Is there a Relativistic Quantum Chemistry Table?

[shintashi]

TL;DR Summary

Looking for a radial velocity of electrons by element list

Wiki said "Arnold Sommerfeld calculated that, for a 1s orbital electron of a hydrogen atom with an orbiting radius of 0.0529 nm, α ≈ 1/137. That is to say, the fine-structure constant shows the electron traveling at nearly 1/137 the speed of light.[9] One can extend this to a larger element with an atomic number Z by using the expression v ≈ Zc/137 for a 1s electron, where v is its radial velocity. For gold with Z = 79, v ≈ 0.58 c, so the 1s electron will be going 58% of the speed of light"

Is there a table with the elements sorted by v = 0.XX c? like how gold is listed as v = 0.58?

or am I making this over complicated and its atomic number/137 = % c?

in retrospect it does appear that the velocities are 1:1 division, so I guess a better question is at what atomic number does it begin to matter? Clearly with Cesium and Gold it matters, but what about Helium? Iron? When is the %c relevant?

 

[Vanadium 50]

Things don't worm that way in QM. Sommerfeld did this work in 1916. Solving the hydrogen atom quantum mechanically was a decade away.