Efficient implementation of effective core potential integrals and gradients on graphical processing units

Effective core potential integral and gradient evaluations are accelerated via implementation on graphical processing units (GPUs). Two simple formulas are proposed to estimate the upper bounds of the integrals, and these are used for screening. A sorting strategy is designed to balance the workload between GPU threads properly. Significant improvements in performance and reduced scaling with system size are observed when combining the screening and sorting methods, and the calculations are highly efficient for systems containing up to 10 000 basis functions. The GPU implementation preserves the precision of the calculation; the ground state Hartree-Fock energy achieves good accuracy for CdSe and ZnTe nanocrystals, and energy is well conserved in ab initio molecular dynamics simulations.