Efficient implementation of molecular CCSD gradients with Cholesky-decomposed electron repulsion integrals

We present an efficient implementation of ground and excited state CCSD gradients based on Cholesky-decomposed electron repulsion integrals. Cholesky decomposition, like density-fitting, is an inner projection method, and thus similar implementation schemes can be applied for both methods. One well-known advantage of inner projection methods, which we exploit in our implementation, is that one can avoid storing large V³ O and V⁴ arrays by instead considering three-index intermediates. Furthermore, our implementation does not require the formation and storage of Cholesky vector derivatives. The new implementation is shown to perform well, with less than 10% of the time spent calculating the gradients in geometry optimizations. The computational time spent per optimization cycle are furthermore found to be significantly lower compared to other implementations based on an inner projection method. We illustrate the capabilities of the implementation by optimizing the geometry of the retinal molecule (C₂0H₂₈O) at the CCSD/aug-cc-pVDZ level of theory.