Real-Time Coupled Cluster Theory with Approximate Triples

In order to explore the effects of high levels of electron correlation on the real-time coupled cluster formalism and algorithmic behavior, we introduce a time-dependent implementation of the CC3 singles, doubles, and approximate triples method. We demonstrate the validity of our derivation and implementation using specific applications of frequency-dependent properties. Terms with triples are calculated and added to the existing CCSD equations, giving the method a nominal $O$(N⁷) scaling. We also use a graphics processing unit accelerated implementation to reduce the computational cost, which we find can speed up the calculation by up to a factor of 13 for test cases of water clusters. In addition, we compare the impact of using single-precision arithmetic compared to conventional double-precision arithmetic. We find no significant difference in polarizabilities and optical-rotation tensor results but a somewhat larger error for first hyperpolarizabilities. Compared to linear response CC3 results, the percentage errors of RT-CC3 polarizabilities and RT-CC3 first hyperpolarizabilities are under 0.1 and 1%, respectively, for a water-molecule test case in a double-ζ basis set. Furthermore, we compare the dynamic polarizabilities obtained using RT-CC3, RT-CCSD, and time-dependent nonorthogonal orbital-optimized coupled cluster doubles (TDNOCCDs) in order to examine the performance of RT-CC3 and the orbital-optimization effect using a set of ten-electron systems.