On the applicability of centroid and ring polymer path integral molecular dynamics for vibrational spectroscopy

2009 ◽  
Vol 130 (19) ◽  
pp. 194510 ◽  
Author(s):  
Alexander Witt ◽  
Sergei D. Ivanov ◽  
Motoyuki Shiga ◽  
Harald Forbert ◽  
Dominik Marx
Keyword(s):  
Molecular Dynamics ◽  
Vibrational Spectroscopy ◽  
Path Integral ◽  
Ring Polymer

scholarly journals Path integral molecular dynamics for bosons

2019 ◽  
Vol 116 (43) ◽  
pp. 21445-21449 ◽  
Author(s):  
Barak Hirshberg ◽  
Valerio Rizzi ◽  
Michele Parrinello
Keyword(s):  
Molecular Dynamics ◽  
Path Integral ◽  
System Size ◽  
Time Step ◽  
Different Temperatures ◽  
Ring Polymer ◽  
The Many ◽  
Trapped Bosons ◽  
Polymer Configurations ◽  
Physical Phenomena

Trapped bosons exhibit fundamental physical phenomena and are at the core of emerging quantum technologies. We present a method for simulating bosons using path integral molecular dynamics. The main difficulty in performing such simulations is enumerating all ring-polymer configurations, which arise due to permutations of identical particles. We show that the potential and forces at each time step can be evaluated by using a recurrence relation which avoids enumerating all permutations, while providing the correct thermal expectation values. The resulting algorithm scales cubically with system size. The method is tested and applied to bosons in a 2-dimensional (2D) trap and agrees with analytical results and numerical diagonalization of the many-body Hamiltonian. An analysis of the role of exchange effects at different temperatures, through the relative probability of different ring-polymer configurations, is also presented.

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

2021 ◽  
Vol 9 ◽  
Author(s):  
Yunfeng Hu ◽  
Phonemany Ounkham ◽  
Ondrej Marsalek ◽  
Thomas E. Markland ◽  
Bala Krishmoorthy ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Path Integral ◽  
Dynamic Properties ◽  
Chemical Reactivity ◽  
Persistent Homology ◽  
Dynamics Simulation ◽  
Ab Initio Molecular Dynamics ◽  
Point Energy ◽  
Ring Polymers ◽  
Ring Polymer

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.

scholarly journals Path-integral approximations to quantum dynamics

2021 ◽  
Vol 94 (7) ◽  
Author(s):  
Stuart C. Althorpe
Keyword(s):  
Molecular Dynamics ◽  
Correlation Function ◽  
Path Integral ◽  
Quantum Dynamics ◽  
Time Correlation ◽  
Time Correlation Function ◽  
Imaginary Time ◽  
Integral Methods ◽  
Ring Polymer ◽  
Recent Extension

Abstract Imaginary-time path-integral or ‘ring-polymer’ methods have been used to simulate quantum (Boltzmann) statistical properties since the 1980s. This article reviews the more recent extension of such methods to simulate quantum dynamics, summarising the chain of approximations that links practical path-integral methods, such as centroid molecular dynamics (CMD) and ring-polymer molecular dynamics (RPMD), to the exact quantum Kubo time-correlation function. We focus on single-surface Born–Oppenheimer dynamics, using the infrared spectrum of water as an illustrative example, but also survey other recent applications and practical techniques, as well as the limitations of current methods and their scope for future development. Graphic abstract

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

2021 ◽  
Author(s):  
Yunfeng Hu ◽  
Phonemany Ounkham ◽  
Ondrej Marsalek ◽  
Thomas E. Markland ◽  
Bala Krishnamoorthy ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Proton Transfer ◽  
Path Integral ◽  
Persistent Homology ◽  
Dynamics Simulation ◽  
Point Energy ◽  
Ring Polymers ◽  
Ring Polymer ◽  
Wasserstein Distances ◽  
Quantum Delocalization

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 tunnelling. 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. Keywords: path integral molecular dynamics, persistent homology, quantum delocalization, proton transfer, Wasserstein distances. <br>

Theoretical study of the dissociative photodetachment dynamics of the hydrated superoxide anion cluster

2021 ◽  
Author(s):  
Yu Hashimoto ◽  
Kohei Saito ◽  
Toshiyuki Takayanagi ◽  
Hiroto Tachikawa
Keyword(s):  
Molecular Dynamics ◽  
Molecular Dynamics Simulation ◽  
Path Integral ◽  
Superoxide Anion ◽  
Theoretical Study ◽  
Dynamics Simulation ◽  
Simulation Methods ◽  
Anion Cluster ◽  
Dissociative Photodetachment ◽  
Ring Polymer

The dissociative photodetachment of the hydrated superoxide anion cluster, O2−·H2O + hν → O2 + H2O + e−, is theoretically investigated using path-integral and ring-polymer molecular dynamics simulation methods, which...

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

2021 ◽  
Author(s):  
Yunfeng Hu ◽  
Phonemany Ounkham ◽  
Ondrej Marsalek ◽  
Thomas E. Markland ◽  
Bala Krishnamoorthy ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Proton Transfer ◽  
Path Integral ◽  
Persistent Homology ◽  
Dynamics Simulation ◽  
Point Energy ◽  
Ring Polymers ◽  
Ring Polymer ◽  
Wasserstein Distances ◽  
Quantum Delocalization

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 tunnelling. 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. Keywords: path integral molecular dynamics, persistent homology, quantum delocalization, proton transfer, Wasserstein distances. <br>

Nuclear quantum effects in the direct ionization process of pure helium clusters: path-integral and ring-polymer molecular dynamics simulations on the diatomics-in-molecule potential energy surfaces

2018 ◽  
Vol 20 (41) ◽  
pp. 26489-26499 ◽  
Author(s):  
Kento Suzuki ◽  
Takaaki Miyazaki ◽  
Toshiyuki Takayanagi ◽  
Motoyuki Shiga
Keyword(s):  
Molecular Dynamics ◽  
Molecular Dynamics Simulations ◽  
Path Integral ◽  
Potential Energy Surfaces ◽  
Direct Ionization ◽  
Helium Clusters ◽  
Pure Helium ◽  
Ring Polymer ◽  
Ring Polymer Molecular Dynamics ◽  
Dynamics Simulations

The ionization dynamics of pure Hen clusters has been theoretically studied using path-integral and ring-polymer molecular dynamics simulations.

scholarly journals From classical to quantum and back: Hamiltonian adaptive resolution path integral, ring polymer, and centroid molecular dynamics

2017 ◽  
Vol 147 (24) ◽  
pp. 244104 ◽  
Author(s):  
Karsten Kreis ◽  
Kurt Kremer ◽  
Raffaello Potestio ◽  
Mark E. Tuckerman
Keyword(s):  
Molecular Dynamics ◽  
Path Integral ◽  
Adaptive Resolution ◽  
Ring Polymer
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