• second-order optimization
• MCSCF
• direct algorithm
• Cholesky decomposition
• CASSCF
• two-electron integrals

CASSCF calculations are often performed in order to get a qualitatively correct description of multi-reference systems.
However, for large molecules with a small active space, the manipulation of the two-electron repulsion integral matrix elements represents the bottleneck of the method.
For this reason, long computational times together with difficult convergence properties led to the search for efficient numerical techniques capable of speeding up the algorithm.
In this thesis we implement a second-order CASSCF algorithm that exploits the Cholesky decomposition of the two-electron repulsion integral matrix.
The Cholesky decomposition technique efficiently reduces the computational cost associated with integral tensor operations, allowing to perform ab initio calculations on extended systems.
Numerical tests on aromatic molecules and on two biologically relevant chromophores show good overall performances that allow us to extend the applicability of the CASSCF method to larger systems.