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We consider the cumulant expansion of the periodic Anderson model (PAM) in the case of a finite electronic correlation U, employing the hybridization as perturbation, and obtain a formal expression of the exact one-electron Green's function (GF). This expression contains effective cumulants that are as difficult to calculate as the original GF, and the atomic approach consists in substituting the effective cumulants by the ones that correspond to the atomic case, namely by taking a conduction band of zeroth width and local hybridization. In a previous work (T. Lobo, M. S. Figueira, and M. E. Foglio, Nanotechnology 21, 274007 (2010)10.1088/0957-4484/21/27/274007) we developed the atomic approach by considering only one variational parameter that is used to adjust the correct height of the Kondo peak by imposing the satisfaction of the Friedel sum rule. To obtain the correct width of the Kondo peak in the present work, we consider an additional variational parameter that guarantees this quantity. The two constraints now imposed on the formalism are the satisfaction of the Friedel sum rule and the correct Kondo temperature. In the first part of the work, we present a general derivation of the method for the single impurity Anderson model (SIAM), and we calculate several density of states representative of the Kondo regime for finite correlation U, including the symmetrical case. In the second part, we apply the method to study the electronic transport through a quantum dot (QD) embedded in a quantum wire (QW), which is realized experimentally by a single electron transistor (SET). We calculate the conductance of the SET and obtain a good agreement with available experimental and theoretical results

General derivation of the Green's functions for the atomic approach of the Anderson model: application to a single electron transistor (SET)