LCAO Molecular Orbitals in Desmos 3D

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Published on October 15, 2024 12:39:09 PM ● Video Link: https://www.youtube.com/watch?v=QqbKRsXnM0w

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By converting spherical coordinate WFs given in chemistry textbooks, (here used Quantum Chemistry by Ira Levine) to cartesian form, we can plot orbitals and their linear combinations on Desmos 3D. [ https://www.desmos.com/3d/svzvkuofms ]
(square of wavefunction) = probability density (here = 0.1 or 0.2)

The most fascinating part of this animation is the part where using the pure m=1 or m=-1 orbital (which are donuts parallel to x-y plane instead of dumbbells along x and y axes) instead of the linear combination obtained real Px and Py, we obtain a Pi bond that is cylindrically symmetric about the bond axis, instead of the popular double Pi bond with 4 sausage shaped lobes.

Timestamps:
00:00 - 1s Sigma bonding and anti bonding MOs
01:25 - 2pz Sigma bonding and anti bonding MOs
03:09 - 2px Pi bonding and anti bonding MOs
04:52 - 2px and 2py Pi double bond
05:22 - 2px and 2py double bond + 2pz sigma bond = Triple Bond
06:45 - 2p cylindrically symmetric Pi bonding and antibonding from considering pure complex orbital (instead of real valued Px and Py obtained by linear combination)
09:46 - Triple bond with cylindrically symmetric Pi bond