A theory is developed to calculate values of the potential-energy barriers to structural relaxation in molecular glass formers from the data of static pair-correlation function. The barrier height is shown to increase due to an increase in the number of "stable bonds" a particle forms with its neighbors and the energy of each bond as liquids move deeper into the supercooled (supercompressed) region. We present results for a system of hard spheres and compare calculated values of the structural relaxation time with experimental and simulation results.