In this research, the optimised structural and vibrational properties of cis–trans isomers of powerful insecticide allethrin were theoretically studied in gas phase and in aqueous and ethanol solutions by using hybrid B3LYP/6–311 + + g(d,p) level of theory. The results revealed that the permittivity of solvent has influence on the properties of both isomers, thus, higher dipole moments and solvation energies are observed in water, a solvent of higher permittivity (78.355) than ethanol. Complete vibrational assignments of both isomers were done by combining the experimental IR spectrum of allethrin with the scaled quantum mechanical force field (SQMFF) methodology and the determination of corresponding scaled force constants in gas phase and aqueous solution are reported. Different signs of dihedral O2C10C6C4 angles of both isomers (negative in cis and positive in trans) support the differences in the vibrational assignments. Natural bond orbital (NBO) calculations suggest that both isomers are highly stable in gas phase and aqueous solution and that the side chains and five member’s rings are involved in the n → σ* interactions. However, atoms in molecules (AIM) studies reveal a higher stability of form cis in both media than the trans one. Merz-Kollman (MK), Mulliken and natural population atomic (NPA) charges for both isomers support the higher hydration of trans isomer in aqueous media and, hence, the higher solvation energy in water (ΔGC/ZPVE = − 80.29 kJ/mol). Changes in the bond orders of O and C atoms of side chain are observed in water as a consequence of hydration. The higher stability of the cis form in the above solutions could be explained by the lower solvation energy in water, as supported by AIM calculations. The studies of frontier orbital reveal that the cis form in both media is sligthly more reactive than the trans form.

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