New and Efficient Implementation of CC3

Area of Science:

• Computational Quantum Chemistry
• Electronic Structure Theory
• Method Development

Background:

• Coupled cluster methods are essential for accurate electronic structure calculations.
• The CC3 method provides a balance of accuracy and computational cost for excited states.
• Efficient implementations are crucial for applying high-level theories to larger systems.

Purpose of the Study:

• To present a new, efficient implementation of the CC3 method in the `e` electronic structure program.
• To detail the computational costs and performance of the new CC3 implementation.
• To validate the implementation by calculating excited states of l-proline.

Main Methods:

• Implementation of the closed-shell coupled cluster singles and doubles with perturbative triples (CC3) method.
• Development of efficient algorithms for ground state and excited state calculations, including transition moments.
• Comparison of the new implementation's performance against existing CC3 codes (CFOUR, DALTON, PSI4).

Main Results:

• The new CC3 implementation achieves an iterative cost of 4n_V⁴n_O³ FLOP for ground state calculations.
• Jacobian and transpose Jacobian transformations for excitation energies and transition moments have a cost of 8n_V⁴n_O³ FLOP.
• Equation of motion transition moments are implemented with noniterative costs of 10n_V⁴n_O³ FLOP for ground state density and 26n_V⁴n_O³ FLOP per state for transition densities.

Conclusions:

• The new CC3 implementation in `e` is computationally efficient and accurate.
• The method successfully calculates valence and core excited states, demonstrating its capability.
• This work provides a valuable tool for researchers studying electronic excited states.