Context. The solar irradiance is known to change on time scales of minutes to decades, and it is suspected that its substantial fluctuations are partially responsible for climate variations.

Aims. We are developing a solar atmosphere code that allows the physical modeling of the entire solar spectrum composed of quiet Sun and active regions. This code is a tool for modeling the variability of the solar irradiance and understanding its influence on Earth.

Methods. We exploit further development of the radiative transfer code COSI that now incorporates the calculation of molecular lines. We validated COSI under the conditions of local thermodynamic equilibrium (LTE) against the synthetic spectra calculated with the ATLAS code. The synthetic solar spectra were also calculated in non-local thermodynamic equilibrium (NLTE) and compared to the available measured spectra. In doing so we have defined the main problems of the modeling, e. g., the lack of opacity in the UV part of the spectrum and the inconsistency in the calculations of the visible continuum level, and we describe a solution to these problems.

Results. The improved version of COSI allows us to reach good agreement between the calculated and observed solar spectra as measured by SOLSTICE and SIM onboard the SORCE satellite and ATLAS 3 mission operated from the Space Shuttle. We find that NLTE effects are very important for the modeling of the solar spectrum even in the visual part of the spectrum and for its variability over the entire solar spectrum. In addition to the strong effect on the UV part of the spectrum, NLTE effects influence the concentration of the negative ion of hydrogen, which results in a significant change of the visible continuum level and the irradiance variability.