Development and implementation of new efficient strategies to evaluate excitation energies and molecular properties for multi-reference systems

In this thesis we develop and implement new strategies to push the limits of the CASSCF method in computing excitation energies using both the State-Average (SA) and Linear Response (LR) formalisms, as well as transition (SA and LR) and response (LR) molecular properties. Concerning SA, our strategy consists in using two distinct alternative Full-CI solvers, namely Many-Body Expansion – Full Configuration Interaction (MBE-FCI) and the Density Matrix Renormalization Group (DMRG). These, coupled with the Cholesky Decomposition (CD) of the two-electron integrals, push the application of the SA–CASSCF method to larger molecules in extended active spaces such as the Fe(II)-tetraphenylporphyrin and the carotenoid lutein. To tackle the numerical problem associated with LR, we develop a new library (DiagLib) featuring several robust eigensolvers, including the new Swapped Metric Orthogonal – Generalized Davidson (SMO-GD) algorithm for the solution of the LR–CASSCF equations both in the resonant case and in presence of an external frequency. SMO-GD proves to be competitive with state of the art methods and it is applied to compute spectra and properties of a large chromophore.