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Analytic second derivatives from auxiliary density perturbation theory.

Rogelio Isaac Delgado-Venegas1, Daniel Mejía-Rodríguez1, Roberto Flores-Moreno2

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This study presents analytic second energy derivatives for auxiliary density functional theory (ADFT), validated for molecular frequencies and showing good parallel scaling for large systems like carbon fullerenes.

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Theoretical Chemistry

Background:

  • Auxiliary Density Functional Theory (ADFT) is a computational method for electronic structure calculations.
  • Analytic second energy derivatives are crucial for predicting molecular properties like vibrational frequencies.
  • Efficient calculation of these derivatives is essential for large molecular systems.

Purpose of the Study:

  • To present the working equations for analytic second energy derivatives within the ADFT framework.
  • To extend Auxiliary Density Perturbation Theory (ADPT) for perturbation-dependent basis and auxiliary functions.
  • To implement and validate the new analytic second ADFT energy derivative approach.

Main Methods:

  • Development of working equations for analytic second energy derivatives in ADFT.
  • Extension of ADPT to handle perturbation-dependent basis and auxiliary functions.
  • Solution of ADPT equation systems using the Eirola-Nevanlinna algorithm.
  • Implementation in the deMon2k software package.
  • Validation against finite difference methods for small molecules.
  • Analysis of parallel scaling using harmonic frequency calculations on C240 fullerenes.

Main Results:

  • Good agreement between the analytic second ADFT energy derivative approach and finite difference methods for harmonic frequencies.
  • Fair parallel scaling of the analytic second ADFT energy derivatives up to 720 processors.
  • Successful application to symmetry-unrestricted optimization and frequency analysis of large icosahedral carbon fullerenes (up to 960 atoms).

Conclusions:

  • The newly developed analytic second ADFT energy derivative approach is accurate and efficient.
  • The method demonstrates good scalability for parallel computations.
  • This approach enables the study of large and complex molecular systems, such as fullerenes.