Isomorphic classical molecular dynamics model for an excess electronin a supercritical fluid Page: 2 of 25
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I. INTRODUCTION
Ring polymer molecular dynamics (RPMD) allows for the direct simulation of quantum mechanical systems. It is a
classical model that both preserves the exact quantum Boltzmann distribution and exhibits time-reversal symmetry.1,2
These features ensure that RPMD trajectories are stable and self-consistent on long timescales, enabling the study
of coupled dynamical timescales in complex systems. In exhibiting these features, RPMD and centroid molecular
dynamics3,4 are unique among quantum dynamical methods. Mixed quantum-classical methods based on mean-
field5'6 and trajectory surface hopping7'8 dynamics do not preserve the correct Boltzmann populations.910'1 Similarly,
methods based on the classical Wigner model12,13,14,15,16,17,18,19 do not yield trajectories that preserve the quantum
Boltzmann distribution and are thus not employed as models for direct dynamical simulation.
Here, we test the RPMD model for the direct simulation of an excess electron in a supercritical fluid. This is the first
application of RPMD to electronic degrees of freedom, a highly quantum mechanical - and presumably challenging -
regime for the model. To evaluate the accuracy of RPMD in this context, we compare the model dynamics against
numerically exact path integral statistics with the aid of analytical continuation techniques. We further explore the
long-timescale features of the dynamics using direct simulation with RPMD.
II. METHODS
An excess electron is simulated in an otherwise classical fluid. The system is described using potentials and
parameters that were previously adopted by Berne, Coker, and coworkers to model an excess electron in helium
at 300 K.20,21,22,23,24,25,26,27 The potential energy function, U(q, Q1, ... , QN), is a sum of pairwise helium-helium
and electron-helium interactions;22 q and Q3 specify the positions of the electron and the helium atoms, and N is
the number of atoms in the fluid. Helium-helium interactions are described using the Lennard-Jones potential with
QHe 2.556 A and EHe 10.22 K; electron-helium interactions are described using the pairwise pseudopotential
Ue-He(r) + 07 B (1)
where r is the electron-helium distance and, in atomic units, A 0.655, B 89099, and C 12608.
The ring polymer molecular dynamics (RPMD) equations of motion for this system arel
v2() =wn(q(& l) + q(&--) - 2q( c)- V, U(q(c), Q1, . .. , QN)
m
V3 nM VQ U(q(), Q1, ..,QN), (2)
a=1
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Miller, Thomas F., III. Isomorphic classical molecular dynamics model for an excess electronin a supercritical fluid, article, August 4, 2008; Berkeley, California. (https://digital.library.unt.edu/ark:/67531/metadc928036/m1/2/: accessed April 19, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.