Since this may be a homework question, I'll just give a few suggestions:
What is conserved in this circuit? You mention energy in the title, you need to think about charge.
In all solutions of this sort you have governing equations and basic assumptions that you make about quantities that are conserved.
\$ Q=CV\$ is a conserved quantity. That means that once charged up, when you attach a new Capacitor you are changing the C value in the equation. But \$CV = \$ constant.
In other words, Energy is NOT conserved.
A more physical view may help. Lets make the capacitors with an air gap and the ability to change the plate spacing (ignoring fringe fields etc. - it's a thought experiment). To change the value of C (increase it) we need to decrease the plate spacing. Since the energy is decreasing that means that the forces present will drag the plates towards each other and do positive work against the system that controls the plate spacing. That means the system in order to decrease the energy must be attractive, i.e. the forces are generated that bring the plates together. We know this is the case because one plate will have +'ve charge and the other plate will have -'ve charge (charge balance again). SO the system is consistent.
For your system of two two caps, work IS done when the displacement current flows during charge equilibration.