<i>n</i> -Mode Quantized Anharmonic Vibronic Hamiltonians for Matrix Product State Dynamics

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 <i>n</i>-mode quantization of all vibronic Hamiltonian terms comprised of general high-dimensional model representations. We expand the existing vibrational DMRG formalism by applying the <i>n</i>-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 <i>n</i>-mode vibronic Hamiltonian, demonstrating that it enables accurate calculations of complex photochemical dynamics.