Self-consistent Formulation of Constricted Variational Density Functional Theory with Orbital Relaxation....

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Accurate calculation of electronic excitation energies is crucial for understanding molecular properties and reactions.
• Existing density functional theory (DFT) methods, such as constricted nth order variational DFT (CV(n)-DFT), have limitations in describing excited states, particularly for nσ→π* transitions.

Purpose of the Study:

• To introduce and validate a new DFT method, the relaxed self-consistent field nth order constricted variational density functional (RSCF-CV(n)-DFT) method.
• To improve the accuracy of calculated excitation energies by allowing relaxation of occupied excited state orbitals.
• To assess the performance of RSCF-CV(n)-DFT for nσ→π* transitions using various functionals (LDA, B3LYP, BHLYP) and compare results with high-level ab initio calculations.

Main Methods:

• Development of the RSCF-CV(n)-DFT method, which allows relaxation of orbitals in response to changes in Coulomb and exchange-correlation potentials.
• Application of the method to 34 nσ→π* transitions in 16 different compounds.
• Comparison of RSCF-CV(n)-DFT results with established CV(n)-DFT, CV(∞)-DFT, and Slater's ΔSCF methods, as well as benchmark 'best estimates' (BE) from ab initio calculations.

Main Results:

• The B3LYP functional within the standard CV(2)-DFT framework provided good agreement with BE (RMSD = 0.33 eV).
• Full orbital relaxation in the RSCF-CV(n)-DFT method significantly improved accuracy for all functionals, with B3LYP yielding the best results (RMSD = 0.32 eV).
• The RSCF-CV(n)-DFT method showed similar performance to Slater's ΔSCF method for excitations described by a single orbital displacement.

Conclusions:

• The RSCF-CV(n)-DFT method represents a significant advancement in calculating electronic excitation energies, particularly for nσ→π* transitions.
• Allowing for full relaxation of orbitals in excited states is essential for achieving high accuracy in DFT-based excitation energy calculations.
• The developed method offers a computationally efficient and accurate alternative to high-level ab initio methods for studying molecular electronic transitions.