In octahedral field, the baricenter remains conserved and there is lowering of energy of $\mathrm{t_{2g}}$ orbitals.
What is a baricenter and why must it be conserved? Why is there lowering of energy of $\mathrm{t_{2g}}$ as ligands approach?
Also when ligands are far there an increase in energy but not when they are nearer. What is going on?
I know energy must be conserved but they are many ways to release/utilise energy like sound, heat, light, kinetic energy.
The baricentre should probably be spelt barycentre. It is something analogous to a centre of mass. Simple models such as some flavours of the crystal field theory will assume a destabilisation only of the metal orbitals. However, for an energetic destabilisation to occur, something else must be stabilised — this is the conservation of energy. Thus, the logic says that the raise in energy of the $\mathrm{e_g}$ orbitals must be offset by a lowering of the $\mathrm{t_{2g}}$ orbitals.
When constructing a proper MO scheme of an octahedral coordination complex, this argument is revealed as bogus. As can be seen in this answer, the $\mathrm{e_g}$ orbitals are actually $\mathrm{e_g^*}$ orbitals, i.e. antibonding with respect to the $\ce{M\bond{<-}L}$ bonds which is the reason why they are raised. Disregarding π interactions, the $\mathrm{t_{2g}}$ orbitals are nonbonding and thus their energy is not affected.
