Thesis outline

The thesis is organized as follows:

• In the first chapter we briefly review QMC methods mainly used in this thesis, the Variational Monte Carlo. Then we introduce the pairing wave-function used to study molecular and solid systems.
• In the second chapter two optimization methods, used in VMC, are presented: Stochastic Reconfiguration(SR) and Stochastic Reconfiguration with Hessian acceleration (SRH). Advantages, limitations, tips and tricks are shown for both of them.

• In the third chapter we show the results obtained by applying the paring wave-function to different molecular systems.

• In the beginning of the fourth chapter we show how to generalize the pairing function to study extended systems. Then we come back for a while to technical aspects of simulation of periodic systems.

• In the fifth chapter a new method to simulate systems at finite temperature is presented. This technique has allowed us to perform ionic dynamics using noisy forces coming from Quantum Monte Carlo.

• In the last chapter we show preliminary results obtained on high-pressure hydrogen, using our new technique. Moreover our results allowed us to guess a new possible exotic phase in high pressure hydrogen driven by the electronic correlation.