Accurate extrapolation of electron correlation energies from small basis sets

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Accurate calculation of electron correlation energies is crucial for predicting molecular properties.
• Extrapolation schemes are used to estimate energies from finite basis sets to the complete basis set limit.
• Existing methods have limitations in accurately capturing convergence rates for different molecular systems.

Purpose of the Study:

• To develop a novel two-point extrapolation scheme for electron correlation energies.
• To improve the accuracy of basis set truncation error estimation.
• To provide a more reliable method for computational chemistry studies.

Main Methods:

• Proposed a new two-point extrapolation formula incorporating an angular momentum offset (xi(i)).
• The formula is deltaE(X) proportional, variant(X + xi(i))(-gamma).
• Calibrated three parameters using 105 reference molecules for MP2 and CCSD energies from double- and triple-zeta (DT) and triple- and quadruple-zeta (TQ) basis sets.

Main Results:

• The new model is 3-5 times more accurate than previous single-parameter two-point schemes.
• TQ extrapolations using the new model outperform conventional asymptotic formula extrapolations from larger basis sets (56).
• Satisfactory results were obtained for boron compounds and neon.

Conclusions:

• The proposed extrapolation scheme offers a significant improvement in accuracy for electron correlation energies.
• The angular momentum offset effectively accounts for differences in convergence rates.
• This method provides a more robust tool for computational chemistry, especially when using smaller basis sets.