n-Mode Quantized Anharmonic Vibronic Hamiltonians for Matrix Product State Dynamics.

Area of Science:

• Quantum chemistry
• Theoretical chemistry
• Computational physics

Background:

• Accurate theoretical predictions of photochemical processes are crucial for understanding spectral features.
• Reliable quantum dynamics calculations necessitate precise modeling of anharmonic effects and nonadiabatic coupling terms in potential energy surfaces.

Purpose of the Study:

• To present the n-mode quantization of all vibronic Hamiltonian terms for high-dimensional model representations.
• To expand the vibrational Density Matrix Renormalization Group (DMRG) formalism by applying n-mode quantization to potential energy surfaces and coupling terms.

Main Methods:

• Implementation of n-mode quantization for all vibronic Hamiltonian terms.
• Development of a novel matrix product state architecture with tailored local site operators for efficient vibronic wave function encoding.
• Application of the time-dependent Density Matrix Renormalization Group (TD-DMRG) algorithm within a second-quantized framework.

Main Results:

• Demonstrated accurate and reliable excited-state quantum dynamics calculations for maleimide.
• Analyzed convergence and parameter choices for the TD-DMRG algorithm applied to the n-mode vibronic Hamiltonian.
• Established a robust framework for complex photochemical dynamics computations.

Conclusions:

• The developed n-mode quantization approach enables accurate calculations of complex photochemical dynamics.
• The novel matrix product state architecture provides an effective tensor-train format for vibronic wave functions.
• This work advances the computational modeling of vibronic systems in theoretical chemistry.