Influence of Charge Transfer on Thermoelectric Properties of Endohedral Metallofullerene (EMF) Complexes

Abstract

A considerable potential advantage of manufacturing electric and thermoelectric devices using endohedral metallofullerenes (EMFs) is their ability to accommodate metallic moieties inside their cavities. Published experimental and theoretical works have explained the usefulness of this resilience feature for improving the electrical conductance and thermopower. Through thorough theoretical investigations of three EMF complexes employing three different metallic moieties involving Sc₃C₂, Sc₃N, and Er₃N and their configurations on a gold (111) surface, this research demonstrates that the thermoelectric properties of these molecular complexes can be tuned by taking advantage of the charge transfer from metallic moieties to Ih-C₈₀ cages. Mulliken, Hirshfeld, and Voronoi simulations articulate that the charge migrates from metallic moieties to cages; however, the amount of the transferred charge depends on the nature of the moiety within the complex.

1. Introduction

Charge transfer (CT), electron transfer (ET), and donor–acceptor (DA) complexes have long been the focus of investigation. Consequently, charge transfer perception is essential in many organic devices, because of its various uses in many disciplines involving chemistry, physics, materials science, medicine, and biology. For example, CT has been extensively explored in organic solar cells [1,2,3], water splitting devices, [4], and single molecule electronics [5,6,7,8,9]. Similarly, there have been varying types of donors and acceptors in complicated charge transfer research [10,11,12,13]. The chemical nature of the molecule determines whether a molecule behaves as a donor or acceptor. In such systems, an electron-rich donor commonly acts as the receptor and the acceptor is often electron-deficient. In measurement methods, the charge transfer through molecular systems is classified into two categories: CT in Donor–Bridge–Acceptor (DBA) molecules and CT in Metal–Bridge–Metal (MBM) junctions [14,15,16].

To probe the charge transfer and density functional theory (DFT), analysis can be employed to determine the nature of two molecular segments (i.e., molecule) in complexes based on their electronic structures, as illustrated in Figure 1. Donor–acceptor interaction energy calculation within the DFT framework plays a crucial role in studying charge transfer behaviours inside a molecular system. DFT analyses have been widely used to investigate CT complexes [17,18,19].

In the present research, we explore the electronic properties of three donor–acceptor complexes. The major investigation here is dedicated to the analysis of three distinct methodologies including the Mulliken population [20], Hirshfeld [21], and Voronoi [22]. These methods were used to trace down the charge transfer between the molecular segments (see Figure 1). CT calculations were first performed in isolated systems (i.e., gas phase), and then on a Au (111) surface (see Section S3 of the SI).

Figure 2 below illustrates the anatomy of three complexes, each of which consists of two molecular segments involving a metallic moiety such as Sc₃C₂, Sc₃N, Er₃N, and Ih-C₈₀ cages. When the metallic moiety is encapsulated inside the fullerene cage, the outcome is endohedral metallofullerene (EMF) complexes. The current research investigates the electronic structure of three EMFs, i.e., Sc₃C₂@C₈₀, Sc₃N@C₈₀, and Er₃N@C₈₀; examples of three EMF complexes and an empty fullerene are shown in Supplementary Figure S1 and Figure S2.

2. Computational Methods

All the theoretical simulations were carried out by employing the density functional (DFT) code SIESTA [23]. The optimum geometries of isolated EMFs were obtained by relaxing the molecules until all forces on the atoms were less than 0.01 eV/Å (for more detail, see Supplementary Figure S1 and Figure S2). A double-zeta plus polarization orbital basis set was used, with norm-conserving pseudopotentials and the local density approximation (LDA) exchange with a functional correlation, and to define the real space grid, an energy cut-off of 250 Rydberg was used. Results using GGA were also calculated and found that the resulting functions were comparable [24,25], with results obtained employing LDA functional exchange (see Section 1). To simulate the likely contact configuration during a break-junction experiment, we employed leads constructed from 6 layers of Au (111), each containing 30 gold atoms and further terminated with a pyramid of gold atoms.

To determine the optimum distance of EMF complexes attaching to the Au (111) metals, density functional theory and the counterpoise method were used, which removes basis set superposition errors (BSSEs). The binding distance was defined as the distance between the gold surface and the EMF complex. The ground state energy of the total system was calculated using SIESTA and is denoted $E_{AB}^{AB}$. The energy of each monomer was then calculated in a fixed basis, which is achieved through the use of ghost atoms in SIESTA (see Section 4). Since the energy of the individual complex in the presence of the fixed basis is defined as $E_A^{AB}$ and for the isolated gold as $E_B^{AB}$, the binding energy $\Delta \left(\mathsf{\theta }\right)$, is then calculated using the following equation [26,27,28]:

$$\mathrm{Binding}\mathrm{Energy}=E_{AB}^{AB}-E_A^{AB}-E_B^{AB}$$

(1)

3. Results and Discussion

The electronic properties of the three EMF complexes involving Sc₃C₂@C₈₀, Sc₃N@C₈₀, and Er₃N@C₈₀ were simulated employing both density functional theory (DFT) and quantum transport theory. To have a deep understanding of thermoelectric properties, the wave function of the investigated complexes, i.e., the lowest unoccupied orbitals (LUMO) and the highest occupied molecular orbitals (HOMO), along with their energies, are explored, as illustrated in Supplementary Figures S3–S5. These isosurface plots clearly demonstrate a significant weight on metallic moieties Sc₃C₂, Sc₃N, and Er₃N, in contrast to Ih-C₈₀ cages. The significant weight occurs on the LUMO orbitals and it is well-known that these complexes possess LUMO dominated transport. This denotes that metallic moieties play a pivotal role in tuning the electronic properties of the EMF complexes.

As a first step, we investigated the charge transfer through these EMF complexes. Charge calculations are common practise in chemical science measurements and calculations. We shall first discuss charge transfer analyses in the gas phase for the three EMFs. We evaluate the net charge transfer from metallic moieties Sc₃C₂, Sc₃N, and Er₃N to Ih-C₈₀ cages using three different DFT analyses methods Mulliken, Hirshfeld, and Voronoi (see Section S3 in the SI).

Table 1. Gas phase, charge transfer calculations employing Mulliken, Hirshfeld, and Voronoi methods of Sc₃C₂@C₈₀, Sc₃N@C₈₀, and Er₃N@C₈₀ complexes. The total number of electrons transferred from metallic moieties (with a charge of +|e|) to Ih-C₈₀ cages (with a charge of –|e|) to form complexes. Note: loss–gain differences gained by C₂, N, and N (numbers in brackets) of Sc₃C₂@C₈₀, Sc₃N@C₈₀, and Er₃N@C₈₀ complexes.

Metallic Moiety	Mulliken		Hirshfeld		Voronoi
	moiety	cage	moiety	cage	moiety	cage
Sc3C2	+1.40	−1.14	+1.15	−0.83	+1.06	−0.72
C2	(−0.26)	-	(−0.32)	-	(−0.34)	-
Sc3N	+1.50	−1.26	+1.31	−0.98	+1.27	−0.96
N	(−0.24)	-	(−0.33)	-	(−0.31)	-
Er3N	+6.96	−5.14	+7.48	−6.14	+7.14	−5.82
N	(−1.82)	-	(−1.34)	-	(−1.32)	-

below demonstrates that the three metallic moieties donate electrons to the C₈₀ cage. However, the total number of the transferred electrons depends on the chemical nature (i.e., atom species) and geometrical shape of the metallic moiety. We find that the donation of erbium nitride Er₃N is the highest followed by scandium nitride Sc₃N and then scandium carbide Sc₃C₂. Furthermore, the charge transfer through the three EMF complexes follows the order Er₃N@C₈₀ > Sc₃N@C₈₀ > Sc₃C₂@C₈₀ for Mulliken, Hirshfeld, and Voronoi analyses.

Surprisingly, there is a difference between the total number of the donated and gained electrons through the complexation (i.e., encapsulating the moiety inside cage). For example, the scandium carbide Sc₃C₂ donates 1.40 electrons to the cage; however, only 1.14 is indeed gained by the cage (loss–gain difference), and this occurs through all the EMF complexes. To answer this question, we tracked down the CT from the donor to receptor, atom by atom. The tracking analyses suggest the missing electrons are gained by the metallic moiety itself.

To accommodate this, we find that loss–gain differences are indeed gained by the moieties. For instance, through Sc₃C₂@C₈₀ complexation, the two carbon atoms of Sc₃C₂, gain 0.26, 0.32, and 0.34 electrons from the moiety’s donation. Similarly, the nitrogen atoms of Sc₃N and Er₃N gain 0.24, 0.33, and 0.31 and 1.82, 1.34, and 1.32 electrons, respectively, when they form complexes with Ih-C₈₀ cages (above analyses evaluated via the Mulliken population, Hirshfeld, and Voronoi). It should be noted that the electron travelled from the moiety to the Ih-C₈₀ cage has a significant effect on the conductance $G$ and thermopower $S$; more details have been given previously [20,29]. Moreover, it should be noted that the total number of electrons donated by erbium nitride Er₃N is significantly larger than of Sc₃C₂ and Sc₃N moieties; we will discuss that later.

To mimic the likely metal–organic contact configuration during a scanning tunnelling microscope break-junction measurement (STM-BJ), we now repeat the above analysis for the case when the EMF forms a complex on a gold surface. Calculations in this section are for three parameters: metallic moiety, Au surface (2nd, 4th, and 6th columns), and a Ih-C₈₀ cage (3rd, 5th, and 7th columns).

Table 2. On a gold surface, charge transfer calculations employing the Mulliken, Hirshfeld, and Voronoi methods of Sc₃C₂@C₈₀, Sc₃N@C₈₀, and Er₃N@C₈₀ complexes. The total number of electrons transferred from metallic moieties and Au surface (with a charge of +|e|) to Ih-C₈₀ cages (with a charge of −|e|) to form complex Au junctions. Note: numbers in brackets correspond to Au donation (+|e|) and C₂, N gaining (−|e|).

Moiety + Au	Mulliken		Hirshfeld		Voronoi
	moiety	cage	moiety	cage	moiety	cage
Sc3C2	+1.33	−1.39	+0.93	–0.81	+0.97	−0.79
Au, C2	(+0.3, −0.24)	-	(+0.2, −0.32)	-	(+0.18, −0.36)	-
Sc3N	+2.15	−2.09	+1.07	–0.98	+1.04	–1.02
Au, N	(+0.22, −0.28)	-	(+0.23, −0.32)	-	(+0.24, −0.26)	-
Er3N	+6.53	−5.20	+6.96	–5.80	+6.66	−5.60
Au, N	(+0.24, −1.57)	-	(+0.28, −1.44)	-	(+0.29, −1.35)	-

suggests that the electronic charge travels from both the metallic moiety and the gold surface to the Ih-C₈₀ cage for the three configurations (i.e., EMF complex + Au surface). This behaviour is expected to occur as both the moiety and Au are metals, unlike the cage.

Table 2 explains that both the Sc₃C₂ and Au lose (+) electrons, and in total, their donation is 1.63 electrons (Sc₃C₂ = +1.33 and Au = +0.3 electrons). Again, only 1.39 is the gained (−) by the Ih-C₈₀ cage, the difference of 0.24 electrons gained by C₂ atoms within the moiety. Summing up the two negative figures (1.39 and 0.24), we obtain the total transferred electrons to be 1.63 electrons. Looking at the numbers in brackets mainly Au donation and C₂, N gaining, one could summarise that Au donation is approximately 0.2–0.3 and C2 and N gaining 0.24–1.60 electrons. Furthermore, in all cases, the gain by C₂ and N is larger than Au donation; we attribute that to the fact that C₂ and N atoms are in direct contact with EMF moieties.

Again, in the erbium nitride configuration (Sc₃N@C₈₀ + Au), net charge transfers are significantly larger than those of the scandium nitride and scandium carbide configurations. Table 1 and Table 2 show that the net charge transfers of Er₃N are more than four times higher than those of Sc₃C₂ and Sc₃N, and the reason for this is that the erbium nitride moiety possesses f-electrons in its outer orbital shells [30]. It is widely known that DFT cannot treat electrons in f-orbitals accurately [31].

The above result explains why the $\Delta \left(\mathsf{\theta }\right)$ of Er₃N is less symmetric than that of Sc₃C₂ and Sc₃N, as shown in Figure 3 (Note: Figure 3 is reported in our previous work [29]). This also applies to the charge inhomogeneity (${\sigma }_q$). In ref. [29], the standard deviations of charge distributions on the three EMFs complexes were evaluated, and the values indicated that the ${\sigma }_q$ of the erbium nitride complex was 10 times less than that of the other complexes, as illustrated in

Table 3. Standard deviations of charge ${\sigma }_q$ for Sc₃C₂@C₈₀, Sc₃N@C₈₀, and Er₃N@C₈₀ complexes. Charges are simulated using the Mulliken, Hirshfeld, and Voronoi methods. Adapted with permission from ref [29]. Copyright 2022 Nanoscale Horizons, 2022.

EMF Complex	$${\mathit{\sigma }}_{\mathbf{Mulliken} }$$	$${\mathit{\sigma }}_{\mathbf{Hirshfeld}}$$	$${\mathit{\sigma }}_{\mathbf{Voronoi}}$$
Sc3C2@C80	0.0154	0.0113	0.0133
Sc3N@C80	0.0163	0.0109	0.0119
Er3N@C80	0.00378	0.00259	0.00268

.

CT analyses that were performed in both the solute and on a Au surface are essential to determine the total number of electrons transferred from metallic moieties to the Ih-C₈₀ cage. These charge transfers have a great influence on the electric and thermoelectric properties of the EMFs. The electrical conductance is boosted in crown ether molecules [32,33], due to charge transfer from the ion to the molecular wire, causing the molecular resonances to shift closer to the electrode Fermi energy. Similarly, CT enhances the Seebeck coefficient in crown ether molecules [34,35,36,37] and endohedral metallofullerenes [38,39,40].

Many experimental and theoretical studies pointed out that EMF–complex junctions retain a high single molecule power factor. For example, Lee and his co-workers [41] reported that the Gd@C₈₂ complex has the biggest power factor for a molecular device (at the time of publication), which is about 16.2 fW K⁻². This is equivalent to approximately 4 × 10 μW K⁻² m⁻¹ for a Gd@C₈₂ monolayer. In another study [29] performed in 2022, the researchers noticed a larger PF of 50 fW K⁻² for Sc₃N@C₈₀ and Sc₃C₂@C₈₀ complexes, and some measurements hit 70–80 fW K⁻² for Sc₃N@C₈₀ and Sc₃C₂@C₈₀ complexes. Statistically, they report larger values for the carbide complex (Sc₃C₂@C₈₀). Considering all their measured conductance and Seebeck coefficient values, the PF can be statistically improved when the charge transfer becomes larger. We attribute this desirable feature to the CT phenomena. Table 3 above clearly illustrates that the charge transfer of Sc₃N@C₈₀ and Sc₃C₂@C₈₀ complexes are approximately 10 times larger than that of the Er₃N@C₈₀ complex, and this explains why their conductance $G$ and Seebeck $S$ (i.e., power factor $G{S}^2$) are larger than those of Er₃N@C₈₀, as shown in Figure 4 below (Note: Figure 4 has been reported in our previous work [29]).

Large power factor $G{S}^2$ and bi-thermoelectric behaviour of the studied EMF complexes underline our initial intuition that charge transfer (CT) results in considerable improvement in the thermoelectric transport properties, compared with an empty cage such as C₆₀. This desirable feature has also been noted previously [41] in some EMF complexes involving Gd@C₈₂ and Ce@C₈₂, and the empty C₈₂ displayed mainly negative Seebeck coefficients, with occasional positive Seebeck coefficients. The positive and negative Seebeck coefficients were ascribed to meta-geometries. The reported findings of the thermopower demonstrate improvements in the EMFs thermoelectric properties compared to the empty C₈₂. Compared to the current investigated EMF complexes, the only difference with the complexes explored in a previous study [41] is the number of metallic atoms within the complex, and in [41], a single atom was positioned out within the cage. This difference could lead only to less migrated charge to the fullerene cage as the metallic moiety is smaller.

4. Conclusions

In conclusion, through a systematic theory study, we have demonstrated that the electrical and thermoelectrical performance of endohedral metallofullerene (EMF) complexes and configurations can be modulated by chemically varying the metallic moiety that encapsulates inside Ih-C₈₀ cages. The electric charge transfer of three EMFs involving Sc₃C₂@C₈₀, Sc₃N@C₈₀, and Er₃N@C₈₀ complexes and their configurations when they are placed on a gold (111) surface have been investigated in three different charge transfer methods. The Mulliken, Hirshfeld, and Voronoi methods all suggest that the charge migrates from metallic moieties such as Sc₃C₂, Sc₃N, and Er₃N to C₈₀ cages; however, the amount of the transferred charge depends on the nature of the moiety inside the EMF complex. Published studies [32,33,38,42,43,44,45] evidenced that the CT improve both conductance and thermopower. This work sheds light on new strategies for designing electric and thermoelectric devices based on tuning the CT by using different metallic moieties with potential practical applications.