**1. Introduction**

In recent years, the field of molecular thermoelectrics has attracted a lot of attention [1–12]. One of the aims is to improve the thermoelectric efficiency of nanoscale devices by controlling the electronic and vibrational degrees of freedom of the molecules. Moreover, useful information on charge and energy transport mechanisms can be extracted by studying the thermoelectric properties of molecular junctions [1,3,4,13,14]. In addition to the charge conductance *G*, the Seebeck coefficient *S* is typically measured in these devices. Measurements in junctions with fullerene ( *C*60) have found a high value of thermopower (of the order or even smaller than −30 μV/K) [4]. Understanding the thermopower is also important for helping advances in thermoelectric performance of large-area molecular junctions [15,16]. Moreover, recently, the application of an Al gate voltage at *Au*–*C*60–*Au* junction has allowed to achieve the electrostatic control of charge conductance and thermopower with unprecedented control [17]. However, the precise transport mechanisms affecting both *G* and *S* remain elusive in these kinds of measurements. Finally, due to experimental challenges [2,18–20], only recently the thermal conductance of single-molecule junctions has been fully characterized [21].

In molecular junctions, relevant contributions to the thermoelectric properties typically result from intramolecular electron–electron and electron–vibration interactions [1,22]. An additional source of coupling between electronic and vibrational degrees of freedom is also provided by the center of mass oscillation of the molecule between the metallic leads [23]. Different theoretical techniques [1,22] have been used to study the effects of local many-body interactions which affect the thermoelectric transport properties [7–9,24–28] in a significant way.

In devices with large molecules such as fullerenes or carbon nanotube quantum dots, a non-perturbative treatment of electron–vibration coupling can be obtained within an adiabatic approach which is based on the slowness of the relevant vibrational modes in comparison with the

fast electron dynamics [29–39]. The adiabatic approach can also include a strong Coulomb repulsion allowing the self-consistent calculation of thermoelectric properties of massive molecules, such as fullerenes, within the Coulomb blockade regime [40].

In this paper, the thermoelectric properties of a molecular junction are analyzed focusing on the role of electron–electron and electron–vibration interactions. An adiabatic approach developed in the literature takes into account the interplay between the low frequency center of mass oscillation of the molecule and the electronic degrees of freedom within the Coulomb blockade regime [40]. Parameters appropriate for junctions with *C*60 molecules are considered in this paper. In particular, a one-level model is taken into account since it describes the relevant transport level of fullerene and its alignment to the chemical potential of the metallic leads.

The aim of this paper is to thoroughly investigate both the charge conductance and the Seebeck coefficient since accurate experimental data are available for *Au*–*C*60–*Au* junction in [17] as a function of the voltage gate. We show that an accurate description of the transport properties is obtained in the intermediate regime for the electron–vibration coupling and in the strong coupling regime for the electron–electron interaction. Moreover, we point out that only the combined effect of electron–vibration and electron–electron interactions is able to predict the correct behavior of both the charge conductance and the Seebeck coefficient finding a very good agreemen<sup>t</sup> with available experimental data.

The paper is organized as follows. In Section 2, a very general model for many electronic levels and multiple vibrational degrees is considered and the adiabatic approach is exposed. In Section 3, the one-level model is presented. In Section 4, the theoretical results are presented together with the precise comparison with experimental data. Finally, in Section 5, conclusions and final discussions are given.
