1 Introduction

Unraveling the mechanism of interaction of organic molecules is of high relevance both for expanding the limits of knowledge in the field of surface science and for opening new perspectives toward improving the behavior (either reactivity or stability) of materials used in different applications [1]. A family of organic molecules that is of interest in surface reactivity is the sulfur-containing compounds. These molecules induce copper metal corrosion, which is a chemical phenomenon that triggers serious failures in power transformers [2, 3]. Dibenzyl disulfide (DBDS) is commonly used as an antioxidant additive in insulating mineral oil employed in power transformers. In this sense, DBDS is known to promote, under certain conditions, copper corrosion in electric equipment, by forming copper (I) sulfide Cu 2 S as the main product along with sulfur-containing derivatives such as benzyl mercaptan and dibenzyl sulfide [4–7]. Although extensive investigations have been carried out on this subject, the mechanisms responsible for the chemical phenomenon still remain unclear. Since DBDS is related to the commonly used thiol molecules in the well-known thiol self-assembled monolayers (SAM) on metal surfaces, the analysis of the metal–sulfur bond is important to complete the already known information on the chemical properties of this type of systems and answer the questions that are still open, such as the reaction mechanism of the SAM formation and S-metal bond [8–11].

In the present paper, the nature of the interaction between copper and DBDS is theoretically studied. A cluster model will be used to simulate the copper surface at reasonable accuracy, i.e., using hybrid functional in combination with all-electron localized basis sets. A discrete or cluster models may result in an advantageous strategy to understand at the local level the interaction between metal and chemical compounds.

Many studies on the interaction and adsorption phenomenon using metal clusters have been described in the literature [12–20]. In this context, density functional theory (DFT) can be considered as the sweet spot between computing time and accuracy, showing to be reliable for molecular calculations of transition metals [21–27].

Therefore, in this work, we attempt to clarify some aspects associated with copper corrosion by DBDS at the DFT level by accounting energetic and electronic properties that govern the interaction between DBDS and copper. The main focus of attention is to characterize locally the copper–sulfur interaction/bonding. This work will constitute the first step or a preliminary study to a periodic DFT calculation, and a cluster will be used taking into account that the cluster all-electron calculations are more reliable concerning the study of electronic properties. Then this paper focuses firstly on the Cu–S bond properties and secondly on the molecule/surface adsorption system. The molecule/surface system will be treated in a subsequent study.

2 Model and computational details

Non-local hybrid exchange–correlation functionals combined with all-electron basis set (e.g., def2-type) have shown good performance in describing both transition metal clusters and organic molecules [28, 29]. As a consequence, molecular geometry optimizations for Cu 7 and DBDS, and the respective Cu 7···DBDS complexes, were carried out using the hybrid PBE0 exchange–correlation functional, which belongs to the non-empirical class of functionals (PBE) including 25 percentage of exact Hartree–Fock exchange [30]. In the present study, it was combined with def2-SVP, (14s9p5d1f)/[5s3p2d1f], basis set for the optimization of isolated systems and complexes. For each optimization, a frequency analysis was performed to confirm that the geometries are minima on the potential energy surface. In order to get more reliable energetic results, single-point energy calculations, using the optimized structure of complexes, was made combining the PBE0 functional with def2-TZVP, (17s11p7d1f)/[6s4p4d1f], basis set. All of these calculations were carried out with the Gaussian 09 suite of programs [31].

Each localized Cu 7···DBDS complex can be characterized by its stabilization or binding energy ∆E BE, which is calculated from the total energy of the ground state optimized geometries of the Cu 7···DBDS complex, Cu 7 and DBDS as:

$$\Delta E_{\text{BE}} = E(Cu_{7} \cdots DBDS){-}\left[ {E\left( {Cu_{7} } \right) + E\left( {DBDS} \right)} \right]$$
(1)

These values were corrected by using the counterpoise method for the basis set superposition error (BSSE) [32].

By following a two-step process as displayed in Fig. 1, in which, firstly, both Cu 7 and DBDS (they are also called reactants along the text) are distorted in their complex geometries and, secondarily, these are being allowed to interact. This thus led to decompose ∆E BE into two contributions as follows:

Fig. 1
figure 1

A two-step model to decompose the binding energy of Cu 7···DBDS complexes: distortion and interaction. Green and red arrows indicate a favorable (negative sign) and unfavorable (positive sign) energy quantities, respectively

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$$\Delta E_{\text{BE}} =\Delta E_{\text{dist}} +\Delta E_{\text{int}}$$
(2)

with

$$\Delta E_{\text{BE}} =\Delta E_{\text{dist}} \left( {Cu_{7} } \right) +\Delta E_{\text{dist}} \left( {DBDS} \right)$$
(3)

where ΔE dist (Cu 7 or DBDS) can be calculated as the difference between the energy of the isolated deformed complex (using the geometry in the complex) and the energy of the ground state of the isolated cluster or DBDS, respectively.

This partition is known as strain/interaction [33] or distortion/interaction model [34] which was also successfully applied to surface adsorption in the limit of low coverage by Scaranto et al. [35]. The energies required to distort reactants (Cu 7 and DBDS) from the ground state geometries to those adopted in the complexes, ΔE dist, can be computed as the following energy differences:

$$\Delta E_{\text{dist}} (X) = E(X\;{\text{distorted}}) - E\left( {X\;{\text{optimized}}} \right);\quad X = Cu_{7} ,\;DBDS$$
(4)

The formation of the complexes from distorted reactants releases the energy, ΔE int, given by a similar expression to Eq. (1), but using the total energy of the distorted geometries of the reactants. It should be noted that ΔE int can also be computed easily using the ΔE BE and ΔE dist terms:

$$\Delta E_{\text{int}} =\Delta E_{\text{BE}} -\Delta E_{\text{dist}}$$
(5)

The formation of Cu 7···DBDS complex was also analyzed from an electronic viewpoint. The amount of total electronic charge transferred between Cu 7 and DBDS was quantified through the global charge transfer descriptor (G-CT). This will help us twofold, first to analyze the direction of electronic flow, and second, to classify the nature of the interaction between copper clusters and DBDS as physisorption or chemisorption. G-CT corresponds to the sum of atomic charges (q A ) on each reactant, i.e., Cu 7 or DBDS:

$$G{ - }CT = \sum\limits_{A} {q_{A} } ;\quad A \in Cu_{7} \;or\;DBDS$$
(6)

For this purpose, the natural atomic charges (NPA) [36] were used.

There exists another important tool, Electron Localization Function (ELF) [37], which enables us to evaluate presence or absence of a bond, S–S in this study. In general, the gradient vector field of ELF divides the space in basins of attractors where electron pairs are located. These basins are either core basins (include a nucleus) or valence basins (do not include a nucleus, except for protons). The number of connections of a given valence basin with core basins is called the synaptic order. A disynaptic valence basin corresponds to a common two-center bond, whereas a monosynaptic basin describes a lone pair [38–40]. This scheme will be used to characterize S–S bond in the formed Cu 7···DBDS complex. The ELF analysis was made using the TOPMOD [41] program, and its graphical representation was obtained using MOLEKEL [42] program.

Previous to the formation of complexes between or DBDS and Cu 7 , stochastic search and optimization techniques were used to localize minimum energy structures of DBDS. An exhaustive search was performed using a Monte Carlo algorithm of molecular mechanics via Merck Molecular Force Field (MMFF) where multiple conformational analyses about five dihedral angles involving S–S, S–C, and C–C(phenyl) bonds were done, finding twenty candidate conformers of DBDS which were optimized using PBE0/def2-SVP level (single-point energy calculations were done at the PBE0/def2-TZVP level). The three most stable conformations of DBDS lie in a narrow energy range less than 1 kcal/mol. The major difference between these structures is given by the dihedral angle involving phenyl rings as displayed Fig. 2.

Fig. 2
figure 2

Structures of three stable conformers of DBDS and copper cluster

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Moreover, it is necessary to remark some features of the cluster model chosen to carry out the present study. The copper cluster is three-dimensional adopting a pentagonal bipyramidal molecular geometry (D 5h), as shown Fig. 2, and describes a building block for bigger clusters (e.g., Cu 13 and Cu 19) [43, 44]. From the electronic viewpoint, the highest occupied molecular orbital is mainly localized in the apical zones (i.e., the two atoms with higher coordination on the main symmetry axis), while the lowest unoccupied molecular orbital (LUMO) is mainly delocalized on the equatorial positions (i.e., five atoms on the perpendicular plane to main axis) [20, 45–48].

Finally, the three conformers of DBDS were randomly placed on the cluster and these then are structurally relaxed giving rise to localize several Cu 7···DBDS complexes which were characterized within three aspects: structures, stability, and electronic viewpoints.

3 Results and discussion

In our investigation, seventeen Cu 7···DBDS complexes were found, which lie in an energy range of 62 kcal/mol, and they are labeled as C1 to C17 in Fig. 3; this displays all structural motifs. It is noteworthy that their formation is mainly driven by Cu···S interaction, no preference between apical or equatorial Cu atom was observed, at least in the cluster used in this work. In addition, in some complexes the phenyl···Cu proximity generates the possibility of a π···Cu interaction, which could confer extra stability to the complexes. It does not determine the stability of the complexes because it was observed in both kinds of complexes, i.e., physi- and chemisorption.

Fig. 3
figure 3

Structures of the Cu 7···DBDS complexes

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In Table 1 are collected the S–S bond length, binding energy, distortion and interaction energies for the set of 17 Cu 7···DBDS complexes. Taking into account the different stabilizing contributions, the set of 17 complexes can be divided into two main groups. The first set encompasses those complexes (C1–C13) with interaction between Cu 7 and DBDS classified as associative type, in the sense that the S–S bond is slightly weakened, as can be seen by the data of S–S bond length in Table 1, while the second group includes those Cu 7···DBDS complexes with interaction between Cu 7 and DBDS of dissociative type, which is partially (C14–C16) or highly dissociative (C17) as it is revealed by an increment of disulfide distance, and the concomitant benzyl sulfide fragments are coordinated around the copper cluster. In other words, it can be possible to distinguish the adsorption of DBDS on the copper cluster as a physisorption process or a partially or totally dissociative chemisorption process. Both kinds of process can be confirmed by ∆E BE values reported in Table 1.

Table 1 S–S bond distance (in Å) and Wiberg index Wi S–S , binding energy ∆E BE, distortion energy ∆E dist (Cu 7) and ∆E dist (DBDS) and interaction energy between distorted species ∆E int
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Notice that a value of ∆E BE by about −15.0 kcal/mol can be considered as the transition between physi- and chemisorption process of DBDS on Cu 7. Moreover, it is interesting to note that ∆E BE values for the Cu 7···DBDS complexes found by here are not higher than the cohesive energy of copper bulk (i.e., 81 kcal/mol). This result explains why Cu 7 does not undergo fragmentation to form Cu 2 S as a consequence of the interaction between Cu 7 and DBDS.

In Fig. 4, a representation of the ELF basins is shown to help visualize the most relevant bonds in the free moieties (I and II) and Cu 7···DBDS complexes (III and IV). In general, the copper cluster (II) is characterized by seven core basins on copper atoms, and valence basins describing multicenter bonds. DBDS presents typical characterization of Lewis representation for C–C, C–H, C–S and S–S bonds and the monosynaptic basins (yellow) representing a lone pair on each sulfur atom. We would like to draw attention to sulfur–sulfur bond, which is represented by a valence disynaptic basin V(S,S) and clearly appears in DBDS conformers (I, left and right upper isosurfaces). It can be observed even when a physisorption (III) process is carried out (C1–C13) but disappears completely in the complex formed by a chemisorption (IV) process, confirming a dissociative process in the most stable complex, C17. The S–S dissociative process in the later kind of complexes was confirmed through Wiberg Bond order index [49] from a Natural Bond Orbital (NBO) analysis for S–S (third column of Table 1). In physisorbed complexes, the index is close to 1 and decreases until it disappears in chemisorbed ones.

Fig. 4
figure 4

Some selected ELF Isosurfaces (ELF = 0.78) for isolated moieties and complexes. I selected DBDS conformers, II Cu7 cluster, and III physi- and IV chemisorption complexes

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3.1 Contributions to the binding energy

According to the decomposition energy scheme, described by Eqs. (1)–(5) and summarized in Fig. 1, all energy data, i.e., ∆E BE, ∆E dist (Cu 7), ∆Edist (DBDS), and ∆E int, are plotted together as displayed Fig. 5, in order to establish which role plays each contribution in the formation of Cu 7···DBDS complexes. It can be noted that other than ∆E BE; ∆E int and ∆E dist (DBDS) are helpful quantities to discriminate the interaction nature between DBDS on \(Cu_{7}\) as chemisorption or physisorption. While the formation of highly stabilized complexes is accompanied with an advanced degree of dissociation of the disulfide bond, which correlates with higher values of ∆E dist (DBDS) in favor of the stronger interaction between distorted species accounted by ∆E int, the formation of weakly stabilized complexes is given by low values of distortion energy and weak interaction between distorted species. In the former case, ∆E dist (DBDS) achieves almost 60 % of the absolute value of ∆E int, whereas it reaches a percentage less than 45 % of the absolute value of ∆E int in the latter case.

Fig. 5
figure 5

Binding energy ∆E BE, distortion energy ∆E dist (Cu 7) and ∆E dist (DBDS), and interaction energy ∆E int for the set of 17 Cu 7···DBDS

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Notice that ∆E dist (Cu 7) data are quite similar along the series of the Cu 7···DBDS complexes and they are in the range of 1 and 2 kcal/mol except for the one labelled as C17 (4.7 kcal/mol), which presents highly dissociative adsorption. This result enables to conclude that the geometry of the copper cluster does not undergo significant modifications by to the formation of the complexes.

3.2 Electronic aspects: global charge transfer

The characterization of the complexes from an electronic viewpoint was done on the basis of the natural atomic charges (NPA). For this we used the global charge transfer (G-CT) between both reactants involved in the formation of the complexes as was described by Eq. (6). In Table 2 are quoted the sum of atomic charge Cu 7, DBDS, and disulfide S–S bond, while their values are confronted with ∆E BE in Fig. 6.

Table 2 Natural atomic charge transfer on Cu 7, DBDS, and disulfide S–S bond in the complexes
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Fig. 6
figure 6

Global charge transfer as a function of the binding energy

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G-CT reveals that the amount of transferred charge in weakly bonded complexes is smaller than those which are strongly stabilized. Moreover, the direction of the electronic flow is opposite; while in the former the charge is transferred from DBDS to Cu 7, in the latter the electronic charge is donated from copper cluster to the disulfide compound. This result allows to suggest that the physisorption process is characterized by lower values of binding energy and amount of electronic charge transferred from DBDS to Cu 7, whereas the higher binding energy in chemisorption process is driven by a higher electronic charge transferred from Cu 7 to DBDS; consequently, the copper cluster undergoes an oxidation process. As can be seen from q S–S , the electron donation or attachment in DBDS is given mainly in the disulfide bond.

Finally, a good correlation between the S–S distances and the charge transfer of disulfide S–S bond was obtained; it can be seen in Fig. 7. Short S–S distances are found in physisorbed complexes and chemisorption is confirmed by the S–S bond dissociation, which is generated by high charge transfer from the cluster to disulfide fragment.

Fig. 7
figure 7

Relationship between S–S charge transfer and S–S bond distance

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The evidences observed in the present study can be interpreted as follows: The copper corrosion problem by sulfur-containing compounds is associated with the formation of highly stable Cu 7···DBDS complexes with dissociation of the disulfide bond as an initial step within the reaction mechanism of the sulfur-induced copper corrosion phenomenon.

4 Concluding remarks

In this work, the adsorption of dibenzyl disulfide on Cu 7 (D5h) cluster has been investigated by using density functional theory methods. Seventeen stable complexes were found, and no preference between apical or equatorial Cu positions was observed. The Cu···S interaction was characterized as the main thermodynamic stabilizing factor. It was also found that an extra stability could be conferred by a π···Cu interaction. On the basis of the binding energy data, two sets of complexes were found and characterized. The former, named as “physisorption complexes,” were characterized by values of binding energies lower than 15 kcal/mol, as well as low distortion energy and weak interaction between distorted fragments. Also, a slight weakening in the disulfide bond and low electronic flow from DBDS to Cu 7 were observed. In contrast, the complexes belonging to the second group, named here as “chemisorption complexes,” were found to have opposite characteristics compared with the former complexes. These were characterized by high values of binding and distortion energies, being the latter counterbalanced with a stronger interaction between distorted fragments. So, the adsorption process can be seen as mildly (C14–C16) and strongly (C17) dissociative accompanied with significant electronic charge transfer from Cu 7 to DBDS. Therefore, it could be possible to interpret these results as the first step of the copper corrosion phenomenon by sulfur-containing compounds, in which an oxidation process takes place on the copper cluster being the disulfide bond dissociation a key step. This supports the initial radical step in the generation of byproducts of copper corrosion process produced by DBDS [50–52].