Spin-adapted open-shell random phase approximation and time-dependent density functional theory. I. Theory.

Area of Science:

• Quantum Chemistry
• Theoretical Chemistry
• Computational Chemistry

Background:

• Calculating excited states of open-shell systems using single-reference quantum chemical methods is challenging due to incomplete spin configurations.
• Existing methods often require complex formalisms or are limited by approximations, hindering accurate predictions.

Purpose of the Study:

• To develop a general and computationally efficient tensor-coupling scheme for spin-adapting quantum chemical methods for excited states of open-shell systems.
• To enable the accurate calculation of all relevant spin states (S(i)-1, S(i), S(i)+1) for excited states.

Main Methods:

• A tensor-coupling scheme is proposed, utilizing all components of a reference multiplet (tensor reference) instead of increasing excitation ranks.
• The formalism is combined with the tensor equation-of-motion approach for compact excitation energy expressions.
• A spin-adapted open-shell random phase approximation and a spin-adapted restricted open-shell Kohn-Sham based time-dependent density functional theory (ROKS-TD-DFT) are developed.

Main Results:

• The new ROKS-TD-DFT scheme can access excited states with spins S(i)-1, S(i), and S(i)+1, unlike standard methods limited to S(i).
• The implementation and computational cost are comparable to unrestricted Kohn-Sham based TD-DFT.
• Spin-contaminated spin-flip configuration interaction approaches can be effectively spin-adapted using this tensor-coupling scheme.

Conclusions:

• The proposed tensor-coupling scheme provides a robust and versatile framework for spin-adapted calculations of excited states in open-shell systems.
• This approach significantly enhances the capability of quantum chemical methods to accurately predict diverse spin states, with broad applicability.