We have investigated the temperature dependence of the magnetic susceptibility $chi(T)$ of rare-earth cobaltites RCoO$_3$ (R= La, Pr, Nd, Sm, Eu) in the temperature range $4.2-300$ K and also the influence of hydrostatic pressure up to 2 kbar on their susceptibility at fixed temperatures $T=78 $ and 300 K. The specific dependence $chi(T)$ observed in LaCoO$_3$ and the anomalously large pressure effect (d ln $chi$/d$Psim -100$ Mbar$^{-1}$ for $T = 78$ K) are analyzed in the framework of a two-level model with energy levels difference $Delta$. The ground state of the system is assumed to be nonmagnetic with the zero spin of Co$^{3+}$ ions, and magnetism at a finite temperature is determined by the excited magnetic spin state. The results of the analysis, supplemented by theoretical calculations of the electronic structure of LaCoO$_3$, indicate a significant increase in $Delta$ with a decrease in the unit cell volume under the hydrostatic pressure. In the series of RCoO$_3$ (R= Pr, Nd, Sm, Eu) compounds, the volume of crystal cell decreases monotonically due to a decrease in the radius of R$^{3+}$ ions. This leads to an increase in the relative energy $Delta$ of the excited state (the chemical pressure effect), which manifests itself in a decrease in the contribution of cobalt ions to the magnetic susceptibility at a fixed temperature, and also in a decrease in the hydrostatic pressure effect on the susceptibility of RCoO$_3$ compounds, which we have observed at $T=300$ K.
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