Extended dissipaton theory for higher-order bath couplings and application to non-Condon spectroscopy with anharmonicity

TL;DR

This work addresses the challenge of simulating open quantum systems with non-Gaussian, anharmonic baths that influence non-Condon vibronic spectroscopy. It develops an extended DEOM formalism that generalizes bath couplings to arbitrary order using dissipaton algebra within a Brownian-vibration environment and Herzberg–Teller-type interactions, enabling exact treatment of complex system-bath dynamics. The authors derive and implement extended DEOM equations incorporating higher-order terms $\bar{\alpha}_r$ and non-Condon coupling $v_B$, and validate the method with condensed-phase linear absorption spectra, illustrating how anharmonicity and solvent effects shape vibronic signatures. This framework provides an accurate, efficient tool for studying open quantum systems in realistic environments and can be integrated with ab initio or machine-learning potentials to broaden applicability to biological pigments, molecular aggregates, and solid-state devices.

Abstract

In this work, we develop an extended dissipaton theory that generalizes the environmental couplings beyond the conventional linear and quadratic forms, enabling the treatment of arbitrary order of bath couplings. Applying this theoretical framework to the condensed-phase non-Condon spectroscopy, we demonstrate the interplay of anharmonicity, non-Condon and solvent effects on optical spectra. Precise simulations are carried out with high efficiency on linear absorption spectra involving the above mentioned correlated effects. We exhibit how an anharmonic potential modulates the vibronic feature, offering insights into the role of nonlinear environmental couplings in spectroscopic signatures and exemplifying the success of the extended dissipaton formalism as an exact and efficient method for higher-order bath couplings.

Figures (5)

• Figure 1: Ground and excited potential energy surfaces. The dotted curve represents the harmonic reference ($g=0$) of the excited state. The dashed and solid curves exhibit the anharmonic excited-state potential surfaces with $g=1$ and $g=2$, respectively.
• Figure 2: The numerically fitted bath spectra $C(\omega)$ compared with exact ones, the Fourier transform of $\langle \hat{q}(t)\hat{q}(0)\rangle_{\hbox{\tiny B}}$, with three specified values of $\zeta=3\Omega$, $1.5\Omega$, $0.75\Omega$.
• Figure 3: The evaluatedlinear absorption spectra with varied $\zeta$ and fixed $v_{\hbox{\tiny B}}=g=1$. The gas phase result is computed via the standard Fermi golden rule approach, where the $\delta$-functions have been broadened as Lorentzian functions.
• Figure 4: The evaluated linear absorption spectra with varied $v_{\hbox{\tiny B}}$ and fixed $g=1$.
• Figure 5: The evaluated linear absorption spectra with varied $g$ and fixed $v_{\hbox{\tiny B}}=1$ (upper panel) and $2$ (lower panel).