Time-Dependent Density Functional Theory (TDDFT) has recently been extended to describe many-body open quantum systems (OQS) evolving under non-unitary dynamics according to a quantum master equation. In the master equation approach, electronic excitation spectra are broadened and shifted due to relaxation and dephasing of the electronic degrees of freedom by the surrounding environment. In this paper, we develop a formulation of TDDFT linear-response theory (LR-TDDFT) for many-body electronic systems evolving under a master equation, yielding broadened excitation spectra. This is done by mapping an interacting open quantum system onto a non-interacting open Kohn-Sham system yielding the correct non-equilibrium density evolution. A pseudo-eigenvalue equation analogous to the Casida equations of usual LR-TDDFT is derived for the Redfield master equation, yielding complex energies and Lamb shifts. As a simple demonstration, we calculate the spectrum of a C$^{2+}$ atom in an optical resonator interacting with a bath of photons. The performance of an adiabatic exchange-correlation kernel is analyzed and a first-order frequency-dependent correction to the bare Kohn-Sham linewidth based on Gorling-Levy perturbation theory is calculated.
Benchmarking and contrasting exchange-correlation functional differences in response to static correlation in unrestricted Kohn-Sham and a hybrid 1-electron reduced density matrix functional theory
Electronic Transitions for a Fully Polarizable QM/MM Approach Based on Fluctuating Charges and Fluctuating Dipoles: Linear and Corrected Linear Response Regimes
基于波动电荷和波动偶极子的完全可极化QM/MM方法，称为QM/QMF μ（J. Chem. Theory Comput. 2019，15 2233-2245），扩展到溶剂化分子系统的垂直激发能的计算。激发能定义在两种不同的溶剂化机制内，即线性响应（LR）和校正线性响应（cLR），在线性响应（LR）中，MM部分的响应被调整为QM跃迁密度，在校正线性响应（cLR）中，MM响应被调整为弛豫QM密度，从而能够解释激发态中的电荷平衡。该模型，这是指定的三个物理参数（电负性，化学硬度，和极化率）适用于对硝基苯胺，吡啶和嘧啶的水溶液的真空到水的溶致变色位移。结果显示出良好的协议与他们的实验同行，从而突出了这种方法的潜力。
