A straightforward a posteriori method for reduction of density-fitting error in coupled-cluster calculations

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Density-fitting approximations are widely used to reduce the computational cost of coupled-cluster (CC) calculations.
• However, these approximations introduce errors in the calculated total energies.
• Accurate removal of these errors is crucial for reliable CC energy predictions.

Purpose of the Study:

• To develop a simple, a posteriori method for correcting density-fitting errors in coupled-cluster energies.
• To assess the effectiveness of the proposed method for various molecular systems and basis sets.
• To evaluate the computational cost associated with the error correction procedure.

Main Methods:

• The method treats the difference between exact and density-fitted integrals as a perturbation.
• Simplified response-like equations are employed to compute corrected amplitudes and energy corrections.
• The approach is tested at the coupled-cluster singles and doubles (CCSD) level of theory.

Main Results:

• Significant fractions of density-fitting error were removed from total coupled-cluster energies.
• Average error reductions of approximately 10-fold and 20-fold were observed with double-zeta and triple-zeta basis sets, respectively.
• Similar error reductions were achieved for interaction energies of model complexes.

Conclusions:

• The proposed method effectively corrects density-fitting errors in coupled-cluster calculations.
• The computational cost is minimal compared to the main CC iterations.
• The method's applicability extends beyond density-fitting to other integral decomposition schemes.