Gold-centered carbene-metal-amides (CMAs) containing cyclic (alkyl)(amino)carbenes (CAACs) are promising emitters for thermally activated delayed fluorescence (TADF). Aiming at design and optimization of new TADF emitters, we report a density functional theory study of over 60 CMAs with various CAAC ligands, systematically evaluating computed parameters in relation to photoluminescence properties. We demonstrate that the efficiency of TADF of CMAs, arising from a compromise of exchange energy and oscillator strength, is governed by the overlap of HOMO and LUMO orbitals, where HOMO is localized on amide and LUMO on Au-carbene. The S0 ground states and excited T1 states of the CMAs adopt approximately coplanar geometries of carbenes and amides, but rotate perpendicular in the excited S1 states, resulting in degeneracy or near-degeneracy of S1 and T1, accompanied with lowering of the S1-S0 oscillator strength from its maximum at coplanar geometries to near zero at rotated geometries. Based on computations, promising new TADF emitters are proposed and synthesized. Bright CMA complex (Et2CAAC)Au(carbazolide) is obtained and fully characterized to demonstrate that high radiative rates up to 106 s-1 can be obtained for the gold-CMA complexes with small CAAC-carbene ligands.