El-Kelany Khaled E, Pascale Fabien, Platonenko Alexander, Ferrari Anna Maria, Dovesi Roberto
Institute of Nanoscience and Nanotechnology, Kafrelsheikh University, 33516 Kafr el-skiekh, Egypt.
Université de Lorraine-Nancy, CNRS, Laboratoire de Physique et Chimie Théoriques, UMR 7019, Vandoeuvre-les-Nancy, France.
J Phys Condens Matter. 2022 May 12;34(28). doi: 10.1088/1361-648X/ac6925.
The relative stability Δof the cubic3¯(C), of the two tetragonal4m(T1) and4m(T2), and of the orthorhombic(O) phases of KVFhas been computed both for the ferromagnetic (FM) and antiferromagnetic (AFM) solutions, by using the B3LYP full range hybrid functional and the Hartree-Fock (HF) Hamiltonian, an all-electron Gaussian type basis set and the CRYSTAL code. The stabilization of the T2 phase with respect to the C one (152Ha for B3LYP, 180Ha for HF, per 2 formula units) is due to the rotation of the VFoctahedra with respect to theaxis, by 4.1-4.6 degrees. The O phase is slightly less stable than the T2 phase (by 6 and 20Ha for B3LYP and HF); it is, however, a stable structure as the dynamical analysis confirms. The mechanism of the stabilization of the AFM solution with respect to the FM one is discussed through the spin density maps, and is related to the key role of the exact exchange term (20% in B3LYP, 100% in HF). The G-AFM phase (the first six neighbors of the reference V ion with spin reversed) is more stable than the FM one by about 500 (HF) and 1800 (B3LYP)Ha per two formula units. A volume reduction is observed in the C to T passage, and in the FM to AFM one, both being of the order of 0.3-0.5A˚3at the B3LYP level. Atomic charges, magnetic moments and bond populations, evaluated according to a Mulliken partition of the charge a spin density functions, complete the analysis. The IR and Raman spectra of the FM and AFM C, T2 and O cells are discussed; the only noticeable difference between the various space groups appears in the modes with wavenumbers lower than 100 cm.
通过使用B3LYP全范围杂化泛函和哈特里-福克（HF）哈密顿量、全电子高斯型基组以及CRYSTAL代码，计算了铁磁（FM）和反铁磁（AFM）解下KVF的立方3¯(C)相、两种四方4m(T1)和4m(T2)相以及正交（O）相的相对稳定性Δ。相对于C相，T2相的稳定性（B3LYP为152哈特里，HF为180哈特里，每2个化学式单元）源于VF八面体相对于轴旋转4.1 - 4.6度。O相比T2相稍不稳定（B3LYP和HF分别低6和20哈特里）；然而，动力学分析证实它是一种稳定结构。通过自旋密度图讨论了AFM解相对于FM解的稳定机制，这与精确交换项的关键作用有关（B3LYP中占20%，HF中占100%）。G - AFM相（参考V离子的前六个自旋反转的相邻原子）每两个化学式单元比FM相稳定约500（HF）和1800（B3LYP）哈特里。在从C相到T相以及从FM相到AFM相的转变中观察到体积减小，在B3LYP水平下两者均约为0.3 - 0.5埃³。根据电荷和自旋密度函数的穆利肯划分评估的原子电荷、磁矩和键布居完成了分析。讨论了FM和AFM的C、T2和O晶胞的红外和拉曼光谱；不同空间群之间唯一明显的差异出现在波数低于100厘米⁻¹的模式中。
