LC tank circuit feeding on op-amp, no oscillation?
In your circuit you are using the tank as the load on the op-amp buffer circuit. The op-amp is trying to produce 4.5 V, but its output is short-circuited by the inductor. 

To generate oscillations in a linear circuit, you need to meet the Barkhausen criterion: 


A feedback mechanism with loop gain equal to unity
Phase shift through the loop equal to a multiple of 2\$\pi\$ radians.


The usual way to use a tank circuit to set the frequency of an oscillator is to put it in the feedback loop where it can cause the Barkhausen criterion to be met at (or very near) its resonance frequency.

In your circuit, the tank is not involved in feedback, so it can have no influence on oscillation.

A relatively similar circuit that can oscillate is shown here:



(source)

Notes:


R1 prevents the op-amp output being short-circuited at DC.
The tank forms a divider with R1 so that positive feedback is very low except when the tank is at resonance.