Cite this Article
Shi Shun-Ping, Zhang Chuan-Yu, Zhao Xiao-Feng, Li Xia, Yan Min, Jiang Gang. Geometries, stabilities, and electronic properties analysis in InnNi(0,±1) clusters: Molecular modeling and DFT calculations . Chinese Physics B, 2017, 26(8): 083103  
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Geometries, stabilities, and electronic properties analysis in InnNi(0,±1) clusters: Molecular modeling and DFT calculations
Shi Shun-Ping1, Zhang Chuan-Yu1, †, Zhao Xiao-Feng1, Li Xia1, Yan Min1, Jiang Gang2
Department of Applied Physics, College of Geophysics, Chengdu University of Technology, Chengdu 610059, China
Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China

 

† Corresponding author. E-mail: zhangchuanyu10@cdut.cn

Project supported by the Cultivating Program of Excellent Innovation Team of Chengdu University of Technology (Grant No. KYTD201704), the Cultivating Program of Middle-aged Backbone Teachers of Chengdu University of Technology (Grant No. 10912-KYGG201512), the National Natural Science Foundation of China (Grant No. 11404042), the Science Fund from the Science & Technology Department of Sichuan Province, China (Grant No. 2016RZ0069), and the Research Foundation of Chengdu University of Technology, China (Grant No. 2017YG04).

Abstract

Density functional theory (DFT) with the B3LYP method and the SDD basis set is selected to investigate In Ni, In Ni , and In Ni ( –14) clusters. For neutral and charged systems, several isomers and different multiplicities are studied with the aim to confirm the most stable structures. The structural evolution of neutral, cationic, and anionic In Ni clusters, which favors the three-dimensional structures for n = 3 – 14. The main configurations of the In Ni isomers are not affected by adding or removing an electron, the order of their stabilities is also nearly not affected. The obtained binding energy exhibits that the Ni-doped In cluster is the most stable species of all different sized clusters. The calculated fragmentation energy and the second-order energy difference as a function of the cluster size exhibit a pronounced even–odd alternation phenomenon. The electronic properties including energy gap , adiabatic electron affinity (AEA), vertical electron detachment energy (VDE), adiabatic ionization potential energy (AIP), and vertical ionization potential energy (VIP) are studied. The total magnetic moments show that the different magnetic moments depend on the number of the In atoms for charged In Ni. Additionally, the natural population analysis of In Ni clusters is also discussed.

PACS: 31.15.E-;36.40.Mr;36.40.Cg
Keyword: n Ni ( 0 , ± 1 ) clusters" target=_blank>In n Ni ( 0 , ± 1 ) clusters;stability;electronic property;density functional theory
1. Introduction

Atomic clusters play a bridge between molecular and condensed matter physics. Therefore, the properties of clusters are widely studied as a function of size and composition with two objectives: First, researcher hopes to learn how they evolve toward bulk properties and to find unique properties for specific cluster sizes that differ largely from their bulk counterparts. Second, when the composition varies, corresponding to the structure, stability, electronic property, magnetic moment, etc. are also changed. These characteristics make a huge potential of clusters studies for a wide range of applications. In recent years, semiconductor nanomaterials have drawn a lot of research efforts both for theoretical and for their potential technological applications. Indium as a good semiconductor element, the technological importance is growing due to its potential mainstream use in future nanoelectronic devices.[1] Thus, over the past decades, the structural and electronic properties of indium clusters have been extensively studied both experimentally and theoretically.[2–11] For example, Staudt and Wucher[11] investigated the yields of neutral and charged In clusters sputtered from a pure indium surface under bombardment with 15-keV Xe ions, the results demonstrated that for clusters containing more than about 20 atoms the detection probability became an exceedingly important parameter that needed to be characterized in order to arrive at a quantitative determination of the true cluster size distribution.

However, a great number of experimental and theoretical works about doped indium clusters have been studied.[12–31] This is motivated by the fact that an atom doped in a small indium cluster can strongly change the properties of the pure indium cluster. Janssens et al.[12] performed the structures and ionization potentials of small In O clusters (n = 1–8) by using experimental and theoretical studies, they found that ionization potentials were slightly lower for the In O species than for pure indium clusters and exceptionally low ionization potentials were obtained for In O and In O. When one N atom is doped In clusters, the In N, In N, and In N clusters possesses relatively higher stability than their neighbor.[13] However, when two N atoms are doped In clusters, In N cluster is the strongest of all the investigated clusters.[16] In addition, the calculated results of In P and In P clusters showed that hollow cages with alternating In–P bonds were energetically preferred over other structures for both the neutral and anionic species within the range x = 6–15.[14] Except the metalloid element is doped, the metal element and the transition metal (TM) element are also doped,[15,17–21,23,24,27,28] because the metal element and TM element alter just one atom’s presence, location, or identity. Based on the above facts, Liu et al.[20] investigated the stabilities and electronic properties of In Na (n = 4–9) clusters, in comparison with the corresponding pure In clusters, the doped Na atoms resulted on a local structural distortion of the mixed clusters. Both the PbIn and Pb In clusters,[19] which had planar, ground state geometries, large HOMO–LUMO (highest occupied molecular orbited–lowest unoccupied molecular orbital) gaps of 1.34 eV and 1.45 eV, respectively. By anionic photoelectron spectroscopy and fist principles calculations, Gupat et al. [27] obtained that the Bi In , Bi In , Bi In , and Bi In were classified as gas phase zintl clusters that followed Wade’s rules and were analogous to known zintl species.

All the time, TM element-doped clusters have attracted attention, because when a transition metal is encapsulated into clusters, some special phenomena appear, for example, when the Ti atom is doped to Ga clusters, the average binding energies exhibit a sequence as Ga Ti > Ga Ti > Ga Ti > Ga , and the HOMO–LUMO gaps of Ga Ti clusters are distinctly higher than those of Ga clusters.[32] When the Nb atom is doped Ga clusters, the results indicated the doping of Nb atom in gallium clusters improved the chemical activities.[33] Ni atom as a TM element, it is usually selected to dope the clusters.[34–40] For instance, the averaged binding energies of the NiGe clusters were obviously higher than those of the pure Ge clusters, which indicated that the doped Ni atom in the Ge clusters contributes to strengthen the stabilities of the germanium framework.[34] Yuan et al. [36] found that the odd–even alterations of vertical detachment energies were shown markedly in Ni-doped gold clusters, therefore, they predicted that the odd–even alteration of the reactivity of O can be found on Ni-doped gold clusters. In this paper, to compare the effect of the doped Ni atom to the indium clusters, using the first-principles method based on density-functional theory, we systematically investigate the indium clusters-doped Ni atom, In Ni (n = 1–14). In the case of doping with nickel, Ni atom delivers just also one itinerant electron because of the small promotion energy from 3d 4s to 3d 4s with respect to other 3d transition elements.[39] Therefore, these systems have a contribution in clarifying the influence of the s-, d-electrons of impurity atoms on geometric, electronic, and bonding properties of dopant indium clusters with respect to pure indium clusters.

2. Computational details

A research is performed for the lowest energy and low-lying structures of In Ni (n = 1–14) clusters, using the density functional theory (DFT). In this paper, we employ a combination functional of Becke’s three-parameter exchange functional (B3)[41] with the Lee–Yang–Parr (LYP)[42] generalized gradient correction functional. In addition, in order to confirm the structures and energies of all neutral, anionic, and cationic In Ni clusters, the basis set SDD[43] is chosen, in which the core electrons is constituted by energy-consistent 21-valence electron relativistic effective core potential (RECP) of the Stuttgart group. The other functionals (B3P86, B3PW91) and other basis sets (LanL2DZ, DZVP) on the two-atom clusters (In and Ni ) are checked, with the purpose to choose the suitable computational method. The calculated results together with the comparable experimental and theoretical results are listed in Table 1. From Table 1, we see that the values of functionals (B3P86, B3PW91) and basis sets (LanL2DZ, DZVP) do not depend on that experimental results, however, it can be found that the experimental results for bond length , vibration frequencies ( ), dissociation energies , and ionization potentials (IP) are quite matched to the choices of B3LYP method and SDD basis set.

Table 1.

Calculated values of bond length (in unit Å), frequency (in unit cm ), dissociation energy (in unit eV), and ionization potentials IP (in unit eV) for the In and Ni molecules at different levels.

.

For small-sized neutral, cationic, and anionic In Ni (n = 1–14) clusters, a great deal of isomers are considered, including all the configurations in the literature. Then, both some independent configurations and we optimized several isomeric structures by placing an Ni atom on each possible site of the In cluster or by adding one In atom to the In Ni cluster as well as by substituting one In by Ni atom form the In cluster, we obtain the lowest energy structures of In Ni clusters. We also implement configurations calculations to gain ground state structures of In Ni (n = 1–14) clusters. For In Ni (n = 1–14) clusters, we consider that the structures of In Ni clusters will be directly developed into the structures of In Ni clusters. In addition, the default self-consistent field convergence to 10 a.u. (The unit a.u. is short for atomic unit) and (75, 302) integral pruned grid are used, which are exactly enough to ensure that the results are valid. For each configuration, three different spin multiplicities for In Ni clusters are considered. The structures with the lowest energies are chosen as the ground-state configurations. All calculations are performed using the Gaussian 03W package.[44]

3. Results and discussion
3.1. Geometrical structures of In Ni (n = 1–14) clusters

For In Ni (n = 1–14) clusters, a lot of initial possible geometries with various possible spin multiplicities are optimized. The optimized most stable and low-lying structures of In Ni, In Ni , and In Ni clusters are plotted in Fig. 1, Fig. 2, and Fig. 3, respectively. According to the relative energy from low to high, the stability orders of each cluster are marked by order of letter, na > nb > nc > and so on (n is the number of In atoms in In Ni clusters), meanwhile, the symmetries of In Ni, In Ni , and In Ni clusters are also listed in Fig. 1, Fig. 2, and Fig. 3, respectively.

Fig. 1. (color online) The lowest energy and low lying structures of In Ni (n = 1–14) clusters.
Fig. 2. (color online) The lowest energy and low lying structures of In Ni (n = 1–14) clusters.
Fig. 3. (color online) The lowest energy and low lying structures of In Ni (n = 1–14) clusters.

(i) InNi, InNi , and InNi

The equilibrium geometries of InNi clusters with symmetry are optimized. The doublet InNi dimmer is the ground state, and the corresponding electronic state is , the bond length of InNi dimmer is 2.656 Å. However, the bond lengths of triplet InNi and triplet InNi dimmer are 2.597 Å and 2.657 Å, which are shorter and longer than the bond length of neutral InNi, reflecting that the In–Ni interaction of the neutral InNi is weaker than the In–Ni interaction of the anionic InNi and stronger than the In–Ni interaction of the cationic InNi , respectively.

(ii) In Ni, In Ni , and In Ni

The possible structures such as , , and isomers are optimized as the stable structures. According to the optimized results, it is worth noting that the lowest-energy structures as shown in Fig. 1 (2a), Fig. 2 (2a ), and Fig. 3 (2a ) are an isosceles triangle in which the bond lengths are 2.63 Å, 2.68 Å, 2.74 Å for In–Ni, respectively. We obtain the bond angles are 69.8°, 68.3°, 129.8° for In–Ni–In, respectively. Although the isomer 2a is similar to the lowest-energy structure of the 2a, the isomer 2a is different to the lowest-energy structure of the 2a. The linear structures 2b and 2b with Ni atom at one end are the next isomer, but the linear structure 2b with Ni atom in the middle is the next isomer.

(iii) In Ni, In Ni , and In Ni

In the case of n = 3, In Ni, In Ni , and In Ni have the same most stable structure (3a, 3a , and 3a in Fig. 1, Fig. 2, and Fig. 3, respectively), which are a three-dimensional tetrahedral configurations, the symmetries are . The other two geometries for the neutral In Ni clusters are a planar quadrilateral structure and a planar Y-shaped structure, whose relative energies are 0.308 eV, 0.873 eV and the symmetries are , and , respectively. Correspondingly the orders of relative energies of anionic and cationic In Ni clusters are same with neutral In Ni clusters, in which the symmetries are also , and , respectively.

(iv) In Ni, In Ni , and In Ni

For n = 4, the lowest-energy structures of the neutral, cationic, and anionic In Ni clusters are same, and the symmetries of all of them are also identical. The ground-state structure of the In Ni cluster with the electron state B is different from the ground state structure of the In cluster.[51] The 4b and 4c isomers with and symmetries are higher in energy than the most stable structure 4a by 0.64 eV and 0.88 eV, respectively. The energy orders of anionic 4b with , 4c with , and cationic 4b with , 4c with are same with neutral 4b and 4c.

(v) In Ni, In Ni , and In Ni

Starting n = 5, the lowest energy structures for neutral and cationic forms are similar, but the most stable structure of anionic cluster is different with neutral and cationic forms, although the symmetries of In Ni, In Ni , and In Ni clusters are identical ( ). The structures and the energy orders of 5b, 5c and 5b , 5c with and symmetries are also similar. Although the structures of 5b and 5c are same with 5c and 5b, respectively, the energy orders are also contrary.

(vi) In Ni, In Ni , and In Ni

By calculations, we obtain that the spin triplet state is the lowest energy for the In Ni cluster (Fig. 1 (6a)), corresponding to the A″ state and the symmetry. The most stable structures of In Ni and In Ni are also prism structures, which are in agreement with the neutral In Ni cluster. The difference is that the energy orders for the isomers of cationic are different with the neutral and the anionic.

(vii) In Ni, In Ni , and In Ni

The global minimum of In Ni cluster can be generated by adding an In atom to the corresponding In Ni cluster. The most stable structures for the cationic and the anionic clusters are similar to those of its neutral counterparts, and the symmetries are also identical, which are . The only difference is that the neutral with the A′ state instead of A′ state of the cationic and the anionic. Also, the other stable isomers for the three clusters, the orders of stabilities are different (7b , 7c , and 7b , 7c are same, 7b, 7c, and 7b , 7c are different).

(viii) In Ni, In Ni , and In Ni

In the case of the most stable In Ni, we optimize the geometry subject to capped octahedron geometry with symmetry. The structure is in reasonable agreement with the anionic but different to the cationic, this structure is the third most stable for In Ni , and the most stable structure of In Ni favors that Ni atom is located in the inside of the distorted capped trigonal prism.

(ix) In Ni, In Ni , and In Ni

The ground state structure obtained for In Ni has symmetry and it can be built from In Ni (8b) wedge, corresponding to the A state. The 3D structure of In Ni (9a ) with symmetry is the lowest energy structure, which is different with the most stable neutral In Ni. Also, the ground state structure of In Ni can be viewed as similar with the neutral In Ni.

(x) In Ni, In Ni , and In Ni

The lowest energy structures of neutral, cationic, and anionic In Ni clusters adopt the similar structures as shown in the three series (Fig. 1 (10a), 2 (10a ), and 3 (10a )). Compared with the other neutral clusters of In Ni, the geometric structures of anionic and cationic clusters are quite similar, the symmetries are also same, but the orders of energy change largely, especially for In Ni clusters.

(xi) In Ni, In Ni , and In Ni

Starting from various initial structures, the In Ni clusters are calculated considering different spin configurations. The state (Fig. 1 (11a)) is the lowest energy geometry, corresponding to the electronic state is A. The most stable structures of In Ni and In Ni clusters are same with the neutral In Ni, which the symmetries and the electronic state are and A, respectively.

(xii) In Ni, In Ni , and In Ni

When the size of In Ni cluster is up to 12, the lowest energy of In Ni with symmetry is obtained by adding one indium atom above the most stable of In Ni. Adding one indium atom in the base of In Ni and In Ni clusters (Fig. 2 (11a ) and Fig. 3 (11a )), the lowest energy structures for In Ni and In Ni can be also obtained, the structures and the symmetries are consistent with the neutral In Ni.

(xiii) In Ni, In Ni , and In Ni

The lowest energy structure for neutral In Ni cluster is similar to its corresponding anionic cluster. This phenomenon is also found for some low-lying isomers (13b and 13b , 13c and 13c , 13d and 13d ). Although the lowest energy structure for cationic In Ni is the same as the most stable of In Ni and In Ni , the orders of energy for low-lying In Ni isomers are different with the corresponding the neutral and anionic In Ni clusters.

(xiv) In Ni, In Ni , and In Ni

Finally, the ground state structure of In Ni cluster is obtained by adding one indium on lowest energy of In Ni cluster (Fig. 1 (14a)), which agrees with the structures of In Ni and In Ni clusters, the symmetries of these clusters are also same, that is . For the other four In Ni and In Ni clusters, they have the similar structure and the order of energy. Although the structures of In Ni are the same as the In Ni and In Ni clusters, the order of energy is different.

3.2. Relative stabilities

In order to investigate the strength of chemical bonds, the relative abundances determined in mass spectroscopy experiments, and the thermodynamic stabilities of most stable In Ni, In Ni , and In Ni (n = 1–14) clusters, we calculated the averaged binding energy , fragmentation energy (D), and the second-order energy difference ( ). The values of the theoretical calculations of In Ni, In Ni , and In Ni (n = 1–14) clusters are defined in the following formula: where E is total energy of relevant system. The values of , D, and for In Ni, In Ni , and In Ni clusters are shown in Figs. 4(a), 4(b), and 4(c), respectively. As seen from Fig. 4(a), the values of averaged binding energy for In Ni and In Ni clusters show the same growing tendency with cluster size n increasing. The of In Ni and In Ni clusters increase as the cluster size grows, except In Ni , In Ni , and In Ni clusters, indicating that their neighboring clusters are relatively more stable than In Ni , In Ni , and In Ni clusters. Furthermore, the binding energies of In Ni clusters are larger than the of neutral In Ni clusters, the results are the same as those reported in Refs. [52]–[54]. However, the curve of In Ni clusters has a decreasing tendency versus n from 2 to 6, and then, it shows a slight alternation when . A visible peak occurs at n = 3, indicating that In Ni cluster is relatively more stable than their neighboring clusters. And figure 4(a) clearly illustrates that the binding energy of In Ni clusters is larger than that of the corresponding In Ni and In Ni clusters.

Fig. 4. (color online) Binding energies, fragmentation energies, and the second-order energy difference for the In Ni, In Ni , and In Ni (n = 1–14) clusters versus the number of indium atoms.

As shown in Fig. 4(b), the D values each exhibit a pronounced odd–even oscillation behavior as a function of cluster size, suggesting that In Ni, In Ni , and In Ni clusters keep higher stabilities than their respective corresponding neighbours. For In Ni, In Ni , and InNi clusters, they have the largest fragmentation energy of 2.31 eV, 2.41 eV, and 3.33 eV, respectively. It means that In Ni, In Ni , and InNi clusters are more stable than other clusters. For the second-order energy difference ( ) of In Ni, In Ni , and In Ni clusters, we observed an odd–even alternation effect in the relative stability as a function of cluster size, that is, maxima are found at n = 1, 4, 7, 10, and 13 for neutrals, n = 2, 4, 6, 9, 11, and 13 for anions, and n = 2, 5, 7, 9, and 13 for cations, respectively, indicating higher stabilities.

3.3. Electronic properties

To obtain the typical electronic properties of In Ni, In Ni , and In Ni (n = 1–14) clusters, we calculate the energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), the electronic properties including adiabatic electron affinity (AEA), vertical electron detachment energy (VDE), adiabatic ionization potential energy (AIP), vertical ionization potential energy (VIP). The AEA, VDE, AIP, and VIP are calculated as follows: where E is the total energies of the corresponding systems.

As presented in Fig. 5(a), for the In Ni, In Ni , and In Ni clusters, we find HOMO–LUMO gaps=1.03 eV–3.48 eV, which indicate that small neutral, cationic and anionic In Ni clusters are far from a true metal system because the large size of the HOMO–LUMO gaps. The HOMO–LUMO gaps for both the neutral and anion In Ni clusters have odd–even alteration as the size n increases, except In Ni, In Ni, In Ni , In Ni , and In Ni , indicating their relatively higher stabilities, which are in agreement with the second-order energy difference. For the cationic counterpart, there is relatively large gap for cluster InNi , indicating its large reactive stabilities.

Fig. 5. (color online) HOMO–LUMO gaps, electron energies, and ionization energies for the In Ni, In Ni , and In Ni (n = 1–14) clusters versus the number of indium atoms.

Other important electronic properties that reflect the stability of clusters are their electron affinities and ionization potentials.[50] Comparing the total energies of In Ni, In Ni , and In Ni clusters, we obtain the AEA, VDE, AIP, and VIP. Figure 5(b) depicts the variations of AEA and VDE of In Ni clusters with the number of indium atoms. The AEA values tend to increase as n increases, except In Ni, In Ni, and In Ni. When n = 2, 6, 8, and 14, the AEA values are higher than those of adjacent clusters, reflecting the higher stability of In Ni , In Ni , In Ni , and In Ni . As for VDE, the calculated maximums at n = 1, 5, 8, 12, and 14, the minima at n = 2, 6, 10, and 13. As shown in Fig. 5(c), the VIP gives the lower bound while the AIP gives the upper bound. The difference of the variation trend of AIP and VIP for the same cluster size is small, because the geometries of these cationic clusters do not differ greatly from the corresponding neural clusters. On the other hand, the difference between AIP and VIP for the same cluster size is great, since the geometries of these cations differ significantly from the corresponding neutral clusters. The AIP values of In Ni and In Ni are smaller, indicating that these clusters are more easily ionized than the others.

3.4. Magnetisms

The total magnetic moments of the studied In Ni (n = 1–14) clusters are plotted as a function of cluster sizes in Fig. 6. From Fig. 6, we see that the total magnetic moments of the In Ni clusters show an obvious odd–even alternative behavior, expect In Ni. When n is odd, the total magnetic moments decrease with cluster size n increases, this phenomenon is also happened when n is even. We also observed that the total magnetic moments of the In Ni clusters show an obvious odd–even alternative behavior, expect for In Ni , In Ni . The In Ni clusters exhibit nonmagnetic moments for odd n, expect for InNi , In Ni . That is because these clusters are a closed-shell system, whose α and spin orbitals degenerate, so the corresponding magnetic moment is zero. Whereas for even n, the magnetic moments of In Ni clusters decrease with cluster size n increases, in which the magnetism may come from the even number of valence electrons.

Fig. 6. (color online) Magnetic moment for the In Ni, In Ni , and In Ni (n = 1–14) clusters versus the number of indium atoms.
3.5. Natural population analysis

The localization of charge and the charge-transfer information of In Ni (n = 1–14) clusters will be provided by the natural population analysis (NPA), the results are displayed in Table 2. In neutral In Ni clusters, the charge on In atom in the ground state isomers has positive values and Ni has negative values. This phenomenon indicates that the electrons in In Ni clusters are transferred from In frames to Ni atom. Thus, the In frames act as electron donor in In Ni clusters. Less than an electron is transferred from In frames to Ni atom, which shows that the bonds between indium and nickel atoms are covalent rather than ionic. The charges on all the In and Ni atoms of anionic In Ni clusters have negative values, which may be related to the arrangement of the internal charge induced by the extra electron. For In Ni clusters, as shown in Table 2, the indium atoms possess positive charges in the range of 0.654–1.444 electrons, while the nickel atoms possess negative charges, except InNi and In Ni . It indicates that the charges are transferred from In frames to Ni atom, which is identical to the situation in neutral clusters.

Table 2.

The total charges (Q) of In atoms and the charges (Q) of Ni atom for the ground state structures of In Ni clusters.

.
4. Conclusions

In this work, we performed a systematic study of the neutral, anionic, and cationic In Ni clusters. We obtained the most stable structures for In Ni clusters, the optimized results indicate that the In Ni and the In Ni clusters keep the similar structures, the lowest energy structures of In Ni clusters also maintain the analogous structures as In Ni clusters, except In Ni and In Ni . On the basis of the structures and energies from our systematic calculations, we analyzed the relative stabilities by calculating the averaged binding energy, the fragmentation energy, and the second-order energy difference. We show that the binding energy of In Ni clusters is larger than that of the corresponding In Ni and In Ni clusters, the fragmentation energy and the second-order energy difference exhibit a pronounced odd–even oscillation behavior as a function of the cluster size. On the basis of the calculated HOMO–LUMO gaps, AEA, VDE, AIP, and VIP, it is found that the neutral, anionic, and cationic In Ni clusters are far from a true metal system due to the large size of the HOMO–LUMO gaps, In Ni and In Ni clusters are more easily ionized than the others because they have smaller AIP. We also observed that the total magnetic moments of the In Ni clusters show an obvious odd–even alternative behavior. The natural population analysis results of In Ni clusters indicate that the charges transfer from In frames to the Ni atom.

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