Does Kirchhoff’s Law Work in Molecular-ScaleStructures?

This study aims to theoretically and comprehensively investigate the single-molecule electrical conductance of symmetric and asymmetric alkane cyclic (<i>SAC</i> and <i>AAC</i>) molecules and their corresponding linear chains with three different terminal end groups including thiol (−<i>SH</i>), direct carbon (−<i>C</i>), and amine (−<i>NH</i>₂). Here, we examine the validity of Kirchhoff’s law concerning sigma nonconjugated molecules at the nanoscale level. Counterintuitively, the electrical conductance (<i>G</i>) of symmetric and asymmetric alkane cyclic molecules with two parallel conductance paths is lower than that of their corresponding single chains with only one conductance path. This completely contradicts classical rules for combining conductances in parallel, regardless of the anchor group type, in light of this study’s use of symmetric and asymmetric cyclic molecules. A comparison of the DFT prediction trends with scanning tunneling microscopy measurements indicates that they are well-supported. The results of this investigation demonstrate an excellent correlation between our simulations and experimental measurements, for both SAC and AAC structures of different cavity size <i>n</i>,<i>m</i> = 3,3; 4,4; 5,5···10,10 and <i>n</i>,<i>m</i> = 3,5; 4,6; 5,7; 6,8; 7,9; 8,10; and 9,11 and for three different terminal end groups.