In colloquial use, relationship chemistry is a term used to metaphorically to qualify the “chemistry” of relationships. [1] The term is a common one in dating site advertisements. The matching site LoveIsSexy, for instance, boldly declares, on its about us page, that it has a “state-of-the-art matching technology” that puts its users in direct contact with “relationships that work” and that: [2]

“Relationship chemistry is more than simply liking the same movies … it’s about shared values, ethics, social, physical, and intellectual characteristics … it’s also about sex … without good sexual chemistry and compatibility, many relationships simply don’t work.”

References
1. (a) Hamburg, Sam R. (2001). Will Our Love Last? A Couple’s Road Map. Scribner.
(b) Relationship Chemistry – theRelationshipGym.com.
(c) Fishman, Barbara M. and Ashner, Laurie. (1994). Resonance: the New Chemistry of Love. San Francisco: HarperSanFrancisco.
2. LoveIsSexy (About) – LoveIsSexy.com.