Direct Unconstrained Optimization of Molecular Orbital Coefficients in Density Functional Theory

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Materials Science

Background:

• Standard Kohn-Sham density functional theory (DFT) requires orthogonal orbitals, complicating optimization.
• Existing methods involve elaborate parameterization and complex algorithms for orbital optimization.

Purpose of the Study:

• To develop a simplified and efficient orbital optimization method for DFT.
• To demonstrate the effectiveness of nonorthogonal orbitals in variational calculations.

Main Methods:

• Introduced variable-metric self-consistent field (VM SCF) optimization.
• Augmented DFT energy functional with a penalty term for linear dependence.
• Utilized molecular orbital coefficients as independent variables for unconstrained minimization.

Main Results:

• Developed simple closed-form expressions for the electronic gradient and Hessian.
• Achieved efficient convergence with a preconditioned conjugate gradient algorithm.
• Successfully applied VM SCF to narrow-gap systems and singlet diradicals.

Conclusions:

• The VM SCF approach offers a straightforward reformulation of variational procedures in DFT.
• This method can be extended to multiconfiguration electron correlation methods and excited-state orbital optimization.