Bring au (atomic units) to Au

[correaa]

… talking about #659 , It's about time we added the Atomic Units!

[chiphogg]

Putting this here for my own easy reference: https://godbolt.org/z/8Kaq83xrf

We discussed on the C++ slack why Au can't provide these units out of the box: they do not have exact definitions relative to other units. However, we can make it as easy as possible for users to define a set of atomic units within their project that behaves very nicely! To wit:

• Within the set of atomic units, all relationships are exact
• When converting to/from regular units, the numerical accuracy is every bit as good as current physics will allow

The precise shape for solving this issue will be:

• A code example page (helps Add code examples to README and doc main page #529) walking the reader through, and providing a drop-in solution
• A discussion page explaining the subtleties of different sets of units

I believe we can do this for 0.6.0.

[correaa]

Thank you for the reference.

I am not sure if I understand the limits of Au correctly, specifically when mixing systems of units.
In any case, many SI definitions these days are redefined or in the process of being redefined exactly in terms of atomic quantities.

For example: "The elementary charge is defined as a fundamental constant in the SI.[8] The value for elementary charge, when expressed in SI units, is exactly 1.602176634×10−19 C.[2]" (wikipedia)

The SI vs au unit mass conversion is still approximate, AFAIK. Is this the obstacle?

Being able to define au units (or non exact units) for a project would be great, thank you.