Optimized Pair Natural Orbitals for the Coupled Cluster Methods

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Coupled-cluster singles and doubles (CCSD) is a high-accuracy quantum chemistry method.
• Standard CCSD methods face computational scaling challenges with system size.
• Pair natural orbitals (PNOs) are used to compress the CCSD wave operator, reducing computational cost.

Purpose of the Study:

• To develop an optimized PNO-based CCSD method that minimizes truncation errors.
• To improve the accuracy of PNO-CCSD calculations, especially for large PNO ranks.
• To assess the effectiveness of iteratively optimized PNOs (iPNOs) and perturbative corrections.

Main Methods:

• Formulation of the CCSD method using truncated PNOs.
• Iterative optimization of PNOs (iPNOs) to minimize truncation effects.
• Combination of iPNO optimization with Neese's perturbative correction for PNO incompleteness.

Main Results:

• iPNOs offer moderate improvements for small PNO ranks and significant gains for large ranks.
• PNO truncation errors in CCSD energy are reduced by orders of magnitude in the asymptotic regime.
• The combined iPNO optimization and perturbative correction yields highly accurate approximations to canonical CCSD energies.
• Benchmark calculations show improvements of up to two orders of magnitude in noncovalent binding energies compared to standard PNO approaches.

Conclusions:

• Iteratively optimized PNOs provide a robust strategy for accurate and efficient CCSD calculations.
• The combination of iPNO optimization and perturbative correction is particularly effective for achieving high precision.
• This method significantly reduces computational cost while maintaining high accuracy for electronic structure calculations.