Low scaling EOM-CCSD and EOM-MBPT(2) method with natural transition orbitals.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Equation-of-motion coupled-cluster (EOM-CCSD) theory is a powerful method for calculating excited states.
• Traditional EOM-CCSD methods suffer from high computational scaling, limiting their application to larger systems.
• Natural Transition Orbitals (NTOs) provide a compact representation of excited states.

Purpose of the Study:

• To develop a low-scaling computational method for EOM-CCSD and its approximations.
• To reduce the computational cost associated with the double excitation vector (R2) in EOM calculations.
• To enable accurate excited-state calculations for larger molecular systems.

Main Methods:

• Selection of dominant occupied and virtual orbitals from NTOs based on transition density matrix eigenvalues.
• Modification of the R2 vector to retain only the most significant excitation contributions.
• Implementation of a low-scaling approach with an overall computational complexity of ~M^5.

Main Results:

• The modified R2 vector effectively captures dominant excitations within reduced subspaces.
• The developed method achieves a computational scaling of ~M^5 for the EOM part.
• Energy deviations due to R2 truncation are minimal (average ~0.03 eV) compared to untruncated EOM-CCSD.

Conclusions:

• The proposed low-scaling method provides an accurate and efficient approach for excited-state calculations.
• This method is compatible with various NTO generation techniques, including time-dependent density functional theory.
• The ~M^5 scaling opens possibilities for applying EOM-CCSD and MBPT(2) to larger and more complex systems.