Exact-exchange density functional theory for hyperpolarizabilities.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Density Functional Theory (DFT) is a powerful quantum mechanical modeling method.
• Standard DFT methods often suffer from self-interaction errors.
• Accurate calculation of molecular hyperpolarizabilities is crucial for understanding nonlinear optical properties.

Purpose of the Study:

• To formulate time-dependent density functional theory (TDDFT) with an exact-exchange functional (TDDFTx) for calculating beta static hyperpolarizabilities.
• To derive and implement analytical formulas for these calculations.
• To investigate the properties of the adiabatic exact-exchange second kernel.

Main Methods:

• Utilizing the optimized effective potential method for TDDFTx.
• Employing a diagrammatic technique to derive functional derivatives for the adiabatic second kernel.
• Implementing derived formulas using Gaussian basis sets.
• Comparing TDDFTx results with time-dependent Hartree-Fock (TDHF).

Main Results:

• The study successfully derived and implemented formulas for beta static hyperpolarizabilities using TDDFTx.
• It was found that no current DFT functional fully satisfies the correct properties of the second kernel.
• TDDFTx, by correcting self-interaction errors and exhibiting correct long-range behavior, yielded results close to TDHF in the static limit.

Conclusions:

• The developed TDDFTx approach provides a more accurate method for calculating static hyperpolarizabilities.
• The findings highlight limitations in current DFT functionals regarding the second kernel properties.
• TDDFTx offers a promising alternative to standard DFT for systems where self-interaction errors are significant.