Excited-State Gradients in Polarizable QM/MM Models: An Induced Dipole Formulation

Charge and structural relaxation of electronically excited states in embedded systems are strongly affected by the environment. It is known that the largest part of environment effects comes from electrostatics. However, polarization can also play a role by tuning the electronic and geometrical properties of the states, finally modifying the fluorescence. Here we present the formulation of analytical excited-state gradients within a polarizable QM/MM approach and their implementation within the ONIOM framework. A time-dependent DFT level of theory is used in combination with an induced dipole formulation of the polarizable embedding. The formation and relaxation of the bright excited state of an organic dye (DAPI) intercalated in a DNA pocket is used to quantify the role played by the mutual polarization between the QM subsystem and the embedding and also to investigate the onset of overpolarization, which is a known limit of the model with potentially detrimental effects. On the one hand, the results indicate the robustness of the QM-classical interface and, on the other hand, show the non-negligible effect of polarization between DAPI and a DNA pocket in determining the fluorescence properties of the embedded dye.嵌入体系中电子激发态的电荷与结构弛豫过程，会受到周围环境的强烈影响。已知环境效应的主要来源为静电相互作用，而极化作用亦可通过调控激发态的电子与几何性质，最终改变体系的荧光特性。本文提出了可极化QM/MM（Quantum Mechanics/Molecular Mechanics，QM/MM）方法框架下的解析激发态梯度公式，并将其实现于ONIOM框架之中。研究采用含时密度泛函理论(Time-Dependent DFT)，结合可极化嵌入的诱导偶极子模型进行计算。以嵌入DNA口袋的有机染料（DAPI）的亮态激发态的形成与弛豫为研究对象，一方面量化QM子体系与嵌入环境之间的相互极化所起到的作用，另一方面探究过极化现象的发生——该现象是该模型已知的局限性之一，可能带来不利影响。研究结果一方面表明QM-经典界面具备良好的鲁棒性，另一方面也证实了DAPI与DNA口袋之间的极化作用，在决定嵌入染料的荧光特性方面具有不可忽视的影响。