Bridging the Gap between Variational and Perturbational DFT-Based Methods for Calculating Excited States

Area of Science:

• Quantum chemistry
• Computational physics
• Theoretical chemistry

Background:

• The delta self-consistent field (ΔSCF) method is crucial for calculating electronic excited states.
• Existing methods may require complex spin purification procedures.
• Restricted-open Kohn-Sham (ROKS) formalism offers a potential alternative for targeting specific electronic states.

Purpose of the Study:

• To thoroughly investigate the ROKS-based ΔSCF method for calculating unmixed singlet excited electronic states.
• To present modifications to enhance the convergence and stability of the ΔSCF method.
• To benchmark ROKS-ΔSCF against time-dependent density functional theory (TDDFT) for excited states.

Main Methods:

• Implementation and application of the ROKS-based ΔSCF method.
• Modification of the maximum overlap method for improved ΔSCF convergence.
• Development of a molecular orbital tracking and order-preserving algorithm.
• Large-scale comparison with TDDFT for excitation energies, electron densities, and transition dipole moments.

Main Results:

• The ROKS-ΔSCF method successfully targets unmixed singlet excited states, eliminating the need for spin purification.
• Modified algorithms demonstrated improved convergence for the ΔSCF calculations.
• ROKS-ΔSCF results showed good agreement with TDDFT for excitation energies and properties across various molecules.
• Both single- and multi-reference excited states were reproduced by the ROKS-ΔSCF method.

Conclusions:

• ROKS-based ΔSCF is a viable and efficient method for calculating excited electronic states, particularly unmixed singlets.
• The presented algorithmic improvements enhance the practical applicability of the ΔSCF method.
• ROKS-ΔSCF serves as a reliable alternative to TDDFT for studying excited-state properties.