Time-dependent vibrational coupled cluster theory: Theory and implementation at the two-mode coupling level.

Area of Science:

• Quantum chemistry
• Computational chemistry
• Molecular dynamics

Background:

• Accurate simulation of molecular vibrations is crucial for understanding chemical reactions and material properties.
• Time-dependent methods are essential for describing dynamic processes in molecules.

Purpose of the Study:

• To derive and implement equations for time-dependent vibrational coupled cluster (TDVCC) wave functions, including both ket and bra states.
• To analyze the behavior of TDVCC under time-dependent Hamiltonians and assess its accuracy and efficiency.

Main Methods:

• Derivation of time evolution equations for TDVCC ket and Λ bra states.
• Implementation for Hamiltonians and cluster operators with at most two-mode coupling.
• Theoretical and numerical analysis of norm, energy, and expectation value evolution.
• Study of state separability for noninteracting systems.
• Numerical experiments on polycyclic aromatic hydrocarbons.

Main Results:

• The TDVCC theory and its implementation capture the complex dynamics of molecular vibrations.
• Analysis revealed non-trivial behavior in norm, energy, and expectation values due to nonunitary time evolution.
• The coupled cluster state exhibits correct separability, while the Λ state shows more intricate behavior.
• TDVCC in incomplete expansions outperforms standard linear variational methods in accuracy.
• Equivalent results are achieved with complete expansions.

Conclusions:

• TDVCC provides a robust framework for studying time-dependent vibrational dynamics.
• The method demonstrates superior accuracy compared to variational approaches for a given number of parameters.
• TDVCC is efficient for large molecular systems, as shown by applications to polycyclic aromatic hydrocarbons.