Getting R2 from alternate regression

I would like to be able to test an outside regression model on my dataset. With my data, I was able to generate a logarithmic model (dark green curve in linked image) and generate a R2 value for that model. The red line represents an model from a different study that I would like to predict its R2 value on my dataset. What is the best way for this to be done?

The functions for the two regressions are (where x=Tout_F_6am):

darkgreen=function(x){10^(-0.022-(0.005*x))} #R2=0.13
red=function(x){10^(-0.046-(0.00367*x))} #R2=???

Stack overflow features a post here but when I try readjusting my coefficients for the alternate model, I just get the same coefficient.

cor(clo, 10^-0.022-0.005*passive$Tout_F_6am) ** 2 #0.134
cor(clo, 10^-0.046-0.00367*passive$Tout_F_6am) ** 2 #0.134???