Open-Ended Recursive Approach for the Calculation of Multiphoton Absorption Matrix Elements.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Molecular Spectroscopy

Background:

• Response theory is essential for understanding molecular interactions with light.
• Calculating multiphoton absorption is computationally demanding and requires accurate theoretical frameworks.
• Previous methods lacked efficient implementations for higher-order response functions.

Purpose of the Study:

• To develop and implement a recursive approach for calculating single residues of response functions to arbitrary order.
• To present explicit expressions for linear, quadratic, cubic, and quartic response function residues.
• To compute one-, two-, three-, and four-photon absorption cross sections for specific molecules.

Main Methods:

• Implemented a recursive algorithm for calculating single residues of response functions.
• Utilized density-matrix-based response theory to derive explicit expressions.
• Employed computational chemistry methods to calculate multiphoton absorption cross sections for para-nitroaniline and para-nitroaminostilbene.

Main Results:

• Successfully calculated one-, two-, three-, and four-photon absorption cross sections.
• Demonstrated that basis set size has minimal impact on cross sections with adequate basis sets.
• Showed that exchange-correlation functional choice significantly influences calculated cross sections, especially for charge-transfer transitions.

Conclusions:

• The developed code provides the first treatment of four-photon absorption within response theory.
• A range-separated exchange-correlation functional with the aug-cc-pVDZ basis set is recommended for accurate multiphoton absorption calculations.
• This work advances the computational study of molecular light-matter interactions.