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Analytic derivatives for perturbatively corrected "double hybrid" density functionals: theory, implementation, and

Frank Neese1, Tobias Schwabe, Stefan Grimme

  • 1Lehrstuhl für Theoretische Chemie, Institut für Physikalische und Theoretische Chemie, Universität Bonn, Wegelerstr. 12, D-53115 Bonn, Germany. theochem@thch.uni-bonn.de

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New double hybrid density functionals (DFT) incorporate nonlocal correlation for improved accuracy. These methods, like B2-PLYP, offer superior molecular geometries and reduced errors in quantum chemical calculations.

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Materials Science

Background:

  • Density Functional Theory (DFT) is a widely used method in quantum chemistry.
  • Standard hybrid DFT methods incorporate a fraction of exact exchange but rely on semilocal functionals for correlation.
  • A new class of double hybrid functionals has been proposed, incorporating a fraction of nonlocal correlation energy.

Purpose of the Study:

  • To extend the applicability of new double hybrid functionals to the calculation of analytic gradients for potential energy surface exploration.
  • To implement and test these functionals for various chemical systems, including main group and transition metal species.
  • To assess the accuracy of the new functionals for molecular geometries compared to existing methods.

Main Methods:

  • Development and implementation of analytic gradient theory for double hybrid functionals, including PT2 gradients with exchange-correlation terms.
  • Inclusion of support for closed-shell and spin-unrestricted reference determinants.
  • Accommodation of external point charge fields and continuum solvation models (conductor-like screening model).
  • Application of the density fitting resolution of the identity (RI) approximation for computational efficiency.

Main Results:

  • The B2-PLYP double hybrid functional demonstrates excellent performance in predicting molecular geometries.
  • Calculated geometries are superior to those obtained from standard DFT and MP2 methods.
  • The computational cost of double hybrid gradients is approximately four times that of standard hybrid DFT gradients for systems with ~500-600 basis functions.

Conclusions:

  • Double hybrid functionals represent a significant advancement in DFT, offering improved accuracy for thermochemical properties and molecular geometries.
  • The analytic gradient implementation enables efficient exploration of potential energy surfaces for these advanced functionals.
  • These methods provide a powerful tool for accurate electronic structure calculations across a range of chemical systems.