Second Linear Response Theory and the Analytic Calculation of Excited-State Properties

Area of Science:

• Quantum Chemistry
• Computational Spectroscopy
• Theoretical Molecular Physics

Background:

• Calculating excited-state properties is crucial for understanding molecular spectra and optical processes.
• Previous methods based on second linear response theory required double linear response time-dependent density functional theory (TDDFT) calculations.
• These calculations are computationally intensive and complex.

Purpose of the Study:

• To present a more efficient method for calculating permanent and transition multipoles of excited states.
• To simplify the computation of excited-state properties needed for spectra and multiphoton processes.
• To improve upon existing theoretical frameworks in computational quantum chemistry.

Main Methods:

• The method is based on second linear response time-dependent density functional theory (TDDFT).
• It requires only a single linear response calculation, unlike previous double calculations.
• Excited-state properties are evaluated analytically using electron repulsion integrals and excitation vectors, focusing on full many-body wave functions.

Main Results:

• The proposed method efficiently computes permanent and transition multipoles of excited states.
• Analytical evaluation through algebraic operations simplifies the process.
• The approach utilizes full many-body wave functions for a more robust derivation.

Conclusions:

• The new method offers a computationally efficient and accurate way to determine excited-state properties.
• It provides a simplified alternative to double TDDFT calculations for molecular spectroscopy.
• Validation against reference calculations shows excellent agreement for excited-state dipoles in various molecules.