  We perform charge density functional theory plus $U$ calculation of
LaMnO$_3$. While all the previous calculations were based on spin density
functionals, our result and analysis show that the use of spin-unpolarized
charge-only density is crucial to correctly describe the phase diagram,
electronic structure and magnetic property. Using magnetic force linear
response calculation, a long-standing issue is clarified regarding the second
neighbor out-of-plane interaction strength. We also estimate the
orbital-resolved magnetic couplings. Remarkably, the inter-orbital
$e_g$-$t_{2g}$ interaction is quite significant due to the Jahn-Teller
distortion and orbital ordering.
