The Ledoux criterion is used to determine which regions of the star are unstable to convection. The diffusion coefficient, \(D\), in convective regions is approximated with where \({\mathrm{H}_{\mathrm{P}}}\) is the pressure scale height, \({v}_c\) is the convective velocity, and \(\alpha\) the mixing length parameter. We fix \(\alpha = 1.5\), which results from evolutionary tracks of the Sun the \(\alpha\) dependence of our scenario will be presented in future work. The convective velocity, \({v}_c\), is calculated using the mixing length theory \cite{BV58} (MLT hereafter) and the convective contribution to the diffusion coefficient becomes: where \(\varkappa\) is the opacity, \(\rho\) is the density, \(\beta\) is the ratio of gas pressure to total pressure, \(g\) is the local gravitational acceleration, and \(c\) is the speed of light. Here, \({\nabla_{\mathrm{\!rad}}}\) and \({\nabla_{\mathrm{\!ad}}}\) are the radiative and adiabatic gradients, respectively.