Zhang Zhan Tong, Vaníček Jiří J L
Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland.
J Chem Phys. 2024 Sep 21;161(11). doi: 10.1063/5.0219005.
In single vibronic level (SVL) fluorescence experiments, the electronically excited initial state is also excited in one or several vibrational modes. Because computing such spectra by evaluating all contributing Franck-Condon factors becomes impractical (and unnecessary) in large systems, here we propose a time-dependent approach based on Hagedorn wavepacket dynamics. We use Hagedorn functions-products of a Gaussian and carefully generated polynomials-to represent SVL initial states because in systems whose potential is at most quadratic, Hagedorn functions are exact solutions to the time-dependent Schrödinger equation and can be propagated with the same equations of motion as a simple Gaussian wavepacket. Having developed an efficient recursive algorithm to compute the overlaps between two Hagedorn wavepackets, we can now evaluate emission spectra from arbitrary vibronic levels using a single trajectory. We validate the method in two-dimensional global harmonic models by comparing it with quantum split-operator calculations. In addition, we study the effects of displacement, distortion (squeezing), and Duschinsky rotation on SVL fluorescence spectra. Finally, we demonstrate the applicability of the Hagedorn approach to high-dimensional systems on a displaced, distorted, and Duschinsky-rotated harmonic model with 100 degrees of freedom.
在单电子振动态（SVL）荧光实验中，电子激发的初始态在一个或几个振动模式中也被激发。由于在大型系统中通过评估所有贡献的弗兰克 - 康登因子来计算此类光谱变得不切实际（且不必要），在此我们提出一种基于哈格多恩波包动力学的含时方法。我们使用哈格多恩函数——高斯函数与精心生成的多项式的乘积——来表示SVL初始态，因为在势能至多为二次的系统中，哈格多恩函数是含时薛定谔方程的精确解，并且可以用与简单高斯波包相同的运动方程进行传播。在开发了一种高效的递归算法来计算两个哈格多恩波包之间的重叠之后，我们现在可以使用单个轨迹来评估任意电子振动态的发射光谱。我们通过将其与量子分裂算符计算进行比较，在二维全局谐波模型中验证了该方法。此外，我们研究了位移、畸变（压缩）和杜什金斯基旋转对SVL荧光光谱的影响。最后，我们在具有100个自由度的位移、畸变和杜什金斯基旋转的谐波模型上证明了哈格多恩方法对高维系统的适用性。
