Direct Unconstrained Optimization of Excited States in Density Functional Theory

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Orbital-optimized density functional theory (DFT) offers an alternative to time-dependent (TD) DFT for excited states.
• TDDFT struggles with excited states involving significant electron density redistribution, like charge-transfer and double-electron excitations.

Purpose of the Study:

• To develop a simple and robust method for excited-state optimization.
• To address the variational collapse problem inherent in excited-state calculations.
• To improve the accuracy of calculating challenging excited states.

Main Methods:

• Introduced variable-metric time-independent DFT (VM TIDFT).
• Allowed nonorthogonal electronic states during optimization, gradually enforcing orthogonality with a penalty function.
• Utilized molecular orbital coefficients as independent variables for a closed-form gradient.

Main Results:

• VM TIDFT successfully overcomes variational collapse.
• The method demonstrates robustness and accuracy in numerical tests across various molecular systems.
• Accurate energies were obtained for both standard and challenging excitations (charge-transfer, double-electron).

Conclusions:

• VM TIDFT provides a reliable approach for excited-state optimization.
• This method extends the capabilities of DFT for describing complex electronic excitations.
• VM TIDFT is a promising alternative to TDDFT for challenging excited-state problems.