• CFOUR
• Cholesky decomposition
• computational chemistry
• Dyall spin separation
• electron-repulsion integrals
• electronic-structure theory
• Hartree Fock
• kinetic balanc
• no-pair approximation
• physical chemistry
• relativistic quantum chemistry
• spin-free Dirac-Coulomb Choleksy decomposition
• spin-free Dirac-Coulomb hamiltonian
• theoretical chemistry

Relativistic effects are classified as scalar effects (or spin-free effects) and spin-orbit coupling effects, and become crucial when dealing with electronic-structure calculations of molecules containing heavy-metal atoms. Due to the dominance of the scalar relativity it is convenient to perform the Dyall spin separation in order to obtain a genuine spin-free Dirac-Coulomb Hamiltonian. The 4-component structure of the wave function leads to a higher number of two-electron integrals to be computed than the non-relativistic case. From a computational point of view the electron repulsion integrals represent one of the main bottleneck, especially the required memory to store them, and in the last decades various algorithms were developed to efficiently reduce the cost. The Cholesky decomposition technique is the one we are interested in. In fact, the central aim of this work is to propose a novel and efficient Cholesky decomposition implementation based on the recent two-step algorithm, for a spin-free Dirac-Coulomb Hamiltonian. Consequently, a Cholesky decomposed spin-free Dirac-Coulomb SCF algorithm was implemented; furthermore, thanks to the no-pair approximation it is provided an implementation of a Cholesky decomposed spin-free Dirac-Coulomb CCSD. The final part of this work focuses on several numerical tests in order to ensure the effectiveness and the efficiency of our novel implementations, using both small molecular systems and larger ones up to 1308 basis functions per component.