The following article appeared in Journal of Chemical Physics 134.6 (2011): 061101 and may be found at http://scitation.aip.org/content/aip/journal/jcp/134/6/10.1063/1.3553204 ; Quantitative side-chain torsion angle χ1 determinations of phenylalanine residues in Desulfovibrio vulgaris flavodoxin are carried out using exclusively the correlation between the experimental vicinal coupling constants and theoretically determined Karplus equations. Karplus coefficients for nine vicinal coupling related with the torsion angle χ1 were calculated using the B3LYP functional and basis sets of different size. Optimized χ1 angles are in outstanding agreement with those previously reported by employing x ray and NMR measurements