Graphics Processing Unit-Accelerated Density-Fitting Coupled-Cluster and Equation-of-Motion Coupled-Cluster Methods with Spin–Orbit Coupling

Coupled-cluster (CC) programs incorporating spin-orbit coupling (SOC) within the density-fitting (DF) approximation have been developed in this work. The implementations include DF-SOC-CCSD and DF-SOC-CCSD(T) for ground-state calculations and DF-SOC-EOM-EE-CCSD for excitation energies. The DF approximation reduces memory and disk usage, while a spin-independent formulation simplifies the code and enables efficient graphics processing unit (GPU) acceleration. Spatial symmetry and single/double precision are also supported to enhance computational efficiency. Benchmark calculations on heavy-element systems show that the DF approximation introduces negligible errors and accurate SOC splittings are maintained even with single-precision arithmetic. GPU acceleration exhibits good scalability, achieving a more than 5-fold speedup for larger systems until I/O operations become the limiting factor. The developed DF-SOC-CC program suite provides an accurate and efficient approach for electronic structure calculations of heavy-element systems involving SOC.