DEVELOPMENT OF ALGORITHMS FOR CLASSICAL AND SEMICLASSICAL DYNAMICS
type: CreativeWork
description: Driven by questions regarding the significance of atom-atom correlations, this research introduces novel concepts and algorithms aimed at discerning whether or not a molecule is composed of a collection of approximately independent vibrating fragments. Specifically, from a time-dependent perspective, the uncorrelated degrees of freedom must obey Liouville theorem or, more generally, conserve the symplectic form of the Hamiltonian flow. We present a practical approach to identify such vibrating fragments utilizing data collected from molecular dynamics simulations. Our method is based on a heuristic evolutionary algorithm that we call the Probability-Graph Evolutionary Algorithm (PGEA). We demonstrate its usefulness with applications on both model systems and ab initio potentials. We implement these analyses for semiclassical theories, in which the symplectic monodromy matrix naturally occurs. When the calculation of the monodromy matrix becomes prohibitively expensive, we show how to use a neural gas algorithm to tessellate the phase space traversed by trajectories and approximate the local curvature of the potential. We further investigate the correlation among atoms with an experimentalist mindset: We want to artificially “decouple” pairs of atoms and see how the sys tem as a whole rearranges. In practice, we run simulations of artificially modified potentials (called the pair-decoupled potential), in which selected pairs of atoms (or degrees of freedom) do not perceive each other’s displacement. When this artificial disturbance takes place, it affects the molecule as a whole, resulting in a loss (or gain) in energy. A measure of the average energy lost allows to understand if the decoupled pairs can or cannot be seen as belonging to approximately independent groups. To evolve a system under the pair-decoupled potential we provide a practical numerical integration rule, which is based on a local harmonic approximation of the potential, yet it preserves the symplec…
abstract: Driven by questions regarding the significance of atom-atom correlations, this research introduces novel concepts and algorithms aimed at discerning whether or not a molecule is composed of a collection of approximately independent vibrating fragments. Specifically, from a time-dependent perspective, the uncorrelated degrees of freedom must obey Liouville theorem or, more generally, conserve the symplectic form of the Hamiltonian flow. We present a practical approach to identify such vibrating fragments utilizing data collected from molecular dynamics simulations. Our method is based on a heuristic evolutionary algorithm that we call the Probability-Graph Evolutionary Algorithm (PGEA). We demonstrate its usefulness with applications on both model systems and ab initio potentials. We implement these analyses for semiclassical theories, in which the symplectic monodromy matrix naturally occurs. When the calculation of the monodromy matrix becomes prohibitively expensive, we show how to use a neural gas algorithm to tessellate the phase space traversed by trajectories and approximate the local curvature of the potential. We further investigate the correlation among atoms with an experimentalist mindset: We want to artificially “decouple” pairs of atoms and see how the sys tem as a whole rearranges. In practice, we run simulations of artificially modified potentials (called the pair-decoupled potential), in which selected pairs of atoms (or degrees of freedom) do not perceive each other’s displacement. When this artificial disturbance takes place, it affects the molecule as a whole, resulting in a loss (or gain) in energy. A measure of the average energy lost allows to understand if the decoupled pairs can or cannot be seen as belonging to approximately independent groups. To evolve a system under the pair-decoupled potential we provide a practical numerical integration rule, which is based on a local harmonic approximation of the potential, yet it preserves the symplec…
author: GANDOLFI, MICHELE
language: eng
date published: 2024-02-13
date modified: 2026-07-27T20:18:56Z
provider: Università degli Studi di Milano
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: Università degli Studi di Milano

PropertyValue
property ID: Handle
value: https://hdl.handle.net/2434/1027890

PropertyValue
property ID: DOI
value: 10.13130/gandolfi-michele_phd2024-02-13