If he was among the wounded left in Murfreesboro and died there, his remains are likely buried in Evergreen Cemetery. I put the link to our local SCV Camp 33 website that can tell you more about that burial site.

Of the nearly 2,000 soldiers buried in the Evergeen Cemetery plot, a mere handful of names are known. I checked the list, and there is a Captain Williams (state and first name not listed). If your guy was a captain, perhaps this is him.