Geometric Transition and Electronic Properties of Titanium-Doped

Article pubs.acs.org/JPCA

Geometric Transition and Electronic Properties of Titanium-Doped Aluminum Clusters: AlnTi (n = 2−24) Yawen Hua,*,† Yiliang Liu,‡ Gang Jiang,*,† Jiguang Du,§ and Jun Chen∥ †

Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China College of Electrical and Information Engineering, Southwest University for Nationalities, Chengdu 610041, China § College of Physical Science and Technology, Sichuan University, Chengdu 610064, China ∥ Science and Technology on Surface Physics and Chemistry Laboratory, Mianyang 621907, China ‡

ABSTRACT: Equilibrium geometries of AlnTi (n = 2−24) clusters were studied using density-functional theory with generalized gradient approximation. The resulting geometries showed that the titanium atom remains on the surface of clusters for n < 20 but is endohedrally doped from n = 20. This structural transition confirms the previous experiment results obtained by studying their abilities for argon physisorption (Lang, S. M.; Claes, P.; Neukermans, S.; Janssens, E. J. Am. Soc. Mass Spectrom. 2011, 22, 1508). The average bond lengths, coordination numbers, relative stabilities, electronic properties, and other relevant properties were discussed. It was found that the doped titanium atoms strengthen the stabilities of the pure aluminum clusters. The coordination numbers of titanium atoms along with the average Al−Ti bond lengths undergo dramatic increases during the structural transition. The intra-atomic hybridization exists in both Ti and Al atoms, and charge transfer from Al atoms to Ti atom were found in these complexes, which should reflect the strength of Al−Ti interactions. Electronic structure analysis based on the partial density of states reveals stronger Al−Ti interactions for the endohedrally doped structures.

1. INTRODUCTION Nanoclusters have attracted much attention because they constitute a new type of material possessing properties, which are distinct from the individual atoms and molecules or bulk matter.1−4 Specially, there are continuous interests in metal clusters due to their great potential applications in many fields, such as catalysis, optics, and nanoelectronics.5−11 A lot of investigations on the structures and electronic properties have been conducted on pure aluminum clusters with various theoretical and experimental methods.12−24 For example, Chuang studied the structures of neutral aluminum clusters Aln (n = 2−23) using a genetic algorithm (GA) coupled with a tight-binding interatomic potential and found that the icosahedral structure of Al13 served as the core for the growth of aluminum clusters from Al14 to Al18.12 Sun obtained that the structures of Aln clusters underwent a transition to the bulk motif above Al23 by discussing the medium-sized aluminum clusters Aln (n = 19−26) using the same method with Chuang.17 Also, Andersson investigated the electronic structure of free aluminum clusters with about 3−4 nm radius by synchrotron radiation-based photoelectron and Auger electron spectroscopy.24 While the additive effect of the second component in hybrid systems plays an important role in some unique catalytic, electronic, magnetic properties, and so on, more and more attention has been turned to doped metal clusters nowadays.25−28 Take the AlnB and AlnB2 (n = 1−7) clusters, for example. The calculations of structures and © 2013 American Chemical Society

stabilities based on the B3LYP and CCSD(T) methods by Jiang indicated that the mixed Al−B clusters exhibit peculiar aromatic behaviors.25 First-principles calculations predicted that doping in aluminum clusters can enhance the stabilities of certain “magic” clusters and modify their physical and chemical properties.26−28 Many chemical elements had been performed as substitutes to search the stabilized doped aluminum clusters, such as the halogens (F, Cl, Br, I).29−32 Bergeron reported that the Al13I2− cluster behaves chemically like the triiodide ion, and Al13Ix− clusters exhibit pronounced stability for even numbers of I atoms, while the Al14Ix− exhibits stability for odd numbers of I atoms.29,30 Some other nonmetals (H, N, S, C),33−38 nontransition metals (Mg, Na, Li, K, Cu),39−49 and transition metals (Fe, Co, Ni, Mn, Cr, Ti, V).50−55 were also added as the dopants in the Al clusters. Some novel properties were explored, accordingly. Among these elements, transition metals especially attracted much more attention for the free electrons of the unfilled 3d shell which carried a finite magnetic moment caused by Hund correlation.52 Kurkina found that the Fe, Co, and Ni impurities may be magnetic or nonmagnetic depending on the size of the Aln cluster.53 Moreover, structural information on free transition metal (Ti, V, Cr) doped cationic aluminum clusters was obtained by Sandra on the basis of their Received: September 27, 2012 Revised: March 2, 2013 Published: March 4, 2013 2590

dx.doi.org/10.1021/jp309629y | J. Phys. Chem. A 2013, 117, 2590−2597

The Journal of Physical Chemistry A

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abilities for argon physisorption.55 Motivated by the above and the potential technological application of Ti−Al alloy, in this article, the Ti atom was taken as the impurity to probe into its influences on the structural and electronic properties of Aln clusters. To investigate the structures and electronic properties of AlnTi (n = 2−24) clusters from a theoretical perspective, this work was organized as follows. In section 2, we emphasized the construction method of the models and the computational details. The results and their discussions were presented in section 3. We paid attention to their geometrical structures, relative stabilities, and electronic properties. The relatively stable models were given for every size. The average binding energies compared with the pure Aln clusters, the second-order difference of energies, and the fragment energies for the most stable structures of every size were computed. The average bond lengths and coordination numbers were given for analyzing the geometrical transition. We discussed the electronic populations for the lowest-energy structures. The partial density of states (PDOS) for Al19Ti and Al20Ti complexes were also plotted to study the bonding mechanism. A brief conclusion was given in section 4.

Self-consistent-field (SCF) electronic structure calculations were performed using a density functional theory (DFT)-based DMOL3 package for all of the models.57−59 All electron (AE) spin-polarized calculations were performed with the double numerical polarization (DND) basis set. The initial value for the number of unpaired electrons for each atom was taken from the formal spin introduced for each atom. Thus, the optimal results could be generally obtained. Spin multiplicities were obtained from the electronic population analysis. The electron density functional was treated by the general gradient approximation (GGA) with the specific exchange-correlation functional of BP, which is a combination of Becke’s exchange functional with the correction functional of Perdew and Wang (PW91).60,61 SCF calculations were carried out with a convergence criterion of 10−6 au on the electron density. Geometry optimizations were performed with the Broyden−Fletcher−Goldfarb−Shanno (BFGS) algorithm,62 and all clusters were relaxed fully without any symmetry constraints. We used the convergence criterion of 4.0 × 10−3 Hartree/Å for the gradient of force, 5.0 × 10−3 Å for the atomic displacement, and 10−5 au for the total energies in the geometry optimizations. In order to evaluate the accuracy of our selected scheme on describing the AlnTi clusters, we carried out the test calculations on Al2 and Ti2 dimers. Among the BP, PW91, PBE, BLYP, and RPBE functionals, the BP seemed to be a suitable functional. The present results with the BP functional as well as some experimental and available theoretical values for the equilibrium bond distances, harmonic vibrational frequencies, and multiplicities were summarized in Table 1. For the Al2 dimer, our calculated bond length of 2.697 Å and harmonic vibrational frequency of 235.4 cm−1 fit well with the experimental values of 2.7 Å and 284.2 cm−1, which were obtained from the vibrational spectra analysis.63 Moreover, our results were also in good agreement with the previous computational values based on LSD/PW/NCPP with the bond length of 2.7 Å and harmonic vibrational frequency of 290 cm−1.64 Additionally, the bond length (1.948 Å) and harmonic vibrational frequency (419.9 cm−1) of the Ti2 dimer were obtained, which were in good agreement with the experimental values of 1.942 Å and 407.9 cm−1, too.65 The spin multiplicities of the experimental and present values were also consistent. It indicated that our calculation method provided an efficient way to apply to the AlnTi clusters. To confirm that the optimized geometries correspond to the local minimums, the stabilities of the AlnTi clusters were further verified with vibrational frequency analyses. For the structures having low energies and few imaginary vibrational modes, we would reconstruct them by carrying out a relaxation along the coordinate of this mode to optimize again. Specifically, along the path of the imaginary vibrational mode, two models beside the optimized structure would be taken as the candidates. After the optimizations, the model with lower energy and without imaginary frequencies would be adopted.

2. MODELS CONSTRUCTING AND COMPUTATIONAL DETAILS The doped models were constructed for two steps. First, the pure Aln clusters were built systematically using a tightbinding genetic algorithm (TB/GA) method combined with first-principles calculations.12,17,56 For clusters containing fewer than 12 atoms, the growing method (GM) was used to search the low-energy structures, that is to say, adding one atom to the cluster with the size of n − 1. It is noteworthy that one Al atom is not only added to the ground state isomer but also to the low-lying isomers. For clusters containing more than eight atoms, an unbiased search for the low-energy structures of pure Aln (n = 9−25) clusters was investigated systematically to examine the motifs of growth, using a genetic algorithm (TB/GA) method combined with first-principles calculations. The Al9, Al10, and Al11 clusters were used to verify the consistency of GA with GM. In our present study, GA optimizations converged if the lowest energy structures remained unchanged after 5000 generations. Interatomic many-body Gupta potential for Al along with the conjugate gradient method was used for energy minimization. At the end of the global mininum structure search, 16 structures remained as the possible candidates for the further optimization using firstprinciples. Then, in order to obtain the lowest energy structures of AlnTi clusters, not only some independent configurations but also we optimized several isomeric structures by placing a Ti atom on each possible site of the Aln cluster or by adding one Al atom to the Aln−1Ti cluster as well as by substituting one Al by Ti atom from the Aln+1 cluster. Thus, the number of possible structures increases dramatically with the size of AlnTi clusters.

Table 1. Theoretical and Experimental Values of the Bond Lengths (Re), Harmonic Vibrational Frequencies (ωe), and Spin Multiplicities (spin) for Al2 and Ti2 Dimers ωe (cm−1)

Re (Å) cal. Al2 Ti2 a

2.697 1.948

theor.

expt.

a

c

2.70 1.93b

2.70 1.94d

cal. 235.4 419.9

theor. a

290 434b

spin expt. c

284.2 407.9d

cal.

expt.

3 3

3c 3d

Reference 64. bReference 66. cReference 63. dReference 65. 2591



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3. RESULTS AND DISCUSSION 3.1. Geometrical Structures of Optimized AlnTi (n = 2−24) Clusters. The number of stable conformations increases dramatically with the cluster size. In order to reduce the length of this article, only the ground state and two typical stable isomers of AlnTi (n = 2−24) clusters for each size were depicted in Figure 1 (for Al2−14Ti) and Figure 2 (for Al15−24Ti),

Figure 2. The stable geometries of AlnTi clusters for n = 15−24; the white spheres represent Ti atoms.

two atoms forming the bond). Besides, the Al−Ti bonds were involved in the average bond lengths and the Ti atom around the Al atoms was involved in the coordination numbers of Al atoms. As can be seen from Figures 1 and 2, for Al2Ti, the lowest energy structure is an isosceles triangle (C2v) with the Ti atom staying at the apex, and the Al−Al distance is slightly shorter than the Al dimer bond length. The linear C∞v (Al−Al−Ti) geometry is found to also be stable, which is 0.76 eV higher than the ground state, while the linear configuration with the Ti atom taking a middle position cannot stay stable. The first three-dimensional (3D) structure occurs at n = 3. Three Al atoms form an equilateral triangle, and the Ti atom caps the surface. It results in a tetrahedral configuration (C3v), whose energy is much lower than the linear structure in which the Ti atom is occupying a terminal position. For Al4Ti, the most stable structure is similar to the Al3Ti but is a rectangular pyramid with C4v symmetry. The structure with a C3v symmetry obtained by capping the Ti atom on the tetrahedral Al4 (4C) and a planar structure (4B) also have low energies. The Al5Ti clusters can be viewed as the addition of one Al atom on the ground state of Al4Ti. The ground state (5A) is an edge-capped structure with Cs symmetry, which is similar with the parent cluster of H2O adsorption we had calculated before.67 The two low-lying isomers (5B and 5C) are face-capped configurations with an Al atom capped on the opposite and adjacent faces of the Ti atom, respectively. The 5B is a square-bipyramid with C4v symmetry. In the case of Al6Ti, the most stable structure is a distorted pentagonal bipyramid (C2v) with the impurity atom Ti as a part of the pentagonal ring. The energy difference between the ground state and the face-capped octahedron (6B) is merely 0.309 eV. A face-capped pentagonal bipyramid is the lowest energy geometry of Al7Ti. The preferred geometry of Al8Ti can be viewed as a tricapped square-bipyramid motif with two face-capped Al atoms and one edge-capped Al atom. The ground states of Al9Ti and Al10Ti have similar structures.

Figure 1. The stable geometries of AlnTi clusters for n = 2−14; the white spheres represent Ti atoms.

respectively. The impurity atom Ti was shown as a white sphere. The isomers were labeled as A, B, and C in increasing order of their total energies or, equivalently, decreasing order of their relative stabilities. The spin multiplicities (spin), point group (PG) symmetries, and relative energies ΔE (meV) with respect to the lowest-energy configurations for the different isomers of Al2−24Ti were summarized in Table 2. According to the computational results, the energetically preferred spin multiplicities of almost all the odd-n AlnTi clusters are doublet, while they are singlet for all the even-n geometries with exception of 2B, 4A, 4C, 13C, and 18A, which are triplet, triplet, quintuplet, quartet, and triplet, respectively. Meanwhile, the average bond lengths, average Al−Ti bond lengths, average coordination numbers (CNs) of Al atoms, and coordination numbers of Ti atoms for the stable isomers of Al2−24Ti were also listed in Table 2. Elements were excluded from bonding if they did not lie within a distance between 60 and 155% of the ideal bond length (defined as the sum covalent radii of the 2592



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Table 2. The Spin Multiplicities (spin), Point Group (PG) symmetry, relative energies ΔE (meV) with Respect to the LowestEnergy Configurations, Average Bond Lengths Rav (Å), Average Al−Ti Bond Lengths RAl−Ti (Å), Average Coordination Numbers (CNav) Together with the Coordination Numbers of Ti Atom (CNTi) for the Different Isomers of Al2−24Ti Clusters 2A 2B 3A 3B 4A 4B 4C 5A 5B 5C 6A 6B 7A 7B 8A 8B 8C 9A 9B 9C 10A 10B 10C 11A 11B 11C 12A 12B 12C 13A 13B 13C 14A

spin

PG

ΔE (meV)

Rav (Å)

RAl−Ti (Å)

CNav

CNTi

1 3 2 2 3 1 5 2 2 2 1 3 2 2 1 1 1 2 2 2 1 1 1 2 2 2 1 1 1 2 2 4 1

C2v C∞v Cs C∞v C4v C1 C3v Cs C4v C1 C2v C3v C1 C1 Cs Cs C1 Cs C1 C1 Cs C2v C1 C5v Cs C1 C5v Cs C1 Cs Cs C3v Cs

0 757 0 1926 0 1179 1198 0 70 87 0 309 0 391 0 137 385 0 123 257 0 110 200 0 194 221 0 317 355 0 501 571 0

2.562 2.663 2.676 2.617 2.655 2.668 2.741 2.676 2.700 2.716 2.742 2.728 2.759 2.765 2.740 2.730 2.769 2.763 2.782 2.759 2.776 2.745 2.743 2.769 2.741 2.788 2.791 2.776 2.760 2.792 2.785 2.801 2.7856

2.567 2.619 2.640 2.652 2.658 2.601 2.599 2.687 2.680 2.736 2.581 2.721 2.631 2.669 2.620 2.628 2.869 2.715 2.619 2.699 2.660 2.796 2.767 2.767 2.803 2.705 2.763 2.777 2.818 2.801 2.803 2.725 2.758

2.0 1.5 3.0 1.7 3.0 3.0 3.8 3.2 4.0 3.4 4.7 4.5 4.7 4.7 5.0 4.8 4.8 4.9 5.3 5.0 5.5 5.0 5.2 6.0 5.3 5.7 6.5 5.8 5.7 6.2 6.4 6.7 6.6

2.0 1.0 3.0 1.0 4.0 2.0 3.0 4.0 4.0 5.0 4.0 3.0 5.0 3.0 4.0 4.0 6.0 6.0 4.0 5.0 5.0 8.0 6.0 6.0 6.0 5.0 6.0 6.0 6.0 6.0 7.0 3.0 6.0

14B 14C 15A 15B 15C 16A 16B 16C 17A 17B 17C 18A 18B 18C 19A 19B 19C 20A 20B 20C 21A 21B 21C 22A 22B 22C 23A 23B 23C 24A 24B 24C

spin

PG

ΔE (meV)

Rav (Å)

RAl−Ti (Å)

CNav

CNTi

1 1 2 2 2 1 1 1 2 2 2 3 1 1 2 2 2 1 1 1 2 2 2 1 1 1 2 2 2 1 1 1

Cs Cs C1 Cs Cs C1 C1 C1 C1 C1 Cs C5v Cs C1 Cs Cs C1 C1 C2 C1 Cs C1 Cs C1 C1 C1 C1 C1 C1 C1 C1 C1

108 367 0 30 33 0 68 104 0 6 69 0 160 184 0 92 128 0 343 351 0 262 352 0 55 175 0 143 145 0 62 235

2.799 2.792 2.800 2.806 2.797 2.796 2.821 2.804 2.832 2.803 2.827 2.796 2.810 2.812 2.824 2.831 2.811 2.852 2.821 2.807 2.815 2.839 2.829 2.828 2.825 2.824 2.797 2.815 2.816 2.826 2.819 2.814

2.824 2.818 2.814 2.736 2.750 2.866 2.826 2.769 2.770 2.820 2.989 2.673 2.834 2.785 2.723 2.810 2.783 3.218 2.775 2.797 3.182 3.237 3.182 3.200 3.174 3.132 2.954 2.842 2.839 3.078 3.123 3.100

6.1 6.5 6.5 6.5 6.7 6.6 6.5 6.4 6.8 6.5 6.5 6.7 6.7 6.5 7.1 7.1 6.6 6.3 6.8 6.8 6.2 6.3 6.3 6.3 6.3 6.4 6.3 6.8 6.8 6.6 6.3 6.3

7.0 7.0 6.0 6.0 6.0 7.0 8.0 7.0 7.0 8.0 10.0 6.0 8.0 7.0 6.0 8.0 7.0 19.0 8.0 8.0 17.0 19.0 18.0 18.0 17.0 17.0 14.0 9.0 9.0 16.0 16.0 16.0

the substitution of the Ti atom for the Al atom on the apex of the well-known double icosahedron pure Al19 cluster. The lowest-energy Al19Ti cluster with Cs symmetry consists of embedding one Al atom into the double icosahedron of 18A. From another point of view, it can also be recognized as the coupling of the icosahedron and a hexagonal bipyramid motif. The Ti atom is placed on the apex position of the pentagonal pyramid. It should be noted that, for the AlnTi clusters with n ranging from 2 to 19, the Ti atoms are prone to lying at the surface. Then, with the cluster size increasing, the motifs become more and more complicated, and the Ti dopant tends to be embedded inside the clusters. Specifically, for n ≥ 20, all the ground states have Ti-trapped structures and with low symmetries of C1 or Cs. This agrees quite well with Sandra’s experimental result obtained by studying the abilities of AlnTi clusters for argon physisorption, who found that bare Aln clusters are inert toward argon, while AlnTM+ (TM = Ti, V, Cr) clusters attach one argon atom up to a critical cluster size.55 The critical size was found to be 19−21 for Ti dopant. They interpreted this size as the geometrical transition from surface-located dopant atoms to endohedrally doped aluminum clusters with the transition metal atom endohedrally residing in an aluminum cage. This consistency confirmed the experimental interpretation and prompted the rationality of our calculations. However, as the stability order of metal clusters is often sensitive to the DFT

One corresponds to the tricapped pentagonal-bipyramid and the other is a tricapped hexagonal-bipyramid, with their Ti atoms staying on the apex and on the surface, respectively. The most stable structure of Al12Ti is an icosahedral structure with the Ti atom in the cage apex, which has been observed in many other metallic clusters, such as Cr, Mn, and Fe.54 Al11Ti forms a structure that is a precursor to an icosahedric structure which can be obtained by removing one Al atom from the Al12Ti. Similarly, the structures for Al13Ti can be obtained by adding one Al atom on the Al12Ti, but both of the formations have distortions. The ground states of Al14Ti can be regarded as a bicapped 12A with two Al atoms face-capped on the opposite position of the Ti atom, while the most stable Al15Ti is formed by embedding another Al atom into the icosahedron cage which seriously distorted the geometry (C1). The pure Al17 cluster consists of capping four atoms on the icosahedron structure, with a couple sets of two adjacent atoms capping on opposite symmetric positions. It is highly symmetric (D2h) with closely packed atoms. The ground state of Al16Ti can be obtained by replacing an Al atom with a Ti atom at the flank position and then undergoing a distortion for the whole structure. The most stable structure of Al17Ti can be seen as two fused hexagonalbipyramids with capping of another three adjacent Al atoms. The most stable Al18Ti cluster with C5v symmetry arises from 2593



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process. Furthermore, the binding energy curve can be roughly divided into four regions: n < 6 where the binding energies increase rapidly as the cluster size increases. The surface effect will be important in these small clusters. Then, 6 < n < 13 where binding energies increase moderately with size, 13 < n < 21 where the binding energies increase slowly, and n > 21 where the binding energies vary slightly. That seems to have an energy convergence to bulk behavior, which suggests that the surface effect will not be dominant compared with the bulk motif. For comparison, the average binding energies for pure Aln clusters were also plotted in Figure 3, which were calculated as follows: Eb = [nE(Al) − E(Aln)]/n. As can be seen, average binding energies of the doped AlnTi clusters are obviously higher than those of the corresponding pure Aln+1 clusters by 0.085−0.394 eV. It suggests that the doping of a Ti atom in the Aln cluster strengthens the stability of the framework. In cluster physics, the fragmentation energy and secondorder difference of energy are sensitive quantities that can reflect the relative stabilities of clusters. On the one hand, the size dependence of the fragmentation energy for AlnTi clusters was investigated and plotted in Figure 4. The fragment energy

functionals, we additionally calculated the low-lying isomers of AlnTi (n = 2−24) clusters with the PBE and BLYP functionals. The results indicated that most of the stability order had no change. Especially, the concluded structure transitions from Al19Ti to Al20Ti cluster for the PBE and BLYP functionals are completely consistent with the result for the BP functional. From Table 2, we can see that, in spite of the fluctuations, the average bond lengths increase with the size of AlnTi as a whole, and the same phenomenon can be found for the average Al−Ti bonds but fluctuated by a larger margin. Especially, the Al−Ti bond lengths for n > 19 are much larger than the smaller size clusters, which can be attributed to the structure transition of the clusters. That is, the radius of the Ti atom is bigger than that of the Al atom, so when the Ti atom was surrounded by the Al atoms, it would make the clusters expand. It is worth noticing that, compared with the other endohedral cage structures, the bond length of Al−Ti for Al23Ti is much shorter. That may be due to the special conformation of Al23Ti, which looks like three layers of bulk Al(111) surface. As we know, the Al(111) surface has a compact shape. In addition, the average coordination numbers of AlnTi clusters have a rising trend with the size increasing. For the specific Ti atoms, their coordination numbers also increase with the size increasing, and an apparent steep increase occurs with the size n transiting from 19 to 20. This confirms the structure transition of Ti atoms from the surface to the interior of AlnTi clusters. 3.2. Stability of the AlnTi (n = 2−24) Clusters. The stability of clusters can be discussed on the basis of the average binding energies (Eb), second difference in energies (Δ2E), and the fragment energies (Efra). For the AlnTi (n = 2−24) clusters, these can be calculated with the following formulas: E b(Al nTi) = [nE(Al) + E(Ti) − E(Al nTi)]/(n + 1)

(1)

Δ2E(Al nTi) = E(Al n + 1Ti) + E(Al n − 1Ti) − 2E(Al nTi)

(2)

Efra(Al nTi) = E(Al n − 1Ti) + E(Al) − E(Al nTi)

(3)

where E is the total energy of the system. From the numerical results in Figure 3, we can see that the average binding energies

Figure 4. The fragment energies of AlnTi clusters (n = 2−24).

curve of small clusters usually exhibits even−odd alternation behavior.68−70 As can be seen, the fragment energy curve of small AlnTi clusters also exhibits a pronounced even−odd alternation behavior as a function of cluster size from n = 3 to 12, indicating that the AlnTi (n = 4, 6, 8, 10, 12) clusters maintain greater stabilities than the clusters in the vicinity. With the cluster size increasing, the complicated motifs start playing more important roles than the number of valence electrons, and the even−odd alternation behavior vanishes accordingly. However, there are two local peaks at n = 16 and 18, which also present a relatively higher stability with respect to their neighbors. In particular, the Al21Ti cluster in terms of the calculated fragment energies has the strongest stability. On the other hand, the size dependences of second-order differences of energies were calculated and plotted in Figure 5. There is also an even−odd alternation behavior from n = 3 to 12, confirming that the AlnTi (n = 4, 6, 8, 10, 12) clusters maintain greater stabilities than their neighbors. In addition, two slight lifts at n = 16 and 18 can also hint the stabilities with respect to their neighbors. It is worth pointing out that the second-order difference of energy for the Al21Ti cluster is also the largest one. These concluded stabilities of AlnTi clusters based on the fragmentation energies and second-order differences of energies are the same.

Figure 3. The average binding energies per atom for AlnTi and the corresponding bare Aln+1 clusters (n = 2−24).

generally increase with the increasing size, indicating these clusters could continue to gain energy during the growth 2594



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For the Ti atoms, we can see that, from n = 2 to 4, the number of 4s electrons decreases and the number of 3d and 4p electrons increases monotonically. This suggests the electrons transfer from 4s to 3d and 4p orbitals; namely, the intra-atomic hybridization effect increases with the cluster size increasing. From n = 5 to 19, the electron numbers of these orbitals approximately keep unvaried. There are more electrons transferred from 4s to 3d than from 4s to 4p, which indicates the stronger intra-atomic hybridization between 4s and 3d orbitals of the Ti atom. It should be mentioned that some electrons of Al atoms also transferred to the 3d and 4p orbitals of Ti atom, as shown in Figure 6c, which may further influence the electron population of Ti atom. Especially for the clusters beyond n = 19, the number of transferred electrons from Al atoms to Ti atoms is larger as a whole, and accordingly there are relatively more Ti-3d and Ti-4p electrons. This increase demonstrates the enhanced interactions between Ti atom and Al atoms. This electronic behavior beyond n = 19 shows that a structural transition occurs from Al19Ti to Al20Ti cluster, which is in conformity with the results from the atomic structures. For the Al atoms as shown in Figure 6b, we could see that the 3p orbitals obtained a few electrons and the 3s orbital lost some electrons. The electronic population reveals that all of the additional 3p electrons come from the 3s orbitals. The electron transition suggests the prevalent hybridization between 3s and 3p orbitals of the Al atoms. It is apparent that more and more electrons transferred from 3s to 3p orbitals, which indicates the enhanced intra-atomic hybridization of Al atoms as a function of the cluster size. As depicted in Figure 6c, the pattern of the total transferred electrons from Al atoms to Ti atom is similar to the trend of the 3d orbitals for the Ti atom, which indicates that the transferred electrons from Al atoms are predominantly obtained by the Ti-3d orbitals. Accordingly, the number of transferred electrons can be used to weigh the interactions between Al and Ti atoms to some extent. Take the Al23Ti cluster, for example. The slightly higher number of transferred electrons suggests the stronger Al−Ti interaction, which agrees well with its compact geometry of Al(111) surface. In order to compare the different Ti−Al interactions for the Ti atoms located at the surface of the cluster and embedded inside the cluster, the PDOS of the Al19Ti and Al20Ti clusters were calculated and compared in Figure 7. The Al atom bonding with the Ti atom was marked with “Al1”, and another Al atom (marked with “Al2”) around the Al1 but not connected with Ti atom was also calculated for comparison. The Fermi levels for Al19Ti and Al20Ti are −3.7 and −4.3 eV, respectively. As can be seen, the hybrid Al−Al, Al−Ti metallic bonds and free electrons coexist at the Fermi levels for both models. For Al19Ti, the weak interactions of Al(3s, 3p)−Ti(3s) at about −59.4 eV and Al(3s, 3p)−Ti(3p) at about −37.4 eV can be found. The similar weak interactions also occur for the Al20Ti cluster at about −59.2 and −37.7 eV, respectively. In fact, the differences of the PDOS for Al1 and Al2 in Al19Ti are not dramatic. However, for the Al20Ti cluster, some electrons of the Al1 atom at the Fermi level shift left to −10.1 eV, and the same phenomenon can also be found for the Ti atom. Therefore, a remarkable Al(3s, 3p)−Ti(3d, 4s, 4p) interaction can be found at about −10.1 eV for Al20Ti. This additional Al−Ti bond may be attributed to the strengthened Al−Ti interaction. The difference for Al19Ti and Al20Ti around the Fermi levels also results from the different coordination numbers of the Ti atom,

Figure 5. The second-order difference of energies for AlnTi clusters (n = 2−24).

3.3. Electronic Properties of AlnTi (n = 2−24) Clusters. To study their interactions and how the physical properties of AlnTi clusters change as the size of the cluster is increasing, we calculated the nature bond orbitals (NBO) using the Gaussian 09 program with the B3LYP functional. The obtained electronic populations and charge transfer of valence orbitals for Al and Ti atoms were depicted in Figure 6. The ground

Figure 6. Natural bond orbital analysis with the B3LYP functional. (a) Electronic population of 3d, 4s, and 4p orbitals for Ti atom, (b) average electronic population of 3s and 3p orbitals for Al atoms, and (c) total charge transfer from Al atoms to Ti atom.

state electronic configurations of the Al atom and Ti atom are 3s23p1 and 4s23d2, respectively. We considered the average electronic populations of the 3s and 3p orbitals for Al atoms; meanwhile, the 3d, 4s, and 4p orbitals were considered for Ti atom. The total charge transfers from Al atoms to Ti atom were also listed. 2595



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Figure 7. The partial density of states (PDOS) for the most stable structures of Al19Ti and Al20Ti, namely, 19A and 20A. The (a) and (b) figures show the PDOS of the Ti atom along with the Al atom bonding with the Ti atom (marked with Al1) of 19A and 20A, respectively. The “Al2” represents the PDOS of an Al atom bonding with the “Al1” atom but not connected with the Ti atom. The “s”, “p”, and “d” orbital contributions are represented by the dashed line, solid line, and dotted line, respectively. The vertical dashed line denotes the Fermi level.

which further confirms the structure transition as mentioned above.

ACKNOWLEDGMENTS

■

REFERENCES

We would like to thank the reviewers for the valuable suggestions on improving our paper.

4. CONCLUSIONS In summary, we studied the structures and electronic properties of Ti-doped Aln clusters AlnTi (n = 2−24) using all electron spin-polarized density-functional theory with generalized gradient approximation. A critical size for the geometrical transition of surface-located dopant atom to endohedrally doped aluminum clusters with the Ti atom residing in an aluminum cage was found from n = 19 to 20, which was consistent with the experimental forecast. The steep increases of the average Al−Ti bond lengths and coordination numbers of Ti atoms from n = 19 to 20 confirm this structural transition. Moreover, the nature bond orbital analysis reveals that the hybridization effect exists in both the Al and Ti atoms, and charge transfer from Al to Ti atoms can be found during the Al−Ti interactions. The PDOS of Al19Ti and Al20Ti clusters were calculated for comparison, which shows that there is an additional strong Al(3s, 3p)− Ti(3d, 4s, 4p) interaction around the Fermi level of the endohedral structure. Both the charge transfer and the PDOS indicate that the interactions between Al and Ti atoms in the endohedral structures are stronger than the surface-located dopant structures, which are in conformity with the result of the structural transition.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (Y.H.); [email protected] (G.J.). Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. All authors contributed equally. Notes

The authors declare no competing financial interest. 2596



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NOTE ADDED AFTER ASAP PUBLICATION Due to production errors, this article was published ASAP on March 18, 2013, with incorrect versions of the Abstract, Figure 1, and Table of Contents graphics. The corrected article was published on March 28, 2013.

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Geometric Transition and Electronic Properties of Titanium-Doped

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