Parameterized attenuated exchange for generalized TDHF@vW applications.

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Theoretical Spectroscopy

Background:

• The time-dependent Hartree-Fock (TDHF) method, combined with the Bethe-Salpeter Equation (BSE), is a powerful tool for studying molecular electronic excitations.
• Accurate calculation of exciton binding energies and optical gaps is crucial for understanding molecular photophysics.
• Previous TDHF@vW methods required system-specific parameterization, limiting their broad applicability.

Purpose of the Study:

• To introduce a novel parameterization scheme for the attenuated exchange kernel (vW) in the TDHF@vW method.
• To develop a broadly applicable and computationally efficient approach for accurate prediction of molecular optical gaps.
• To reduce the computational cost associated with high-accuracy electronic structure calculations.

Main Methods:

• Parameterization of the inverse dielectric function using a low-order polynomial with error function apodization.
• Leveraging photophysical similarities in exciton binding energies among molecules with comparable static dielectric responses.
• Calibrating the seven-parameter scheme on a few representative molecules.

Main Results:

• The parameterized vW is grid-independent and broadly applicable within molecular families.
• Achieved a mean absolute error of approximately 0.1 eV compared to experimental optical gaps.
• Demonstrated a five- to tenfold improvement in accuracy over conventional TD density functional theory (TDDFT) or TDHF.
• Reduced computational cost to that of standard TDHF.

Conclusions:

• The new parameterization scheme significantly enhances the accuracy and applicability of the TDHF@vW method for predicting optical gaps.
• This approach offers a balance between high accuracy (BSE-level) and computational efficiency.
• The method provides a promising tool for theoretical spectroscopy and materials science applications.