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

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.