# The Effect of Anchor Group on the Phonon Thermal Conductance of Single Molecule Junctions
## 1 Introduction
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Molecule**} & \multicolumn{3}{c}{**Calculated \(\kappa\) (pW/K)**} & **Measured \(\kappa\)** \\ \cline{2-5}  & \(\kappa_{p}\) & \(\kappa_{e}\) at DFT Fermi Energy & **(pW/K)** & **Ref.** \\ \hline Biphenyl–4,4\({}^{\prime}\)–dithiol (BDT) & 19.6 & 2.3 & - & [17] \\ \hline
2,2\({}^{\prime}\)–dinitro–BDT & 11.7 & \(<\)0.01 & - & [17] \\ \hline oligo(2–phenylene–4,4\({}^{\prime}\)–ethynylene)–dithiol (OPE2) & 9.9 & \(<\)0.01 & - & [17] \\ \hline
2,2\({}^{\prime}\)–dinitro–OPE2 & 9.7 & 16.7 & - & [17] \\ \hline
4,4\({}^{\prime}\)–bipyridyl (BP) & 34.8 & \(<\)0.01 & - & [17] \\ \hline
3,3\({}^{\prime}\),5,5\({}^{\prime}\)–tetrachloride–BP & 14.8 & \(<\)0.01 & - & [17] \\ \hline
3,3\({}^{\prime}\)–dinitro–BP & 23.6 & \(<\)0.01 & - & [17] \\ \hline oligo(3–phenylene–4,4\({}^{\prime}\)–ethynylene)–dithiol (OPE3) & 19 & 0.1 & 20 \(\pm\) 6 & [19] \\ \hline Octane–dithiol & 23 & 0.02 & 29 \(\pm\) 8 & [19] \\ \hline Alkanes with dihydrogeno[b]thiophene (BT) anchor (\(N=\) number of C2H4) & \(N=\) 1 & 25.4 & 0.03 & - & [24] \\ \hline \multirow{2}{*}{\begin{tabular}{c} Alkanes with dihydrogeno[b]thiophene \\ (\(N=\) number of C2H4) \\ \end{tabular} } & \(N=\) 2 & 33.4 & \(<\)0.01 & - & [24] \\ \cline{2-5}  & \(N=\) 4 & 30.3 & \(<\)0.01 & - & [24] \\ \hline \multirow{2}{*}{\
\begin{tabular}{c} Alkanedithiol \\ (\(N=\) number of C2H4) \\ \end{tabular} } & \(N=\) 8 & 5.6 & \(<\)0.01 & - & [24] \\ \cline{2-5}  & \(N=\) 1 & 17–22 & 5.7 & 14.6 \(\pm\) 3 & [20] \\ \cline{2-5}  & \(N=\) 2 & 18–27 & 1.1 & 13.4 \(\pm\) 5 & [20] \\ \cline{2-5}  & \(N=\) 3 & 17–29 & \(<\)0.01 & 16.9 \(\pm\) 3 & [20] \\ \cline{2-5}  & \(N=\) 4 & 20–33 & \(<\)0.01 & 26.3 \(\pm\) 7 & [20] \\ \cline{2-5}  & \(N=\) 5 & 17–33 & \(<\)0.01 & 28 \(\pm\) 8 & [20] \\ \hline \multirow{2}{*}{
\begin{tabular}{c} Oligoyne with BT anchor \\ (\(N=\) number of C2H4) \\ \end{tabular} } & \(N=\) 1 & 15.6 & 0.4 & - & [24] \\ \cline{2-5}  & \(N=\) 2 & 9.2 & 0.5 & - & [24] \\ \cline{2-5}  & \(N=\) 4 & 7.7 & 0.25 & - & [24] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Room temperature thermal conductance due to electrons (\(\kappa_{e}\)) and phonons (\(\kappa_{p}\)) of single molecules between gold electrodes using DFT–NEGF calculations and single molecule measurements. In most of the molecular junctions, molecules are contacted to the electrodes via suitable anchor groups [30]. From Table 1, the calculated thermal conductance of alkanes is different in [24] (Alkanes with dihydrobenzzo[b]thiophene (BT) anchor) and [20] (Alkanedithiol). While the electrodes and the molecular backbone are the same, these calculations use different anchor groups for alkanes. Therefore, it seems that the anchor group plays a significant role in the thermal conductance of molecules. In order to understand the effect of anchor groups on thermal conductance, a systematic study of a given molecular backbone with different anchor groups is needed. For this reason, we choose OPE3 and exploited its thermal conductance with different anchor groups including pyridyl (PY), thiol (S), methyl sulphide (SMe) and carbodithioate (CS) between two gold electrodes (see Figure 1). We found that thermal conductance due to phonons is affected significantly by the choice of anchor groups. For example, thermal conductance of OPE3 decreased by a factor of 2 from CS to SMe. This is significant because the thermoelectric figure of merit (ZT) is inversely proportional to thermal conductance, and therefore ZT can be enhanced by a factor of 2 using the choice of a suitable anchor group.