Combining spin-adapted open-shell TD-DFT with spin–orbit coupling

Big picture of relativistic molecular quantum mechanics

Any quantum mechanical calculation on electronic structure ought to choose first an appropriate Hamiltonian H and then an Ansatz for parameterizing the wave function Ψ, from which the desired energy/property E(λ) can finally be calculated. Therefore, the very first question is: what is the most accurate many-electron Hamiltonian H? It is shown that such a Hamiltonian i.e. effective quantum electrodynamics (eQED) Hamiltonian, can be obtained naturally by incorporating properly the charge conjugation symmetry when normal ordering the second quantized fermion operators. Taking this eQED Hamiltonian as the basis, various approximate relativistic many-electron Hamiltonians can be obtained based entirely on physical arguments. All these Hamiltonians together form a complete and continuous ‘Hamiltonian ladder’, from which one can pick up the right one according to the target physics and accuracy. As for the many-electron wave function Ψ, the most intriguing questions are as follows. (i) How to do relativistic explicit correlation? (ii) How to handle strong correlation? Both general principles and practical strategies are outlined here to handle these issues. Among the electronic properties E(λ) that sample the electronic wave function nearby the nuclear region, nuclear magnetic resonance (NMR) shielding and nuclear spin-rotation (NSR) coupling constant are especially challenging: they require body-fixed molecular Hamiltonians that treat both the electrons and nuclei as relativistic quantum particles. Nevertheless, they have been formulated rigorously. In particular, a very robust ‘relativistic mapping’ between the two properties has been established, which can translate experimentally measured NSR coupling constants to very accurate absolute NMR shielding scales that otherwise cannot be obtained experimentally. Since the most general and fundamental issues pertinent to all the three components of the quantum mechanical equation HΨ = EΨ (i.e. Hamiltonian H, wave function Ψ, and energy/property E(λ)) have fully been understood, the big picture of relativistic molecular quantum mechanics can now be regarded as established.

Influences of Conjugation Extent on the Aggregation-Induced Emission Quantum Efficiency in Silole Derivatives: A Computational Study

The photophysical properties of a series of silole derivatives, with hydrogen (TPS), bromine (BrTPS), and conjugated phenyl (HPS), triphenylsilyethynyl (BTPES), and dimethylfluorene (BFTPS) substituents at 2,5-positions in both gas and aggregate phases have been investigated computationally by employing the correlation function rate formalism coupled with a hybrid quantum/molecular mechanics (QM/MM) approach. It is found that the solid-state fluorescence quantum efficiency first increases sharply with the degree of π-conjugation of the 2,5-substituents, then levels off, and finally starts to decrease slightly. This is because the side-group conjugation tends to enhance the radiative decay rate in both gas and solid phases. However, a further increase in conjugation leads to saturation in the radiative decay rate but increases the non-raditiave decay rate due to the decreased energy gap.