**Sophya Garashchuk, PhD**, University of South Carolina

Research in our group is focused on studies of quantum-mechanical (QM) behavior of nuclei and its effects on reactivity of molecular systems in gas and condensed phases. The dominant quantum-mechanical effects, present even in large molecular systems, are tunneling, internal energy flow and nonadiabatic dynamics involving excited electronic states. In large molecular systems, however, one expects that not all nuclei exhibit quantum effects, but just a few selected degrees of freedom describing, for example, proton motion leading to tunneling at low energies. The zero-point energy (ZPE) of the vibrational degrees of freedom may affect the energy flow even for heavier particles. Inclusion of the ZPE into (quasi)classical trajectory simulations is an outstanding conceptual problem. Thus, a rigorous yet practical hybrid quantum/classical dynamics approach is a long-standing goal of theoretical chemistry. We are using the quantum trajectory (QT) formulation of the Schrödinger equation to define and analyze quantum/classical or, more precisely approximate-quantum/nearly-classical dynamics. The approximate Mixed Quantum/Classical Trajectory (MQCT) dynamics developed in our group is used for conceptual and for system-oriented studies, such as isotope effects in proton transfer and adsorption in systems of 10-100 atoms. Within the quantum trajectory formalism the approximations -- necessary for applications to large systems -- are driven by physical considerations and well-identifiable. The approach is particularly appealing since it treats all nuclear degrees of freedom on equal footing and is readily compatible with electronic structure solved on-the-fly.

The specific research goal supported by this grant is a
study of quantum effects in systems consisting of carbon and hydrogen atoms. To
test the MQCT formalism we modeled nonreactive collision of He (classical
degree of freedom, *y*) with HBr (quantum degree of freedom, *x*). The
quantum correction is a function of the coordinate *x*, but parametrically
depends on the domains defined in the *y*-coordinate. The conceptual challenge
is description of the energy transfer between these two degrees of freedom, without
losing the zero-point energy of the quantum degree of freedom to the classical
degree of freedom. Figure 1 illustrates the model system (left panel) and application
of MQCT (central and right panels).

Figure 1. Left panel: He+HBr model system. Average positions (central panel) and vibrational energy of HBr (right panel) as functions of time, obtained with exact quantum-mechanical propagation (black), approximate quantum trajectory propagation in two dimensions (red), without the quantum correction (green), Ehrenfest (blue dash) and MQCB (magenta).

Next, the MQCT approach has been applied
to explore nuclear quantum effects on adsorption of hydrogen on a graphene
flake C_{37}H_{15} (also C_{87}H_{23}). The
dominant quantum effect is due to localization of the initial proton wavefunction
affecting dynamics of the “flake” depending if the quantum correction for the
proton is included (labeled “LQF” on graphs) or not (“classical”).

Figure 2. H colliding with C_{37}H_{15}
at energies 0.1-1 eV. Quantum proton is represented with an ensemble of quantum
trajectories (white spheres above the graphene flake) . Vibrations of the flake
dissipate collision energy and are necessary for hydrogen adsorption. The
wavepacket was represented with 2400 quantum trajectories that were propagated
for 1000 time steps with the classical forces coming from the Density
Functional Tight Binding method.

Figure
3. Adsorption probability (left) as a function of collision energy and
displacement of the central carbon atom (right) as a function of time for C_{37}H_{15}
(a) and C_{87}H_{23} (b).

The paper *“A Hybrid Quantum
Trajectory-Electronic Structure Approach for Exploring Nuclear Effects in the
Dynamics of Nanomaterials”* S. Garashchuk, J. Jakowski, L. Wang, B.G.
Sumpter is in review in the Journal of Chemical Theory and Computation. Current
work includes analysis of scattering off various sited on the graphene flake;
future work will focus on a more challenging scattering of molecular hydrogen.

The grant has been also used to support
development of the analytical triplet and singlet surfaces for O+C_{2}H_{2
} (diagram below) reaction carried out in conjunction with experimental
work from the Minton group from Montana State University. Extensive
benchmarking of the surface against electronic structure reaction path
calculations for the major channels have been performed. The surfaces are
described, analyzed and prepared for distribution to researchers through *Chemical
Physics Letters*. The manuscript “Analytical potential energy surface for
O+C_{2}H_{2} system” by S. Garashchuk, V. A. Rassolov and B. J.
Braams is in review.

Figure 4. Reaction channels included into the triplet surface (left) and a representative reaction path obtained from the developed surface and coupled cluster calculation (for geometries optimized using Density Functional Theory).

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