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Abstract Quantum Monte Carlo (QMC) is one of the most promising methods for solving quantum many body problems. However, in QMC methodology it is generally desirable to use the simplest possible trial wavefunction since the most computationally intensive part of any QMC simulation is evaluating the trial wavefunction and its derivatives. Therefore, using highly correlated methods for wavefunction construction in QMC are limited to comparatively small molecular systems. Instead, density functional theory DFT is an efficient and popular way for constructing the QMC initial orbitals and at the same time maintaining a reasonable scaling with system size. However, the mean obstacle of DFT is that the true exchange-correlation density functional is unknown and the accuracy of these exchange-correlation functionals depends on a particular application. On the other hand, studying rare-earth containing systems is still a challenge for both experimentalists and theoreticians. Despite, their technologically importance, many of their properties remain unknown. In this regard, the objective of this work is to use the QMC, and more specifically the DMC method, employing the suitable DFT trial function to provide insights and predictions of some physical properties of species involving these elements. To this aim, we assess the performance of a range of DFT, including pure, hybrid, and long-range corrected functionals as well as Hartree-Fock function in order to select the best starting place for our QMC trial function for systems containing rareearths. This thesis is also relevant to calculate the potential energy curves PECs for the lowlying states of lanthanum monoboride, monocarbide and monophosphide neutrals and anions using the DMC method combined with three different trial functions. from the fitted PECs, spectroscopic constants have been numerically determined and the ground states have been assigned. For diatomic lanthanum boride and carbide, our results have been compared with the only theoretical work exists in literature; however, predictions have been provided for lanthanum phosphide which has not been explored yet. Moreover, variations of the dipole moments with internuclear distances for the low-lying states of the former neutral species have been studied and analyzed. Having obtained the best DFT exchange-correlation functional convenient for actinides, we also present in this thesis the first attempts to study the electronic structure of actinide monohydrides and monofluorides by means of the DMC method. Ground state total energies, bond lengths, dissociation energies, and dipole moments have been reported. Our results compare well with the few data available in literature, confirming the ability of the DMC method to successfully describe the physical properties of these molecules. Finally, an outlook on future topics of interest has been presented. |