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Excited-State Properties for Extended Systems: Efficient Hybrid Density Functional Methods.

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Two new methods, auxiliary density matrix method (ADMM) and simplified Tamm-Dancoff approximation (sTDA), accelerate calculations for excited-state properties in materials. These approaches improve computational efficiency for time-dependent density functional theory (TDDFT) without sacrificing accuracy.

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Area of Science:

  • Computational Chemistry
  • Materials Science
  • Quantum Chemistry

Background:

  • Time-dependent density functional theory (TDDFT) is crucial for modeling photophysical and photochemical processes in extended materials.
  • Accurate TDDFT calculations require including exact exchange, which is computationally expensive for excited-state properties, hindering large-scale applications.
  • Existing methods for efficient exact exchange treatment are limited for excited-state calculations in periodic systems.

Purpose of the Study:

  • To develop and evaluate computationally efficient schemes for treating exact exchange in excited-state TDDFT calculations.
  • To enable accurate and cost-effective modeling of photophysical and photochemical processes in extended materials.
  • To facilitate large-scale applications and screening of materials with desired optical and electronic properties.

Main Methods:

  • Proposed the auxiliary density matrix method (ADMM) to approximate exact exchange using a smaller auxiliary basis set, with error compensation.
  • Introduced a simplified Tamm-Dancoff approximation (sTDA) using semiempirical tight-binding for Coulomb and exchange interactions in the excited-state kernel.
  • Benchmarked both methods against accurate reference data for molecular test sets and applied them to covalent-organic frameworks.

Main Results:

  • ADMM showed mean absolute errors below 0.3 pm for bond lengths and 0.02-0.04 eV for excitation energies, achieving a speed-up of over 10x for geometry optimizations.
  • sTDA demonstrated accuracy comparable to approximated hybrid DFT, with mean absolute errors of 1.1 pm for bond lengths and 0.2-0.5 eV for excitation energies.
  • sTDA accelerated broad-band excitation spectra computation by an order of magnitude compared to ADMM-approximated hybrid functionals.

Conclusions:

  • ADMM and sTDA offer significant computational speed-ups for excited-state calculations in extended materials.
  • These methods provide a good balance between accuracy and efficiency, making them suitable for large-scale material screening.
  • The developed schemes pave the way for more accessible and extensive studies of photophysical and photochemical phenomena in materials.