The electron–phonon (e–ph) interaction in lead halide perovskites (LHPs) plays a role in a variety of physical phenomena. Unveiling how the local lattice distortion responds to charge carriers is a critical step toward understanding the e–ph interaction in LHPs. Herein, we advance a fundamental understanding of the e–ph interaction in LHPs from the perspective of stereochemical activity of 6s2 lone-pair electrons on the Pb2+ cation. We demonstrate a model system based on three LHPs with distinctive lone-pair activities for studying the structure–property relationships. By tuning the A-cation chemistry, we synthesized single-crystal CsPbBr3, (MA0.13EA0.87)­PbBr3 (MA+ = methylammonium; EA+ = ethylammonium), and (MHy)­PbBr3 (MHy+ = methylhydrazinium), which exhibit stereo-inactive, dynamic stereo-active, and static stereo-active lone pairs, respectively. This gives rise to distinctive local lattice distortions and low-frequency vibrational modes. We find that the e–ph interaction leads to a blue shift of the band gap as temperature increases in the structure with the dynamic stereo-active lone pair but to a red shift in the structure with the static stereo-active lone pair. Furthermore, analyses of the temperature-dependent low-energy photoluminescence tails reveal that the strength of the e–ph interaction increases with increasing lone-pair activity, leading to a transition from a large polaron to a small polaron, which has significant influence on the emission spectra and charge carrier dynamics. Our results highlight the role of the lone-pair activity in controlling the band gap, phonon, and polaronic effect in LHPs and provide guidelines for optimizing the optoelectronic properties, especially for tin-based and germanium-based halide perovskites, where stereo-active lone pairs are more prominent than their lead counterparts.

We perform model calculations for a stretched LiF molecule, demonstrating that nonadiabatic charge transfer effects can be accurately and seamlessly described within a density functional framework. In alkali halides like LiF, there is an abrupt change in the ground state electronic distribution due to an electron transfer at a critical bond length R = R, where an avoided crossing of the lowest adiabatic potential energy surfaces calls the validity of the Born-Oppenheimer approximation into doubt. Modeling the R-dependent electronic structure of LiF within a two-site Hubbard model, we find that nonadiabatic electron-nuclear coupling produces a sizable elongation of the critical R by 0.5 bohr. This effect is very accurately captured by a simple and rigorously derived correction, with an M prefactor, to the exchange-correlation potential in density functional theory, M = reduced nuclear mass. Since this nonadiabatic term depends on gradients of the nuclear wave function and conditional electronic density, ∇χ(R) and ∇n(r, R), it couples the Kohn-Sham equations at neighboring R points. Motivated by an observed localization of nonadiabatic effects in nuclear configuration space, we propose a local conditional density approximation-an approximation that reduces the search for nonadiabatic density functionals to the search for a single function y(n).

We provide a rigorous proof that the Hartree Fock energy, as a function of the fractional electron number, E(N), is piecewise concave. Moreover, for semi-local density functionals, we show that the piecewise convexity of the E(N) curve, as stated in the literature, is not generally true for all fractions. By an analysis based on exchange-only local density approximation and careful examination of the E(N) curve, we find for some systems, there exists a very small concave region, corresponding to adding a small fraction of electrons to the integer system, while the remaining E(N) curve is convex. Several numerical examples are provided as verification. Although the E(N) curve is not convex everywhere in these systems, the previous conclusions on the consequence of the delocalization error in the commonly used density functional approximations, in particular, the underestimation of ionization potential, and the overestimation of electron affinity, and other related issues, remain unchanged. This suggests that instead of using the term convexity, a modified and more rigorous description for the delocalization error is that the E(N) curve lies below the straight line segment across the neighboring integer points for these approximate functionals.

We explore effects of orbital relaxation on Kohn-Sham frontier orbital energies in density functional theory by using a nonempirical scaling correction approach developed in Zheng et al. [J. Chem. Phys. 138, 174105 (2013)]. Relaxation of Kohn-Sham orbitals upon addition/removal of a fractional number of electrons to/from a finite system is determined by a systematic perturbative treatment. The information of orbital relaxation is then used to improve the accuracy of predicted Kohn-Sham frontier orbital energies by Hartree-Fock, local density approximation, and generalized gradient approximation methods. The results clearly highlight the significance of capturing the orbital relaxation effects. Moreover, the proposed scaling correction approach provides a useful way of computing derivative gaps and Fukui quantities of N-electron finite systems (N is an integer), without the need to perform self-consistent-field calculations for (N ± 1)-electron systems.