## Journal of Self-Assembly and Molecular Electronics

### Robustness of DFT predictions of the charge transfer mechanism for self-assembled monolayers modi ed with Ferrocene on Au(111)

Author: Filipe C. D. A. Lima, Arrigo Calzolari, Helena M. Petrilli, and Marilia J. Caldas

Thematic Issue:  2015

Article No: 002     doi: 10.13052/jsame2245-4551.2015004

 001 002 003 004 005 006 007

Robustness of DFT Predictions of the Charge Transfer Mechanism for Self-Assembled Monolayers Modified with Ferrocene on Au(111)

Received 14 July 2015; Accepted 19 August 2015;
Publication 19 August 2015

Filipe C. D. A. Lima,1 Arrigo Calzolari,2 Helena M. Petrilli1*, and Marilia J. Caldas1

• 1Departamento de Física dos Materiais e Mecânica, Instituto de Física, Universidade de São Paulo, 05508-090, São Paulo, SP, Brasil
• 2CNR-NANO Istituto Nanoscienze S3 National Center, I-41100, Modena, Italia
• 1,*Corresponding Author: hmpetril@if.usp.br

## Abstract

The charge transfer mechanism of ferrocene-modified monolayers is a controversial topic in the literature. Recently, theoretical results of the ferrocenyl-glycyl-cystamine (Fc-Gly-CSA) on Au(111) have shown evidences of electronic tunneling from the ferrocene center to the electrode. Here we study the Fc-Gly-CSA molecule using the Density Functional Theory with the Perdew-Burke-Ernzerhof (PBE) and hybrid-PBE (PBEh) functionals in order to investigate the robustness of the electronic structure to the inherent Kohn-Sham scheme approximations. For PBEh, we tested different values for the Hartree-Fock exact exchange (Exx). Our results show that as the Exx increases, the Highest Occupied Molecular Orbital (HOMO)- Lowest Unoccupied Molecular Orbital (LUMO) energy difference also increase. Nevertheless, the states located over the Gly-CSA always remained at least 1 eV below the HOMO in all cases here investigated. These results indicate that the evidences of electronic tunneling charge transfer mechanism for the Fc-Gly-CSA/Au(111) are robust concerning the exchange correlation functionals.

## Keywords

• Electronic Structure
• DFT
• Exact Exchange
• Self-Assembled Monolayers (SAMs)
• Molecular Electronics
• Ferrocene

## 1 Introduction

Self assembled monolayers modified with ferrocene (Fc-SAMs) are systems well defined in terms of thickness and composition, being very good candidates to investigate electron transfer (ET) properties in electrochemistry due to the reversible oxidization properties of the ferrocene (Fc) moiety [1]. Fc-SAMs have been studied since the early 1990’s when Chidsey et al. [2] worked with alkanethiols modified with Fc, while the results using peptides as linker molecules appeared years later. The realization of these Fc-SAMs has deserved much attention in view of their potential applications as biosensors for artificial photosynthesis, and molecular electronics [1, 36].

The charge transfer mechanism in Fc-SAMs is a controversial topic of discussion, with mainly two different proposals [7]. From one hand, it has been explained as a dynamic tunneling process [5, 8, 9] from the Fc center to the electrode [1012]. On the other hand, there is the suggestion of a hopping hole-transfer process, in which case the molecular orbitals of the linking peptide participate in the process, oxidizing and creating a pathway for the electron in the charge transfer [1316].

Recently, our theoretical results have shown evidences of electronic tunneling even in the presence of solvent environment [17]. Our work focused on ferrocenyl-glycyl-cystamine (Fc-Gly-CSA) absorbed on the Au(111) surface through the thiol group, and has been carried out within the Kohn-Sham (KS) scheme of the Density Functional Theory (DFT) [18] using the Generalized Gradient Approximation (GGA) of Perdew- Burke- Ernzerhof (PBE) exchange correlation functional [19]. For the isolated molecule, we found that the highest occupied molecular orbital (HOMO) is degenerate and spatially localized on the Fc region, while the electronic energy levels mainly localized on the peptide, glycyl-cystamine (Gly-CSA), are found around 1.2 eV below the HOMO. We also found that, when the Fc-Gly-CSA was absorbed on Au(111), this energy difference remained unchanged, suggesting that the gold electrode does not modify the frontier orbitals of the Fc-Gly-CSA. It is important to stress that our results for the overall alignment (metal Fermi energy and molecular HOMO) placed the molecular HOMO very close to, but below the Au Fermi energy, that is, no spurious charge transfer was detected in the absence of an external electric field.

We are here referring to the following discussion. It is known that DFT, and specifically the PBE exchange correlation functional (Exc), usually provides very good results for the electronic description of noble metal surfaces, which mostly behave as the free electron gas, with electrons delocalized over the system. On the other hand, carbon based molecules may have a very localized electronic structure, and plain DFT underestimates ionization potentials (IP), what has lead to several different proposals focusing on avoiding this problem [2024]. When both systems are simulated together, the PBE Exc functional may fail to describe the molecular states properly, usually upshifting the position of the molecular energy levels relative to those of the metal.

Coming back to the electronic structure of carbon based molecules, among the alternative Exc functionals proposed and in use at this time, the simplest are “hybrid” functionals that mix a fraction of Exact Exchange $\left({\text{E}}_{xx}={E}_{x}^{EX}\right)$ in the semi-local Exc of the PBE formalism, which we will call PBEh [23]. Recent studies, that build on the connection between the eigenvalue of the HOMO and the IP through Koopmans theorem, show that the amount of Exx to be added is system-dependent [25, 26], and that it is much higher for organic molecules (α ≈ 0.7) than the usually adopted (0.20–0.25) for other systems.

${E}_{xc}=\alpha {E}_{x}^{\text{EX}}+\left(1-\alpha \right){E}_{x}^{\text{PBE}}+{E}_{c}^{\text{PBE}}\text{​},\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}0\le \alpha \le 1\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(1\right)$

The use of such Exc functionals for the study of a coupled bi-component system, such as a metal/molecule interface, is thus unfortunately not feasible, since the results for the metal bulk or surface would be clearly far from reasonable. Here, we explore the robustness of our previous results by employing PBEh to study the isolated Fc-Gly-CSA molecule, with different fractions of Exx: α = 0.25 (PBE0), α = 0.50 and α = 0.75. We also refine the technicalities of the calculations, by passing from ultrasoft to norm-conserving pseupotentials. The impact of using the hybrid functional is, as we expected, strong, and consolidates the indication of tunneling as the possible charge transfer mechanism.

## 2 Theoretical Methods

The Fc-Gly-CSA is found, in crystalline form, as a dimer linked by a S-S bond that breaks when interacting with the gold electrode [27, 28]. Here we consider only one monomer of the Fc-Gly-CSA in gas phase form, with a H saturating the thiol termination, as shown in Figure 1. The structure is extracted from the literature [29] X-Ray results.

Figure 1 Two dimensional representation of the Fc-Gly-CSA monomer considered here.

The calculations were carried out in the KS scheme of the DFT, using the QUANTUM ESPRESSO computational package [30]. The supercell dimensions were 10.2 × 8.8 × 40.6 Å3, and we considered only the gamma point in the Brillouin zone. For the geometry optimization, the molecule was relaxed until the forces were smaller than 0.02 eV/A, using the PBE functional and the Vanderbilt’s ultrasoft pseupotentials [31] (USPP) with 28 Ry as kinetic energy and 280 Ry as charge density cutoffs. The valence shell included the following sets of orbitals: [3s2, 3p6, 3d6, 4s2] for Fe, [2s2, 2p2] for C, [2s2, 2p6] for O, [2s2, 2p3] for N, [3s2, 3p4] for S and [1s1] for H.

For the electronic structure calculations we employed, in addition to the PBE functional, the above mentioned hybrid functionals PBEh with different fractions of Exx: α = 0 (PBE), α = 0.25 (PBE0), α = 0.5 and α = 0.75. In this case, we used norm-conserving pseudopotentials (NCPP) [32], including the following sets of orbitals, in the valence shell: [4s2, 3d6] for Fe, [2s2, 2p2] for C, [2s2, 2p6] for O, [2s2, 2p3] for N, [3s2, 3p4] for S and [1s1] for H. The cutoffs used were: 100 Ry for the wave functions, 400 Ry for the charge density and 120 Ry for the Exx grid.

## 3 Results and Discussion

The projected density of states (PDOS) over the different atomic species of Fc-Gly-CSA, obtained using different α values is shown in the Figure 2. The PDOS were aligned by the electrostatic potential vacuum level, obtained in each case. In order to discuss the changes observed in the electronic structure, we present in Figure 3 chosen KS electronic isosurfaces, starting from the highest occupied molecular orbital (HOMO), which is doubly degenerate (HOMO and H-1), and going down in energy through the 6 energy levels below (H-2, H-3, H-4, H-5, H-6, H-7). The relevant orbitals for the present discussion are then identified by visual similarity inspection and labeled HM, HM1, Hm, HS, HF. The HM, HM1 and HF states are mostly located on the Fc region, whereas the Hm state is mostly located on the Gly-CSA and the HS on the CSA thiol site [17].

Figure 2 PDOS of the atoms for the 4 cases investigated here: C (shaded gray), Fe (red line), O (black line), N (blue line) and S (orange line). a) PBE; b) α = 0.25 (PBE0); c) α = 0.5; d) α = 0.75. The states HM, HM1, Hm, HS and HF are according to Figure 3.

Figure 3 KS molecular orbitals (light blue spheroids) for the Fc-Gly-CSA using different α values, starting from the highest occupied molecular orbital (HOMO) and going down in energy through the 7 orbitals below (see text). a) PBE; b) α = 0.25 (PBE0); c) α = 0.5; d) α = 0.75. Atom colors: light yellow (S), gray (C), blue (N), orange (Fe), red (O) and white (H).

The comparison of the PBE Exc results between USPP and NCPP calculations does not show remarkable differences in the overall PDOS, except for a splitting of the triple degenerate HM state (USPP) into two peaks (NCPP) separated by 0.46 eV, now labeled HM and HM1 in Figure 2. From the molecular KS plots, shown in Figure 3a, we can observe that HM and HM1 maintain the same character on the Fc region. Moving to lower energies, we identify orbitals located on the peptide (Hm and HS) at ~1.23 eV below the HM state and the HF orbital, which is mostly on the Fc region, at ~1.77 eV below the HM state. Accordingly with the PDOS, these orbital characters are in general very good agreement with our previous USPP [17] results.

Now examining the PBEh results, shown in Figure 2b, Figure 2c and Figure 2d, we see that the energy difference between the HOMO and the Lowest Unoccupied Molecular Orbital (LUMO) becomes larger as the α fraction increases, correcting the HOMO-LUMO gap underestimation, typical of KS-DFT. The HM state (together with the other occupied states) systematically moves to lower energies as the α fraction increases: 1.3 eV for α = 0.25, 2.6 eV for α = 0.5 and 4.1 eV for α = 0.75.

Interestingly, the splitting between HM and HM1 states (located on the Fc) increase with the α fraction (ranging from 0.46 eV in the PBE case to 1.42 eV in the α = 0.75 case), since the HM1 state is more sensitive to the Exx, changing the relative orbital order at lower energies: for α = 0.75, HM1 crosses the Hm, the HS and the HF, states. The HF orbital that was initially placed at ~1.77 eV for the PBE Exc, seems to move into the opposite direction.

The Hm and HS states are located on the Gly-CSA. As the α fraction increases, these orbitals are always at least at 1 eV below the Fc located HM states. This is important, since it shows that the Gly-CSA states are “pinned” below the HM, being separated by an almost constant energy difference. Referring to the charge transfer mechanism [7, 17] of Fc-Gly-CSA/Au(111), the pathway for electronic hopping would be created by the Hm and HS states, which orbital character remain mostly unaffected in the Fc-Gly-CSA isolated form studied here. Therefore, we are led to reinforce our previous conclusion that the electronic tunneling is the Fc-Gly-CSA/Au(111) charge transfer mechanism.

## 4 Conclusions

Here, we addressed a throughout discussion regarding the description of the molecular orbitals and energy levels of the Fc-Gly-CSA isolated molecule using the PBEh Exc with different α values. As it could be expected, when the percentage of the Exx fraction increases, the HOMO-LUMO difference also increases. Nevertheless, the energy difference between the highest occupied Fc and the Gly-CSA states are very stable, always larger than 1 eV.

Previous DFT results [17] for Fc-Gly-CSA/Au(111) have shown evidences of electronic tunneling as the charge transfer mechanism from the Fc center to a gold electrode. This conclusion was reached due to the existence of a ~1 eV energy gap between the Fc and the Gly-CSA electronic states: in the case of the application of an electric field to the system, the first electronic levels, localized on the molecule, that would be excited are on the Fc region. Our present results show that the evidences of the charge transfer mechanism is not affected by the inclusion of the Exx fraction, since the energy barrier between Fc and Gly-CSA states have not changed in any case.

In theoretical general perspective, our results confirm the capability of DFT in describing Fc-SAMS on gold surface, otherwise unaccessible with higher level simulation techniques: although generally DFT quantitatively fails in describing electronic alignment, in this case it provides a qualitative good description of carbon based molecules adsorbed on metal surfaces. Thus we reinforce that the approach used here is robust and other Fc-SAMS can be investigated in order to develop a deep knowledge of the charge transfer mechanism in these important systems.

## Acknowledgement

The authors acknowledge computing time provided on the Blue Gene/Q supercomputer supported by the Research Computing Support Group (Rice University) and Laboratório de Computação Científica Avançada (Universidade de São Paulo). Also, the financial support provided by FAPESP (projects: 2012/02326-8 and 2011/50318-1), CNPq, INCT-INEO and CAPES.

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## Biographies

F. C. D. A. Lima received his Ph.D. in Physics in 2015 at the Institute of Physics of the So Paulo State University (USP), Brazil where he is now a post-doc. His research activity is on the investigation of molecules on inorganic interfaces using multi-scale approach (Ab Initio and Classical Molecular Dynamics).

A. Calzolari graduated in physics in 2003 at University of Modena and Reggio Emilia in Modena, Italy. He is researcher at the Instituto Nanoscienze of the National Research Council of Italy (CNR-NANO) since 2010. He is also adjunct professor at Physics Dept., University of North Texas, Denton TX, USA since 2012; and Member of Aflowlib Consortium, Duraham NC USA since 2015. His research activity is focused on the ab initio study of the structural, electronic, optical, vibrational and transport properties of nanostructures, molecules, surfaces and interfaces, for solar cells, molecular electronics and nanotechnology applications.

H. M. Petrilli received her Ph.D. in Physics in 1989 at the Institute of Physics of the So Paulo State University (USP), Brazil, where she has been working since then. Her main interest is on electronic structure calculations applied to systems involving metals: alloys, nanostructures, metal complexes with applications in Biology and Medicine, interfaces.

M. J. Caldas received her Ph.D. in Physics in 1981 at the Institute of Physics of the So Paulo State University (USP), Brazil, where she is now full professor. She has been working with Condensed Matter Physics, mainly on the following subjects: theoretical computational physics and chemical physics, electronic structure, semiconductors, organic polymers and hybrid organic/inorganic systems and nanosystems.

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