Automatic derivation and evaluation of vibrational coupled cluster theory equations

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Vibrational coupled cluster (CC) theory is essential for accurate molecular vibrational analysis.
• Deriving and evaluating complex CC expressions computationally is challenging.
• Existing methods may lack generality or efficiency for higher excitation levels and mode couplings.

Purpose of the Study:

• To introduce an automated scheme for deriving and evaluating expressions in vibrational CC theory.
• To develop a general method applicable to various excitation and mode coupling levels.
• To improve computational efficiency by automatically detecting and utilizing low-scaling intermediates.

Main Methods:

• Utilizing a Baker-Campbell-Hausdorff expansion of the similarity-transformed Hamiltonian.
• Developing a commutator-based algorithm for expression derivation and evaluation.
• Implementing automatic detection of computational intermediates to reduce scaling.
• Extending the method for response theory calculations.

Main Results:

• The developed scheme successfully automates the derivation and evaluation of vibrational CC expressions.
• The method demonstrates generality across different excitation and mode coupling levels.
• Computational efficiency is improved through the identification of key intermediates.
• Accurate fundamental excitation energies for ethylene oxide were computed.

Conclusions:

• The automated scheme provides a powerful and general tool for vibrational CC theory.
• The method offers significant advantages in computational efficiency and applicability.
• This approach facilitates more complex molecular vibrational analyses and response theory calculations.