Higher-order diagrammatic vibrational coupled-cluster theory

Area of Science:

• Quantum Chemistry
• Theoretical Chemistry
• Computational Spectroscopy

Background:

• Accurate calculation of molecular vibrational energies is crucial for spectroscopy and chemical reaction understanding.
• Existing methods often face limitations in accuracy, computational cost, or basis-set dependence.

Purpose of the Study:

• To develop a diagrammatically size-consistent and basis-set-free vibrational coupled-cluster (XVCC) theory.
• To establish quantum-field-theoretical tools for deriving working equations for XVCC and equation-of-motion XVCC (EOM-XVCC).
• To implement and optimize XVCC and EOM-XVCC for potential energy surfaces (PES) up to 8th order excitations.

Main Methods:

• Definition of XVCC theory for nth-order Taylor-series PES.
• Application of normal-ordered second quantization and Feynman-Goldstone diagrams.
• Implementation using computer algebra with optimizations like strength reduction and intermediate reuse.
• Derivation of working equations for mth-order excitation operators (1 ≤ m ≤ 8).

Main Results:

• Optimized cost scaling of O(N(m+⌊n/2⌋)) for mth-order XVCC/EOM-XVCC on nth-order PES.
• Demonstrated rapid and nearly monotonic convergence of calculated energies and frequencies with increasing excitation rank (m).
• Identified m = n as the optimal balance between cost and accuracy, achieving high precision for vibrational transitions.

Conclusions:

• XVCC theory provides a robust and accurate framework for molecular vibrational calculations.
• The developed method offers significant improvements in computational efficiency and accuracy.
• The study elucidates relationships between XVCC and other advanced vibrational theories.