Oxazole yellow (YOPRO), a cyanine dye consisting of benzoxazole and quinoline rings connected by a linker, is almost nonfluorescent in water, but its fluorescence is greatly enhanced after intercalation in double-stranded DNA, forming the basis of DNA concentration assays. To explore this difference, new potential energy surfaces for the two linker dihedral angles in the ground S0 and first excited S1 electronic states are developed. Umbrella sampling molecular dynamics is used to obtain the free energy of rotation around the two dihedral angles of the linker. The two-dimensional free energy surface of the S1 state, spanning the Franck-Condon transition point from the S0 electronic state minimum (dihedral 1 around 180°, dihedral 2 around 0°) to the S1 state minimum (∼90, ∼0), is obtained in water and when intercalated. In water, YOPRO's S1 free energy surface is completely downhill from the Franck-Condon point, whereas when intercalated, there is a barrier on the path. Thus, when intercalated in DNA, S1 YOPRO is more constrained than in water, supporting the hypothesis that intercalation does inhibit ring rotational motion around the linker and therefore strongly reduces the nonradiative relaxation, resulting in higher fluorescence intensity.