The CH stretch vibrations of M(+)[cyclohexane][Ar] (M = Li, Na, and K) cluster ions were theoretically modelled. Results were compared to the corresponding infrared photodissociation spectra of Patwari and Lisy [J. Chem. Phys A 111, (2007) 7585]. The experimental spectra feature a substantial spread in CH stretch vibration frequencies due to the alkali metal cation binding to select hydrogens of cyclohexane. This spread was observed to increase with descreasing metal ion size. Exploring the potential energy landscape revealed the presence of three conformers whose energy mimina lie within ∽ 1 kcal of each other. It was determined that in all conformers the metal ion interacts with three hydrogen atoms; these hydrogen atoms can either be equatorial or axial. The corresponding spectra for these conformers were obtained with a theoretical model Hamiltonian [J. Chem. Phys. {\bf 138} (2013) 064308] that consists of local mode CH stretches bilinearly coupled to each other and Fermi coupled to lower frequency modes. Frequencies and coupling parameters were obtained from electronic structure calculations that were subsequently scaled based on previous studies. Theoretical spectra of a single low energy conformer were found to match well with the experimental spectra. The relative frequency shifts with changing metal ion size were accurately modelled with parameters generated using ωB97X-D/6-311++(2d,p) calculations.