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 ${\mathrm{Nb}}_{\mathrm{x}}{\mathrm{Al}}_{\mathrm{y}}$ 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.

先前针对铌团簇建议的方法在此适用于预测掺杂有铝原子的铌团簇的基态自旋态。通过使用具有Douglas-Kroll-Hess校正的全电子密度泛函理论，该材料的自旋态，几何形状，硬度，结合能，电离势，电子亲和力和平均静态偶极极化率${\mathrm{铌}}_{\mathrm{X}}{\mathrm{铝}}_{\mathrm{ÿ}}$检查群集。从能量最小化获得的基态自旋态面临最大硬度原理（MHP）和最小极化率原理（MPP）提供的结果。通常，MHP和MPP产生了预期结果，即与从最小能量获得的结果一致。此外，将极化率，电离势和反应性的理论结果与可用的实验值进行了比较。