Understanding the gaff2.dat proper dihedral parameters

I have a project where I'm trying to program my own force field, and I decided to use the AMBER gaff2.dat force field parameters.


However, I am really struggling parsing the gaff2.dat file when it is about the dihedral angle parameters.


I am now trying to replicate the rotation around -O-C-C-O, for which I know the profile :


$$ V\_{std} = 0.25 [1+ \cos 3\omega] + 0.15[1+\cos 2\omega]$$


I read that for gaff you have to take every parameters into account, so for $\ce{-O-CH\_2-CH\_2-O-}$ I have to use the parameters for O-C-C-O, H-C-C-O and H-C-C-H. In the gaff2.dat file I get :



```
os-c3-c3-os   1    0.000         0.000          -3          p28,suger5ring,suger6ring,coccoc GA AUE=1.1750 RMSE=1.6708 TorType=2
os-c3-c3-os   1    0.000       180.000          -2
os-c3-c3-os   1    0.170       180.000           1

hc-c3-c3-os   1    0.000         0.0            -3.         Junmei et al, 1999 TorType=1
hc-c3-c3-os   1    0.250         0.0             1.         Junmei et al, 1999 TorType=1

hc-c3-c3-hc   1    0.120         0.000           3          m1 SS AUE=0.2420 RMSE=0.2944 TorType=2

```

Which I guess would mean that :


$$ V\_{gaff} = 0.170[1+\cos (\omega -\pi)] + 0.25[1+ \cos \omega] + 0.12[1+\cos 3\omega]$$


However, this gives this profile :


[![enter image description here](https://i.stack.imgur.com/VesNQ.png)](https://i.stack.imgur.com/VesNQ.png)


Which is not what I expected to get.


I have spent the past week reading a lot about the AMBER force field parameters and I ran out of ideas. So if anyone know how these dihedral angle are parametrized I could really use some explanation.


