Introduction

Norbornadiene (bicyclo[2.2.1]hepta-2,5-diene, NBD), norbornene (bicyclo[2.2.1]hept-2-ene, NBE) and their derivatives have attracted the attention of researchers for many years [1, 2]. These compounds are widely used in the production of polymers with desired properties [3,4,5,6,7,8] and pharmaceuticals [9,10,11,12], in the perfumery industry [13, 14] and microelectronics [15, 16], and also as solar energy converters [17,18,19,20,21]. The use of NBD and NBE is not limited to the role of prospective semiproducts for organic syntheses. In the Catellani reaction, i.e. Pd-catalyzed C-H functionalization of arenes, NBE is actually a co-catalyst for the synthesis of polyfunctionalized arenes [22,23,24].

The NBD molecule has two double bonds and C2V symmetry, while NBE has one double bond and Cs symmetry (Fig. 1). The presence of a methylene (C7) bridge leads to a significant strain in both molecules (ring strain energies = 32.3 (NBD) and 21.6 (NBE) kcal/mol [25]). In particular, the bond angles C1C7C4, C2C1C6, and C2C1C7 are much smaller [26, 27] than the tetrahedral angle. Due to the high ring strain the double bonds of NBD and NBE have an increased reactivity. Unlike conjugated dienes, the double bonds in the NBD molecule are separated by a CH2 group. However, recent works [28] show that NBE does not enter into the hydrogenation reaction in the presence of NBD. The development of new selective catalysts and the selection of the conditions for carrying out the partial hydrogenation of unsaturated compounds are fundamental tasks of catalysis. In addition, the hydrogenation of one of the two double bonds of cyclic dienes is of interest for the subsequent synthesis of their functional derivatives. Pd-based catalysts are among the most active and selective in the partial hydrogenation of alkynes and dienes [29,30,31,32,33,34,35].

Fig. 1
figure 1

Carbon atom numbering and structures of NBD and NBE molecules

Full size image

It is known from the literature that the selective hydrogenation of one double bond is also possible in cyclodienes with non-conjugated double bonds, for example, the hydrogenation of 1,4-cyclohexadiene [36, 37] and 1,5-cyclooctadiene [33,34,35]. The sequential nature of the hydrogenation of double bonds is possible if the hydrogenation rates of the first and second double bonds are noticeably different. Under the conditions of heterogeneous catalysis, an important role is played by the selective adsorption of the diene on the active site [36]. The selectivity depends on the relative adsorption strength, configuration of substrates and the structure of active sites [38]. Thus, the study of adsorption of unsaturated substrates on a metal surface is extremely important for understanding the mechanisms of reactions involving them and, in particular, the hydrogenation. Detailed information about the ways by which the substrate molecules interact with the catalyst surface can be obtained using quantum chemical modeling.

On the basis of UV-photoelectron spectroscopy (UPS), high-resolution X-ray photoelectron spectroscopy (XPS), and near edge X-ray absorption fine structure (NEXAFS) in combination with DFT calculations it was shown [39] that during NBD adsorption, the double bonds are parallel to the Ni(111) surface and form an η2:η2 adsorption configuration (Fig. 2a) with an adsorption energy of 54.0 kcal/mol. The presence of CN groups at the C2 and C3 atoms of the NBD molecule does not interfere with the interaction of the disubstituted double bond with the Ni(111) surface [40]. The adsorption energy of the NBD molecule in the η2:η1 configuration with the agostic C-H bond [39] of the CH2-bridge group (Fig. 2b) is significantly lower (38.5 kcal/mol). Similar adsorption structures of the NBD molecule were identified on the Pt(111) surface [41, 42], corresponding to two configurations η2:η2 and η2:η1. The corresponding adsorption energies are noticeably higher (~ 83 and 56 kcal/mol) as compared to the Ni(111) surface. Chemisorption of NBD is also possible on non-metallic surfaces. For example, the adsorption energy of the NBD molecule on the Si(001) surface varies within 72–96 kcal/mol [43]. There are significantly fewer works in the literature related to the study of NBE adsorption as compared to NBD. According to DFT calculations [44], the adsorption energy of NBE on the Ge(100) surface is 24.4 kcal/mol.

Fig. 2
figure 2

NBD η2:η2 (a) and η2:η.1 (b) adsorption configurations on Ni(111) [39] and Pt(111) surfaces [41, 42]

Full size image

The main goal of this work was a DFT study of the structure and energy of possible adsorption configurations of NBD and NBE molecules on Pd(111) and Pd(100) surfaces.

Computational methods and models

The quantum chemical calculations were performed using the PRIRODA computer code [45, 46]. The generalized-gradient approximation of density functional theory (DFT) with the Perdew-Burke-Ernzerhof exchange–correlation functional (PBE) [47] was used. Relativistic effects were considered using the SBK effective core potential [48] with TZ2P basis set (Table S1). The use of effective core potential makes it possible to noticeably reduce computational costs, while the accuracy decreases insignificantly. Previously, it was shown that PBE/SBK calculated binding energies in Pd2 and PdH molecules are in good agreement with the all-electron scalar-relativistic calculations [49]. In this work, to verify the adequacy of the PBE/SBK method, we calculated the adsorption of an ethylene molecule in the di-σ configuration on the surface of a Pd39 particle. The atomic structure of the Pd39 surface corresponds to the (111) facet (Figure S1). For comparison, calculations were performed in the all-electron scalar-relativistic approximation of DFT-PBE and the L22m basis set [50, 51], as well as in the PBE0 hybrid functional with 25% Hartree – Fock exchange energy [52]. The calculation results are presented in Table 1.

Table 1 Adsorption energy (Eads) of C2H4 on Pd39, C = C and C–Pd bond distances for di-σ configuration
Full size table

Table 1 shows that the PBE/SBK calculated adsorption energy Eads of C2H4 (24.6 kcal/mol) agrees well with the all-electron PBE/L22m calculations (24.0 kcal/mol). According to the PBE0/SBK calculations, the Eads(C2H4) value is slightly higher than in the PBE/SBK calculations (by 4.1 kcal/mol). The periodic DFT-PW91 calculations [53,54,55] of Eads(C2H4) and the geometric parameters of the di-σ configuration are also in good agreement with our PBE/SBK calculations. It should be noted that the computational costs of the PBE/L22m and PBE0/SBK methods are much higher. In addition, convergence problems arise with an increase of the number of Pd atoms.

In our study of the adsorption of NBD and NBE, a Pd86 nanoparticle with (111) and (100) facets, obtained by truncating an octahedral Pd140 cluster, was used as a model of the palladium surface. The optimized structure of Pd86 is shown in Fig. 3. Previously, this model was used to study the adsorption of phenylacetylene and styrene on the Pd surface [56]. Table 2 illustrates the values of the relative energies of Pd86 in various electronic states and the ranges of the Pd–Pd bond lengths R111 and R100 for the (111) and (100) facets, respectively. The triplet and quintet spin states of Pd86 have lower energies [56]. However, geometry optimization of these states leads to structural deformation of Pd86, which manifests itself in the elongation of one diagonal on the (100) facet and the shortening of the other (d1 and d2, Fig. 3). As can be seen from the last column of Table 2, the diagonals d1 and d2 are markedly different. In turn, the asymmetry of the d1 and d2 diagonals leads to a distortion of the shape of the (111) and (100) faces. The deformation of Pd86 increases with increasing multiplicity. Adsorption of NBD or NBE molecules also enhances the deformation of the Pd86 particle. To exclude a noticeable symmetry breaking, the singlet state for Pd86 was taken in further calculations.

Fig. 3
figure 3

Side view of the (100) and (111) facets of the Pd86 cluster

Full size image
Table 2 Calculated properties of Pd86 in various spin multiplicities (2S + 1): relative energy (ΔE), Pd–Pd bond distances (min–max) on the (111) and (100) facets, d1 and d2 diagonals of the (100) facet
Full size table

The adsorption energy of NBD and NBE molecules on the palladium surface was calculated by the relation:

$${E}_{\mathrm{ads}}=-\left[E\left(\mathrm{molecule}/{\mathrm{Pd}}_{86}\right)-E\left(\mathrm{molecule}\right)-E\left({\mathrm{Pd}}_{86}\right)\right]$$
(1)

where E(molecule/Pd86), E(molecule), and E(Pd86) are the total energies of the Pd86 cluster with the adsorbed NBD/NBE molecule, the Pd86 cluster, and the free NBD/NBE molecule, respectively. In this work, to calculate the adsorption energy, Eq. (1) was chosen, which coincides in sign with the binding energy and is opposite in sign with the adsorption enthalpy to eliminate confusion when discussing the relative stability of adsorption configurations. Vibrational frequency analysis of the optimized adsorption structures was utilized to ensure that it was true local minimum having no imaginary frequencies. The adsorption energy including zero-point vibrational energy (ZPVE) corrections is designated as Eads,0.

Results and discussion

Based on the data on the adsorption of NBD and NBE molecules on Ni and Pt surfaces [39, 41, 42], it can be concluded that the interaction of these molecules with metal atoms is in many respects similar to the endo/exo coordination of the double bond of these molecules on one metal atom [41]. In the same way, when approaching the surface, NBD and NBE molecules can have an endo-orientation if the surface atoms and the CH2-bridge group are on opposite sides of the plane of the adsorbed double bond (C2C3C5C6), and an exo-orientation if the surface atoms are on the same side with the CH2-bridge group (Fig. 4). According to our calculations, NBD and NBE molecules are adsorbed on the Pd surface in several possible ways and are not limited to two configurations (Fig. 2) described for other metals [39,40,41,42,43,44].

Fig. 4
figure 4

Endo- (left) and exo- (right) orientation of NBD relative to a surface

Full size image

Adsorption of NBD and NBE molecules on Pd(111)

For the NBD molecule, the type of adsorption configuration formed depends, first of all, on its endo/exo orientation when approaching the surface. In the case of endo-orientation, both double bonds of the NBD molecule interact with surface Pd atoms, resulting in the formation of 3 adsorption configurations, tetra-σ, di-σ,π, and di-π. The tetra-σ configuration corresponds to the η2:η2 configuration (Fig. 2a). Optimized structures are shown in Fig. 5. Calculated adsorption energies, C = C and C‒Pd bond lengths, and C2C1C7 bond angle are presented in Table 3.

Fig. 5
figure 5

Optimized structures of NBD (tetra-σ, di-σ,π, and di-π) and NBE (di-σ and π) endo-adsorption configurations on Pd(111): a – side views of Pd86, b – top views of NBD/NBE (the first layer of the Pd atoms are shown), c – side views of the C1(4) atom of NBD/NBE molecule (the first layer of the Pd atoms are shown)

Full size image
Table 3 Adsorption energies (Eads and Eads,0, kcal/mol), C = C and C‒Pd bond lengths (RC=C and RC‒Pd, Å), C2C1C7 bond angle (deg.) of endo-adsorption configurations of NBD and NBE on Pd(111)
Full size table

In the tetra-σ, di-σ,π, and di-π configurations the carbon atoms of NBD are bonded with 4, 3, and 2 Pd atoms, respectively. The adsorption energy of the NBD molecule on Pd(111) decreases in the same order. The strongest is the tetra-σ configuration, in which both NBD double bonds are di-σ-adsorbed. The energy of interaction of the di-σ-adsorbed double bond with Pd atoms is approximately equal to half of Eads(tetra-σ), i.e., 21.85 kcal/mol, which is slightly less than the adsorption energy of ethylene (24.6 kcal/mol, Table 1). The length of the NBD double bond in the tetra-σ configuration is markedly increased (1.48 Å). This distance is closer to the single bond of the norbornane molecule than to the double bond of the NBD molecule. For comparison, the C2C3 bond lengths in free NBD and norbornane (C7H12) molecules are 1.34 Å [26, 57] and 1.57 Å [58], respectively.

Both double bonds are π-adsorbed in the di-π configuration. This mode of interaction with Pd atoms activates the double bond less, so the length of the double bond (1.42 Å) is longer than in the case of the tetra-σ configuration. The binding energy of each π-adsorbed double bond with a Pd atom is approximately equal to 12.95 kcal/mol.

The threefold site of Pd(111) stabilizes an intermediate di-σ,π configuration in which one double bond is di-σ-adsorbed and the other is π-adsorbed. The lengths of NBD double bonds in the di-σ,π configuration are 1.49 Å and 1.42 Å, respectively, and correspond to the tetra-σ and di-π configurations (Table 3).

The NBE molecule has only one double bond, which forms with Pd(111) two possible configurations upon endo-adsorption, di-σ and π. The lengths of the adsorbed double bonds of NBE and NBD molecules are close, but in the case of NBE, the binding energy of the double bond with Pd atoms is noticeably lower, 18.1 and 9.5 kcal/mol for di-σ- and π-adsorbed double bonds (Table 3). For comparison, in the NBD molecule these energies are 21.85 and 12.95 kcal/mol. The additional energy gain during NBD adsorption is associated with the prevalence of ring strain energy of the NBD molecule. Thus, the C2C1C7 bond angle for the NBD tetra-σ configuration is larger than for the NBE di-σ configuration (99.0º and 98.2º, Table 3). According to experimental data, this angle in free NBD and norbornane molecules is 98.4° [59] and 102.0° [58], respectively. Two hydrogen atoms in the endo-di-σ and endo-π configurations of NBE interact with surface Pd atoms. In the case of endo-di-σ configuration each H atom is not above one Pd atom, but between two (di-σ, Fig. 5) due to the triangular geometry of the threefold sites of Pd(111). As a result, the H–Pd interaction is not strong, and the shortest H–Pd distances are 2.38 and 2.54 Å.

The exo-approach of NBD and NBE molecules to Pd(111) leads to the formation of di-σ and π configurations, in which only one double bond interacts with two (for di-σ) or one (for π) Pd atoms. The exo-di-σ configuration corresponds to the η2:η1 configuration (Fig. 2b). Optimized structures are shown in Fig. 6. Calculated adsorption energies, C2 = C3 and C‒Pd bond lengths, and C2C1C7 bond angle are presented in Table 4. The adsorption energy of NBD in the exo-di-σ and exo-π configurations is 6.4–6.9 kcal/mol higher than the adsorption energy in the endo-tetra-σ and endo-di-π configurations (per one double bond). The main contribution to this difference is made by the interaction energy of the H atom of the methylene bridge with the Pd atom. The distance between metal and hydrogen in the exo-di-σ and exo-π configurations is 2.11–2.18 Å, and the C-H–Pd angle is 155.7º and 170.9º, respectively. These geometrical values of the H–Pd interaction do not allow us to attribute it to the agostic type, and it is closer to the anagostic one [60].

Fig. 6
figure 6

Optimized structures of exo-adsorption configurations of NBD and NBE on Pd(111): a – side views of Pd86, b – top views of NBD/NBE (the first layer of the Pd atoms are shown), c – side views of the C1(4) atom of NBD/NBE molecule (the first layer of the Pd atoms are shown)

Full size image
Table 4 Adsorption energies (Eads and Eads,0, kcal/mol), C2 = C3 and C‒Pd bond lengths (RC2C3 and RC‒Pd, Å), C2C1C7 bond angle (deg.) of exo-adsorption configurations of NBD and NBE on Pd(111)
Full size table

Similarly to NBD, in the exo-di-σ and exo-π configurations of NBE, there is an anagostic H‒Pd interaction. From the energy difference between di-σ and π configurations in the exo- and endo-orientation of the NBE molecule, one can approximately estimate the energy of the H‒Pd interaction:

$$\begin{array}{c}{E}_{\mathrm{ads}}\left(exo-\textbf{di-}\boldsymbol{\sigma} \right)-{E}_{\mathrm{ads}}\left(endo-\textbf{di-}\boldsymbol{\sigma} \right)=7.7\; \mathrm{kcal}/\mathrm{mol}\\ {E}_{\mathrm{ads}}\left(exo-\boldsymbol{\pi}\right)-{E}_{\mathrm{ads}}\left(endo-\boldsymbol{\pi}\right)=9.5\; \mathrm{kcal}/\mathrm{mol}\end{array}$$

These values are slightly bigger than for NBD (6.4–6.9 kcal/mol). The point is that part of this energy is related not to the H‒Pd interaction, but to the fact that the exo-configurations of the adsorbed NBE molecule are less strain than the endo-configurations. This is indicated by increased C2C1C7 angles (103º and 102.7º, Table 4).

From a comparison of the adsorption energies of NBD and NBE molecules on the (111) facet (Tables 3 and 4), it follows that for NBD, endo-adsorption with the formation of the tetra-σ configuration is extremely preferable, and for NBE, exo-adsorption with the formation of di-σ configuration.

Adsorption of NBD and NBE molecules on Pd(100)

The adsorption energies and the main geometrical parameters of the adsorption configurations of NBD and NBE on the (100) facet are given in Table 5. Optimized structures are shown in Fig. 7. We failed to detect the di-σ,π and di-π configurations of the endo-adsorbed NBD molecule on Pd(100). During the geometry optimization these configurations transform into the only possible tetra-σ configuration without an activation barrier. In the case of NBE, the endo-adsorption leads to the formation of the di-σ configuration.

Table 5 Calculated C2 = C3 and C‒Pd bond lengths (RC2C3 and RC‒Pd, Å), C2C1C7 bond angle (deg.), adsorption energy (Eads and Eads,0, kcal/mol) and energy gain (ΔEads, kcal/mol) of adsorption configurations of NBD and NBE on Pd(100)
Full size table
Fig. 7
figure 7

Optimized structures of adsorption configurations of NBD (upper structures) and NBE (lower structures) on Pd(100): a – side view of C1(4) atom of the NBD/NBE molecule, b – top view of the NBD/NBE molecule (the first layer of the Pd atoms are shown)

Full size image

As can be seen from Table 5, the interaction of NBD and NBE with Pd(100) is stronger. The energy gain ΔEads is especially noticeable for the endo-tetra-σ configuration of NBD (4.8 kcal/mol). This can be explained by the fact that the fourfold sites of the (100) facet are geometrically better suited for the adsorption of the NBD molecule than the threefold sites of Pd(111).

As in the case of Pd(111), the exo-adsorbed NBD and NBE molecules on Pd(100) may exist in two possible configurations, di-σ and π. The structures of these configurations on the (100) and (111) facets are very close, but the adsorption energies on the (100) facet are higher, especially for the π configurations of NBD and NBE (ΔEads = 3.7–3.8 kcal/mol, Table 5). A possible explanation is that the surface atoms of Pd(100) are coordinatively more accessible.

Comparison of Eads for different configurations of NBD and NBE (Table 5) leads to the conclusion that the most energetically favorable configurations on the (100) facet are endo-tetra-σ (NBD) and exo-di-σ (NBE) configurations. This means that on Pd(100) the NBD molecule is adsorbed in the endo-orientation, while the NBE molecule is adsorbed in the exo-orientation. This conclusion is valid for the two considered facets. The adsorption process proceeds without an activation barrier, as evidenced by the energy profiles of NBD desorption from the (100) and (111) facets (Figure S2).

According to [61] the adsorption energy can be decomposed into 3 components: the stabilizing interaction energy (Eint) between a molecule and a surface and the destabilizing distortion energy of molecule (Edis,mol) and surface (Edis,Pd):

$${E}_{\mathrm{ads}}={E}_{\mathrm{int}}-\left({E}_{\mathrm{dis},\mathrm{mol}}+{E}_{\mathrm{dis},\mathrm{Pd}}\right)$$

Such a decomposition of the adsorption energy for all configurations is presented in Table 6. The distortion energy Edis,mol calculated as difference between the energies of an isolated molecule in relaxed and in adsorbed geometries; the distortion energy Edis,Pd calculated as difference between the energies of a surface in relaxed and substrate geometries; and the interaction energy Eint calculated as difference between the sum of energies of an isolated molecule in adsorbed geometry and a surface in substrate geometry and the energy of a surface with an adsorbed molecule. As can be seen from Table 6, a strong interaction of NBD and NBE molecules with the Pd surface (31.1–113.4 kcal/mol) compensated by a larger deformation of NBD and NBE molecules (8.7–64.0 kcal/mol).

Table 6 Calculated interaction energy (Eint, kcal/mol) and distortion energies of NBD and NBE molecules (Edis,mol, kcal/mol) and Pd surface (Edis,Pd, kcal/mol) for all adsorption configurations
Full size table

There are no experimental data on the adsorption of NBD on the palladium surface, however, experiments on the NBD adsorption [41, 42] and the hydrogenation of NBD with dideuterium on Pt(111) [62] indicate the presence of the exo-di-σ configuration, but not the endo-tetra-σ configuration. A specific feature of the adsorption of phenylacetylene and styrene on the Pd surface was noted earlier [56]. These molecules interact with the metal not only with the ethynyl or vinyl group, but also with the aromatic ring. In this case, very strong di-μCC + πAr configuration are formed, the hydrogenation rate of which is much lower [63, 64] than configurations in which the ring is tilted to the Pd surface. DFT calculations [56] showed that adsorption of two phenylacetylene molecules in the di-μCC configuration on the same number of Pd atoms is energetically more preferable than one molecule in the di-μCC + πAr configuration.

It is also possible that in the case of NBD, the experimentally observed exo-di-σ configuration on Pt(111) is preferable due to more compact adsorption. Figures 5b and 6b show that the endo-tetra-σ configuration occupies 2 sites with a common side, while the exo-di-σ configuration occupies 1 threefold site. The binding energy per one Pd atom is:

$$\begin{array}{c}{E}_{\mathrm{ads}}\left(endo-\textbf{tetra-}\boldsymbol{\sigma} \right)/4=10.9 \:\mathrm{kcal}/\mathrm{mol}\\ {E}_{\mathrm{ads}}\left(exo-\textbf{di-}\boldsymbol{\sigma} \right)/3=9.6 \:\mathrm{kcal}/\mathrm{mol}\end{array}$$

These values are close, but still the endo-tetra-σ configuration according to the binding energy (per Pd atom) remains more preferable.

The approximate area of adsorption of one NBD molecule in the endo-tetra-σ and exo-di-σ configurations is shown in Fig. 8. It can be seen from the figure that the direction of the second double bond away from the Pd surface leads to a significantly smaller area of the exo-adsorbed NBD molecule (Fig. 8b), which in turn leads to less steric hindrance for neighboring adsorbed NBD molecules. A simple calculation of the area of these shapes gives the values of 24.4 Å2 (Sa) and 16.1 Å2 (Sb) for the endo-tetra-σ and exo-di-σ configurations, respectively, and amounts to 7.6 and 5 areas of threefold site. The ratio Sa/Sb ≈ 1.5 is approximately the same as the ratio of the Eads(endo-tetra-σ) and Eads(exo-di-σ) values. Thus, more compact NBD adsorption in the exo-di-σ configuration can compensate for the difference in the adsorption energy ΔEads(endo-tetra-σ/exo-di-σ) due to the interaction of a larger number of NBD with the Pd(111) surface. An example of a compact arrangement of several NBD molecules on Pd(111) is shown in Figure S3.

Fig. 8
figure 8

Estimation of adsorption area of one NBD molecule for the endo-tetra-σ (a) and exo-di-σ (b) configurations on (111) facet of Pd86. Distances (Å) between the purple dots are shown

Full size image

The feature of the (100) facet leads to the fact that the endo-tetra-σ and exo-di-σ configurations of the NBD molecule occupy the same adsorption area corresponding to 4 fourfold sites. The NBD molecule directly occupies one fourfold site, and an area corresponding to 3 fourfold sites surrounds this molecule. In this regard, in contrast to the (111) surface, the exo-adsorption of NBD on the Pd(100) surface seems unlikely.

Multiple adsorption of NBD and NBE on Pd surface

In order to elucidate the possible effect of the environment of neighboring adsorbed NBD molecules on the adsorption energy, calculations for 2 to 4 adsorbed NBD molecules on the Pd surface were made (Figure S4). Figure 9 shows the dependence of the average adsorption energy (per one molecule) on the number of the endo-tetra-σ adsorbed NBD and exo-di-σ adsorbed NBE molecules on Pd(100). It follows that the average adsorption energy of NBD decreases by about ~ 6 kcal/mol, while for NBE this value is lower (~ 3 kcal/mol). Thus, the repulsion between endo-adsorbed NBD molecules is stronger. Another factor in favor of the exo-adsorption of the NBD molecule on Pd(111).

Fig. 9
figure 9

Dependence of the average adsorption energy (Eads/molecule) on the number (n) of the adsorbed NBD and NBE molecules on Pd(100)

Full size image

Interconversion and migration of adsorption configurations on Pd surface

Another important aspect of surface chemistry concerns the interconversion and mobility of adsorption configurations on the Pd surface. According to our calculations, the endo-di-π adsorbed NBD molecule transforms into a di-σ,π configuration with the very low (~ 0.5 kcal/mol) activation barrier. Then, with the same barrier, the di-σ,π configuration passes into the energetically more favorable tetra-σ configuration. Figure 10 shows a graph of the energy change along the reaction coordinate (C–Pd distance). The approach of the C3 atom of the di-σ,π configuration to the Pd1 atom leads to the formation of the tetra-σ_1 configuration. The tetra-σ_2 configuration is formed if the movement of the C2 atom of the di-σ,π configuration is directed to the Pd5 atom. It turns out that the di-σ,π configuration is an intermediate in the two-stage transformation of tetra-σ_1 to tetra-σ_2 with the low activation barriers (6.1–6.7 kcal/mol). Therefore, the di-π and di-σ,π configurations are not stable despite the high adsorption energy (25.9 and 37.8 kcal/mol, Table 3).

Fig. 10
figure 10

Energy profile of interconversions of di-π, di-σ,π and tetra-σ configurations of the endo-adsorbed NBD molecule on Pd(111). The energies are given with respect to the tetra-σ_1 configuration. The corresponding structures are shown on the right (top view of NBD)

Full size image

However, the di-σ,π configuration plays an important role as an intermediate in the migration of the NBD molecule. In contrast to the (111) facet, π-adsorption of double bonds of the endo-adsorbed NBD molecule on the (100) facet is impossible and, accordingly, the di-σ,π configuration is not formed. This leads to significant difficulties in the migration of the NBD molecule on Pd(100). According to our calculations, the activation barrier to migration of the NBD molecule is ~ 28 kcal/mol (Figure S5).

The configurations of the exo-adsorbed NBE molecule are also capable of interconversions on the (111) face. Thus, the π configuration easily transforms into a more energetically favorable di-σ configuration with the activation barrier of ~ 1 kcal/mol. Figure 11 shows the energy change in during the transition from one di-σ configuration to the same one through the intermediate formation of the π configuration. The activation barriers of the two-stage migration of the NBE molecule from the Pd1 and Pd2 atoms (di-σ_1, Fig. 11) to the Pd2 and Pd3 atoms (di-σ_2, Fig. 11) do not exceed 8 kcal/mol. The transition from di-σ_1 to di-σ_2 is possible in one stage without intermediate formation of the π configuration. For example, the approach of the C2 atom to the Pd3 atom leads to the di-σ_2 configuration, but the activation barrier in this case is higher (~ 10 kcal/mol, Figure S6).

Fig. 11
figure 11

Energy profile of interconversions of di-σ and π configurations of the exo-adsorbed NBE molecule on Pd(111). The energies are given with respect to the di-σ_1 configuration. The corresponding structures are shown on the right (top view of NBE)

Full size image

Migration of the exo-adsorbed NBE molecule is also possible on the (100) facet. The activation barrier of π → di-σ transformation is ~ 0.5 kcal/mol (Figure S7). Therefore, the transformation of one di-σ configuration into another di-σ through the intermediate formation of the π configuration will proceed with the activation barrier:

$$E^{\ne} ={E}_{\mathrm{ads}}\left(\textbf{di-}\boldsymbol{\sigma} \right)-{E}_{\mathrm{ads}}\left(\boldsymbol{\pi} \right)+E^{\ne} \left(\boldsymbol{\pi} \to \textbf{di-}\boldsymbol{\sigma} \right)=5.1 \; \mathrm{kcal}/\mathrm{mol}$$

Conclusions

In summary, the interaction of norbornadiene (NBD) and norbornene (NBE) molecules with the Pd(111) and Pd(100) surfaces have been investigated using the density functional theory (DFT-PBE) calculations. Five configurations of adsorbed NBD may be formed on Pd(111): endo-tetra-σ, endo-di-σ,π, endo-di-π, exo-di-σ and exo-π. The most energetically stable configuration is the endo-tetra-σ configuration with the adsorption energy of 43.7 kcal/mol. The NBE molecule adsorbed on Pd(111) may exist in 4 configurations: endo-di-σ, endo-π, exo-di-σ and exo-π. The most preferred is the exo-di-σ configuration (Eads = 25.8 kcal/mol).

On the Pd(100) surface, a smaller number adsorption configurations of NBD and NBE are formed, since the double bonds of these molecules in the endo-orientation are bound only in a di-σ configuration. Therefore, 3 NBD adsorption configurations (endo-tetra-σ, exo-di-σ and exo-π) and 3 NBE adsorption configurations (endo-di-σ, exo-di-σ and exo-π) are formed on Pd(100). The most stable adsorption configurations are endo-tetra-σ (NBD) and exo-di-σ (NBE) with the adsorption energies are 48.4 and 27.3 kcal/mol, respectively. Therefore, the adsorption of NBD and NBE on Pd(100) was found to be on about 2–5 kcal/mol stronger as compared to Pd (111).

Thus, on both clean Pd surfaces, the endo-adsorption with the formation of the tetra-σ configuration is preferred for NBD, while the NBE molecule is adsorbed in the exo-di-σ configuration. However, the possibility of NBD adsorption in the exo-di-σ configuration on Pd(111) cannot be ruled out. Due to smaller adsorption area of the exo-di-σ configuration on Pd(111), a larger number of NBD molecules may adsorbed on the surface. In addition, repulsion between endo-adsorbed NBD molecules is stronger.

In the exo-di-σ and exo-π configurations of NBD and NBE, the hydrogen atom of the CH2-bridge group interacts with the Pd atoms. Geometric parameters (bond length H–Pd is 2.11–2.18 Å, ∠CHPd = 156-171º) make it possible to classify this H–Pd interaction as anagostic, and the interaction energy is approximately equal to 6.4–7.7 kcal/mol.

The most energetically favorable endo-tetra-σ (NBD) and exo-di-σ (NBE) configurations are highly mobile on Pd(111) and their migration occurs with the low activation barriers (~ 6–8 kcal/mol). Migration of NBD on the (111) facet proceeds through the intermediate di-σ,π configurations, and NBE migrates through the π configurations. On Pd(100), only NBE molecules with the activation barriers of ~ 5 kcal/mol can migrate, while NBD migration is hindered due to the high activation barriers (~ 28 kcal/mol).