A Density-Based Basis-Set Correction for Wave Function Theory.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Basis-set incompleteness is a significant source of error in quantum chemical calculations.
• Accurate prediction of molecular properties requires extrapolation to the complete basis-set (CBS) limit.
• Existing methods for basis-set correction often lack universality or require empirical parameters.

Purpose of the Study:

• To introduce a universal density-based correction for basis-set incompleteness.
• To enable accurate energy calculations near the CBS limit using compact Gaussian basis sets.
• To avoid the need for ad hoc range-separation parameters in density-functional theory.

Main Methods:

• Development of a density-based correction utilizing short-range correlation density functionals.
• Application of range-separated density-functional theory (RS-DFT) with an adaptive, spatially dependent range-separation function μ(r).
• Estimation of basis-set incompleteness error based on the spatial nonhomogeneity of the error.

Main Results:

• The proposed correction accurately vanishes in the complete basis-set (CBS) limit.
• Demonstrated accurate calculation of CCSD(T) atomization and correlation energies for the G2 set of molecules.
• Achieved near-CBS limit accuracy using compact Gaussian basis sets.

Conclusions:

• The universal density-based correction effectively addresses basis-set incompleteness.
• This method provides a robust and parameter-free approach to improve wave function calculations.
• The adaptive RS-DFT scheme offers a promising avenue for high-accuracy computational chemistry.