Results of a high resolution infrared study of the spectroscopy of monodeuterated methyl fluoride, CH₂DF, have been reported for the first time. Spectra ranging from 500 - 3300 cm^-1 have been obtained and cover all the fundamental bands at resolutions down to 0.005 cm^-1. The two lowest energy fundamentals, the v₅ and v₆ bands, have been analyzed in detail and spectroscopic constants determined. Hence six empirical vibration-rotation interaction constants have been calculated. These constants have been used, along with literature high resolution spectroscopic data for five other isotopomers to assess the accuracy of existing potential energy surfaces of methyl fluoride. A perturbation-resonance approach to the calculation of the observables from the force constants has been utilized. Problems associated with using a data set consisting of mixed symmetry isotopomers are discussed and discrepancies in the observed minus calculated fits have been rationalized. Using the compiled data set, a new optimised set of cubic force constants has been determined. Two approaches to the problem of calculating, variationally, energy levels of polyatomic molecules have been developed. In the first approach, Watson's complete rovibrational Hamiltonian has been transformed into boson creation and annihilation operators. A computer code has been written in FORTRAN77 in order to calculate the terms in the Hamitonian which are used to construct and diagonalise the matrix representation of the Hamiltonian yielding the eigenvalues and eigenfunctions. In the second approach, a FORTRAN77 computer program has been written which calculates, variationally, stretching energy levels of a centrally bonded five atomic molecule. The approach involves construction of a basis set of Morse oscillator-like functions. The program then constructs a matrix representation of the Hamiltonian operator in this basis and diagonalises the subsequent matrix to obtain the eigenvalues and eigenvectors.

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