The dataset comprises the experimental and computational studies that form the basis of the publication: "Structure and vibrational spectroscopy of lithium and potassium methanesulfonates" by Parker, Revill-Hivet, Nye and Gutmann, published in Royal Society Open Science (2020). The dataset consists of three zip files: "A-Crystallographic_information.zip", "B-Experimental_spectra.zip", "C-CASTEP.zip", . "A-Crystallographic_information.zip" contains cif files of the structures. These can be read by any text reader or loaded into any suitable program e.g. Jmol (available from: http://jmol.sourceforge.net/ ) to display the structure. "B-Experimental_spectra.zip" contains the vibrational spectra: infrared, Raman and inelastic neutron scattering (INS), all have a .dat extension and can be viewed with any text reader or can be loaded into programs such as Excel or Origin to display the spectra. The filename is the name of the compound and ends in _IR for infrared, _Raman for Raman and _INS for INS data. The infrared and Raman data consists of two columns of ASCII data. Column 1 is the energy transfer in wavenumber (cm-1), column 2 is the intensity (Absorbance for the infrared data, arbitrary units for the Raman data). The INS data consists of three columns: column 1 is the energy transfer in wavenumber (cm-1), column 2 is the intensity, S(Q,w) (arbitrary units), and column three is the error bar of the intensity given in column 2. There are three spectra listed sequentially in each file and separated by 0,1,2. The first "0" are the data from the backscattering detectors, "1" are the data from the forward scattering detectors and "2" is the arithmetic average of the forward and back scattering detectors. "2" is the spectrum that is normally displayed and is that shown in the Royal Society Open Science paper and on the INS database. "C-CASTEP.zip" contains the input (.cell and .param) and output (.castep) from the geometry optimisation using the CASTEP (version 17.21) program. The output file includes the geometry optimised structure. The CASTEP input files (.cell and .param) and the output files (.castep and .phonon) for the vibrational calculation have the same stem as for the geometry optimisation but have _Efield appended. The .phonon file includes both the transition energies and atomic displacements for all the atoms in each mode. The .phonon files for the calculations of the isotopomers are also included. These include the mass of the isotopomer in the title.