Efficient Implementation of Relativistic Coupled Cluster Linear Response Theory in Combination with Perturbation Sensitive Natural Spinors and Cholesky Decomposition Treatment of Two-electron Integrals

Abstract: We present an efficient implementation of the low-cost linear-response coupled-cluster singles and doubles (LR-CCSD) method for computing static and frequency-dependent polarizabilities in systems with significant relativistic and electron-correlation effects. The approach employs X2C-based Hamiltonians (X2CAMF and X2CMP) and incorporates Cholesky decomposition to reduce memory requirements. In the current implementation, costly three- and four-external index integrals are generated on the fly, eliminating the need for their storage. Benchmark results indicate that the X2CMP Hamiltonian provides more consistent performance than X2CAMF, particularly for large and highly augmented basis sets. The proposed FNS++CD-X2CMP-LR-CCSD method shows excellent agreement with four-component reference values across a wide range of systems. Additionally, different strategies for constructing the FNS++ basis were assessed, and an averaged density approach was found to offer a favorable balance between accuracy and computational cost. On average, about 73% of the virtual spinor space is removed, demonstrating the efficiency and consistency of the FNS++ density-based truncation approach. The present implementation enables accurate and scalable relativistic response calculations for large molecular systems, as demonstrated by the calculation of the static polarizability of the Uranium Hexafluoride complex with a triple-zeta basis set more than 1400 basis functions.