Energy correction and analytic energy gradients due to triples in CCSD(T) with spin-orbit coupling on graphic processing units using single-precision data

Calculating the contribution of triples ((T)) to the correlation energy, the density matrices and the constant terms in the ? equation is the most expensive steps in obtaining analytic energy gradients for the CCSD(T) approach. In this work, we report the implementation of these steps for the CCSD(T) method with spin-orbit coupling (SOC) included in post-self-consistent-field calculations (SOC-CCSD(T)) using single-precision data on a consumer GPU card to accelerate calculations. The developed program can be used for calculations on GPU with single-precision data or on CPU with either single- or double-precision data. According to our results, calculating the (T) correlation energy in SOC-CCSD(T) on GPU with single-precision data is about 7-10 times faster for the investigated molecules than that on CPU with double-precision data, and it is 5-9 times faster in calculating the (T) part of analytic energy gradients for the SOC-CCSD(T) method. Our results indicate that loss of accuracy for energy gradients and equilibrium structures using single-precision data is negligible, while a mixed-precision calculation is needed for the (T) correlation energy. In calculating harmonic frequencies based on finite difference of analytic energy gradients, a larger step size is required to achieve accurate results for certain vibrational modes with single-precision data.