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I have a number of trajectories of alanine dipeptide molecule and I'm interested in computing dihedral angles of each configuration.

$\quad\quad\quad\quad$Attempt to depict phi and psi peptide angles

Have I selected the right atoms for computing each angle in the above image? Is possible to compute both angles, $\phi$ and $\psi$, given only the coordinates of the heavy atoms (without the hydrogen in the green circle)?

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Proteopedia suggests that the $\phi$ and $\psi$ angles of a Ramachandran plot only involve carbon and nitrogen atoms in their definition and specifically the carbons and nitrogens in the backbone of the protein or $n$-peptide. These definitions are also used in an article from BioMol Concepts, describing new ways of presenting Ramachandran plots, which suggests these definitions are standard.

$\phi$ should be the dihedral from a carbonyl carbon $\ce{C}_{i-1}$, to the following nitrogen $\ce{N}_i$, to the alpha carbon $\ce{C(\alpha)}_{i}$, to the next carbonyl carbon $\ce{C}_{i}$.

$\psi$ should be the dihedral from nitrogen (the same from the definition of $\phi$) $\ce{N}_{i}$, to the alpha carbon $\ce{C(\alpha)}_{i}$, to the carbonyl carbon $\ce{C}_{i}$, to the next nitrogen $\ce{N}_{i+1}$.

So to answer your questions, your drawing depicts two different dihedral angles and the actual $\phi$ and $\psi$ angles only involve heavy, backbone atoms. In your image, $\phi$ is given by the (2,4,5,7) angle while $\psi$ is the (4,5,7,9) angle.

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