# The Effect of Anchor Group on the Phonon Thermal Conductance of Single Molecule Junctions
## 1 Introduction  
Currently, nearly 10% of the world's electricity is used by computers and the internet and converted to heat. This waste heat could be used to generate electricity economically, provided materials with a high thermoelectric efficiency could be identified [1]. The demand for new thermoelectric materials has led to a worldwide race to develop materials with a high thermoelectric efficiency [2, 3, 4, 5, 6, 7, 8, 9, 10, 11]. The efficiency of a thermoelectric device is inversely proportional to its thermal conductance \(\kappa=\kappa_{p}+\kappa_{e}\) due to electrons (\(\kappa_{e}\)) and phonons (\(\kappa_{p}\)) [12]. Therefore, low-thermal-conductance materials are needed for an efficient conversion of heat into electricity. The state of the art thermoelectric figure of merit (ZT) was found in inorganic materials, e.g., 2.2 at high temperatures 900 K [13]. These inorganic materials are toxic, and their global supply is limited. Therefore, organic materials are now being considered [14]. Molecules are attractive candidates for thermoelectricity because their structure can be modified with atomic precision and desirable properties can be induced by the engineering of their structure [15, 16]. They are also expected to show intriguing properties, such as room temperature quantum and phonon interference, that can be used to simultaneously increase their electrical conductance and Seebeck coefficient and to suppress their thermal conductance [17, 18]. Just recently the technological challenge of measuring the thermal conductance of single molecules was overcome [19, 20]. This opens new avenues to study the thermoelectric efficiency of single molecules [21, 22]. To optimize molecular junctions for a maximumefficiency, strategies to increase their electrical conductance and Seebeck coefficient simultaneously and to suppress their thermal conductance should be developed. So far, thermal conductance of a few molecules, including C60 [23], alkanes [19; 24], OPE2 derivatives [17], OPE3 [19; 23], Benzene [25; 26], Oligoyne [24], biphenyl-dithiol [17], bipyridyl and its radical counterpart [18], between gold electrodes has been calculated. Among these, thermal conductance of alkanes [19; 20] and OPE3 [27] molecules with thiol anchor were measured. Table 1 shows a summary of room temperature thermal conductance calculations due to electrons (\(\kappa_{e}\)) and phonons (\(\kappa_{p}\)) of single molecules between gold electrodes using density functional theory (DFT) combined with the non-equilibrium Green's function (NEGF) method for transport calculations and comparison with single molecule thermal conductance measurements. Previous studies show that the thermal conductance of single molecules is dominated by phonons. For example, the measured thermal conductance of OPE3 is 20 \(\pm\) 6 pW/K [27]. The calculated contribution from electrons and phonons are 0.1 pW/K and 19 pW/K, respectively [27]. The thermal conductance can be controlled using electrically inert side groups and phonon interference through multipath molecular backbones [17; 25; 26; 28; 29].