The restriction on the strong coupling constant in the IR region from the 1D-1P splitting in bottomonium

The $b\bar{b}$ spectrum is calculated with the use of a relativistic Hamiltonian where the gluon-exchange between a quark and an antiquark is taken as in background perturbation theory. We observed that the splittings ${\mathrm{\Delta }}_1=\mathrm{{\rm Y}}(1\mathrm{D})-{\chi }_b(1\mathrm{P})$ and other splittings are very sensitive to the QCD constant ${\mathrm{\Lambda }}_V(n_f)$ which occurs in the Vector scheme, and good agreement with the experimental data is obtained for ${\mathrm{\Lambda }}_V(2$-loop, $n_f=5)=325\pm 10$ MeV which corresponds to the conventional ${\mathrm{\Lambda }}_{\overline{MS}}(2-$loop, $n_f=5)=238\pm 7$ MeV, ${\alpha }_s(2-$loop, $M_Z)=0.1189\pm 0.0005,$ and a large freezing value of the background coupling: ${\alpha }_{\mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}}(2$-loop, $q^2=0)=\alpha_{\rm crit} (2$-loop,$r\to \infty)=0.58\pm 0.02$. If the asymptotic freedom behavior of the coupling is neglected and an effective freezing coupling $\alpha_{\rm static}=const$ is introduced, as in the Cornell potential, then precise agreement with ${\mathrm{\Delta }}_1(\mathrm{e}\mathrm{x}\mathrm{p})$ and ${\mathrm{\Delta }}_2(\mathrm{e}\mathrm{x}\mathrm{p})$ can be reached for the rather large value ${\alpha }_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{c}}=0.43\pm 0.02$. We predict a value for the mass M(2D) = 10451\pm2 MeV.