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Analytical excited state forces for the time-dependent density-functional tight-binding method.

D Heringer1, T A Niehaus, M Wanko

  • 1General Electrics, Consumer & Industrial--Lighting, 1340 Budapest, Vaci ut 77, Hungary.

Journal of Computational Chemistry
|June 15, 2007
PubMed
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This study presents a new analytical formulation for geometrical derivatives of excitation energies using time-dependent density-functional tight-binding (TD-DFTB). The TD-DFTB method offers a balance of accuracy and efficiency, making it suitable for molecular dynamics and luminescence spectra calculations.

Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Theoretical Chemistry

Background:

  • Accurate calculation of excitation energies and molecular geometries in excited states is crucial for understanding photochemical processes.
  • Existing methods like Configuration Interaction Singles (CIS) and Random Phase Approximation (RPA) have limitations in accuracy or computational cost.
  • Time-dependent density-functional theory (TD-DFT) offers a good balance but can be computationally expensive for large systems.

Purpose of the Study:

  • To develop an analytical formulation for geometrical derivatives of excitation energies within the time-dependent density-functional tight-binding (TD-DFTB) method.
  • To assess the accuracy of TD-DFTB for excited-state properties, including potential energy surfaces, geometries, and vibrational frequencies.
  • To evaluate the computational efficiency and scalability of the TD-DFTB approach for large molecular systems.

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Main Methods:

  • Derivation of geometrical derivatives of excitation energies using the auxiliary functional approach within TD-DFTB.
  • Calculation of adiabatic excitation energies, excited-state geometries, and harmonic vibrational frequencies for a test set of molecules.
  • Comparison of TD-DFTB performance against Configuration Interaction Singles (CIS), Random Phase Approximation (RPA), and ab initio TD-DFT.

Main Results:

  • The TD-DFTB method provides accurate potential energy surfaces for excited states.
  • TD-DFTB demonstrates superior performance compared to CIS and RPA for the studied properties.
  • The method's accuracy is lower than that of ab initio TD-DFT but offers significantly improved computational efficiency.
  • The scaling exponent of TD-DFTB for excitation energy calculations is reduced to three, similar to ground-state calculations.

Conclusions:

  • The developed analytical formulation for TD-DFTB enables efficient calculation of excited-state properties.
  • TD-DFTB offers a favorable balance between accuracy and computational cost, making it suitable for large-scale simulations.
  • The method is particularly well-suited for molecular dynamics simulations of systems with dozens of atoms and for computing luminescence spectra of systems with hundreds of atoms.