Over the past number of years multiple frequency capacitively coupled plasmas have achieved widespread usage in plasma based nano-fabrication. However,the control of charged particle dynamics in such discharges is often limited by poor understanding of the non-linear coupling between the frequencies used. This is particularly true for plasmas produced in molecular gases. such as oxygen. where long-lived reactive neutral species can significantly affect the dynamics of charged particles. As these gases are used frequently in industry. it is crucial to achieve better understanding of their characteristics under multiple frequency excitation. In order to understand the dynamics of non-linear frequency coupling. this work proposes a novel dual frequency excitation scheme utilizing odd harmonics. The odd harmonic approach has been studied systematically utilizing both numerical simulations and experiments in plasmas produced in molecular oxygen gas. Through these Investigations it has been demonstrated that the frequencies used and the ratio to which they contribute to the resultant voltage waveform have significant influence over the final plasma parameters. This occurs through electron heating and ionization mode transitions which are non~linearly dependent upon the frequency contributions to the overall voltage waveform. A specific scheme for controlling the ion bombardment energy and ion flux to the substrate in Industrial plasma applications. using frequencies of 13.56 MHz and 40.68 MHz has been proposed. It has been predicted. through numerical simulations. and confirmed through experimental measurements. that the proposed scheme offers enhanced control of plasma properties over a wide parameter range. Furthermore. a critical benchmark study has been performed by undertaking a quantitative comparison between the results of state-of-the-art numerical simulations and experimental data. This has identified areas where further improvement in the understanding and modelling of oxygen plasmas is required in order to utilize numerical simulations in a truly quantitative manner for process design and control.