Computational Chemistry 4.4 - Spin Orbitals

Short lecture on spin orbitals in molecular systems.
An orbital is a one-electron wavefunction. A spatial orbital depends on the Cartesian coordinates (x, y, z) of one electron. A spin orbital depends on the spatial coordinates and spin coordinate (omega) of one electron. The spin coordinate can be one of two orthonormal spin functions, alpha (spin-up) or beta (spin-down). The product of an orbital with its complex conjugate gives the probability density function of the electron's location, which when multiplied by a small region of space gives the probability of finding the electron within that small region of space. A "complete" set of spin orbitals can exactly represent any function of Cartesian space as a linear combination of themselves.
Notes Slide: i.imgur.com/bW...
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[@daylton945]

I'm late to the party, just wanted to let you know that your videos are absolutely amazing and I appreciate you finding a middle-ground between keeping it short while still going in depth. It is very appreciated, thanks a lot!

[@TMPChem]

Thanks Daylton. It is the key trade off.

[@GhastlyDesigns]

Fantastic and accurate review. Thanks a tonne for this!

[@OwenChen-e4r]

there is something missing at the last expression it should be ai = instead of phi

[@timpilz3157]

Some question about the spin orbital: Is it really either \phi(r)|alpha> or \phi(r)|beta> or a superposition, like \phi(r)*(a*|alpha> + b*|beta>) with |a|^2+|b|^2=1?

[@ibrahimnazemqader9153]

Thanks..

[@apburner1]

First.