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Snapshots of trajectory for photoexcited Au₆H₂that shows fast dissociation to gold hydride. 

This paper presents an approximate yet practical methodology for calculating two-photon absorption (TPA) cross sections with time-dependent density functional theory (TDDFT), including spin–orbit coupling (SOC). The approach is based on the second-order perturbative sum-over-states (SOS) expression for the TPA cross section and is referred to as the SOS-SOC-TDDFT method. To investigate the influence of SOC on TPA, we apply our approach to the calculation of TPA cross sections that include singlet and triplet states in fac-Ir(ppy)3, which is a phosphorescent complex known for its strong SOC effects. Due to the high angular momentum orbitals in Ir, SOC induces substantial mixing between many singlet and triplet states, although the ground state is predominantly of singlet character. Our evaluation of the TPA cross section involves constructing transition dipole matrix elements between SOC excited states by transforming the dipole matrix elements of singlet and triplet excited states obtained from scalar-relativistic TDDFT calculations, using the excited-state wavefunctions from SOC-included calculations. Our TPA results reveal that SOC leads to spectral broadening, redistribution of TPA intensities, and activation of spin-forbidden transitions. In particular, the presence of intermediate states with mixed spin character allows new excitation pathways to triplet-dominated two-photon excited states, which are inaccessible in spin-pure calculations. This highlights the importance of including SOC for accurate modeling of TPA for heavy-element systems, with results that are more sensitive to relativity than for one-photon excitation, providing insights for using the present approach in future studies of relativistic effects in nonlinear optical properties. 

Aluminum nanocrystals offer a promising platform for plasmonic photocatalysis, yet a detailed understanding of their electron dynamics and consequent photocatalytic performance has been challenging thus far due to computational limitations. Here, we employ density functional tight-binding methods (DFTB) to investigate the optical properties and H2 dissociation dynamics of Al nanocrystals with varying sizes and geometries. Our real-time simulations reveal that Al’s unique free-electron nature enables efficient light-matter interactions and rapid electronic thermalization. Cubic and octahedral nanocrystals ranging from 0.5 to 4.5 nm exhibit size-dependent plasmon resonances in the UV, with distinct spectral features arising from the particle geometry and electronic structure. By simulating H2 dissociation near Al nanocrystals, we demonstrate that hot electrons generated through plasmon excitation can overcome the molecule’s strong chemical bond within tens of femtoseconds. The laser intensity threshold is comparable to previous reports for Ag nanocrystals, though significantly lower than that of Au. Notably, the dipolar plasmon mode demonstrates higher efficiency for this reaction than the localized interband transition for particles at these sizes. Taken together, this work provides mechanistic insights into plasmon-driven catalysis and showcases DFTB’s capability to study quantum plasmonics at unprecedented length and time scales. 

This work presents a new approach for simulating the interaction between molecular aggregate systems and multi-modal energy–time entangled light by solving the Lindblad master equation. The density matrix that describes both molecular and photonic states is propagated on a time grid, with excited-state dephasing included via the Lindblad superoperator. Molecular exciton entanglement, induced by entangled photons, is analyzed from the time-evolved density matrix. The calculations are based on a model of a molecular dimer introduced by Bittner et al. [J. Chem. Phys. 152, 071101 (2020)], along with entangled light that is approximated by a finite number of modes. Our results demonstrate that photonic entanglement plays a significant role in influencing molecular exciton entanglement, highlighting the interplay between the photonic and excitonic subsystems in such interactions.