> The increased nuclear mass causes orbiting electrons to speed up to a significant fraction of the speed of light, where the rules of Einstein’s theory of relativity are important.
> In the relativistic regime, an electron’s spin — the magnetic moment that points either up or down — and the electron’s orbit are no longer independent of each other, a state known as spin-orbit coupling.
Interesting stuff. I've never heard of sigma or pi bonds.
Could electrons orbit a neutron star if we gave it a positive charge?
As written that sentence is wrong. The increased nuclear mass is not the cause of the effects. It's the increase in the nuclear charge and subsequent modification of the coulomb potential that is relevant.
Sigma and Pi bonds are typically covered in AP Chemistry, even if the “why/how” is hand waved pretty heavily. The valence cloud shapes get wild for heavier atoms and bonds between two or more atoms add even more to the mix.