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Extensions of the Time-Dependent Density Functional Based Tight-Binding Approach.

A Domínguez1, B Aradi1, T Frauenheim1

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This study enhances the time-dependent density functional based tight-binding (TD-DFTB) method for improved accuracy in molecular excitation calculations. The revised TD-DFTB approach offers reliable results at a reduced computational cost.

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Theoretical Chemistry

Background:

  • The time-dependent density functional based tight-binding (TD-DFTB) method is a computationally efficient approach for studying electronic excitations.
  • However, the original TD-DFTB method exhibits limitations in accurately describing certain types of electronic transitions, such as σ → π* and n → π* excitations, and triplet states.

Purpose of the Study:

  • To generalize the TD-DFTB approach to incorporate fractional occupations and introduce an on-site correction.
  • To overcome the known limitations of the original TD-DFTB method in describing electronic excitations.
  • To evaluate the performance of the revised TD-DFTB method for organic molecules and spin-polarized systems.

Main Methods:

  • Generalization of the time-dependent density functional based tight-binding (TD-DFTB) approach to include fractional occupations.
  • Introduction of an on-site correction term to the TD-DFTB Hamiltonian.
  • Development of a formalism for spin-polarized TD-DFTB calculations consistent with ground-state DFTB.
  • Benchmark calculations on a diverse set of organic molecules.

Main Results:

  • The revised TD-DFTB method with fractional occupations and on-site correction significantly improves the description of electronic excitations, particularly σ → π* and n → π* transitions.
  • Benchmark calculations demonstrate enhanced accuracy for triplet states in organic molecules.
  • The accuracy of the improved TD-DFTB method is comparable to first-principles time-dependent density functional theory (TD-DFT) but with substantially lower computational expense.
  • A consistent formalism for spin-polarized TD-DFTB calculations has been established.

Conclusions:

  • The generalized TD-DFTB method with fractional occupations and on-site corrections provides a more accurate and reliable tool for studying electronic excitations in molecules.
  • This revised approach overcomes key limitations of the original TD-DFTB, offering a computationally efficient alternative to TD-DFT for various chemical systems.
  • The developed formalism also extends the applicability of TD-DFTB to spin-polarized systems.