Analytic energy gradients for the coupled-cluster singles and doubles method with the density-fitting approximation

Area of Science:

• Computational Chemistry
• Quantum Chemistry

Background:

• Coupled-cluster singles and doubles (CCSD) is a high-accuracy quantum chemistry method.
• Analytic gradients are crucial for molecular property calculations.
• Conventional CCSD gradient calculations can be computationally expensive for large systems.

Purpose of the Study:

• To present an efficient implementation of analytic gradients for the density-fitting CCSD (DF-CCSD) method.
• To accelerate the computation of gradient terms in CCSD calculations.
• To assess the accuracy and efficiency of the DF-CCSD gradient method.

Main Methods:

• Implementation of analytic gradients for DF-CCSD, including frozen core approximations.
• Optimization of key computational steps: particle density matrix (PDM) and generalized Fock-matrix (GFM) computation, Z-vector equation solution, and back-transformations.
• Avoidance of four-index electron repulsion integrals and the four-index two-particle density matrix (TPDM) by utilizing 2- and 3-index TPDMs.

Main Results:

• DF-CCSD analytic gradients show significant acceleration compared to conventional CCSD for larger molecules.
• An 8-fold speedup was observed for the gradient terms of C10H22 using the cc-pVTZ basis set.
• The DF approach avoids the costly computation and storage of four-index integrals and TPDMs.

Conclusions:

• The developed DF-CCSD method provides a computationally efficient approach for calculating analytic gradients.
• The method introduces negligible errors in equilibrium bond lengths and harmonic vibrational frequencies.
• This advancement enables more accurate and feasible calculations for larger molecular systems.