Ab initio molecular dynamics of water by quantum Monte Carlo

The chapter 2, we deal with the challenge b). It focuses on the variational Monte Carlo (VMC) and the wavefunction optimization methods based on VMC. The performance of different methods are displayed through the op- timization of the Jastrow factor in our test case Beryllium dimer and the efficiency is improving surprisingly during the evolution of these methods. In chapter 3, we focus on the challenge a). It describes the wavefunc- tion ansatz used by our simulation. In this thesis, we introduce the atomic hybrid orbitals which significantly increase the compactness of our wavefunc- tion without hurting accuracy. This chapter also explain how to optimize the determinant in a way that the number of variational parameters scales only linearly with the system size. This further helps the efficiency of the wavefunction optimization. In chapters 4 and 5, the issue c) is explained in detail. In chapter 4, a second order Langevin dynamics (SLD) scheme is devised particularly for QMC and this thesis improves this scheme by developing a better integration method. Here, we also highlight the remarkable power of the force covari- ance matrix which can be defined only in QMC and is capable of accelerating the slow modes of a dynamics. In chapter 5, this SLD for QMC is validated through intensive benchmarking on the calculation of the vibrational frequen- cies of water and other small molecules. It is shown that many systematic biases in our MD scheme and QMC evaluation can be controlled so that we are confident to push forward this ab initio molecular dynamics for applica- tions on large systems. Finally in chapter 6, we perform the simulation of liquid water with all the preparation done in the previous chapters. The results are encouraging since we’ve closed the discrepancy of the peak positions of RDFs between experi- ments and ab initio simulations. The power of QMC is also demonstrated by the fact that the shapes of our RDFs are much less structured than previous DFT-based ab initio simulations even if the two water molecule interaction is dealt with the same level of accuracy as the DFT/BLYP calculation. In this chapter, we have also studied the features of hydrogen bonds in our simulation of liquid water. All our results indicate that it is important to consider the quantum nature of the ions for a faithful description of liquid water. This will be left for future studies, possible in principle even within the QMC approach.