Abstract: Main cause for uncertainty of atomic structure theory is indicated. A method for uncertainty of temperature-and-density-dependent atomic models in radiative opacity calculation is described via various functional exchange potentials. Uncertainty quantification(UQ) calculation of atomic structures in density-functional at arbitrary temperature and density is carried out by definition of algorithms of modulus. Several procedures indispensable for uncertainty study, and formulae about UQ of electron energy levels and of matrix elements are given. A criterion is proposed to estimate atomic models quantificationally. Feasibility of UQ method is verified by of data of mercury, gold and iron compared with data from‘quasi true’atomic model.

Key words: uncertainty quantification, radiative opacity, atomic structure, slef-consistent field