At present, at least for engineering purposes, the most successful predictive models for activity coefficients are those based on functional groups such as UNIFAC and its variants. While these models require large amounts of experimental data, the ones based on COSMO-RS require the calibration of a small set of universal parameters. However, the resolution required by many engineering tasks is usually higher than that obtained by COSMO-RS models. Thus, in this work, a novel functional-segment activity coefficient (F-SAC) model is proposed. This new model is also based on the concept of functional groups, but the interaction energy between groups comes from the COSMO-RS theory. The model parameters were calibrated for 21 groups and 43 subgroups by using infinite dilution activity coefficient (IDAC) data only. Only non-hydrogen bonding mixtures were investigated while associating mixtures are studied in an accompanying paper. For the considered IDAC data set, the F-SAC fit was superior to the predictions obtained with both UNIFAC (Do) and COSMO-SAC. Finally, the predictive strength of the model was assessed by using vapor liquid equilibrium data not considered in the model fitting process. Very good agreement with experimental data was possible over the entire composition range, as well as in the prediction of azeotropes.