### Abstract

- Top of page
- Abstract
- 1 Introduction
- 2 Model and method of calculation
- 3 DFT calculations, density of states (DOS), the IDIS-model, and the molecule charging energy
- 4 Pillow effects and the transport energy gap of the molecule
- 5 Conclusions
- Acknowledgements
- Biographical Information
- Biographical Information

The C_{60}/Au(111) metal/organic (MO) interface barrier formation is analyzed from the single molecule limit to the full monolayer case by means of density functional theory (DFT) calculations taking into account charging energy effects to properly describe the electronic structure of the interface and van der Waals (vdW) interactions to obtain the molecule-surface adsorption distance. In our calculations we obtain the density of states (DOS) projected on the C_{60}-molecule, the energy position of its charge neutrality level (CNL), its highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) levels, as well as the interface Fermi level. From these calculations we also obtain the charge transfer, the induced potential on the molecule and the interface screening parameter, *S*. We find a significant evolution from the single molecule to the full monolayer, with the energy barrier for electrons decreasing with the molecule deposition: this reflects an increasing interface screening effect for larger molecule coverages. We also analyze the relationship between *S* and the molecule charging energy, *U*, and deduce an effective interaction between electrons in different C_{60} molecules.

### 1 Introduction

- Top of page
- Abstract
- 1 Introduction
- 2 Model and method of calculation
- 3 DFT calculations, density of states (DOS), the IDIS-model, and the molecule charging energy
- 4 Pillow effects and the transport energy gap of the molecule
- 5 Conclusions
- Acknowledgements
- Biographical Information
- Biographical Information

The growing field of organic electronics relies on the use of organic conjugated molecules as components of multilayer devices. The performance of these devices depends critically on the energy barriers that control the carrier transport between layers, energy barriers that are determined by the relative alignment of the molecular levels at metal–organic (MO) or organic–organic (OO) interfaces 1, 2. This problem, which is typically analyzed by depositing an organic monolayer on a metal or an organic compound, is closely related to the problem of understanding the barrier formation for a single organic molecule sandwiched between two metals 3–5, a case of growing importance within the field of molecular electronics.

In this paper, we consider the paradigmatic case of a C_{60}/Au(111) interface, and analyze how its interface barrier evolves when going from the isolated molecule to the full monolayer case. This approach will allow us to understand how these two limits are interconnected. The advantage of working with C_{60} is its chemical simplicity, which makes the density functional theory (DFT) calculations used in this paper and its corresponding analysis much simpler. Besides we should mention that these molecules have been widely studied deposited on metals 6, forming interfaces 7, 8, encapsulated as a film between two metals as a part of a solar cell 9, or in nanogap organic molecular junctions 10–12.

On the other hand, molecular level alignment at organic junctions has been widely investigated in the last decade 13–15. Since the Schottky–Mott limit (where use of the vacuum level alignment is made) was disproved 16, 17, many different mechanisms have been proposed to explain the barrier formation at MO interfaces: chemical reactions and the formation of gap states in the organic gap 15, 18–20; orientation of molecular dipoles 21, 22; or compression of the metal electron tails at the MO interface due to the Pauli exclusion principle 20, 23–25. It has also been suggested that the tendency of the charge neutrality level (CNL) of the organic material to align with the interface Fermi level 26, 27 plays also an important role; this mechanism is associated with the induced density of interface states (IDIS) and the charge transfer between the organic and the metal. More recently, this approach has been extended to the unified-IDIS model by inclusion of the dipole due to Pauli exclusion principle and intrinsic molecular dipoles 25, 28.

An extra problem appearing when analyzing organic interfaces is related to the standard DFT calculation, that do not yield an appropriate description of the organic transport energy gap 29. In particular, the Kohn–Sham (KS) eigenvalues calculated using the local density approximation (LDA) or generalized gradient approximation (GGA) exchange-correlation functionals yield a transport gap that is too small. It has been argued elsewhere 12, 30 that the effective charging energy of the molecule, *U*, can be used to correct the KS LDA energy gap, *E*^{LDA}, to yield the following transport gap

- ((1))

an equation that will be used below to determine *E*^{t} self-consistently. Another problem is that many MO systems cannot be characterized accurately in a standard (*e.g*., LDA, GGA) DFT formalism due to the poor description of van der Waals (vdW) interactions in these methods 31–36 (the vdW interaction is nonlocal and long-range, while exchange-correlation functionals in standard DFT methods are local and short range, with a typical exponential decay).

The paper is organized as follows: in Section 2, we discuss in detail our approach, while in Sections 3 and 4 present our results. Finally, in Section 5 we present our conclusions.

### 2 Model and method of calculation

- Top of page
- Abstract
- 1 Introduction
- 2 Model and method of calculation
- 3 DFT calculations, density of states (DOS), the IDIS-model, and the molecule charging energy
- 4 Pillow effects and the transport energy gap of the molecule
- 5 Conclusions
- Acknowledgements
- Biographical Information
- Biographical Information

We analyze all these cases using the local-orbital DFT code (FIREBALL) 37 as our basic computational tool. As commented above and discussed in detail below, these DFT calculations are combined with a calculation of the charging energy *U* of the molecule on the metal surface to properly obtain the transport gap, and vdW interactions are also taken into account. We stress that a standard (LDA or GGA) DFT calculation for MO systems like the one analyzed in this work, might be problematic due to the poor description of the organic energy gap and/or of the vdW interactions.

FIREBALL is a real-space DFT technique that uses basis sets of numerical atomic-like orbitals (NAOs) that are strictly zero beyond a given cut-off radius (the Fireball orbitals 38) and that is based in a self-consistent implementation 39 of the Harris–Foulkes 40, 41 functional. In this way, the DFT calculation is cast in a tight-binding-like form 42 where all the required integrals (orbital interactions) are at most three-center, and can be calculated beforehand and placed in data-tables, speeding up the calculations. In these particular calculations we use the LDA exchange-correlation functional and an optimized basis set of sp^{3}d^{5} NAOs for Au, and sp^{3} for C 43, with the following cut-off radii (in a.u.): s = 4.5, p = 4.9, d = 4.3 (Au) and s = 4.5, p = 4.5 (C). For the C_{60} molecule this calculational approach yields CC nearest neighbors distances of 1.40 and 1.47 Å (to be compared with 1.39 and 1.44 obtained in DFT in a plane wave basis 8 and experimental values 1.40, 1.45 Å 44), and a highest occupied molecular orbital (HOMO)/lowest unoccupied molecular orbital (LUMO) energy gap of 2.1 eV, to be compared with 1.6 eV for converged basis set LDA or GGA calculations 30. It is also worth mentioning that the experimental HOMO/LUMO gap (difference between affinity and ionization levels) for the gas-phase C_{60} is 4.9 eV 45, 46. For Au we obtain a bulk lattice parameter of 4.12 Å (experiment 4.07 Å 47). We have checked that with four layers we obtain converged results, that means that we are dealing with systems with a number of atoms between 108 (for the case) and 360 (for the one); that force us to use a very efficient local basis code. We have used 32 *k*-points to map the Brillouin zone at the case, while 8, 8, and 2 *k*-points have been used for the , , and , respectively. Regarding the cluster, an 8 × 8 × 4 size is enough to avoid border effects.

The main approximations of this calculational method are:

- (i)
The use of the LDA exchange-correlation functional. It is well-known that the LDA KS eigenvalues do not provide a good approximation for the transport gap of the organic material. On the other hand, as LDA–DFT exchange-correlation functionals do not take into account properly weak London dispersive forces, in physisorbed systems LDA adsorption energies and distances are not fully reliable.

- (ii)
In the Fireball approach a self-consistent version

39 of the so-called Harris–Foulkes

40,

41 functional is used; in this approximation the Hartree potential is calculated by approximating, in a self-consistent fashion, the total input charge by a superposition of spherical charges around each atom.

- (iii)
Use of a non-fully converged basis set of NAOs.

In the present calculations we correct the deficiencies introduced by these approximations in the following way:

(1) We correct the transport gap using Eq. (1). The point to stress here is that in order to determine *U*, we have first analyzed the case of an isolated molecule on the surface; from our DFT–LDA calculation, *U* can be related to the potential induced in the molecule, *V*^{IDIS} (see below), and to the number of electrons transferred to it, δ*n*, by the equation: Then, *E*^{t} is calculated by introducing in our Hamiltonian the following scissor operator, , () being the empty (occupied) orbitals of the isolated, but deformed, molecule (with the actual geometry of the molecule on the surface). Obviously *U* depends on *E*^{t}, and this forces us to calculate *E*^{t} and *U* self-consistently.

Using this result together with Eq. (1) we can calculate the charging energy for the isolated molecule, *U*^{0}.

Once we have determined *U* from the single molecule case, we calculate the other adlayer cases introducing the same scissor operator which, in this way, takes into account the molecule charging effects. We also use to correct the error in the LDA gap due to the basis set.

(3) The Harris–Foulkes functional neglects off-diagonal contributions of the induced charge (dipolar contributions) whose effects, although not important for the self-consistent calculation itself, introduces non-negligible contributions to the Hartree potential. One of these effects is due to the induced pillow-dipole (or Pauli-exclusion dipole), which is created by the compression of the electron metal tails due to their overlap with the organic molecule wavefunctions. The second effect we consider in this paper is associated with the charge induced on the metal surface and the accompanying induced “metal surface” dipole, that tends to shift that surface charge from practically the last metal layer to the image plane located outwards. Regarding the pillow-dipole, we calculate it following Ref. 25, and analyze how that dipole can be associated with the overlap between the MO wavefunctions. In particular, we calculate the charge rearrangement due to the orthogonalization of the organic/metal orbitals, by expanding the organic/metal many-body interactions up to second order in the wavefunction overlap using the Löwdin symmetric orthogonalization procedure; this rearrangement corresponds to the “push-back” effect experienced by the tail of the metal wavefunctions, and creates the following dipole, *D*^{p}, per molecule

- ((6))

in this equation, *ϕ*_{j} and are the wavefunctions of the molecule and the metal local orbitals, respectively, is its overlap; and *n*_{jσ} and are their occupancies; *d* is the vector joining the atomic positions of orbitals *j* and *j*′ and Δ*r*′ joins *d*/2 with the integration variable *r*′. In our FIREBALL calculation, however, part of this dipole (in particular, the second term) is already taken into account through the potential created by the diagonal charges . Thus we only need to consider here the following off-diagonal contribution

- ((7))

We stress that this “pillow”-dipole is only the off-diagonal contribution of the total induced charge associated with the Pauli exclusion principle. Adding this off-diagonal term to the induced diagonal charge yields the total “push-back” contribution [Eq. (6)] that has been analyzed in detail by other researchers 24, 52.

On the other hand, the induced “metal surface” dipole is calculated by means of the off-diagonal induced charge: ; *e* being the electron charge and being the Green function of our system, defined by the Hamiltonian, as obtained from our DFT–LDA calculation in the local orbital basis. From *en*_{ij} we calculate straightforwardly the corresponding induced Hartree potential.

(4) vdW forces are analyzed using an extension of the LCAO-*S*^{2}-vdW formalism, developed specifically for weakly interacting systems, like graphitic materials 53, 54. In this approach, we consider two different contributions to the interaction energy, a short-range interaction associated with the overlap, *S*, between the wavefunctions of both systems, and the long range fluctuating dipole-dipole interaction leading to the vdW forces. In the present calculations we have used a simplified version of this approach, adding a semiempirical atom–atom vdW term to the short range interaction energy (see below). This way of including vdW interactions is a practical alternative to more *ab initio* approaches to include vdW in DFT (*e.g*., see Refs. 31, 55, 56), that are computationally very demanding for MO systems.

In the case of weakly interacting systems, the short range interaction can be calculated in an approximate way by means of a *corrected* LDA calculation, as follows: first, define the electron density for each subsystem (say, Au and C_{60}); then, approximate the exchange-correlation energy for the complete system as the sum of the exchange-correlation energies for each subsystem taken each one independently, neglecting in this way the effect of the overlapping densities in the exchange-correlation energy. In the following we refer to the short-range interaction energy calculated in this way as the weak chemical interaction (WCI). This way of proceeding tries to avoid the double counting that would appear including both, the exchange-correlation energy provided by a conventional LDA and the correlation energy associated with the long-range vdW potential discussed below: in particular, Lang 52 has clearly shown how the LDA exchange-correlation hole for rare-gas atoms on metal surfaces mimics partially the vdW polarization hole induced in the metal. We should also mention that other authors 35 have analyzed how to avoid this double counting by means of an approach similar to the one presented in this paper, using a short-range exchange-correlation energy. Regarding the CAu long-range (vdW) part, we use a typical atom–atom interaction with the standard form, (*R* is the distance between atoms), where the factor eliminates the vdW contribution for short distances 34. Following Refs. 34, 57, we take for CAu *R*_{vdW} = 3.3 Å 34 or *R*_{vdW} = 4.1 Å 57 (see below) and *d* = 20, while the *C*_{6} parameter (*C*_{6} = 36 eV^{6}) is taken from Ref. 58. The C_{60}C_{60} interaction is a constant that we calculate from Ref. 54, including the damping factor *f*_{D}(*R*) (with *R*_{vdW}(CC) = 2.9 34 or 3.8 57, and *d* = 20).

### 3 DFT calculations, density of states (DOS), the IDIS-model, and the molecule charging energy

- Top of page
- Abstract
- 1 Introduction
- 2 Model and method of calculation
- 3 DFT calculations, density of states (DOS), the IDIS-model, and the molecule charging energy
- 4 Pillow effects and the transport energy gap of the molecule
- 5 Conclusions
- Acknowledgements
- Biographical Information
- Biographical Information

In a first step, we calculate the relaxed geometries and the C_{60}/Au distance using both the standard LDA and the WCI approaches described above. Regarding the C_{60} geometry, we have found a very small relaxation, with C bonds changing less than 5% with respect to the gas-phase geometry, similar to the results by Wang and Cheng 8. Figure 2 shows our results for the adsorption energy of a C_{60} ML on Au(111): the black line represents our LDA-DFT energy, while the blue line corresponds to the WCI result. These two curves can be considered as two limiting cases for the short-range C_{60}Au interaction (basically the interaction of Au and the six nearest C atoms of C_{60}): the WCI corresponds to weakly interacting systems, and the LDA to covalently bonded systems. In order to obtain the total adsorption energy we must add the long-range vdW interactions to this short-range energy. The C_{60}Au(111) vdW interaction is the result of many distant CAu atom–atom interactions (the damping function *f*_{D}(*R*) eliminates the contributions for CAu atom pairs at closer distances). The purple and red curves in Fig. 2 show the energies calculated adding the vdW energy to both short-range curves. In this figure we have used *R*_{vdW}(AuC) = 4.1 Å and *R*_{vdW}(CC) = 3.8 Å 57. The minimum energy for the LDA + vdW result (purple curve) is located at a distance *z* (between the upper Au-layer and lower C-atoms of C_{60}) of 2.25 Å, and at 2.67 Å for the WCI + vdW one (red curve). The adsorption energy is 2.17 and 1.89 eV, respectively; for comparison, the experimental value is 1.87 eV 7. This good agreement is probably fortuitous because of the minimal basis set used in our calculations; in particular, our LDA-adsorption energy is around 0.8 eV smaller than the one calculated using a LDA plane-wave converged basis 8, while an LDA-approach yields adsorption energies typically a few tenths of eVs larger than a GGA-calculation. Moreover, taking *R*_{vdW}(AuC) = 3.3 Å and *R*_{vdW}(AuC) = 2.9 Å 34 in the long range vdW interaction yields *z* = 2.20 Å (LDA + vdW) and 2.45 Å (WCI + vdW), with adsorption energies of 2.9 and 2.5 eV, respectively (see Table 1). Notice that the adsorption energies change significantly when changing the value of *R*_{vdW}, while the equilibrium distance is much less affected. This is in line with a recent analysis of the semiempirical vdW forces for azobenzene on Ag(111) 59: these authors have concluded that, in the Tkatchenko–Scheffler approach 57, even if the adsorption energy is overestimated, the molecule/metal distance seems to be accurately described. Notice also that the sum of C and Au covalent radii is 2.1 Å, not too far from the values obtained above for the C_{60}Au(111) equilibrium distances. This suggests that the actual C_{60}Au(111) equilibrium distance should be in between the *z* values obtained in the LDA + vdW and WCI + vdW calculations. We conclude that 2.4 Å is a good guess to the distance between C_{60} and Au(111). Incidentally, this distance is similar to the minimum energy distance obtained in the LDA calculation (black curve).

Table 1. Distance, *z*, between the upper Au-layer and lower C-atoms of C_{60}, and adsorption energy, *E*_{ads}, for the different cases discussed in the text. Lengths are in Å and energies in eV.technique | *z* | *E*_{ads} | *R*_{vdW}(AuC) | *R*_{vdW}(CC) |
---|

LDA | 2.45 | 0.39 | – | – |

WCI | 2.80 | 0.23 | – | – |

vdW + LDA | 2.25 | 2.17 | 4.1 57 | 3.8 57 |

vdW + WCI | 2.67 | 1.89 | 4.1 57 | 3.8 57 |

vdW + LDA | 2.20 | 2.82 | 3.3 34 | 2.9 34 |

vdW + WCI | 2.45 | 2.40 | 3.3 34 | 2.9 34 |

Once we have obtained the interface geometries, we calculate the interface electronic properties of: (i) the single molecule; and (ii) the other C_{60}-layers, as well as the corresponding charging energy effects. The single molecule case allows us to determine *U* (Eq. (1)), while the other cases can be related to a kind of effective *U*

- ((8))

where *J*_{i} is the effective intersite Coulomb interaction between charges in different molecules (see below for more details).

#### 3.1 C_{60} molecule on Au(111)

Figure 3 shows the electron DOS projected on the C_{60} orbitals for the case of a single molecule adsorbed on Au(111) (Fig. 1, left). In the same figure we also show the molecule energy levels of the isolated (but deformed) molecule; the energy window around the energy gap is enlarged in the inset. The initial (*Φ*_{M}) and the final (*E*_{F}) Fermi energy (this is the metal Fermi level after the contact is established), the HOMO and LUMO levels, as well as the CNL, are shown. This last quantity is calculated integrating the molecule DOS up to charge neutrality conditions. The main effect of the contact is to broaden the molecular levels (also shown in Fig. 3), and to shift the relative position of the metal Fermi energy with the molecular levels from *Φ*_{M} to *E*_{F}, the final Fermi level. In this figure the vacuum level for the adsorbed molecule is kept aligned to the vacuum level for the isolated molecule. Also, in this figure the molecule transport gap (for both the isolated and the molecule on the surface) has been corrected using Eq. (1) with *U* = 1.5 eV. Notice that the first few peaks below the HOMO level are in good agreement with the ones observed in angle-resolved valence-band photoemission spectroscopy for a monolayer of C_{60} on Au; see also the case of a monolayer below 7.

As in a typical MO interface, the C_{60}/Au contact reacts creating a mean potential, *V*^{t}, between the molecule and the metal that tries to align the organic CNL and the metal workfunction; notice that *Φ*_{M} and *E*_{F} define respectively the initial and the final Fermi energy with respect to the molecular levels (which are defined with respect to the vacuum level of the isolated molecule), so that . Following the Unified IDIS model 25, *eV*^{t} has two components, the “pillow” and the IDIS potentials, *V*^{p} and *V*^{IDIS}, respectively: ; in the results presented in this section we neglect *V*^{p}, so that *V*^{t} = *V*^{IDIS}, this potential being associated with the charge transfer between the molecule and the metal, and is given by

- ((9))

where *S* is a screening parameter related to the interface properties (see below); Eq. (9) implies that

- ((10))

Notice that 0 < *S* < 1, with *S* 0 or 1 for high or low screening, respectively 29. In the limit of large screening the CNL and *E*_{F} tend to be aligned, while for *S* 1, we recover the Schottky–Mott limit with no interface IDIS-potential. In order to calculate *S* with good accuracy, we have calculated (CNL − *E*_{F}) versus (−*Φ*_{M}) for the different interfaces analyzed in this work by changing fictitiously *Φ*_{M} using the shift operator mentioned in Section 2, see Fig. 4. In particular, from the slope of the curve for the single C_{60} molecule on Au(111) we obtain *S* = 0.53 for this case.

In order to obtain a convenient description of the screening parameter, *S*, we first consider the equation relating the molecule charging energy, *U*, to the potential induced by the charge transfer, *e*δ*n*

- ((11))

On the other hand, one can define a mean DOS (spin included), *D*, between CNL and *E*_{F} so that δ*n* is given by

- ((12))

Combining Eqs. (9)–(12), one can easily find

- ((13))

Equation (11), or equivalently , has been used to obtain the molecule charging energy (see Fig. 4): our calculations yield *U* = 1.65 eV, with an error bar of ±0.1 eV, coming from the error bars in the slopes of *eV*^{IDIS} and δ*n*. We should mention, as a comment to this result, that introducing the “metal surface” dipole (see Section 2) reduces this value to *U* = 1.5 eV.

#### 3.2 Monolayer and fraction of monolayer cases

Figure 5 shows the molecule local DOS for the geometry (the full monolayer case); we show here the same quantities as in Fig. 3: *Φ*_{M}, *E*_{F}, the CNL and the HOMO and LUMO levels. As in the previous case, we also see how the quantity (CNL − *Φ*_{M}), the initial misalignment between the energy levels of the metal surface and the molecule, has been screened to (CNL − *E*_{F}), so that Eq. (10) is also valid for the monolayer case, but with a different screening parameter, which we have found in this case to be *S* = 0.19; see Fig. 4. It is interesting to realize that this parameter, *S*, is now significantly smaller than in the case of the single molecule on the surface, reflecting a larger screening effect. Similar effects are found for other coverages, the geometries, that show an intermediate screening between the monolayer and the single molecule limits: Fig. 6 shows their DOS projected on the C_{60}-orbitals, around the energy gap; notice how (CNL − *E*_{F}) changes monotonously, being smaller for the compact monolayer and larger for the structure. The values of *S* for the different adlayers are 0.19, 0.23, 0.29, and 0.31 for *m* = 2, 3, 4, and 5, respectively. Notice also that the results shown in Figs. 3–6 indicate that the position of the CNL is practically the same, 0.8 eV above *Φ*_{M} (−5.2 eV), in all the cases studied, with an error bar of ±0.02 eV.

We can also relate *S* to *U*^{eff}, defined for the adlayer case as , by replacing *U* by *U*^{eff} in Eqs. (11) and (13); this yields

- ((14))

Notice that for these cases *V*^{IDIS} depends also on the interaction between molecules, such that

- ((15))

this equation indicating that the effective charging energy of the isolated molecule, *U*, is modified for an adlayer, by the interaction, *J*_{i}, between charges in different molecules 60. From our calculations we obtain the following values of *U*^{eff} (without including the “metal surface” dipole correction): 4.8, 3.3, 2.7, and 2.35 eV for *m* = 2, 3, 4, and 5, respectively; “metal surface” dipole reduces these values to 4.4, 3.0, 2.4, and 2.1 eV.

### 5 Conclusions

- Top of page
- Abstract
- 1 Introduction
- 2 Model and method of calculation
- 3 DFT calculations, density of states (DOS), the IDIS-model, and the molecule charging energy
- 4 Pillow effects and the transport energy gap of the molecule
- 5 Conclusions
- Acknowledgements
- Biographical Information
- Biographical Information

In this paper we have studied the C_{60}/Au(111) MO interface formation for different coverages, going from the single C_{60} molecule adsorbed on the Au(111) surface to the monolayer case (the structure). In our analysis we determine the atomic geometry for the C_{60}/Au(111) interface by means of a local orbital DFT technique, taking into account vdW forces. We analyze the MO barrier formation for the following coverages of C_{60} molecules: *θ* = 1, 4/9, 1/4, and 4/25, corresponding to the adsorption of C_{60} molecules with (*m* = 2, 3, 4, 5) adlayer structures. We have also calculated the single molecule limit, adsorbing one C_{60} molecule on a 8 × 8-Au(111)-cluster. From these calculations we obtain the DOS on the C_{60} molecules, the position of the interface Fermi level, and the position of HOMO and LUMO levels. An important step in our calculations is the self-consistent correction of the transport gap of the organic material, using Eq. (1). The MO interface barrier formation is analyzed in terms of the IDIS model. For this purpose we also calculate the charge transfer at the interface, the CNL of the organic layer, the interface dipole potential and the interface screening parameter *S*. In all the cases analyzed in this paper the C_{60} CNL is found at the same position, within ±0.02 eV. Regarding this screening parameter, we obtain an important change from the isolated molecule on the Au(111) surface, *S* = 0.53, to the monolayer case, *S* = 0.19 (notice that *S* = 1 corresponds to no screening while *S* = 0 corresponds to perfect screening). This indicates the important role played by other adsorbed molecules in the screening properties of the interface and in the interface barrier height formation.

The analysis in terms of the IDIS model allows us to calculate ; this quantity, for the single molecule case, corresponds to the charging energy of the molecule *U* used in Eq. (1) to correct the KS LDA gap to obtain the transport gap: . This correction is introduced in our calculations using a scissor operator, and is calculated self-consistently. We obtain *U* = 1.5 eV, and a transport gap for C_{60} of 3.1 eV in good agreement with scanning tunneling spectroscopy experiments 6 and other theoretical calculations 30 based on a GW-approach. In the adlayer cases, *U*^{eff} is a combination of the intra-site charging energy *U* and intersite electron–electron interaction *J*_{i} for electrons in different C_{60} molecules. The values obtained for *U*^{eff} (4.4, 3.0, 2.4, and 2.1 eV for , *m* = 2, 3, 4, 5) can be used to calculate *J*_{i} and thus obtain an effective many-body Hamiltonian for the adlayers 60.