The sp Hybrid Orbital in Bohmian Mechanics

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Hybrid orbitals are linear combinations of degenerate (equal energy) hydrogen atom orbitals of different angular momentum [1, 2]. The orbitals are spherical, while the orbitals have lobes that can point in different directions.

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In this Demonstration, the -hybridization of a hydrogen atom with a constant phase shift is investigated in the Bohmian mechanics description. In this case, the orbital is combined with one of the orbitals to yield two hybrid orbitals [1], but here only one lobe of the orbital is shown. These hybridized orbitals result in higher electron density, depending on the phase shift , in the bonding region for a bond. The hybrid orbital is plotted in three dimensions. In the Bohm picture [3, 4], the electron acts like an actual particle, its velocity at any instant being fully determined by the gradient of the phase function, and here the constant phase shift influences only the magnitude of the resultant velocity vector but not the shape of the orbits.

In the graphic, you see the wave density (if enabled); the magnitude of the resultant velocity vector (if enabled); nine possible orbits of one electron, where the trajectories (colored) depend on the initial starting point (, , ), the initial starting points of the trajectories (black points, shown as small spheres) and the actual position (colored points, shown as small spheres).

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Contributed by: Klaus von Bloh (June 2019)
Open content licensed under CC BY-NC-SA


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