Analytic energy gradients for the coupled-cluster singles and doubles with perturbative triples method with the...

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Analytic gradients are crucial for molecular property calculations.
• Coupled-cluster singles and doubles with perturbative triples [CCSD(T)] is a high-accuracy electronic structure method.
• Computational cost can be a bottleneck for large systems.

Purpose of the Study:

• To develop and implement an efficient density-fitting (DF) approximation for CCSD(T) analytic gradients.
• To assess the computational speedup and accuracy of the DF-CCSD(T) method.
• To reduce the computational burden of high-accuracy quantum chemical calculations.

Main Methods:

• Implementation of analytic gradients for the density-fitting approximation of CCSD(T) [DF-CCSD(T)].
• Utilized 2- and 3-index two-particle density matrices (TPDMs) instead of 4-index TPDMs.
• Avoided the use of four-index two-electron integrals in gradient term evaluation.

Main Results:

• The DF-CCSD(T) method achieved a speedup of more than 2-fold for analytic gradients compared to conventional CCSD(T).
• Computational time for C6H14 analytic gradients reduced from 106.2 h [CCSD(T)] to 49.8 h [DF-CCSD(T)].
• Errors introduced by the DF approximation were found to be negligible for equilibrium geometries and harmonic vibrational frequencies.

Conclusions:

• The density-fitting approximation provides a substantial acceleration for CCSD(T) analytic gradients.
• DF-CCSD(T) is a computationally efficient and accurate method for electronic structure calculations.
• This approach significantly reduces computational cost without compromising accuracy.