In this letter, we discuss an expression of the continuous fractal entropy. The expression proposed fulfills in a rigorous way the dimensionless criterion and it is strictly positive overall space, the applications were done on the first thirty-six neutral atoms and in a set of 1863 molecules. The results obtained in molecules, permit us to introduce the concept of par-paene-entropic molecules, which means molecules with almost the same entropic content, this permits us to identify some groups of molecules that could be structurally different but some of them could be equivalent from the chemical reactivity point of view. (C) 2018 Elsevier B.V. All rights reserved.