Approaches in Deciphering Zero-Point Energy Effects for Molecular Clusters Using Diffusion Monte Carlo

Abstract

Deciphering the differences of the structures formed with bulk water and the effects of isotopic substitution has been of interest. Studies of water clusters provide a connection to the intermediate cases between a water monomer and bulk water. Water clusters are an attractive system to study due to the fact that experimental and theoretical methods can be used to study the same cluster. However, one main challenge are the amounts of low-lying minima that are exhibited as the size of the cluster increases. When only the electronic energy is considered, finding the minimum energy structure of these clusters is an active field of work. However, when zero-point energy is added, determining the minimum energy structure of a particular sized cluster becomes even more difficult. Deuteration can also change the structures that are relevant in the vibrational ground state. One prime example is the water hexamer, where the minimum energy structure is the prism. Once zero-point energy is considered, the minimum energy structure is the cage. However, the deuterated form of water hexamer has been assigned as the prism structure based on microwave spectroscopy. Diffusion Monte Carlo (DMC) is a method that has been used to study water clusters in the vibrational ground state. However, large ensemble sizes are needed to ensure reliable results. For these calculations, this is due to the nature of the couplings between the high and low frequency vibrations. One method to reduce the ensemble sizes needed for these calculations is to introduce a guiding function. The guiding function, $\Psi_{T}$, is used to enhance sampling in the relevant regions of the potential energy surface. When a guiding function is introduced into the DMC algorithm, the local energy, $\hat{H}\Psi_{T}/\Psi_{T}$, is evaluated, rather than just the potential energy. In this thesis, I first explore the choice of $\Psi_{T}$ and use this approach to evaluate the overlap integral of $\Psi_{T}$ and the wave function calculated using DMC. I show that even using guiding functions as simple as a product of harmonic oscillators can accurately compute the ground state energies of extremely anharmonic molecules, such as the partially deuterated analogues of H$_{3}^{+}$. Based on these results, I construct a simple guiding function that describes the intramolecular vibrations of each isolated water monomer within a water cluster. I find that the ensemble size needed to calculate ground state energies and ground state wave functions of various sized water clusters is reduced by at least an order of magnitude. This DMC approach can be extended beyond water clusters, and can be used to study a broad range of molecules that exhibit couplings in the high and low frequency vibrations. I use this guiding function to study the effects of isotopic substitution in water hexamer. I find that for (H$_{2}$O)$_{6}$, the ground state wave function is the cage. I also find that (D$_{2}$O)$_{6}$ is also a cage, but the ground state energy difference between the cage and prism structures is only 9 cm$^{-1}$. These studies provide the groundwork for further investigation of the strength of hydrogen bonds in water hexamer.