Double-hybrid density-functional theory with density-based basis-set correction

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.