Probing chirality across the electromagnetic spectrum with the full semi-classical light–matter interaction

Unraveling the Mechanism of Circularly Polarized Thermally Activated Delayed Fluorescence (CP-TADF) in Chiral Two-Coordinated Cu(I) Emitters: A Comprehensive Theoretical Exploration

The circularly polarized thermally activated delayed fluorescence (CP-TADF) processes of four pairs of Cu(I)-based chiral enantiomers were calculated by employing the path integral approach to dynamics. The calculated results reveal that the introduction of different substituents at various positions on the planar chiral CzP units significantly impacts on the dissymmetry factor gCPL of CP luminescence (CPL). Substituting the sixth position hydrogen on the chiral CzP unit with -CN or -Cl groups increases the gCPL factor to 2.1 × 10-3 and 2.2 × 10-3 in Sp-MAC-Cu-CNCzP-1 and Sp-MAC-Cu-ClCzP, respectively. This is due to a small electric transition dipole moment |μ| and a relatively large magnetic transition dipole moment |m|. The small |μ| results from the CT excitation with spatially separated highest-occupied molecular orbital (HOMO) and lowest-unoccupied molecular orbital (LUMO) transitions in the S1 state, leading to a small ΔE(S1 - T1) and more efficient TADF. Interestingly, the seventh-substituted MAC-Cu-CNCzP-2 complex exhibits a substantial increase in the ΔE(S1 - T1) of 0.346 eV, which consequently leads to a significant decrease in the kRISC rate, down to 3.32 × 103 s-1, indicating that further efficient reverse intersystem crossing (RISC) processes are failed. Thus, to design efficient CP-TADF molecules, the key lies in regulating and balancing the factors affecting both TADF and CPL properties.

Vibronic Coupling and Multiple Electronic States Effect in ABS and ECD Spectra: Three [7]Helicene Derivatives

Vibronic coupling and multiple electronic states effect play a pivotal role in the molecular spectroscopy of large systems. Herein, we present a detailed theoretical study on the absorption (ABS) and electronic circular dichroism (ECD) spectra of three [7]helicene derivatives in chloroform, with a particular emphasis on the significance of vibronic coupling and the multiple electronic states effect in spectral simulations. The vertical gradient (VG) and vertical Hessian (VH) models, incorporating the Franck-Condon (FC) effect and Herzberg-Teller (HT) contribution, are considered in the vibronic calculations. The results indicate that the simulated vibrationally resolved spectra obtained by the VG model combined with the FC effect are more reliable, showing advantages in the rationality of spectral shapes, the accuracy of the relative heights of absorption peaks, and the correctness of positive and negative signals. Reliable predictions of the three [7]helicene derivatives allowed us to further explore the importance of the multiple electronic states effect in the vibrationally resolved spectra, demonstrating that the high-energy electronic excited states, particularly the fifth (S5) and sixth (S6) excited states, are essential for accurately capturing the fine structures observed in the experimental spectra. Our study predicts reliable theoretical reference spectra for the family of [7]helicene derivatives and provides a fundamental understanding of the vibronic coupling of chiral organic molecules with multiple electronic states.

Transition moments beyond the electric-dipole approximation: Visualization and basis set requirements

In the simulation of x-ray absorption spectroscopy, the validity of the electric-dipole approximation comes into question. Three different schemes exist to go beyond this approximation: the first scheme is based on the full semi-classical light-matter interaction, whereas the latter two schemes, referred to as the generalized length and velocity representation, are based on truncated multipole expansions. Even though these schemes have been successfully implemented in several quantum chemistry codes, their basis set requirements remained largely unknown. Here, we assess basis set requirements of these three schemes. We have considered 1s1/2 and 7s1/2 → 7p1/2 transitions in the radium atom, representative of core and valence excitations, respectively, and carried out calculations with dyall.aeXz (X = 2, 3, 4) basis sets at the four-component relativistic TD-HF level of theory. Our basis set study was greatly facilitated by the generation and visualization of radial distributions of transition moment densities, allowing for a straightforward comparison with equivalent finite-difference calculations. Pertaining to the truncated interaction, we find that the length representation electric multipole is the easiest to converge, requiring the dyall.ae2z basis for low-order multipoles and the dyall.ae4z basis at higher orders. The magnetic multipole moments follow a similar trend although they are more difficult to converge. The velocity representation electric multipoles are the most difficult to converge: at high orders, the dyall.ae3z and dyall.ae4z basis sets introduce artificial peaks and oscillations, which increase the overall error. These artifacts are associated with linear dependence issues in the small component space of larger basis sets. The full interaction operator, however, does not suffer from these problems, and we therefore recommend its use in the simulation of x-ray spectroscopy.

Going beyond the Electric-Dipole Approximation in the Calculation of Absorption and (Magnetic) Circular Dichroism Spectra including Scalar Relativistic and Spin-Orbit Coupling Effects

In this work, a time-dependent density functional theory (TD-DFT) scheme for computing optical spectroscopic properties in the framework of linearly and circularly polarized light is presented. The scheme is based on a previously formulated theory for predicting optical absorption and magnetic circular dichroism (MCD) spectra. The scheme operates in the framework of the full semi-classical field-matter interaction operator, thus generating a powerful and general computational scheme capable of computing the absorption (ABS), circular dichroism (CD), and MCD spectra. In addition, our implementation includes the treatment of relativistic effects in the framework of quasidegenerate perturbation theory, which accounts for scalar relativistic effects (in the self-consistent field step) and spin-orbit coupling (in the TD-DFT step), as well as external magnetic field perturbations. Hence, this formalism is also able to probe spin-forbidden transitions. The random orientations of molecules are taken into account by a semi-numerical approach involving a Lebedev numerical quadrature alongside analytical integration. It is demonstrated the numerical quadrature requires as few as 14 points for satisfactory converged results thus leading to a highly efficient scheme, while the calculation of the exact transition moments creates no computational bottlenecks. It is demonstrated that at zero magnetic field, the CD spectrum is recovered while the sum of left and right circularly polarized light contributions provides the linear absorption spectrum. The virtues of this efficient and general protocol are demonstrated on a selected set of organic molecules where the various contributions to the spectral intensities have been analyzed in detail.