Here we present an ab initio insight into the electronic structure and sodium diffusion in A_3−хNa_1+х(MoO₄)₂ with trigonal (A = Cs) and monoclinic (A = K) glaserite-type structures. Our DFT calculations predict the stability of К_3−xNa_1+x(МoO₄)₂ to high sodium content and a significantly smaller homogeneity region for Cs_3−xNa_1+x(МoO₄)₂ in accordance with experimental findings. These molybdates are wide-gap insulators with a band gap of 4.2 eV, which is very weakly dependent on the sodium content. The calculated electric field gradients at the Na and A sites were related to the anisotropy of electronic charge distribution and used to predict the quadrupole frequencies of the ¹³³Cs, ³⁹K and ²³Na NMR lines in Cs_3−хNa_1+х(MoO₄)₂ and K_3−хNa_1+х(MoO₄)₂. We examined the possible diffusion paths of Na⁺ ions and showed that the direct Na−Na migration is unlikely due to a large energy barrier in both molybdates. Instead, the Na⁺ ions can migrate through the A positions with much lower barriers in A_3−xNa_1+x(МoO₄)₂. Therefore, designing stable non-stoichiometric compositions may be a way to reach good sodium-ion diffusion in double molybdates with the glaserite-type structure.

这里，我们提出一个从头洞察的电子结构和钠扩散甲_{3- х}的Na _{1+ х}氧化钼（MoO ₄）₂与三角（甲 = Cs）的和单斜（甲 = K）芒硝型结构。我们的DFT计算预测К的稳定性_{3- X}的Na _{1+ X}（МoO ₄）₂至钠含量高和Cs的一个显著较小均匀性区域_{3- X}的Na _{1+ X}（МoO ₄）₂根据实验结果。这些钼酸盐是带隙为4.2 eV的宽带隙绝缘体，其对钠含量的依赖性非常弱。在Na和所计算出的电场梯度阿位点相关的电子电荷分布的各向异性和用于预测的四极频率^133个CS，³⁹ K和^23条的Na NMR线Cs的_{3- х}的Na _{1+ х}（的MoO ₄）₂和K _{3- х}的Na _{1+ х}氧化钼（MoO ₄）₂。我们研究了Na ⁺可能的扩散路径离子，并表明由于两种钼酸盐中的能量垒较大，直接Na-Na迁移不太可能。取而代之的是，钠⁺离子可通过迁移甲以低得多的屏障位置甲_{3- X}的Na _{1+ X}（МoO ₄）₂。因此，设计稳定的非化学计量组成可能是在具有玻璃石型结构的双钼酸盐中达到良好的钠离子扩散的方法。