Metal-organic frameworks (MOFs) combining the merits of both organic and inorganic functional building structures are fundamentally important and can meet the requirement of vast scientific and technological applications. Intrigued from the fact that transition metals (TMs) are widely embedded in the carbon sp(2) network or strongly interact with a bare graphene edge, the single transition metal atom may work as a linker to connect carbon chains to build nanoarchitectures. A new MOF building structure, [Metal-Carbon-(Benzene)-Chain](n) ring abbreviated as [M-CBiC](n) (M = Ti, V, and Cr), with increasing carbon chain length i (= 0, 1, 2, ... ), was proposed as carbon chains CBiC connected by a single transition metal atom M to form a ring structure with multiedges n (= 2-6), based on advanced computational methods. They are thermodynamically stable and chemically and physically versatile with ring shape, electronic structures, optical response, as well as hydrogen adsorption energy that vary by changing the length of the carbon chain, the edge number of rings, or the type of connecting metal atoms. The optical response to incoming light of [M-CBiC](n) rings can be adjustable to cover the entire visible solar spectrum range and exhibit a red shift by either increasing the edge number n or filling the d bands in connecting transition metals. In combination with their ideal adsorption energy of hydrogen atoms, vertical bar Delta G(H*)vertical bar Gwd, the proposed [M-CBiC](n) building structure is attractive for photocatalytic or photoelectrochemical hydrogen evolution applications when they are extended in space to build up 1D, 2D, and 3D MOF frameworks.