Density functional studies are performed to understand the role of chelating bi-phosphine ligands [(Ph₂P(CH₂)_mPPh₂); m=1–4] in modulating the regio-selectivity of benzoic acid addition to 1-hexyne, in presence of ruthenium(II) catalyst [(Ph₂P(CH₂)_mPPh₂)Ru(methallyl)₂]. The Markovnikov addition to 1-hexyne is observed when catalyst 1_a [(Ph₂P(CH₂)PPh₂)Ru(methallyl)₂] is employed, whereas a reverse regio-selectivity is witnessed in presence of 1_d [(Ph₂P(CH₂)₄PPh₂)Ru(methallyl)₂]. Anti-Markovnikov addition occurs via the neutral vinylidene intermediates (5_a/d) formed after 1,2-hydrogen shift in hexyne coordinated ruthenium(II) complexes 3_a/d. The energy profile shows clear preference for Markovnikov addition by 15.0 kcal/mol (𝛥$G^S$_L) in case of catalyst system 1_a. In contrast, anti-Markovnikov pathway following neutral vinylidenes are more favourable by 9.1 kcal/mol (𝛥$G^S$_L) for catalyst system 1_d. The Z-enol ester formation is more predominantin the anti-Markovnikov pathway since the activation barrier for this step requires less energy (5.9 kcal/mol, 𝛥$G^S$_L) than the one furnishing the E-product. The calculated results are in good agreement with the reported experimental findings.