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arXiv:2610.01771

Nonadiabatic Quantum Dynamics of Hexatriene via the Extended Hubbard-Peierls Model and Time-Dependent DMRG

Timothy N. Georges, Darren J. Valentine, William Barford

Published Oct 1, 2026• 0 citations
arXivHTMLPDF

Abstract

Propagating the electronic and nuclear degrees of freedom of a molecule simultaneously is a challenging task, because the number of vibronic states grows exponentially with system size. We use the adaptive time-dependent density matrix renormalization group to perform simulations of the extended Hubbard-Peierls Hamiltonian, in which both the electronic and nuclear degrees of freedom are quantized. We describe our approach, and demonstrate it through converged calculations of the nonadiabatic dynamics of hexatriene. This simulation predicts a lifetime of the `bright' $\mathrm{1B_u}$ electronic state of approximately 40 fs. Our predictions for the population of the $\mathrm{1B_u}$ electronic state are in qualitative agreement with those obtained using the linear vibronic coupling model derived from the extended Hubbard-Peierls Hamiltonian in previous work.

DOI
10.48550/arxiv.2610.01771

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Propagating the electronic and nuclear degrees of freedom of a molecule simultaneously is a challenging task, because the number of vibronic states grows exponentially with system size. We use the adaptive time-dependent density matrix renormalization group to perform simulations of the extended Hubbard-Peierls Hamiltonian, in which both the electronic and nuclear degrees of freedom are quantized. We describe our approach, and demonstrate it through converged calculations of the nonadiabatic dynamics of hexatriene. This simulation predicts a lifetime of the `bright' 1Bu\mathrm{1B_u}1Bu​ electronic state of approximately 40 fs. Our predictions for the population of the 1Bu\mathrm{1B_u}1Bu​ electronic state are in qualitative agreement with those obtained using the linear vibronic coupling model derived from the extended Hubbard-Peierls Hamiltonian in previous work.
The accurate theoretical interpretation of ultrafast time-resolved spectroscopy experiments relies on full quantum dynamics simulations for the investigated system, which is nevertheless computationally prohibitive for realistic molecular systems with a large number of electronic and/or vibrational degrees of freedom. In this work, we propose a unitary transformation approach for realistic vibronic Hamiltonians, which can be coped with using the adaptive time-dependent density matrix renormalization group (t-DMRG) method to efficiently evolve the nonadiabatic dynamics of a large molecular system. We demonstrate the accuracy and efficiency of this approach with an example of simulating the exciton dissociation process within an oligothiophene/fullerene heterojunction, indicating that t-DMRG can be a promising method for full quantum dynamics simulation in large chemical systems. Moreover, it is also shown that the proper vibronic features in the ultrafast electronic process can be obtained by simulating the two-dimensional (2D) electronic spectrum by virtue of the high computational efficiency of the t-DMRG method.
Recent advances in experimental techniques have enabled precise characterization of fundamental nonadiabatic and even electronic dynamics in molecules, on ultrafast time scales reaching femtosecond to attosecond resolution. However, accurate theoretical simulation of these ultrafast chemical dynamics processes in large systems remains challenging, largely due to the overwhelming number of degrees of freedom (DoFs) and the pronounced many-body correlations. In recent years, by leveraging efficient decomposition schemes for high-dimensional wave function and operator tensors, the time-dependent density matrix renormalization group (TD-DMRG) has emerged as a powerful and accurate quantum dynamics method for simulating nonadiabatic and electron dynamics in large chemical systems, in conjunction with realistic electron/exciton-vibration/phonon models or ab initio quantum chemistry many-electron Hamiltonians. This review outlines the fundamentals of TD-DMRG for chemical dynamics, covering matrix product state/operator (MPS/MPO) frameworks and algorithms from ground-state calculations to time evolution. We discuss thermal/environmental effects and compare TD-DMRG with other tensor network methods such as multiconfiguration time-dependent Hartree (MCTDH) and multilayer MCTDH (ML-MCTDH). Demonstrated applications include simulations of pyrazine absorption, singlet fission in rubrene crystal, and charge migration in chloroacetylene cation. These show TD-DMRG’s capability for modeling complex ultrafast processes from femtoseconds to attoseconds with controlled accuracy.
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Theoretical predictions of photochemical processes are essential for interpreting and understanding spectral features. Reliable quantum dynamics calculations of vibronic systems require precise modeling of anharmonic effects in the potential energy surfaces and off-diagonal nonadiabatic coupling terms. In this work, we present the n-mode quantization of all vibronic Hamiltonian terms comprised of general high-dimensional model representations. We expand the existing vibrational DMRG formalism by applying the n-mode quantization to all potential energy surfaces entering the Hamiltonian as well as to all off-diagonal coupling terms. This is accompanied by the introduction of a novel matrix product state architecture employing tailored local site operators, which allow an effective encoding of the vibronic wave function in a tensor-train format. This results in a second-quantized framework for accurate vibronic calculations employing the density matrix renormalization group algorithm. We demonstrate the accuracy and reliability of this approach by calculating the excited-state quantum dynamics of maleimide. We analyze convergence and the choice of parameters of the underlying time-dependent density matrix renormalization group algorithm for the n-mode vibronic Hamiltonian, demonstrating that it enables accurate calculations of complex photochemical dynamics.
Substantial progress of the time-dependent density matrix renormalisation group (t-DMRG) method in the recent 15 years is reviewed in this paper. By integrating the time evolution with the sweep procedures in density matrix renormalisation group (DMRG), t-DMRG provides an efficient tool for real-time simulations of the quantum dynamics for one-dimensional (1D) or quasi-1D strongly correlated systems with a large number of degrees of freedom. In the illustrative applications, the t-DMRG approach is applied to investigate the nonadiabatic processes in realistic chemical systems, including exciton dissociation and triplet fission in polymers and molecular aggregates as well as internal conversion in pyrazine molecule.