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Edwin E. Quashie edited figures/radial_force/caption.tex
over 8 years ago
Commit id: 460378618125aa96cd8a2a6a3206226519cc7414
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The force is obtained by the application of the Hellmann-Feynman theorem \cite{Hellmann_2015,1941,Feynman_1939}.
The adiabatic force is recovered for $v \to 0$ with no oscillations as expected.
The maximum value for the force is obtained at the closest distance between $\mathrm{H^+}$ and neighbor $\mathrm{Cu}$ atom.
As the proton moves away from the $\mathrm{Cu}$ atom, the force decreases significantly and eventually reduces to zero. As the velocity increases the position of the maximum value of the force shifts due to the complex shape-structure of the curves and results oscillations. These oscillations becomes persistent as the velocity of the proton increases.%