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We present a theory for accelerating basis convergence in double-hybrid approximations using the density-based basis-set correction (DBBSC) method. Our findings show DBBSC efficiently improves accuracy for molecular calculations.

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Theoretical Chemistry

Background:

  • Double-hybrid approximations are widely used in quantum chemistry for accurate molecular property predictions.
  • Basis set convergence, the process of achieving results independent of the chosen basis set, is crucial for reliable calculations.
  • Accelerating basis set convergence in double-hybrid methods is an ongoing challenge.

Purpose of the Study:

  • To develop the theoretical framework for applying the density-based basis-set correction (DBBSC) method to double-hybrid approximations.
  • To investigate the impact of uniform coordinate scaling on the accuracy of DBBSC in double-hybrid calculations.
  • To demonstrate the efficiency of DBBSC in accelerating basis set convergence for double-hybrid methods.

Main Methods:

  • Development of the theoretical justification for DBBSC applied to one-parameter double hybrids.
  • Analysis of the exact dependence of the basis-set correction functional on the coupling-constant parameter (λ).
  • Inclusion of uniform coordinate scaling of density and basis functions by a factor of 1/λ.

Main Results:

  • The exact theory reveals that uniform coordinate scaling is integral to the DBBSC functional for double hybrids.
  • Test calculations on molecular atomization energies and reaction barrier heights confirm DBBSC's effectiveness.
  • Neglecting uniform coordinate scaling in DBBSC for double hybrids was found to be a reasonable approximation in practice.

Conclusions:

  • The DBBSC method significantly accelerates basis set convergence for double-hybrid approximations.
  • The developed theory provides a robust foundation for applying DBBSC to enhance computational efficiency and accuracy.
  • The study validates the practical utility of DBBSC, even when simplifying assumptions regarding coordinate scaling are made.