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Efficient implementation of isotropic cubic response functions for two-photon absorption cross sections within the

Karan Ahmadzadeh1, Mikael Scott2, Manuel Brand1

  • 1Department of Theoretical Chemistry and Biology, School of Engineering Sciences in Chemistry, Biotechnology and Health, KTH Royal Institute of Technology, SE-106 91 Stockholm, Sweden.

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|January 15, 2021
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Summary

This study introduces a faster method for calculating two-photon absorption cross sections by simplifying hyperpolarizability computations. The new approach significantly reduces computational resources while maintaining high accuracy for molecular properties.

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Molecular Spectroscopy

Background:

  • Accurate calculation of molecular properties like two-photon absorption (TPA) cross sections is crucial for materials science and drug discovery.
  • Existing methods for calculating TPA often require significant computational resources, limiting their application to larger systems.

Purpose of the Study:

  • To develop computationally efficient expressions for isotropic second-order hyperpolarizability within the self-consistent field approximation.
  • To implement these expressions for calculating TPA cross sections, reducing computational cost.

Main Methods:

  • Derivation of computationally tractable expressions for isotropic second-order hyperpolarizability.
  • Development of a novel tensor average formulation for evaluating isotropic damped cubic response functions.
  • Implementation and application to molecular systems including alanine-tryptophan and organic molecules.

Main Results:

  • The tensor average formulation requires substantially fewer auxiliary Fock matrices compared to explicit tensor component calculation (∼3.3% in off-resonance, ∼10% in resonance regions).
  • Numerical examples for TPA cross sections demonstrate the method's applicability.
  • Reduced and approximate forms of the cubic response function show a relative error of less than ∼5% compared to the full form.

Conclusions:

  • The developed method provides a computationally efficient and accurate approach for calculating two-photon absorption cross sections.
  • This advancement can enable the study of larger and more complex molecular systems.
  • The findings offer a valuable tool for researchers in computational chemistry and related fields.