We address a recent controversy concerning the magnetic state of holmium adatom on platinum surface. Within a combination of the density functional theory (DFT) with the exact diagonalization (ED) of Anderson impurity model, the $\left \langle J_{z} \right \rangle = 0$ paramagnetic ground state $\left |J = 8, J_{z} = \pm 8 \right \rangle$ is found. In an external magnetic field, this state is transformed to a spin-polarized state with $〈J _{z} 〉$ ≈ 6.7. We emphasize the role of $5d–4f$ interorbital exchange polarization in modification of the $4f$ shell energy spectrum.