# Real-Time Coupled Cluster Theory with Approximate Triples

## TL;DR

This paper introduces a real-time coupled cluster method with approximate triples to study electron correlation effects efficiently.

## Contribution

A new time-dependent CC3 implementation with approximate triples and GPU acceleration is introduced for real-time calculations.

## Key findings

- GPU acceleration speeds up calculations by up to 13 times for water clusters.
- Single-precision arithmetic shows negligible errors in polarizabilities but larger errors in hyperpolarizabilities.
- RT-CC3 results are within 1% error of linear response CC3 for water molecule properties.

## Abstract

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 (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.