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Parity oscillations of Kondo temperature in a single molecule break junction

We study the Kondo temperature ($T_K$) of a single molecule break junction. By employing a numerical renormalization group calculations we have found that $T_K$ depends dramatically upon the position of the molecule in the wire formed between the contacts. We show that $T_K$ exhibits strong \emph{oscillations} when the parity of the left {and/or} right number of atomic sites ($N_L,N_R$) is changed. For a given set of parameters, the maximum value of $T_K$ occurs for ($odd,odd$) combination, while its minimum values is observed for ($even,even$). These oscillations are fully understood in terms of the effective hybridization function.