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Area of Science:

  • Computational Chemistry
  • Theoretical Chemistry
  • Quantum Chemistry

Background:

  • Time-dependent auxiliary density perturbation theory (TD-ADPT) is a recent advancement in quantum chemistry.
  • Solving the associated linear equation systems can be computationally intensive, limiting its application to larger systems.

Purpose of the Study:

  • To develop and validate a new iterative solver for TD-ADPT.
  • To improve the computational scaling of TD-ADPT calculations.
  • To enable the study of larger and more complex molecular systems.

Main Methods:

  • Implementation of the Eirola-Nevanlinna algorithm for large nonsymmetric linear systems.
  • Application of the new iterative solver to static and dynamic polarizability calculations.
  • Validation against analytic solutions for small molecules.

Main Results:

  • The iterative solver reduces formal computational scaling from O(N^4) to O(N^3).
  • Observed computational scaling for linear alkane chains is N(1.6), demonstrating subquadratic behavior.
  • Excellent agreement between iterative and analytic solutions for polarizabilities was achieved.
  • Static polarizabilities of giant fullerenes (up to C960) were successfully calculated.

Conclusions:

  • The new iterative solver offers a significant speed-up for TD-ADPT.
  • This methodology expands the scope of TD-ADPT to much larger molecular systems.
  • The subquadratic scaling opens new avenues for computational studies in chemistry and materials science.