Lone Pair Rotational Dynamics in Solids

Traditional classifications of crystalline phases focus on nuclear degrees of freedom. Through the examination of both electronic and nuclear structure, we introduce the concept of an electronic plastic crystal. Such a material is classified by crystalline nuclear structure, while localized electronic degrees of freedom—here lone pairs—exhibit orientational motion at finite temperatures. This orientational motion is an emergent phenomenon arising from the coupling between electronic structure and polarization fluctuations generated by collective motions, such as phonons. Using ab initio molecular dynamics simulations, we predict the existence of electronic plastic crystal motion in halogen crystals and halide perovskites, and suggest that such motion may be found in a broad range of solids with lone pair electrons. Such fluctuations in the charge density should be observable, in principle, via synchrotron scattering.

Figure 1

(a) Snapshots illustrating a lone pair rotation of 120° in solid ${\mathrm{Cl}}_2$ at $T=100\mathrm{K}$. Cl atoms are colored green and the maximally localized Wannier function centers (MLWFCs) of the Cl lone electron pairs are shown as pale blue spheres. The ${\mathrm{Cl}}_2$ molecule undergoing the rotation is colored red. Orange lines indicate halogen bonds. (b) Free energy as a function of the W-Cl-Cl-W dihedral angle, where W indicates the center of a maximally localized Wannier function. (c) Time correlation function for halogen bonds in liquid and solid ${\mathrm{Cl}}_2$. Results for the solid are shown for the same temperatures as in panel (b). (d) Intermediate scattering function $F_k(t)$ determined according to Eq. (2), normalized by its value at $t=0$. The value of $k=2.886{\AA }^{-1}$ corresponds approximately to typical distances between lone pairs on opposite ends of the ${\mathrm{Cl}}_2$ molecule.

Figure 2

(a),(b) Snapshots highlighting the coordination environment around a central (a) Sn in ${\mathrm{CsSnBr}}_3$ and (b) Ca in ${\mathrm{CsCaBr}}_3$. Cs are colored purple, Br are orange, Sn is blue, and Ca is cyan. In both panels, maximally localized Wannier function centers (MLWFCs) of Br, Sn, and Ca are shown as gray spheres. (c) Rotational time correlation functions for $B$ sites as defined in Eqs. (3) and (4) for the Sn-lone pair MLWFC dipole moment in CSC/CSB and the Ca MLWFCs in CCB, respectively. The Ca correlation functions are indicated by their value of $\gamma$. (d)–(f) Rotational correlation functions for $X$ sites (Cl or Br) defined in Eq. (4) for $\gamma =1$, 2, 5.