mechanical energy for a membrane with natural curvature of both radii

I’d like to study the following mechanical energy :

$$F_{my,energy}=int Big(frac{1}{R_1}-c_1Big)^2+Big(frac{1}{R_2}-c_2Big)^2 dA $$

I noticed that this energy cannot be written as a Canham-Helfrich energy of the form :

$$F_{CH}=int alphaBig(frac{1}{R_1}+frac{1}{R_2}-c_aBig)^2+betafrac{1}{R_1R_2} dA $$

Although my energy $F_{my,energy}$ is very intuitive and natural, I can’t find a way to write it in function of the gaussian and principal curvature. Is there a way to proceed to do so ?