Persistent Homology Metrics Reveal Quantum Fluctuations and Reactive Atoms in Path Integral Dynamics.

Yunfeng Hu,Phonemany Ounkham,Ondrej Marsalek,Aurora E. Clark,Thomas E. Markland,Bala Krishmoorthy

doi:10.3389/fchem.2021.624937

Abstract

Nuclear quantum effects (NQEs) are known to impact a number of features associated with chemical reactivity and physicochemical properties, particularly for light atoms and at low temperatures. In the imaginary time path integral formalism, each atom is mapped onto a “ring polymer” whose spread is related to the quantum mechanical uncertainty in the particle’s position, i.e., its thermal wavelength. A number of metrics have previously been used to investigate and characterize this spread and explain effects arising from quantum delocalization, zero-point energy, and tunneling. Many of these shape metrics consider just the instantaneous structure of the ring polymers. However, given the significant interest in methods such as centroid molecular dynamics and ring polymer molecular dynamics that link the molecular dynamics of these ring polymers to real time properties, there exists significant opportunity to exploit metrics that also allow for the study of the fluctuations of the atom delocalization in time. Here we consider the ring polymer delocalization from the perspective of computational topology, specifically persistent homology, which describes the 3-dimensional arrangement of point cloud data, (i.e. atomic positions). We employ the Betti sequence probability distribution to define the ensemble of shapes adopted by the ring polymer. The Wasserstein distances of Betti sequences adjacent in time are used to characterize fluctuations in shape, where the Fourier transform and associated principal components provides added information differentiating atoms with different NQEs based on their dynamic properties. We demonstrate this methodology on two representative systems, a glassy system consisting of two atom types with dramatically different de Broglie thermal wavelengths, and ab initio molecular dynamics simulation of an aqueous 4 M HCl solution where the H-atoms are differentiated based on their participation in proton transfer reactions.

Highlights

In recent years, path integral (PI) methods have seen significant application as a means to study nuclear quantum effects (NQEs), such as those arising from zero-point energy and tunneling, in chemical systems
We examine the ability of the shape and persistent homology metrics to identify proton-transferring (PT) vs. non-PT H-atoms in an ab initio path integral simulation of an aqueous 4 M HCl solution
While a few metrics exist that identify variations in atomic position uncertainty, they are optimal for systems where the difference in uncertainty is large between different atom types

Summary

Introduction

Path integral (PI) methods have seen significant application as a means to study nuclear quantum effects (NQEs), such as those arising from zero-point energy and tunneling, in chemical systems. As the mass of the nuclei or the temperature of the system increases, the stiffness of the harmonic spring between the beads is increased, the polymer shrinks, and the ring polymer representation of the atom becomes more “localized”. For lower temperatures or for lighter particles, the weaker coupling between the beads allows the ring polymer to adopt a range of shapes reflecting the quantum mechanical delocalization in the atom’s position. The structure and dynamics of the species within acidic media has received significant attention. NQEs are observed to increase delocalization within protonated structures and as such enhance proton transfer within acidic systems (Ivanov et al, 2015; Marsalek and Markland, 2017; Napoli et al, 2018; Kawashima et al, 2018)

Methods

Results

Conclusion