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## Full-Text Articles in Physics

Incorporation Of Quantum Effects For Selected Degrees Of Freedom Into The Trajectory-Based Dynamics Using Spatial Domains, Sophya V. Garashchuk, M. V. Volkov

#### Incorporation Of Quantum Effects For Selected Degrees Of Freedom Into The Trajectory-Based Dynamics Using Spatial Domains, Sophya V. Garashchuk, M. 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 ...

Stable Long-Time Semiclassical Description Of Zero-Point Energy In High-Dimensional Molecular Systems, Sophya V. Garashchuk, V. A. Rassolov

#### Stable Long-Time Semiclassical Description Of Zero-Point Energy In High-Dimensional Molecular Systems, Sophya V. Garashchuk, V. A. Rassolov

*Faculty Publications*

Semiclassical implementation of the quantum trajectory formalism [J. Chem. Phys.120, 1181 (2004)] is further developed to give a stable long-time description of zero-point energy in anharmonic systems of high dimensionality. The method is based on a numerically cheap linearized quantum force approach; stabilizing terms compensating for the linearization errors are added into the time-evolution equations for the classical and nonclassical components of the momentum operator. The wave function normalization and energy are rigorously conserved. Numerical tests are performed for model systems of up to 40 degrees of freedom.

Semiclassical Nonadiabatic Dynamics Based On Quantum Trajectories For The *O( ^{3}P,^{1}D)* +

*H*System, Sophya V. Garashchuk, V. A. Rassolov, G. C. Schatz

_{2}#### Semiclassical Nonadiabatic Dynamics Based On Quantum Trajectories For The O(3P,1D) + H2 System, Sophya V. Garashchuk, V. A. Rassolov, G. C. Schatz

*Faculty Publications*

The O(P3,D1)+H2→OH+Hreaction is studied using trajectory dynamics within the approximate quantum potential approach. Calculations of the wave-packet reaction probabilities are performed for four coupled electronic states for total angular momentum J=0 using a mixed coordinate/polar representation of the wave function. Semiclassical dynamics is based on a single set of trajectories evolving on an effective potential-energy surface and in the presence of the approximate quantum potential. Population functions associated with each trajectory are computed for each electronic state. The effective surface is a linear combination of the electronic states with the contributions of individual ...

Semiclassical Nonadiabatic Dynamics Using A Mixed Wave-Function Representation, Sophya V. Garashchuk, V. A. Rassolov, G. C. Schatz

#### Semiclassical Nonadiabatic Dynamics Using A Mixed Wave-Function Representation, Sophya V. Garashchuk, V. A. Rassolov, G. C. Schatz

*Faculty Publications*

Nonadiabaticeffects in quantum dynamics are described using a mixed polar/coordinate space representation of the wave function. The polar part evolves on dynamically determined potential surfaces that have diabatic and adiabatic potentials as limiting cases of weak localized and strong extended diabatic couplings. The coordinate space part, generalized to a matrix form, describes transitions between the surfaces. Choice of the effective potentials for the polar part and partitioning of the wave function enables one to represent the total wave function in terms of smooth components that can be accurately propagated semiclassically using the approximate quantum potential and small basis sets ...

Modified Quantum Trajectory Dynamics Using A Mixed Wave Function Representation, Sophya V. Garashchuk, V. A. Rassolov

#### Modified Quantum Trajectory Dynamics Using A Mixed Wave Function Representation, Sophya V. Garashchuk, V. A. Rassolov

*Faculty Publications*

Dynamics of quantum trajectories provides an efficient framework for description of various quantum effects in large systems, but it is unstable near the wave function density nodes where the quantum potential becomes singular. A mixed coordinate space/polar representation of the wave function is used to circumvent this problem. The resulting modified trajectory dynamics associated with the polar representation is nonsingular and smooth. The interference structure and the nodes of the wave function density are described, in principle, exactly in the coordinate representation. The approximate version of this approach is consistent with the semiclassical linearized quantum force method [S. Garashchuk ...

Bohmian Dynamics On Subspaces Using Linearized Quantum Force, V. A. Rassolov, Sophya V. Garashchuk

#### Bohmian Dynamics On Subspaces Using Linearized Quantum Force, V. A. Rassolov, Sophya V. Garashchuk

*Faculty Publications*

In the de Broglie–Bohm formulation of quantum mechanics the time-dependent Schrödinger equation is solved in terms of quantum trajectories evolving under the influence of quantum and classical potentials. For a practical implementation that scales favorably with system size and is accurate for semiclassical systems, we use approximate quantum potentials. Recently, we have shown that optimization of the nonclassical component of the momentum operator in terms of fitting functions leads to the energy-conserving approximate quantum potential. In particular, linear fitting functions give the exact time evolution of a Gaussian wave packet in a locally quadratic potential and can describe the ...

Semiclassical Dynamics With Quantum Trajectories: Formulation And Comparison With The Semiclassical Initial Value Representation Propagator, Sophya V. Garashchuk, V. A. Rassolov

#### Semiclassical Dynamics With Quantum Trajectories: Formulation And Comparison With The Semiclassical Initial Value Representation Propagator, Sophya V. Garashchuk, V. A. Rassolov

*Faculty Publications*

We present a time-dependent semiclassical method based on quantum trajectories. Quantum-mechanical effects are described via the quantum potential computed from the wave function density approximated as a linear combination of Gaussian fitting functions. The number of the fitting functions determines the accuracy of the approximate quantum potential (AQP). One Gaussian fit reproduces time-evolution of a Gaussian wave packet in a parabolic potential. The limit of the large number of fitting Gaussians and trajectories gives the full quantum-mechanical result. The method is systematically improvable from classical to fully quantum. The fitting procedure is implemented as a gradient minimization. We also compare ...