Why does Ruthenium only have one electron in its 5s orbital in the neutral oxidation state?
From Oxtoby et al, Principles of Modern Chemistry, 7th edi p219 and Levine, Quantum Chemistry, 5th edi, p314, the orbital energies of Sc and the elements beyond, 3d&lt;4s. The electrostatic repulsion makes energy of 3d$^3$ higher than 3d$^1$4s$^2$. 

Just my pure guess, Ru is bigger than Fe, electrostatic repulsion is smaller, so 5s$^1$. However, the 6s$^2$ electrons in Os are extra stable due to relativistic effect, so again 6s$^2$.

Quantitative calculation will be highly appreciate for justifying this hand-waving argument