ge7 cluster [11], the ZnGe6 6a isomer can be obtained when one Ge atom is substituted by the Zn atom Another stable 6b structure can be formed if the bottom Ge atom in the tricapped rhombic Ge7 cluster is replaced by the Zn atom In addition, the stable 6c structure is yielded when the Zn atom is directly capped on the boat-like Ge6 cluster As compared to the calculated total energies of the 6a and 6c isomers, the 6b isomer is selected as the lowest-energy ZnGe6 cluster, the most stable 6b geometry is different from those of the NiGe6 and CuGe6 clusters [11,12] The exohedral ZnGen structures, however, are still dominant structures when the size of clusters increases to The 7a is optimized to be the lowest-energy structure while two multi-rhombus 7b and 7c isomers are found as the stable structures as compared to the 7a isomer As seen from all optimized low-lying ZnGe7 structures, no stable Zn-concaved Ge7 structure appears at this size It should be mentioned that the obvious divergence of the growth behaviors for the TMGen (TM = Ni and Zn) clusters appears at n = as compared to the previous investigation on the NiGen clusters The stable endohedral NiGen structures emerge at n = and gradually become dominant structures when the size of n > [12] As far as the ZnGe8 clusters are concerned, the low-lying stable geometries are different from those of the stable NiGe8 structures [12] The initial geometry obtained with one Zn atom being capped on the multi-rhombic Ge8 frame is finally optimized to be the Zn-convex 8a structure Another tetrahedral pyramidal 8b geometry is optimized to be a stable isomer and its total energy is lower than that of the 8a isomer; one stable 8d structure is generated when one Ge atom is capped on the low-rhombus Ge4 unit of the J Wang, J.-G Han / Chemical Physics 342 (2007) 253–259 255 Table Geometries and total energies of the ZnGen (n = 1–13) Clustersa Clusters Sym Freq (cmÀ1) ZnGe C1v 219.4 À3853.8951672 ZnGe2 Cs(a) Cs(b) 154.5 39.5 À5928.7460122 À5928.7487606 ZnGe3 Cs(a) Cs(b) 92.0 39.9 À8003.6857308 À8003.6462131 ZnGe4 C1(a) C1(b) 48.1 19.9 À10078.5513132 À10078.5547701 ZnGe5 Cs(a) C2v(b) 16.7 51.4 À12153.5067159 À12153.4944199 ZnGe6 C1(a) C2v(b) C1(c) 29.1 87.9 41.1 À14228.3883442 À14228.4097478 À14228.3645709 ZnGe7 C1(a) C1(b) Cs(c) 56.7 29.3 37.5 À16303.3033272 À16303.2917688 À16303.2839307 C1(a) C1(b) C1(c) C1(d) C1(e) 19.1 69.7 53.9 45.7 50.8 À18378.2097996 À18378.2111839 À18378.2018176 À18378.2047752 À18378.1662103 C1(a) C1(b) Cs(c) 65.0 56.2 60.7 À20453.1469357 À20453.1125729 À20453.1091569 0.94 1.03 C1(a) C1(b) C1(c) 31.1 58.1 53.3 À22528.0729217 À22528.0668902 À22528.0530808 0.16 0.54 C1(a) C1(b) C1(c) C1(d) C1(e) C1(f) 49.8 60.4 65.8 45.9 27.9 38.7 À24602.9258323 À24602.9596197 À24602.9867675 À24602.9548540 À24602.9642856 À24602.9355404 1.66 0.74 ZnGe12 C1(a) C1(b) C1(c) C1(d) C1(e) 33.1 72.7 42.4 33.8 104.1 À26677.9023734 À26677.8444670 À26677.8789696 À26677.8704576 À26677.9289224 0.72 2.30 1.36 1.59 ZnGe13 C1(a) C1(b) C1(c) 29.1 31.2 40.9 À28752.7847589 À28752.7810418 À28752.7889657 0.11 0.22 ZnGe8 ZnGe9 ZnGe10 ZnGe11 ET (hartree) DE (eV) 0.08 1.08 0.09 0.33 0.58 1.23 0.31 0.53 0.04 0.25 0.17 1.22 0.87 0.61 1.39 a Sym means point-group symmetry Freq represents the lowest vibrational frequency ET denotes the total energies of different ZnGen structures DE denotes relative energy of every conformer and the lowestenergy identical sized cluster Fig All the equilibrium geometries of ZnGen (n = 1–9) clusters, stars show the lowest-energy ZnGen (n = 1–9) structures multi-rhombic ZnGe7 7c isomer As for the ZnGe8 isomers, the doped Zn is not concaved into the germanium frame However, the Ni-concaved NiGe8 geometry is the most stable isomer [12] indicating that the growth behavior of the NiGe8 isomers is actually different from ZnGe8 isomer and the doped Ni atom tends to form the Ni-encapsulated Gen structure when the size of n P (Fig 2) The stable Zn-absorbed 9a is generated when one Zn atom is capped on the outside of the irregular polyhedron 256 J Wang, J.-G Han / Chemical Physics 342 (2007) 253–259 Table Natural charge population, HOMO–LUMO gap, and dipole moment of the located-energy structures with the spin singlet state of different sized ZnGen (n = 3–13) clusters Clusters Natural population HOMO–LUMO gap (eV) Dipole moment (D) ZnGe3 ZnGe4 ZnGe5 ZnGe6 ZnGe7 ZnGe8 ZnGe9 ZnGe10 ZnGe11 ZnGe12 ZnGe13 0.765 1.015 0.936 1.125 1.010 1.028 1.032 1.056 1.103 1.011 1.179 3.200 1.733 2.286 2.216 2.230 1.859 2.195 2.106 1.896 3.160 1.851 2.733 2.259 2.647 1.952 1.554 1.736 1.331 0.393 0.571 0.013 0.819 Ge9 cluster Based upon the ZnGe8 8a structure, the Ge edge-capped pattern gives rise to a stable ZnGe9 9b structure with the Zn atom being localized at outside of the Ge9 polyhedron On the basis of the optimized geometries and calculated total energies of the ZnGe9 isomers, it should be mentioned that the stability of the ZnGe9 isomers with Zn-absorbed on the germanium polyhedron is relative weaker as compared to the Zn-convex Ge9 9c structure in that the total energy of 9c is higher than that of the lowest-energy 9a structure by 1.03 eV 3.2 Zn-encapsulated ZnGen (n = 10–13) clusters Beginning from the ZnGe10 clusters, an obvious divergence of growth behaviors between small-sized ZnGen clusters and relatively large-sized ZnGen clusters is revealed When the number of Ge atoms in the Zn-doped Gen clusters is up to n = 10, the Zn-encapsulated Gen structures are formed Similar to the multi-rhombic or bicapped tetragonal antiprism TMGe10 (TM = Ni and Cu) isomers [11,12], the analogous ZnGe10 10a geometry is also optimized to be the most stable isomer The stability of the 10a isomer is stronger than that of the surface-substituted ZnGe10 10b isomer because the 10a is lower in total energy than the 10b isomer The previous investigation on the NiGen isomers is a guide, the Zn-convex 11a and 11b structures, the Zn-concaved 11c, 11d, and 11e structures, and the Zn surface-inserted 11f structure are optimized to be the stable geometries For the stable ZnGe11 clusters, the Ge-capped pentagonal antiprism 11c geometry is found to be the lowest-energy structure Furthermore, the most stable 11c isomer keeps the geometry that is analogous to that of the most stable NiGe11 cluster [12] As far as the ZnGe12 isomers are concerned, the bicapped pentagonal prism, which is analogous to the most stable NiGe12 geometry [12], is not optimized to be the lowest-energy structure Among all the optimized stable isomers, the Zn capped basket-like 12b isomer is determined to be the weakest structure in stability Surprisingly, the icosahedral stable 12e structure is much lower in total Fig All the equilibrium geometries of the ZnGen (n = 10–13) clusters, stars show the lowest-energy ZnGen (n = 10–13) geometries energy than those of other isomers and is selected as the most stable isomer, which is in good agreement with the previous icosahedral ZnGe12 isomer calculated by using ab initio ultrasoft pesudopotential plane wave method [22] On the basis of the calculated results and the natural charge analyses, it is found that the Zn atom in the most stale 12e isomer acts the same behavior as the Cu atom in the most stable CuSi12 isomer [23]; furthermore, the d orbitals of the Zn atom in the most stable 12e act as core without taking part in the chemical bonds According to the previous investigation on the TM-encapsulated silicon clusters, the metal encapsulated hexagonal prism is proven to be the lowest-energy geometry [23]; however, the analogous TM at Ge12 (TM = Ni, Cu, and Zn) geometries are J Wang, J.-G Han / Chemical Physics 342 (2007) 253–259 not the most stable ones; furthermore, the growth behaviors of the TM-doped Gen clusters are obviously different from those of the TM-doped Sin clusters [8,23] In addition, it should be mentioned that the icosahedral NiGe12 is proven to be an unstable structure which has one imaginary vibrational frequency On the basis of the two typical ZnGe12 structures, i.e., the bicapped pentagonal prism and hexagonal prism, two stable ZnGe13 13b and 13c isomers are considered and optimized, the calculated results show that the 13c isomer is the most stable geometry To sum up, in analogy to the TM with unfilled d orbitals doped Gen clusters, the critical size of the Zn-encapsulated caged germanium clusters emerges at n = 10 Different from the TM at Ge12 (TM = Ni, Cu) clusters, the icosahedral ZnGe12 geometry is proved to be the lowest-energy structure in comparison to the irregular basket-like or bicapped pentagonal ZnGe12 structures 257 Fig Sized dependence of the atomic averaged binding energies of ZnGen (n = 3–13) clusters 3.3 Sized selectivity of the ZnGen clusters The sized selectivity of the Zn-doped germanium clusters can be reflected from the atomic averaged binding energy and fragmentation energy The atomic averaged binding energies and fragmentation energies of the Zn-doped germanium clusters can be calculated from the following formula: Eb ðnÞ ¼ ½ET ðZnÞ þ nET ðGeÞ À ET ðZnGen ފ=n þ Dðn; n À 1Þ ¼ ET ðZnGenÀ1 Þ þ ET ðGeÞ À ET ðZnGen Þ where ET(ZnGenÀ1), ET(Ge), ET(Zn), and ET(ZnGen) represent the total energies of the lowest-energy ZnGenÀ1, Ge, Zn, and ZnGen clusters, respectively The calculated results of the atomic averaged binding energies are plotted as the curves which show the sized dependence of the atomic averaged binding energies of the ZnGen clusters Because the ground states of the small-sized ZnGen (n = 1–2) correspond to triplet spin state, the discussions on the atomic averaged binding energies of different sized clusters with the size n > correspond to spin singlet state As shown in Fig 3, the atomic averaged binding energy of the ZnGen clusters is monotonously increased to the maximum when the size of the NiGen goes from n = to n = 12; then, the atomic averaged binding energy of the ZnGen clusters begins to be decreased when the size of the ZnGen exceeds 12 On the other hand, the sized dependence of the fragmentation energies of the ZnGen clusters is also investigated As seen from Fig 4, the local maxima of D(n, n À 1) of the ZnGen clusters localize at n = 5, 9, and 12 As compared to the TM at Ge10 (TM = Co, Ni, and Cu), the ZnGe10 does not show the stronger relative stability as compared to the adjacent sized clusters although the bicapped tetragonal antiprism is optimized to be the lowest-energy structure On the contrary, the ZnGe12 shows the strongest stability because of the special stable icosahe- Fig Sized dependence of the fragmentation energies of ZnGen (n = 4–13) clusters dral geometry which does not correspond to the minima for the NiGe12 and CuGe12 clusters On the basis of the calculated results above, one can concluded that the most stable geometry depends on the doped transition metal, which is analogous to the transition metal doped silicon clusters [8,25] 3.4 Electronic properties of the ZnGen clusters Charge-transfer phenomena of the ZnGen clusters can be obtained by natural population analyses Different from the Ni-doped germanium clusters [12] however, charges transfer from the Zn to the Ge atoms in all sized ZnGen clusters because the Zn atom with filled 3d occupied orbitals does not obtain the extra charge from the germanium 258 J Wang, J.-G Han / Chemical Physics 342 (2007) 253–259 frame This finding is confirmed that the charge-transfer direction in the TM-doped germanium clusters depends on the doped transition metal The electronic property of the metal doped germanium clusters can be reflected from the energy gap between the highest occupied molecular orbitals (HOMO) and the lowest unoccupied molecular orbitals (LUMO) Previous calculated results on the NiGen clusters indicated that the HOMO–LUMO gap of NiGe10 cluster is much larger than other sized clusters [12] However, in the case of ZnGen clusters, the most stable ZnGe12 has remarkably large HOMO–LUMO gap (3.160 eV) with the weakest chemical stability as compared to the ZnGe10 (2.106 eV) and other sized clusters As mentioned above, the ZnGe12 isomer has the largest atomic averaged binding energy and biggest fragmentation energy; implying that the icosahedral ZnGe12 has the strongest stability and is appropriate for building-block of novel cluster-based nanomaterials Furthermore, in order to examine the special stable properties of the icosahedral ZnGe12 cluster, the spatial distribution of the highest occupied molecular orbitals are analyzed As shown in Fig 5, the molecular orbitals in the icosahedral 12e structure are delocalized on the two pentagonal planes and uniform distribution of electronic density can be formed; furthermore, the HOMO of the 12e isomer is indicative of covalent bonding between the metal Zn and Ge12 frame However, in the case of hexagonal prism, electronic density of four germanium atoms is much smaller than other germanium atoms and the doped Zn atom does not contribute to forming uniform distribution of electronic density in the caged germanium clusters Similar to the most stable stability of the TM at Si12 (TM = Ta, W, and Cr) [3,24], the ZnGe12 is also more stable as compared to other sized clusters However, geometry is the essential Fig Representations of the HOMO and LUMO orbitals of the icosahedral and hexagonal prism ZnGe12 clusters The different gray tones of the orbitals denote the positive and the negative regions difference among them; the stability of the formers is due to the stable hexagonal prism geometry while the stability of the latter is because of the stable icosahedral geometry Previous investigation on the bicapped tetragonal antiprism TM at Ge10 (TM = Cu and Ni) clusters reveal that their dipole moments are almost zero and appears nearly to be non-polar molecule [11,12] However, the dipole moment of the bicapped tetragonal antiprism ZnGe10 isomer is 0.393 D and has obvious the polarity As for as the icosahedral ZnGe12 is concerned, its dipole moment is quite small (0.013 D) and the weak electrostatic interactions between the encapsulated Zn and all germanium atoms are balanced because of the higher symmetrical geometry Hence, it can be expected that the polarity and distribution of electronic density in the frontier orbitals of the Zn-encapsulated caged germanium Gen clusters are correlated with the spatial distribution of germanium atoms Conclusions The geometries, stabilities, and electronic properties of the ZnGen (n = 1–13) clusters are investigated at the B3LYP/6-31G level All the results are summarized as follows: 1) The optimized geometries of the Zn-doped Gen clusters reveal that the Zn atom is encapsulated in caged germanium clusters at n = 10 Moreover, the stable bicapped tetragonal antiprism ZnGe10 cluster in term of the investigated relative stability is not stronger than its neighbors Furthermore, the Zn capped pentagonal antiprism ZnGe11 is more stable than the Zn capped pentagonal prism Ge11 isomer; however, the Cu capped pentagonal prism CuGe11 is more stable than the Cu capped pentagonal antiprism CuGe11 isomer Interestingly, the lowest-energy TMGe12 geometries depend on the different kinds of the encapsulated transition metals For example, the irregular basket-like CuGe12 structure, the bicapped pentagonal prism NiGe12 structure, and the special high-symmetry icosahedral ZnGe12 structure are optimized to be the lowest-energy TMGe12 geometries Consequently, the different sized and shaped lowest-energy TM-encapsulated Gen building blocks for mew cluster-based nanomaterials will lead to the new material with the novel properties 2) The natural population analyses indicate that different charge-transfer mechanisms depend on different transition metal being doped into germanium clusters Charges in the Zn-doped Gen clusters transfer from the Zn atom to the Gen frame, which is different from those of the NiGen clusters with the chargetransfer directions between the Ni and germanium framework being changed at certain size of cluster 3) The atomic averaged binding energy of the ZnGen is increased to maxima at n = 12 when the size increases According to the calculated fragmentation J Wang, J.-G Han / Chemical Physics 342 (2007) 253–259 energies, the magic numbers of the relative stabilities are confirmed to be n = 5, 9, and 12 Furthermore, the icosahedral ZnGe12 is stronger in stability as compared to the adjacent sized clusters Simultaneously, the polarity of the icosahedral ZnGe12 is obviously weakened because of the symmetric distribution of germanium atoms around Zn atom Hence, it is quite interesting that the Zn atom with filled d orbitals is encapsulated into the Ge12 frame to forming highsymmetry icosahedral geometry Acknowledgement [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] This work is supported by Natural Science Foundation of China (20173055) and starting fund(985029) of USTC References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] S.M 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