The following results provide information about bar counts for the sublevelset persistence barcodes for branched alkanes. In Lemma A.1, we show that an additive function over a product space that is defined using Morse building block functions is also a Morse function. Furthermore, the critical points of the additive function are formed from the critical points of the building block function. Once we have this structure, we can use it to establish bar counts. Theorem A.2 counts the number of bars of each length in a barcode.