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Question

The mwfn filetype includes fields for alpha and beta electrons/orbitals/density matrices.

What is the definition of alpha and beta electrons; what distinguishes them?

For future research, where is this definition typically recorded?

Clues:

  • Orbitals are recorded as either $\alpha$, $\beta$, or $\alpha+\beta$.
  • $\beta$ orbitals implicitly come after $\alpha$ orbitals in indexing (with $n$ basis functions, the $i$th $\beta$ orbital is $n$ ahead of the $i$th $\alpha$ orbital. Do they overlap, or do $\alpha$ orbitals stop at $n$?).
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Alpha and beta basically denote spin-up (+1/2 for electrons) and spin-down (-1/2 for electrons).

This tells us how the spin would align if we have a magnetic field. A spin of +1/2 actually means that the spin is aligned with the magnetic field, and a spin of -1/2 means that it's aligned 180 degrees from the magnetic field, but since we conventionally say that the positive z-axis is the direction in which the magnetic field is theoretically applied, a spin of +1/2 becomes "up" and -1/2 becomes "down".

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