Universal perturbative explicitly correlated basis set incompleteness correction.

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Basis set incompleteness is a significant error source in electronic wave function approximations.
• Accurate correlation energies are crucial for predicting molecular properties and reaction pathways.

Purpose of the Study:

• To develop a robust method for reducing basis set incompleteness error.
• To introduce a computationally efficient second-order perturbative correction using explicitly correlated geminal functions.

Main Methods:

• Employing a second-order perturbative correction with explicitly correlated, internally contracted geminal functions.
• Utilizing R12 technology and screening approximations to reduce computational cost.
• Evaluating the Hylleraas functional for the energy correction.

Main Results:

• The [2](R12) correction significantly reduces basis set incompleteness error.
• The method requires only two-electron reduced density matrices and integrals with R12 technology.
• Achieved aug-cc-pVQZ quality correlation energies using only an aug-cc-pVDZ basis for HF and N2.

Conclusions:

• The [2](R12) correction offers a computationally feasible way to obtain high-accuracy correlation energies.
• This method can be combined with a wide range of existing quantum chemistry computational methods.
• It enables accurate electronic structure calculations with smaller, more manageable basis sets.