chemistry between him and her

chemistry
〔学問の分野の〕化学
〔物質の〕化学的性質［構造］
〔複雑なものの〕要素、性質、相互関係
〔二人の間の〕相性、親和力

If there weren't any personal chemistry between us, I wouldn't be sitting here right now. 
私たちの相性がよくないのなら、私は今ここに座ってはいない。

The chemistry between you two has gone sour. 
あなたたち二人の相性はこじれてきています。

There's no chemistry between that guy and me. 
あいつとは肌が合わない。

chemistry between administrators and instructors
管理する側と教える側の相性

chemistry between him and her
《the ～》彼と彼女との相性

a blind date
an arranged meeting for two people who have never met each other before, in order to try to start a romantic relationship