arXiv subjects

Thomas F. Miller III

Publications and source records attributed to Thomas F. Miller III.

42 records · Page 3Linked to original sources

arXiv2011

Exact quantum statistics for electronically nonadiabatic systems using continuous path variables

We derive an exact, continuous-variable path integral (PI) representation of the canonical partition function for electronically nonadiabatic systems. Utilizing the Stock-Thoss (ST) mapping for an N-level system, matrix elements of the Boltzmann operator are expressed in Cartesian coordinates for both the nuclear and electronic degrees of freedom. The PI discretization presented here properly constrains the electronic Cartesian coordinates to the physical subspace of the mapping. We numerically demonstrate that the resulting PI-ST representation is exact for the calculation of equilibrium properties of systems with coupled electronic and nuclear degrees of freedom. We further show that the PI-ST formulation provides a natural means to initialize semiclassical trajectories for the calculation of real-time thermal correlation functions, which is numerically demonstrated in applications to a series of nonadiabatic model systems.

cond-mat.stat-mech↗

arXiv2011

Direct simulation of electron transfer using ring polymer molecular dynamics: Comparison with semiclassical instanton theory and exact quantum methods

The use of ring polymer molecular dynamics (RPMD) for the direct simulation of electron transfer (ET) reaction dynamics is analyzed in the context of Marcus theory, semiclassical instanton theory, and exact quantum dynamics approaches. For both fully atomistic and system-bath representations of condensed-phase ET, we demonstrate that RPMD accurately predicts both ET reaction rates and mechanisms throughout the normal and activationless regimes of the thermodynamic driving force. Analysis of the ensemble of reactive RPMD trajectories reveals the solvent reorganization mechanism for ET that is anticipated in the Marcus rate theory, and the accuracy of the RPMD rate calculation is understood in terms of its exact description of statistical fluctuations and its formal connection to semiclassical instanton theory for deep-tunneling processes. In the inverted regime of the thermodynamic driving force, neither RPMD nor a related formulation of semiclassical instanton theory capture the characteristic turnover in the reaction rate; comparison with exact quantum dynamics simulations reveals that these methods provide inadequate quantization of the real-time electronic-state dynamics in the inverted regime.

cond-mat.stat-mech↗

arXiv2011

Embedded density functional theory for covalently bonded and strongly interacting subsystems

Embedded density functional theory (e-DFT) is used to describe the electronic structure of strongly interacting molecular subsystems. We present a general implementation of the Exact Embedding (EE) method [J. Chem. Phys. 133, 084103 (2010)] to calculate the large contributions of the non-additive kinetic potential (NAKP) in such applications. Potential energy curves are computed for the dissociation of Li+-Be, CH3-CF3, and hydrogen-bonded water clusters, and e-DFT results obtained using the EE method are compared with those obtained using approximate kinetic energy functionals. In all cases, the EE method preserves excellent agreement with reference Kohn-Sham calculations, whereas the approximate functionals lead to qualitative failures in the calculated energies and equilibrium structures. We also demonstrate an accurate pairwise approximation to the NAKP that allows for efficient parallelization of the EE method in large systems; benchmark calculations on molecular crystals reveal ideal, size-independent scaling of wall-clock time with increasing system size.

cond-mat.other↗

arXiv2008

Isomorphic classical molecular dynamics model for an excess electron in a supercritical fluid

Ring polymer molecular dynamics (RPMD) is used to directly simulate the dynamics of an excess electron in a supercritical fluid over a broad range of densities. The accuracy of the RPMD model is tested against numerically exact path integral statistics through the use of analytical continuation techniques. At low fluid densities, the RPMD model substantially underestimates the contribution of delocalized states to the dynamics of the excess electron. However, with increasing solvent density, the RPMD model improves, nearly satisfying analytical continuation constraints at densities approaching those of typical liquids. In the high density regime, quantum dispersion substantially decreases the self-diffusion of the solvated electron. In this regime where the dynamics of the electron is strongly coupled to the dynamics of the atoms in the fluid, trajectories that can reveal diffusive motion of the electron are long in comparison to $β\hbar$.

cond-mat.stat-mech↗

arXiv2007

Sampling diffusive transition paths

We address the problem of sampling double-ended diffusive paths. The ensemble of paths is expressed using a symmetric version of the Onsager-Machlup formula, which only requires evaluation of the force field and which, upon direct time discretization, gives rise to a symmetric integrator that is accurate to second order. Efficiently sampling this ensemble requires avoiding the well-known stiffness problem associated with sampling infinitesimal Brownian increments of the path, as well as a different type of stiffness associated with sampling the coarse features of long paths. The fine-feature sampling stiffness is eliminated with the use of the fast sampling algorithm (FSA), and the coarse-feature sampling stiffness is avoided by introducing the sliding and sampling (S&S) algorithm. A key feature of the S&S algorithm is that it enables massively parallel computers to sample diffusive trajectories that are long in time. We use the algorithm to sample the transition path ensemble for the structural interconversion of the 38-atom Lennard-Jones cluster at low temperature.

cond-mat.stat-mech↗

arXiv2007

Solvent coarse-graining and the string method applied to the hydrophobic collapse of a hydrated chain

Using computer simulations of over 100,000 atoms, the mechanism for the hydrophobic collapse of an idealized hydrated chain is obtained. This is done by coarse-graining the atomistic water molecule positions over 129,000 collective variables that represent the water density field and then using the string method in these variables to compute the minimum free energy pathway (MFEP) for the collapsing chain. The dynamical relevance of the MFEP (i.e. its coincidence with the mechanism of collapse) is validated a posteriori using conventional molecular dynamics trajectories. Analysis of the MFEP provides atomistic confirmation for the mechanism of hydrophobic collapse proposed by ten Wolde and Chandler. In particular, it is shown that lengthscale-dependent hydrophobic dewetting is the rate-limiting step in the hydrophobic collapse of the considered chain.

cond-mat.stat-mech↗