Calculating zero-point energy for the Varshini potential

As per my understanding, for a harmonic oscillator, we can find the zero-point energy by the relation below:


$$ E\_0 = \left(0 + \frac{1}{2}\right)\hbar \omega$$


The equation for the potential in question is:


$$ V(x) = D\_e \left(1 - \frac{r\_e}{x} e^{-\alpha(x^2-r\_e^2)}\right)^2 + T\_e$$


How would one go about finding the value of $E\_0$ for this potential surface?


Edit: All values aside from $x$ are known.


