When corals are first discussed, there relationship with zooxanthellae is often mentioned. Zooxanthellae provide the coral sugar, and the coral provided protection and fertilizers. However, many corals far outside the tropic areas or in deep water do not contain zooxanthellae. They basically get there energy from food. After all, corals are animals. There are even many corals in the tropic and subtropics that can live with or without zooxanthellae. These tend to find low light places to live. Tubaestrae, Gorgonians and Dendrophilia are examples. In fact, at one time, reefs were made up of corals without zooxanthellae. But corals with zooxanthellae tend to out compete those without. You might find the corals under the NPS label for nonphotosynthetic. Examples are chili coral, carnation tree, flower tree coral, Christmas tree coral, red finger gorgonian, blueberry sea fan, & tube coral.
If you are interested in a tank like this, watch this video. It also shows what fish may be good for that type of tank.
https://www.bing.com/videos/search?q=nonphotosynthetic+corals&&view=detail&mid=CB1D683CE11BA88A8B7ACB1D683CE11BA88A8B7A&FORM=VRDGAR
https://www.bing.com/videos/search?q=nonphotosynthetic+corals&&view=detail&mid=D3D5973FD1F63C6D7B6AD3D5973FD1F63C6D7B6A&FORM=VRDGAR
If you are interested in a tank like this, watch this video. It also shows what fish may be good for that type of tank.
https://www.bing.com/videos/search?q=nonphotosynthetic+corals&&view=detail&mid=CB1D683CE11BA88A8B7ACB1D683CE11BA88A8B7A&FORM=VRDGAR
https://www.bing.com/videos/search?q=nonphotosynthetic+corals&&view=detail&mid=D3D5973FD1F63C6D7B6AD3D5973FD1F63C6D7B6A&FORM=VRDGAR