Project Details
Projekt
Ground states of nanoconfined water chains via density matrix renormalization group and restricted Boltzmann machines
Applicant
Dr. Tobias Serwatka
Subject Area
Theoretical Chemistry: Electronic Structure, Dynamics, Simulation
Term
from 2022 to 2024
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 503971734
The objective of this project is the theoretical modelling and investigation of water chains, which includes free chains as well as chains for which every molecule is placed inside a fullerene. These nanoconfined 1D-systems are experimentally available and show, compared to their naturally occuring phases, rather unusual physical effects, e.g. quantum phase transitions and relatively long lifetimes of excited nuclear spin states. The development and implementation of quantum mechanical methods to calculate exact ground states of such high dimensional systems is a challenging task which will be approached in two ways.On the one hand, the existing density matrix renormalization group (DMRG) method shall be extended to treat also molecular translations in addition to molecular rotations. In doing so, it shall be investigated if the chains form zig-zag structures or motifs with different intermolecular distances within a chain. Also the nuclear spin conversion mechanism shall be studied which requires the inclusion of spin degrees of freedom and spin-rotation coupling in the existing DMRG method. Besides, the influence of electric fields as well as fullerene cages on the water-water interactions shall be investigated, in particular with regard to the occurrence and modelling of quantum phase transitions.On the other hand, the ground states shall be calculated by using a special class of neural networks, so-called restricted Boltzmann machines (RBM). RBMs shall be developed to reconstruct the ground state from precalculated input data. Such a network would also be able to reconstruct the wave function from experimental data which makes it a valuable tool for the experimental study of quantum systems. Afterwards the RBM shall be used as ansatz for the wave function in combination with a Monte-Carlo technique in order to calculate the ground state variationally. The appealing feature of that approach is the flexibility of the generic ansatz of the wave function, i.e. it is no longer necessary to find a system specific, physically motivated model for the wave function. Besides, compared to DMRG the stochastic method allows the calculation of larger systems and stronger interactions. This shall be used to describe water chains with small intermolecular distances at which the formation of hydrogen bonds becomes a dominant factor.
DFG Programme
WBP Fellowship
International Connection
Canada
