Elsevier

Chemical Physics

Volume 535, 1 July 2020, 110778
Chemical Physics

Theoretical study of the electronic structure and electrical properties of Al-doped niobium clusters

https://doi.org/10.1016/j.chemphys.2020.110778Get rights and content

Abstract

A methodology previously suggested for niobium clusters is here applied to the prediction of the ground spin-state of the niobium clusters doped with aluminum atoms. By using all-electron density functional theory with Douglas-Kroll-Hess correction, the spin-state, geometry, hardness, binding energy, ionization potential, electron affinity, and mean static dipole polarizability of the NbxAly clusters are examined. The ground spin-states obtained from the energy minimization were confronted with the results provided by the maximum hardness principle (MHP) and by the minimum polarizability principle (MPP). In general, the MHP and MPP have yielded the expected results, i.e., in agreement with the ones obtained from the minimum energy. Additionally, were compared the theoretical results for polarizability, ionization potential, and reactivity with the available experimental values.

Introduction

It is well established that small atomic clusters have different properties depending on the size of the systems, that is, the physical and chemical properties of clusters are not intermediate between isolated molecules (or atoms) and microscopic particles. Additionally, doped clusters can provide different physical and chemical properties when compared with pure systems. These characteristics have motivated many theoretical and experimental studies intending to understand the electronic structure of these systems. Among the Al-doped clusters [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], we highlight the Al-doped niobium clusters [4], [5], [6], [7], [8], already used in some practical applications [6].

A mass spectroscopy investigation [8] about the reactivity of the pure and Al-doped niobium cluster with the H2 molecule revealed a sudden decrease in the reactivity rate when added aluminum atoms in the small NbxAly systems. For the larger clusters, adding one Al atom decreases the reactivity, while by attaching two or three aluminum atoms the rate presents an increase. Pramann et al. [5] also studied the size-dependent evolution of the electronic structure of the NbnAl- (n=4-12) clusters using photodetachment photoelectron spectroscopy, They performed a comparison of the electronic structure (hybridization effects) of pure and Al-doped clusters founding a direct correlation between electronic structure and H2 chemisorption rate constants for n=5-8 and n>9. For the studied clusters, they concluded that the origin of chemisorption reactivity is mainly electronic for small clusters (n<9), and for the larger (n=9-12), the geometry plays an important role [5].

Wang and coworkers [4], [7] studied the structure, electronic, and magnetic effects of Al-doped niobium clusters by using the B3PW91, B3LYP, and PBEPBE functionals together with the 6-311G(d) basis set for the Al atom and the effective core potential (ECP) LANL2DZ basis set for the Nb elements (6-311G(d)/Al//LANL2DZ/Nb). From the Saunders kick global search method, combined with DFT (density functional theory) geometrical optimization, the authors [4], [7] did not find structure transition from the Al-capped frame to the Al-encapsulated structure. As a result, the Al atom always occupies the surface of the NbnAl or NbnAl- (for n=210) clusters. Thus, the geometry of the NbnAl systems (for n=210) can be obtained by replacing one Nb atom in the Nbn+1 pure cluster by one Al, with small local distortion [4].

In previous work [11], we studied the effects of all-electron basis set and the Douglas-Kroll-Hess (DKH) scalar relativistic corrections [12], [13], [14] on the structure and electronic properties of small pure niobium clusters, Nbn (n=2,4,6, and 10). Our results showed that one d function must be added to the ADZP-DKH [15], [16] basis set to improve the description of the valence orbitals in the studied systems. Only with the new basis set, ADZP-DKH(+d), and DKH relativistic corrections the binding energy (BE), ionization potential, and electron affinity results were close to the experimental ones [11]. According to the observed results, we proposed [11] an accurate methodology, M06/ADZP-DKH(+d), to be used in all-electron DFT calculations in the clusters formed by niobium atoms. In the present paper, we will apply this methodology [11] in the study of the Al-doped niobium clusters.

The conceptual Density Functional Theory is a powerful tool that allows us to understand some of the most important aspects of theoretical chemistry and provides a mathematical basis to predict chemical reactivity parameters. It was on this ground, that properties such as hardness (η), electronegativity (χ), chemical potential (μ), first ionization potential (Ip), electron affinity(Ea), and electronic band-gap at the Fermi level (ΔEF) were formally presented by Pearson, Parr, and Yang [17], [18], [19], [20]. Thus, with this set of chemical parameters, we can better understand the mechanism of the stability and reactivity of molecular systems. In this framework, the electron chemical potential (μ) and chemical hardness (η) were exactly defined [19], [20], respectively, asμ=ENν(r)andη=2EN2ν(r)=μNν(r),where the ν(r) is an external potential. From the energies of the systems containing (N-1),N, and (N+1) electrons (denoted as E(N-1),E(N), and E(N+1) respectively) we can write the ionization potential and the electron affinity as follows:Ip=E(N-1)-E(N)Ea=E(N)-E(N+1).Now, taking into account the numerical differentiation and the Eqs. (1), (2), we assume that-μ=χM=12(Ip+Ea)η=(Ip-Ea).The chemical potential can be associated with the Mulliken electronegativity (χM=-μ), which provides the capacity of the system to attract electrons, and the hardness can give important information about the stability of the systems [19], [20], [21]. One can also approximate the Ip and Ea with the energies of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbitals (LUMO), respectively [21]. Thus, the hardness and chemical potential are obtained from the equationsμ=-χM=12(LUMO+HOMO),η=(LUMO-HOMO).It is expected that the η and μ values calculated from the Eqs. (4), (5) yield different results [22], [11]. This is partly because the theoretical DFT values for the LUMO energies are inaccurate when compared with the HOMO energies [21].

The dipole polarizability (α), which measures the distortion in the electron cloud around the system due to a locally applied external electric field, represents one of the most important observables for understanding both electric and optical properties [23], [24], [25], [26]. From the mathematical viewpoint, the polarizability is defined as:αij=-2E(F)FiFj(i,j=x,y,z),where E(F) is the total energy of the system under a small external electric field F. The average isotropic polarizability (α) can be defined as:α=13(αxx+αyy+αzz).For the correct determination of the polarizability, the basis set functions must be sufficiently flexible to describe the distortion of the external orbitals when the electric field is applied [27], [28], [29]. In this sense, the ADZP [15], [16] basis sets family has shown good performance in electrical properties calculations for transition metal systems [30], [31], [32]. Thus, we also expect accurate results for polarizability when the ADZP-DKH(+d) and ADZP-DKH basis sets are used, respectively, for niobium and aluminum atoms.

The Maximum Hardness Principle (MHP) says to be a rule of nature that molecules arrange themselves to be as hard as possible [19], [20], [21], while the Minimum Polarizability Principle (MPP) [33], [34] says that the natural direction of evolution of any system is towards a state of minimum polarizability. Thus, it is expected from the MPP and MHP that the system with the lower energy is the one that provides the minimum polarizability and the maximum hardness. In this way, the understanding of the MPP together with the MHP in transition metal clusters could be useful to check the spin ground state predicted by the total energy [33], [30].

Section snippets

Computational methods

In this work, were performed DFT calculations with M06 [35] and B3PW91 [36], [37] exchange and correlation functionals. Additionally, were used the all-electron basis sets ADZP-DKH(+d) [15], [16], [11] and ADZP-DKH [15], [16], [38], [39], respectively, for the Nb and Al atoms. For simplicity, the level of theory M06/ADZP-DKH(+d)//ADZP-DKH will be labeled as M06/ADZP-DKH(+d). The all-electron calculations were performed with second-order DKH corrections with computational chemistry programs

Results

Fig. 1 shows the final structure of the NbxAly clusters and the respective ground spin-state when the minimum energy criterion is used. In Supplementary Material the geometric coordinates are also presented for the singlet and triplet clusters. As expected [4], the aluminum atoms tend to remain on the surface of the clusters (see Fig. 1). Besides that, in general, the aluminum atoms arrange themselves to form a few bonds as possible between them, i.e., in the NbxAly clusters, the binding

Concluding remarks

In the present work, we apply a previously suggested methodology, M06/ADZP-DKH(+d), to calculate the geometrical parameters, polarizability, ionization potential, electron affinity, hardness, HL-gap, and binding energy for Al-doped niobium clusters. The predictions of the spin-states by maximum hardness principles were compared to those obtained by the energy minimization procedure. The results presented here reveal that MHP can provide the same spin-state generated by the total energy

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

To FAPES (Fundação de Amparo à Pesquisa e Inovação do Espírito Santo).

References (60)

  • I.B. Bersuker et al.

    The jahn-teller effect in dipole (multiple) moments and polarizabilities of molecules

    Adv. Quantum Chem.

    (1986)
  • J. Xiang et al.

    A density-functional study of Al-doped Ti clusters: TinAl (n= 1–13)

    J. Chem. Phys.

    (2004)
  • G.-F. Zhao et al.

    A density functional study of YnAl (n= 1–14) clusters

    J. Chem. Phys.

    (2007)
  • F.-Y. Tian et al.

    Structure, stability, and magnetism of ScnAl (n= 1–8, 12) clusters: density-functional theory investigations

    Phys. Rev. A

    (2008)
  • H.-Q. Wang et al.

    Structural, electronic and magnetic effects of Al-doped niobium clusters: a density functional theory tudy

    J. Mol. Model.

    (2012)
  • X. Feng et al.

    A dft study on the catalytic CO oxidative coupling to dimethyl oxalate on Al-doped core-shell Pd clusters

    J. Phys. Chem. C

    (2017)
  • R. Shastri et al.

    A comparative ab intio study on structural evolution, stability and electronic properties of undoped and Al-doped gaxny (x+y=4-25) clusters

    Eur. Phys. J. Plus

    (2017)
  • F.N.N. Pansini et al.

    Effects of all-electron basis sets and the scalar relativistic corrections in the structure and electronic properties of niobium clusters

    J. Phys. Chem. A

    (2017)
  • B.A. Hess

    Applicability of the no-pair equation with free-particle projection operators to atomic and molecular structure calculations

    Phys. Rev. A

    (1985)
  • B.A. Hess

    Relativistic electronic-structure calculations employing a two-component no-pair formalism with external-field projection operators

    Phys. Rev. A

    (1986)
  • C.L. Barros et al.

    Gaussian basis set of double zeta quality for atoms Rb through Xe: Application in non-relativistic and relativistic calculations of atomic and molecular properties

    Mol. Phys.

    (2010)
  • R.G. Pearson

    Hard and soft acids and bases

    J. Am. Chem. Soc.

    (1963)
  • R.G. Parr et al.

    Absolute hardness: companion parameter to absolute electronegativity

    J. Am. Chem. Soc.

    (1983)
  • R.G. Parr et al.

    Density Functional Theory of Atoms and Molecules

    (1989)
  • R.G. Pearson

    Chemical Hardness: Aplications from Molecules to Solids

    (1997)
  • R.G. Pearson

    Chemical hardness and density functional theory

    J. Chem. Sci.

    (2005)
  • M. Torrent-Sucarrat et al.

    Global hardness evaluation using simplified models for the hardness kernel

    J. Phys. Chem. A

    (2002)
  • D.R. Kanis et al.

    Design and construction of molecular assemblies with large second-order optical nonlinearities. quantum chemical aspects

    Chem. Rev.

    (1994)
  • J. Zyss et al.

    Nonlinear optics in multipolar media: theory and experiments

    Chem. Rev.

    (1994)
  • H.A. Kurtz et al.

    Calculation of the nonlinear optical properties of molecules

    J. Computat. Chem.

    (1990)
  • Cited by (11)

    • Hydrogen storage capacity of the niobium atom adsorbed on carbon and boron nitride planar nanoflakes

      2023, International Journal of Hydrogen Energy
      Citation Excerpt :

      In this work, we will focus on the niobium atom adsorbed on the carbon, h-BN, and hybrid planar flakes. The capacity of the niobium atom to form clusters with interesting physical and chemical properties that depend on the size of the systems is well-known [28–36]. Due to a large number of d electrons in its ground state, [Kr]4d45s1, and the power to make bonding, specifically with hydrogen, the niobium has also been tested as a surface dopant/adsorbent to improve hydrogen storage mechanisms [6,37–45].

    • The role of tagging atoms on the thermal stability and vibrational behavior of Nb<inf>9</inf> clusters

      2022, Journal of Physics and Chemistry of Solids
      Citation Excerpt :

      Also, for niobium compounds, good results have been obtained when using hybrid potentials. For example, for Al-doped niobium clusters, Pansini et al. had good agreement with the experimental data for the ionization potential [50]. Here it is worth mentioning that, the goal of this article is to present a comparative study between hybrid functionals to analyze the connection of tagging atoms with the coexistence of isomers of Nb9 and, in this case, under what conditions this process is carried out, taking into account that there are experimental IR spectra with which to compare our results.

    • Control of cluster coalescence during formation of bimetallic nanoparticles and nanoalloys obtained via electric explosion of two wires

      2022, Advanced Powder Technology
      Citation Excerpt :

      Simulating the structural transformations in binary Nb–Ag and Nb–Al nanoparticles and assessing the degree of stability of such nanostructures are of interest because they have prospects for applications as both ensembles of individual nanoparticles and nanostructured materials obtained using nanopowders synthesized using powder metallurgy technologies [50,51]. It was theoretically predicted [52] that doping of niobium with aluminum atoms in clusters considerably affects its properties without providing obvious tendencies for polarizability, ionization potential, electron affinity, and hardness. A review of the literature has shown that the size mismatch of atoms in a binary system is an essential factor for surface segregation: larger atoms emerge on the particle surface.

    View all citing articles on Scopus
    View full text