Theoretical understanding of mechanochemical (ball-milling) synthesis of thioethers: a CDFT approach

Abstract

Mechanochemical synthesis has gained much attention owing to its environment-friendly nature. The synthesis of organic thioethers starting from organic diazonium and disulfide compounds under the ball-milling process is considered to study the corresponding theoretical aspect. The calculated rate constant values are found to be very small. The force required to cleave the C–N and S–S bonds in diazonium and disulfides are calculated following the constrained geometries simulate external force (COGEF) methodology. The presence of the electron donating group increases the C–N bond strength in diazonium compounds while it decreases the S–S bond strength in disulfides. The force-dependent ionization energy (I), and electron affinity (A) descriptors related rules: (i) if r_neutral > r_cation, then ${\left(\frac{\partial I}{\partial {F}_{e}}\right)}_{{F}_{e}=0}>0$, and (ii) if r_neutral < r_anion, then ${\left(\frac{\partial A}{\partial {F}_{e}}\right)}_{{F}_{e}=0}>0$ are followed by both systems. However, rules related to electronegativity (χ), hardness (η) and electrophilicity (ω) are not followed by diazonium compounds. In diazonium ${\left(\frac{\partial \chi }{\partial {F}_{e}}\right)}_{{F}_{e}=0}<0$ (with the applied external force, the electronegativity decreases) but in disulfide ${\left(\frac{\partial \chi }{\partial {F}_{e}}\right)}_{{F}_{e}=0}>0$ (with the applied external force, the electronegativity increases) as ${r}_{\text{c}\text{a}\text{t}\text{i}\text{o}\text{n}}< {r}_{\text{a}\text{n}\text{i}\text{o}\text{n}}$. In diazonium ions, ${\left(\frac{\partial \eta }{\partial {F}_{e}}\right)}_{{F}_{e}=0}>0$ but in disulfide ${\left(\frac{\partial \eta }{\partial {F}_{e}}\right)}_{{F}_{e}=0}<0$.