The ground-state fermion second-order reduced density matrix (2-RDM) is determined variationally using itself as a basic variable. As necessary conditions of the N-representability, we used the positive semidefiniteness conditions, P, Q, and G conditions that are described in terms of the 2-RDM. The variational calculations are performed by using recently developed semidefinite programming algorithm (SDPA). The calculated energies of various closed- and open-shell atoms and molecules are excellent, overshooting only slightly the full-CI energies. There was no case where convergence was not achieved. The calculated properties also reproduce well the full-CI results.

Artificial molecular switches and machines that enable the directional movements of molecular components by external stimuli have undergone rapid advances over the past several decades. Particularly, overcrowded alkene-based artificial molecular motors are highly attractive from the viewpoint of chirality switching during rotational steps. However, the integration of these molecular switches into solid-state devices is still challenging. Herein, we present an example of a solid-state spin-filtering device that can switch the spin polarization direction by light irradiation or thermal treatment. This device utilizes the chirality inversion of molecular motors as a light-driven reconfigurable spin filter owing to the chiral-induced spin selectivity effect. Through this device, we found that the flexibility at the molecular scale is essential for the electrodes in solid-state devices using molecular machines. The present results are beneficial to the development of solid-state functionalities emerging from nanosized motions of molecular switches.

Theory predicts that double-core-hole (DCH) spectroscopy can provide a new powerful means of differentiating between similar chemical systems with a sensitivity not hitherto possible. Although DCH ionization on a single site in molecules was recently measured with double- and single-photon absorption, double-core holes with single vacancies on two different sites, allowing unambiguous chemical analysis, have remained elusive. Here we report that direct observation of double-core holes with single vacancies on two different sites produced via sequential two-photon absorption, using short, intense X-ray pulses from the Linac Coherent Light Source free-electron laser and compare it with theoretical modeling. The observation of DCH states, which exhibit a unique signature, and agreement with theory proves the feasibility of the method. Our findings exploit the ultrashort pulse duration of the free-electron laser to eject two core electrons on a time scale comparable to that of Auger decay and demonstrate possible future X-ray control of physical inner-shell processes.

Multijunction photovoltaics (PVs) are gaining prominence owing to their superior capability of achieving power conversion efficiencies (PCEs) beyond the radiative limit of single-junction cells^1–8, for which improving narrow-bandgap (NBG) tin–lead perovskites is critical for thin-film devices⁹. Here, with a focus on understanding the chemistry of tin–lead perovskite precursor solutions, we find that Sn(ii) species dominate interactions with precursors and additives and uncover the exclusive role of carboxylic acid in regulating solution colloidal properties and film crystallization and ammonium in improving film optoelectronic properties. Materials that combine these two functional groups, amino acid salts, considerably improve the semiconducting quality and homogeneity of perovskite films, surpassing the effect of the individual functional groups when introduced as part of separate molecules. Our enhanced tin–lead perovskite layer allows us to fabricate solar cells with PCEs of 23.9%, 29.7% (certified 29.26%) and 28.7% for single-junction, double-junction and triple-junction devices, respectively. Our 1-cm² triple-junction devices show PCEs of 28.4% (certified 27.28%). Encapsulated triple-junction cells maintain 80% of their initial efficiencies after 860 h maximum power point tracking (MPPT) in ambient. We further fabricate quadruple-junction devices and obtain PCEs of 27.9% with the highest open-circuit voltage of 4.94 V. This work establishes a new benchmark for multijunction PVs.