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A neutral atom consists of a positively charged nucleus surrounded by a negatively charged electron cloud. When placed in an external electric field, the external electric force pulls the electrons and nucleus apart, opposite to the intrinsic attraction between the nucleus and the electrons. The opposing forces balance each other with a slight shift between the center of masses of the nucleus and the electron cloud, resulting in a polarized atom. On the other hand, a few molecules, like water,...
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Efficient pole-search algorithm for dynamic polarizability: Toward alternative excited-state calculation for large

Hiromi Nakai1,2,3,4, Takeshi Yoshikawa1, Yutaro Nonaka1

  • 1Department of Chemistry and Biochemistry, School of Advanced Science and Engineering, Waseda University, Tokyo, 169-8555, Japan.

Journal of Computational Chemistry
|October 6, 2016
PubMed
Summary

This study introduces an efficient algorithm for finding excited states in large systems by accurately calculating dynamic polarizability. The method enhances accuracy and efficiency for nonlocal excitations.

Keywords:
dynamic polarizabilityexcited statelinear scalingtime-dependent density functional theory

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Area of Science:

  • Computational Chemistry
  • Quantum Mechanics
  • Theoretical Physics

Background:

  • Accurate determination of excited states is crucial for understanding molecular properties and reactions.
  • Large systems with nonlocal excitation nature pose significant challenges for traditional computational methods.
  • Dynamic polarizability calculations are essential for predicting spectroscopic properties.

Purpose of the Study:

  • To develop an efficient and accurate algorithm for locating poles of dynamic polarizability.
  • To enable the computation of excited states in large molecular systems, particularly those with nonlocal excitation characteristics.
  • To improve the extraction of excitation energies and oscillator strengths.

Main Methods:

  • A homogeneous search with a constant frequency interval combined with a bisection search for high accuracy.
  • A subtraction process to isolate and extract contributions from undetected poles in dynamic polarizability.
  • Integration with divide-and-conquer-based dynamic polarizability calculations for large system treatment.

Main Results:

  • The algorithm accurately and efficiently determines excitation energies and oscillator strengths for all dipole-allowed excited states.
  • Numerical assessments validate the precision and speed of the developed pole-search algorithm.
  • The subtraction method effectively retrieves contributions from previously undetected poles.

Conclusions:

  • The presented pole-search algorithm is a significant advancement for calculating excited states in large systems.
  • The combination of this algorithm with divide-and-conquer methods shows great promise for tackling complex nonlocal excitations.
  • This work provides a robust computational tool for theoretical spectroscopy and quantum chemistry.