The sublevelset persistent bars of 2-methylpentane (Figure ) can be obtained directly from the PEL, V : (S 1 ) 2 → R, and also leveraging the critical points of the building block functions. As illustrated in Figure , let a be the global minimum, b 1 and b 2 be the two local minima, c 1 and c 2 be the two local maxima, and d be the global maximum critical point of g 1-2-2-1 . Similarly, let a 1 , a 2 , b , c , d 1 , d 2 be the analogous critical points of g 1-3-2-1 . Since each energy function is a Morse function, the critical points correspond to birth or death times of bars (Lemma A.1). Thus, we can find the length, birth, and death time of each bar. This characterization gives the births and deaths of the bars in Figure as shown in Table , which has been reproduced with permission from Ref. 35.