• configuration interaction
• density matrix renormalization group
• electronic correlation
• quantum chemistry
• quantum monte carlo

The purpose of this thesis work is to present a new ab-initio strategy to perform molecular electronic structure calculations on medium size systems.
Such a strategy goes beyond the Hartree-Fock level of the theory and implements efficient post Hartree-Fock methods.
In principle, the most accurate approach to the problem is the Full-Configuration Interaction (FCI) method (or exact diagonalization) but its exponential scaling with the dimension of the system makes it intractable except for small molecules. Therefore, we utilized an approximated way to perform FCI calculations with a reduced computational cost, namely the Density Matrix Renormalization Group (DMRG) method. It consists in a variational optimization over a class of wave functions called Matrix Product State (MPS) which gives a polynomial scaling with the size of the system, instead of exponential, allowing the treatment of medium-large systems. We applied DMRG with the purpose of accounting for all valence electrons in their valence shell. This choice is shown to be able to account for almost all the so-called static correlation contribution between electrons. We than added the dynamical contribution by the Quantum Monte Carlo (QMC) method which has been used in a second step starting from the leading configurations extracted from the DMRG calculation. In quantum chemistry the application of both these methods used together represents a state of the art computational methodology for strong electronic correlation in medium and large size molecular systems. As illustrative examples, we compute the ground and excited
state energies for four different types of molecules focusing our work on the analysis of the computational time scaling with respect to the dimension of the system, the calculation of vertical transition energies and the construction of a total energy surface. We compared our results with the literature and we found a good agreement. All calculations have been done with the inclusion of a large number of electrons.
These same calculations would have been difficult to perform with standard methods.