where the coefficients α ikl control the Gaussian function widths, Y lm are the set of spherical harmonic functions, and C iklm are the set of coefficients for the auxiliary basis. The coefficients C iklm in the auxiliary density basis are both the outputs of the machine learning model and the data set that the model is trained on. The loss function of the model is calculated by comparing the mean square error of the output coefficients against the training data coefficients. The def2-universal-jfit auxiliary basis was used for this study , since expressing the density in this form has been shown to be highly efficient in other machine learning density models .