Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 3 of 3
Full-Text Articles in Physical Sciences and Mathematics
Incorporation Of Quantum Effects For Selected Degrees Of Freedom Into The Trajectory-Based Dynamics Using Spatial Domains, Sophya V. Garashchuk, Mikhail V. Volkov
Incorporation Of Quantum Effects For Selected Degrees Of Freedom Into The Trajectory-Based Dynamics Using Spatial Domains, Sophya V. Garashchuk, Mikhail V. Volkov
Faculty Publications
The approach of defining quantum corrections on nuclear dynamics of molecular systems incorporated approximately into selected degrees of freedom, is described. The approach is based on the Madelung-de-Broglie-Bohm formulation of time-dependent quantum mechanics which represents a wavefunction in terms of an ensemble of trajectories. The trajectories follow classical laws of motion except that the quantum potential, dependent on the wavefunction amplitude and its derivatives, is added to the external, classical potential. In this framework the quantum potential, determined approximately for practical reasons, is included only into the “quantum” degrees of freedom describing light particles such as protons, while neglecting with …
Efficient Quantum Trajectory Representation Of Wavefunctions Evolving In Imaginary Time, Sophya V. Garashchuk, James Mazzuca, Tijo Vazhappilly
Efficient Quantum Trajectory Representation Of Wavefunctions Evolving In Imaginary Time, Sophya V. Garashchuk, James Mazzuca, Tijo Vazhappilly
Faculty Publications
The Boltzmann evolution of a wavefunction can be recast as imaginary-time dynamics of the quantum trajectory ensemble. The quantum effects arise from the momentum-dependent quantum potential – computed approximately to be practical in high-dimensional systems – influencing the trajectories in addition to the external classical potential [S. Garashchuk, J. Chem. Phys.132, 014112 (2010)]. For a nodelesswavefunction represented as ψ(x, t) = exp ( − S(x, t)/ℏ) with the trajectory momenta defined by ∇S(x, t), analysis of the Lagrangian and Eulerian evolution shows that for bound potentials the former …
Semiclassical Calculation Of Cumulative Reaction Probabilities, David J. Tannor, Sophya V. Garashchuk
Semiclassical Calculation Of Cumulative Reaction Probabilities, David J. Tannor, Sophya V. Garashchuk
Faculty Publications
Calculation of chemical reaction rates lies at the very core of theoretical chemistry. The essential dynamical quantity which determines the reaction rate is the energy-dependent cumulative reaction probability, N(E), whose Boltzmann average gives the thermal rate constant, k(T). Converged quantum mechanical calculations of N(E) remain a challenge even for three- and four-atom systems, and a longstanding goal of theoreticians has been to calculate N(E) accurately and efficiently using semiclassical methods. In this article we present a variety of methods for achieving this goal, by combining semiclassical initial value …