  A Cholesky decomposition (CD)-based implementation of relativistic
two-component coupled-cluster (CC) and equation-of-motion CC (EOM-CC) methods
using an exact two-component Hamiltonian augmented with atomic-mean-field
spin-orbit integrals (the X2CAMF scheme) is reported. The present CD-based
implementation of X2CAMF-CC and EOM-CC methods employs atomic-orbital-based
algorithms to avoid the construction of two-electron integrals and
intermediates involving three and four virtual indices. Our CD-based
implementation extends the applicability of X2CAMF-CC and EOM-CC methods to
medium-sized molecules with the possibility to correlate around 1000 spinors.
Benchmark calculations for uranium-containing small molecules have been
performed to assess the dependence of the CC results on the Cholesky threshold.
A Cholesky threshold of $10^{-4}$ is shown to be sufficient to maintain
chemical accuracy. Example calculations to illustrate the capability of the
CD-based relativistic CC methods are reported for the bond-dissociation energy
of the uranium hexafluoride molecule, UF$_6$, with up to quadruple-zeta basis
sets, and the lowest excitation energy in solvated uranyl ion
[UO$_2^{2+}$(H$_2$O)$_{12}$].
