  The effect of pressure on magnetic properties of LaCoO$_3$ is studied
experimentally and theoretically. The pressure dependence of magnetic
susceptibility $\chi$ of LaCoO$_3$ is obtained by precise measurements of
$\chi$ as a function of the hydrostatic pressure $P$ up to 2 kbar in the
temperature range from 78 K to 300 K. A pronounced magnitude of the pressure
effect is found to be negative in sign and strongly temperature dependent. The
obtained experimental data are analysed by using a two-level model and DFT+U
calculations of the electronic structure of LaCoO$_3$. In particular, the fixed
spin moment method was employed to obtain a volume dependence of the total
energy difference $\Delta$ between the low spin and the intermediate spin
states of LaCoO$_3$. Analysis of the obtained experimental $\chi(P)$ dependence
within the two-level model, as well as our DFT+U calculations, have revealed
the anomalous large decrease in the energy difference $\Delta$ with increasing
of the unit cell volume. This effect, taking into account a thermal expansion,
can be responsible for the temperatures dependence of $\Delta$, predicting its
vanishing near room temperature.
