Mineral oils, synthetic and natural esters are the predominate insulating liquids used world-wide in electrical equipment. In view of the shortfalls of the complex fluid formulations, development of the alternatives in oil-filled transformers remains a challenge. Since the physical properties and the functionality of the liquids depend strongly on the chemical compositions, rational design and predictive screening on the molecular structures of the insulating fluid alternatives on the basis of the structure-activity relationship (SAR) models is highly desired besides the trial-and-error tests. Herein various SAR models for the key properties including the pulse breakdown strengths, AC breakdown voltages, dielectric constants, flash points, and kinetic viscosities have been proposed for the first time by means of the first-principle electrostatic potential surface and group-addition scheme. Dependence of the specific properties on the molecular structures has been illustrated quantitatively in terms of the surface area, the balanced positive and negative potential separation, local polarity, molecular size/weight, density, and topography. Moreover, the individual contributions of the functional groups to the desired properties have been clarified. The predicted properties are in good agreement with the experimental data and the correlation coefficients are greater than 0.95. The present theoretical work sheds new lights on the development of novel dielectric fluids for transformers.