Introduction

Well-defined ruthenium alkylidene complexes (Fig. 1) are commonly used as highly efficient catalysts for olefin metathesis. These systems show a high tolerance towards most of the functional groups in the substrates, air and moisture insensitivity, and thermal stability [1,2,3,4].

Fig. 1
figure 1

Example ruthenium alkylidene catalysts

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The key step during the olefin metathesis process is initial formation of a 14-electron active complex [5,6,7,8,9,10,11,12,13,14]. In the case of the Grubbs-type catalysts (1–3), it occurs by dissociation of ligands L, whereas for the Hoveyda-Grubbs catalysts (4–6), it requires decoordination of the ether moiety (Fig. 2). Electron and steric properties of these ligands significantly affect the rate of the catalyst activation [6,7,8, 10,11,12, 14, 15]. In addition to this often postulated dissociative mechanism, where the dissociation/decoordination is the first step, associative and interchange mechanisms for the activation of the second and third generation ruthenium alkylidene catalysts were also proposed [8, 9, 12, 14, 16, 17]. In the case of the associative mechanism, the alkene molecule coordinates to the metal centre before dissociation of the appropriate ligand, whereas for the interchange mechanism, both steps take place simultaneously. Experimental kinetic studies for the Hoveyda-Grubbs catalysts indicated that two mechanisms, dissociative and interchange, are in work, depending on the steric and electronic properties of the ruthenium complex and the substrate employed [8]. Accordingly, the dissociative pathway was theoretically shown to be preferred over the interchange one in the case of the Hoveyda-Grubbs complexes bearing a large chelating alkoxy ligand, although the Hoveyda ligand decoordination during the cross-metathesis reaction is the rate-determining step [12]. For the Grubbs-type catalysts, the dissociative mechanism was rather computationally predicted as the kinetically favoured one, with the dissociation step being rate determining [12, 17]. Calculations also showed that the Gibbs energy barrier for phosphine dissociation from the Grubbs complex is solvent- and entropy-related [18].

Fig. 2
figure 2

Mechanism of olefin metathesis catalysed by ruthenium alkylidene complexes [7]

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In this work, the formation of the propagating 14-electron alkylidene species from the Grubbs-type (1–3) and Hoveyda-Grubbs-type (4–6) initiators has been investigated using density functional theory (DFT). Our main objectives are to compare the activation parameters for catalysts with different ligands within a given family of compounds and to analyse in detail the nature of the interactions between the dissociating ligand L and the rest of the system. Bonding between the ligand L and the remaining Ru-based fragment is characterized for catalysts 1–3 and the corresponding transition state structures, using the extended-transition-state method combined with the natural orbitals of the chemical valence (ETS-NOCV) [19,20,21,22]. The Hoveyda-Grubbs catalysts have been additionally characterized by means of the interacting quantum atoms (IQA) [23] energy decomposition. This is the first time when these complementary theoretical approaches (ETS-NOCV and IQA) are used to get deeper insight into formation of active species from olefin metathesis catalysts.

Computational methods

Geometry optimization of all structures was carried out using the hybrid GGA PBE0 functional [24] combined with the split-valence def2-SVP basis set [25]. The 28 innermost electrons of Ru were replaced by the Stuttgart effective core potential [26]. Further single point energy calculations were performed with the hybrid meta-GGA M06 functional [27] and the triple-zeta valence def2-TZVPP basis set [25, 26]. The M06 method is recommended for main-group and transition metals thermochemistry, kinetics, and studies of noncovalent interactions [27]. A good performance of the M06 functional in predicting energies of reactions involving ruthenium alkylidene complexes [28,29,30,31,32,33], including the dissociation energy for the Grubbs catalysts [28,29,30,31], was proved and it was often used for investigations of real ruthenium systems [28,29,30,31,32,33,34,35,36]. On the other hand, the PBE0 method was shown to be accurate in reproducing experimental geometry of the second generation Grubbs catalyst (1) [28, 37], being even better than the M06 one [28].

Solvent effects were estimated by single point calculations on gas phase-optimized structures using the polarizable continuum model (PCM) [38]. In selected cases, the geometry optimization (PBE0/def2-SVP) has been also checked within the PCM framework.

Harmonic vibrational frequencies were calculated for each structure to confirm the potential energy minimum or the transition state structure and to obtain thermochemical quantities. The transition states were additionally verified by the IRC calculations [39, 40]. The PBE0/def2-SVP zero-point energy and thermal corrections were added to the gas phase single point energies to obtain a better estimate of gas phase enthalpies (Hg) and Gibbs energies (Gg). Enthalpies (Hs) and Gibbs energies (Gs) of the compounds in a solvent (toluene) were estimated analogously, involving the PCM single point energies. The counterpoise method [41] was used to estimate the basis set superposition error (BSSE). The reaction pathways are mainly discussed in terms of Gibbs energies calculated at the M06/def2-TZVPP//PBE0/def2-SVP level for simulated toluene solution.

It is well-established that the ground state for 16-electron and 14-electron ruthenium alkylidene complexes, studied in this work, is singlet [18, 42]. According to the PBE0/def2-SVP calculations, the triplet and quintet states of the 16-electron complex 1 are less stable than the singlet state, by 93 and 191 kJ mol−1, respectively. In the case of the 14-electron species 1_dis, formed after dissociation of 1, the corresponding differences are 75 and 171 kJ mol−1. Hence, the spin-restricted formalism is used for other computations. Furthermore, the DFT approach was proved sufficiently accurate in studying the reactivity of ruthenium alkylidene complexes [12, 13, 18, 28,29,30,31,32,33]. However, it shall be noticed, that for more difficult cases (e.g., open-shell transition metal complexes), single-determinant DFT shall be applied with special caution due to the approximated character of electron correlation, as well as a possible multireference character of wavefunction.

All the above calculations were done with the Gaussian 09 software [43].

For the Grubbs type catalysts, the charge and energy decomposition ETS-NOCV [19, 20] analysis was performed. DFT (BLYP [44, 45]) calculations were carried out with the Amsterdam Density Functional (ADF) program [21, 22], in which the ETS-NOCV scheme was implemented. The presented energies include DFT-D3(BJ) dispersion corrections [46, 47]. The standard triple-zeta STO basis set containing one set of polarization functions (TZP) was used for the ruthenium atom, whereas the double-zeta basis set (DZP) was employed for other elements as implemented in the ADF [21, 22]. The contours of deformation densities were plotted based on the ADF-GUI interface [21, 22].

ETS-NOCV charge and energy decomposition method

The natural orbitals for chemical valence (NOCV) ψi constitute the canonical representation for a differential density matrix ΔP (it is formed by subtracting the appropriate molecular fragments density matrices from a density matrix of a molecule under consideration) in which ΔP adopts a diagonal form. It gives rise to the corresponding eigenvalues vi and the related vectors ψi. NOCVs occur in pairs (ψ–k,ψk) related to |vk| and they decompose overall deformation density Δρ into bonding components with different symmetries (Δρk):

$$ \Delta \rho (r)=\sum \limits_{k= 1}^{M/ 2}{v}_k\left[\hbox{-} {\psi}_{\hbox{-} k}^2(r)+{\psi}_k^2(r)\right]=\sum \limits_{k= 1}^{M/ 2}{\varDelta \rho}_k(r) $$

Usually, a few k allow to recover a major shape of Δρ. ETS-NOCV [19, 20] allows for obtaining the related energetics, ΔEorb(k), in addition to qualitative picture emerging from Δρk. ETS originally divides the total bonding energy between fragments, ΔEtotal, into five distinct components: ΔEtotal = ΔEelstat + ΔEPauli + ΔEorb + ΔEdispersion + ΔEdist. The ΔEelstat is an energy of quasi-classical electrostatic interaction between fragments. The next term, ΔEPauli, is responsible for repulsive Pauli interaction between occupied orbitals on the two fragments. The third component, ΔEorb, is stabilizing and shows formation of a chemical bond (including polarizations). In the ETS-NOCV scheme, ΔEorb is expressed in terms of the eigenvalues vk and diagonal Fock energy matrix elements \( {F}_{i,i}^{TS} \) (transformed into NOCV representation) as:

$$ \varDelta {E}_{orb}=\sum \limits_k\varDelta {E}_{orb}(k)=\sum \limits_{k=1}^{M/2}{v}_k\left[-{F}_{-k,-k}^{TS}+{F}_{k,k}^{TS}\right] $$

The ΔEdispersion denotes the semiempirical Grimme dispersion correction (D3), whereas the last term ΔEdist describes a change in the fragment’s energy when going from the optimized configurations to those present in the final complex. This method is applied for 1–3.

IQA energy decomposition method

IQA method [23] divides the total electronic energy E into atomic (\( {E}_{self}^A \)) and diatomic (\( {E}_{\mathrm{int}}^{AB} \)) contributions:

$$ E=\sum \limits_A{E}_{self}^A+\frac{1}{2}\sum \limits_A\sum \limits_{B\ne A}{E}_{\mathrm{int}}^{AB} $$

Diatomic part covers all interactions between particles of different atoms A and B: nucleus-nucleus (\( {V}_{nn}^{AB} \)), nucleus-electron(\( {V}_{ne}^{AB} \)), electron-nucleus (\( {V}_{en}^{AB} \)), and electron-electron (\( {V}_{ee}^{AB} \)):

$$ {E}_{int}^{AB}={V}_{nn}^{AB}+{V}_{en}^{AB}+{V}_{ne}^{AB}+{V}_{ee}^{AB}={V}_{nn}^{AB}+{V}_{en}^{AB}+{V}_{ee C}^{AB}+{V}_{ee X}^{AB}={E}_{Coul}+{E}_{XC} $$

where \( {V}_{eeC}^{AB} \) and \( {V}_{eeX}^{AB} \) are Coulomb and exchange contributions of \( {V}_{ee}^{AB} \). The former three terms together with \( {V}_{eeC}^{AB} \) are often combined into the overall Coulomb component ECoul, whereas the last, consisting of the exchange and correlation terms, describes the overall exchange-correlation contribution EXC. This complementary (to ETS-NOCV) method is applied for analyses of intramolecular contacts in the Hoveyda-Grubbs complexes. IQA analyses were performed on the wavefunction obtained in Gaussian 09 at the HF/def2-TZVP level of theory for the PBE0 geometries.

Results and discussion

Activation of the Grubbs-type catalysts

Assuming the commonly accepted dissociative mechanism [5, 6, 12, 13, 17, 18], the activation of the Grubbs-type complexes of general formula (H2IMes)(L)(Cl)2Ru=CHR requires dissociation of the ligand L (Fig. 2). For the phosphine-containing catalysts (1 and 2), rate determining transition states have been localized (Figs. 3 and 4), but the calculated enthalpy profiles (T = 298 K) are monotonic, indicating that these transition states do not affect the enthalpy barriers, which are determined by the reaction, not activation, enthalpies (Table 1). Hence, the Gibbs energy barriers for the reverse reaction (phosphine coordination to the 14-electron ruthenium alkylidene species) are mainly due to the entropy effect, as it was reported elsewhere [13, 18].

Fig. 3
figure 3

Gibbs energy profile (ΔGs, kJ mol−1) for the activation of the catalyst (H2IMes)(PCy3)(Cl)2Ru=CHPh (1). M06/def2-TZVPP//PBE0/def2-SVP calculations for simulated toluene solution

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Fig. 4
figure 4

Gibbs energy profile (ΔGs, kJ mol−1) for the activation of the catalyst (H2IMes)(PCy3)(Cl)2Ru=CH-CH=CMe2 (2). M06/def2-TZVPP//PBE0/def2-SVP calculations for simulated toluene solution

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Table 1 Enthalpies (ΔH, kJ/mol), Gibbs energies (ΔG, kJ/mol), and the corresponding activation parameters (ΔH‡, ΔG‡) of the dissociation/decoordination reactions for the catalysts 1–6, in gas phase (g)and toluene solution (s). Values in parenthesis are BSSE-corrected. The M06/def2-TZVPP//PBE0/def2-SVP calculations
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The calculated activation parameters (ΔHs‡, ΔGs‡) for dissociation of the catalyst 1 are in a very good agreement with the corresponding experimental data, determined for the phosphine ligand exchange in toluene solution (Table 1). Other reported theoretical values of the activation Gibbs energy for phosphine dissociation from 1 are in the same range (90–99 kJ mol−1, toluene solution) [13, 17, 18] or significantly higher (123 kJ mol−1, dichloromethane solution) [12], compared to the present result (99 kJ mol−1).

There are two possible rotational isomers of the active ruthenium alkylidene species [18, 28,29,30, 35, 48]. Perpendicular orientation of the benzylidene group to the mesityl group (1_dis, Fig. 3) is energetically preferred, compared to the parallel orientation (1_dis′), which can be explained by electronic structure analysis [48]. The more stable isomer 1_dis is formed by dissociation of the 16-electron ruthenium complex 1. Rotation of the alkylidene ligand in the 14-electron species requires low activation barrier to overcome (ΔGs‡ = 37 kJ mol−1), which is accompanied by slight elongation of the carbene bond in the transition state 1_TS′, by about 0.025 Å. The less stable isomer 1_dis′ can be also generated directly from 1 by decoordination of the phosphine ligand according to a monotonic pathway.

In the case of the complex (H2IMes)(PCy3)(Cl)2Ru=CH-CH=CMe2 (2), the calculated activation Gibbs energy of phosphine dissociation (Fig. 4) is slightly higher, compared to 1 (Table 1). Hence, the latter can be more active than catalyst 2 in metathesis reactions. It was experimentally shown for ruthenium catalysts of general formula (L1)(L2)(Cl)2Ru=CHR that the substituent R significantly influences the rate of phosphine ligand exchange [6]. The activity of the ruthenium catalysts increases as R = H < < CH=CMe2 < Ph < Et, in accordance with the present results. Generally, bulky substituents R with electron-donor ability more effectively promote phosphine dissociation [6].

It is known that type of ligand L has a great impact on the activity of the Grubbs-type catalysts [6, 7]. As 3-bromopyridine is a much more labile ligand than PCy3, the phosphine free catalyst 3 is highly active in olefin metathesis, with the initiation rate constant higher by several orders of magnitude, compared to 1 [7]. It can also effectively catalyse polymerization [35, 49] and other transformations of terminal alkynes [36, 50, 51].

The computational results clearly indicate that (H2IMes)(3-Br-py)2(Cl)2Ru=CHPh (3) most easily forms the active species, among all the tested catalysts (Table 1). Due to the presence of two 3-bromopyridine ligands, the two-step dissociation pathway is expected (Fig. 5). Considering decoordination of the first ligand, 3-bromopyridine in cis position to the NHC group (pathway a) should dissociate faster than the 3-Br-py ligand located in the trans position (pathway b), based on the calculated Gibbs energy barriers. As it has been suggested in other theoretical studies [17], where the pathway a was also calculated, the higher lability of 3-bromopyridine in cis position to the NHC moiety can be also predicted on the basis of the Ru-N distance which is significantly longer, compared to the ligand in trans position (2.398 and 2.221 Å, respectively).

Fig. 5
figure 5

Gibbs energy profiles (ΔGs, kJ mol−1) for two possible pathways of the activation of the catalyst (H2IMes)(3-Br-py)2(Cl)2Ru=CHPh (3): a dissociation of the first 3-Br-py ligand in cis position to the NHC ligand, b dissociation of the first 3-Br-py ligand in trans position to the NHC ligand. M06/def2-TZVPP//PBE0/def2-SVP calculations for simulated toluene solution

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In the partially dissociated complex (H2IMes)(3-Br-py)(Cl)2Ru=CHPh (3_dis1a and 3_dis1b), the 3-bromopyridine ligand is located in trans position to the NHC ligand, with the Ru-N distance in the range of 2.160–2.169 Å. Not surprisingly, further dissociation to form 14-electron ruthenium alkylidene species 1_dis requires a higher activation barrier to overcome (ΔGs‡ = 56 kJ mol−1), compared to the first step, in agreement with other authors [17]. However, this process is still much more kinetically accessible than dissociation of the phosphine-containing catalysts 1 and 2 (ΔGs‡ = 99 and 100 kJ mol−1, respectively). Moreover, the latter reactions are also highly endergonic (ΔGs = 73 and 83 kJ mol−1, respectively), in contrast to only slightly endergonic dissociation of both 3-bromopyridine ligands (ΔGs = 23 kJ mol−1). Consequently, the concentration of the active 14-electron ruthenium species should be larger for catalyst 3 than for 1 and 2, in agreement with the experimentally observed higher activity of initiator 3, compared to 1 [7]. On the other hand, the thermodynamic equilibrium between the initiator 3 and the mono(3-bromopyridine) ruthenium alkylidene species (3_dis1a, 3_dis1b) can be expected (Fig. 5).

The estimated BSSE correction slightly reduces the calculated dissociation energies for the catalysts 1–3 by about 10 kJ mol−1, and the activation barriers by approximately 3–7 kJ mol−1 (Table 1). The dissociation and activation energies computed for the simulated toluene solution are lower by 10–17 and 5–14 kJ mol−1, respectively, compared to the gas phase values. The solvent effects influence most significantly the dissociation energy of two 3-bromopyridine ligands. Even if relatively small, the solvent effects can change the conclusions concerning the relative activities of the catalysts (compare the ΔGg‡ and ΔGs‡ values for the catalysts 1 and 2, Table 1). As both BSSE and simulation of the solvent cause decrease of the dissociation energies and activation barriers, the summary correction to these quantities may be quite significant, in the range of 9–27 kJ mol−1.

In the case of the dissociation pathways for 1 and 2, we have also examined how including the solvent effects already at the geometry optimization stage influences the final Gibbs energy profiles (Fig. S1, Supplementary Material). It can be seen that the differences are quite small, up to 5 kJ mol−1, compared to the single point PCM calculations based on the gas phase optimized geometries. Importantly, the predicted trends in the activation barriers and dissociation energies have been preserved. Indeed, the structures calculated using the continuum solvent model are slightly changed, compared to the gas phase geometry optimization, particularly in the case of the minima. For instance, the differences in Ru=C and Ru-P bond lengths are up to 0.002 and 0.009 Å, respectively. On the other hand, the Ru-P distance in the transition states is more significantly affected by the inclusion of the solvent effects, being longer up to about 0.1 Å, compared to the gas phase geometry.

Activation of the Hoveyda-Grubbs-type catalysts

The absence of released phosphine, which might re-coordinate to the 14-electron ruthenium alkylidene species, is the key feature of the Hoveyda-Grubbs-type catalysts. The activation of the Hoveyda-Grubbs-type complexes occurs by breaking the Ru–O bond and simultaneous rotation of the Ccarbene–Caromatic bond in the benzylidene moiety (Fig. 2) if the dissociative mechanism [8, 12, 52,53,54] is assumed. It is known that the activity of this type of catalysts can be significantly modified by changing the steric and/or electronic properties of the Ru-chelating isopropoxy fragment. Experimental works [55, 56] showed that introduction of the strong electron-withdrawing nitro group into the aromatic ring of 4, resulting in complex 5, known as the Grela catalyst, causes a significant increase in the catalytic activity. This might be explained by the fact that electron-withdrawing substituents located in position para to the alkoxy group mostly reduce the electron density at the oxygen atom and, consequently, weaken the Ru–O interaction, just facilitating the activation process [57]. However, the sterically activated ruthenium complex 6 [58] is even more active than 5 [56]. The calculated activation barriers (ΔGs‡) for the decoordination of the isopropoxy moiety in the catalysts 4–6, being of 77, 73 and 54 kJ mol−1, respectively (Fig. 6, Table 1), are in agreement with these experimental observations.

Fig. 6
figure 6

Gibbs energy profiles (ΔGs, kJ/mol) for the activation of the Hoveyda-Grubbs-type catalysts: a (H2IMes)(Cl)2Ru=CH(o-OiPrC6H4) (4), b (H2IMes)(Cl)2Ru=CH(5-NO2–2-OiPrC6H3) (5), c (H2IMes)(Cl)2Ru=CH(2-OiPr-3-PhC6H3) (6). M06/def2-TZVPP//PBE0/def2-SVP calculations for simulated toluene solution

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We have further performed IQA energy decomposition study in order to better understand the most facile breaking of the Ru–O bond in 6. Since the Ru–O bond distances are quite similar for 5 and 6 and they are different than in 4 (2.28 Å for 4 and 2.30 Å for 5 and 6), we have focused our attention on comparison between 4 and 6. We have determined, in line with the trend in bond distances, that the overall diatomic Ru–O interaction energy \( {E}_{int}^{AB} \) in 6 is higher (less negative), by 16 kJ mol−1 than in 4 (Fig. 7). IQA further indicates, in line with the previous suggestion [57], that Ru–O is electrostatically dominated (ECoul covers ~86% of the overall stabilization ECoul + EXC), though, the non-classic quantum exchange-correlation term (EXC) is also non-negligible (~14%) (Fig. 7).

Fig. 7
figure 7

Selected IQA diatomic interaction energies Eint (kJ mol−1) and their constituents for catalysts 4 and 6. Eint = EXC + ECoul

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Interestingly, we have further revealed by the IQA calculations that bulky OiPr fragment is able to form the ancillary non-covalent interactions CH…Cl and agostic CH…Ru with the neighbouring metal-fragment (Fig. 7). We have determined that the overall chlorine–hydrogen interaction energy \( {E}_{int}^{AB} \) (CH43…Cl) + \( {E}_{int}^{AB} \) (CH47…Cl) = −36 kJ mol−1 in 4, whereas the corresponding value for 6 is significantly more pronounced, i.e. –69 kJ mol−1 (Fig. 7). Furthermore, solely in the case of 6 additional CH…π interactions are recovered between the C–H43 bond of OiPr and the phenyl substituent, \( {E}_{int}^{AB} \)(CH43…C75) = −21 kJ mol−1 (Fig. 7). Such efficient and more pronounced non–covalent interactions in 6 with respect to 4 and 5 might be responsible for both the Ru–O interaction energies and accordingly for the observed activation energies. These are very intriguing outcomes in the light of the intuitive claim on the solely steric-hindrance power of the isopropoxy group. It is to be added, consistently with the above discussion, that the removal of the mentioned non-covalent interactions due to the simple substitution of bulky OiPr by the significantly smaller in size metoxy unit (OMe) results in the significant elongation of Ru–O distances by ~ 0.02 Å (Fig. S2, Supplementary Material).

Previous computations suggested that the initiator 4 should more easily decoordinate than the initiator 5, only the computational analysis of the full metathesis pathway, including the addition of the first olefin molecule, indicated a higher activity of the catalyst 5 [12]. However, in that work, the isopropoxy group was replaced by ethoxy group—the latter, due to smaller size, can exert different non-covalent interactions with the metal-fragment and accordingly diverge the Ru–O distances (and activation barriers). The present study (which considers real bulky OiPr unit) shows that both the catalysts 5 and 6 are better metathesis initiators than 4, already at the step of the ether moiety decoordination (Fig. 6, Table 1).

Finally, the solvent effects estimated for the initiation step of the Hoveyda-Grubbs-type catalysts 4–6 are less significant than in the case of the Grubbs complexes 1–3 (Table 1). The energies of the decoordination reactions obtained for the simulated toluene solution are decreased by 5–9 kJ mol−1, compared to the gas phase calculations, whereas the predicted activation barriers are lower by approximately 5 kJ mol−1.

ETS-NOCV analysis

In order to understand factors which determine bond energies in the Grubbs-type catalysts, we have performed the ETS-NOCV analysis for the substrates 1–3. Subsequently, we have done similar analysis for the corresponding transition states in order to shed some light on the calculated energy barriers. The ETS energy decomposition results are gathered in Table 2 (for more details on the method, see Section 2 and Refs. [19, 20]).

Table 2 ETS energy decomposition results (kJ mol−1) from BLYP-D3/TZP describing bonding between the dissociating ligand and the remaining Ru-based fragment in substrates
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Among the systems under study, the lowest total bonding energy ΔEtotal (the strongest bond) is predicted for the catalysts 1 and 2 (Table 2). The small difference between the ΔEtotal values and between the corresponding constituents obtained for 1 and 2 is consistent with the similar electronic energy barriers ΔE0‡ (137 and 131 kJ mol−1, respectively). The highest total interaction energy (the weakest bond) is predicted for the complex 3, which consequently most easily dissociates. The dissociation energies for both 3-bromopyridine ligands are very close to each other (ΔEtotal for 3cis and 3trans; see also Fig. 5). On the other hand, the 3-bromopyridine ligand located in cis position to the NHC moiety dissociates with lower activation barrier, compared to that in trans position (27 and 53 kJ mol−1, respectively; see also Fig. 5). This difference is mainly due to stronger stabilization of the latter, arising from the electrostatic and orbital interaction terms, although the Pauli repulsion term is less favourable for 3trans than for 3cis (Table 2). In accordance with the calculated Gibbs energy profiles (Fig. 5), the total interaction energy for the partially dissociated complex 3_dis1a is lower, compared to 3cis and 3trans.

It shall be emphasized that the electrostatic stabilization ΔEelstat dominates in each case, followed by the orbital interaction and dispersion terms (Table 2). The dispersion contributions ΔEdispersion appeared to cover from 9.4% (for 3_dis1a) of the overall stabilization (ΔEdispersion + ΔEorb + ΔEelstat) up to 18.2% (for 3cis). Particularly, ΔEdispersion is extremely significant at absolute level; it is −141 kJ mol−1 for 2 and − 144 kJ mol−1 for 1 (Table 2). It is in accord with the recent findings which highlight that bulky substituents might lead to enhancement of the molecular stability since their London dispersion donating properties might easily outweigh the corresponding steric (Pauli/kinetic) repulsion [59,60,61,62,63,64]. In the forthcoming paragraphs, electron density reorganization channels due to formation of various types of non-covalent interactions are identified and discussed in detail.

It is seen from Fig. 8 that the most relevant deformation density channel, Δρ1, that characterizes the Ru–P bond in 1 depicts donation from the lone electron pair of phosphorus to the metal centre (ΔEorb(1) = −164 kJ mol−1). Quantitatively less important are the π-contributions Δρ2 and Δρ3 related to ΔEorb(2 + 3) = −42 kJ mol−1 which stem from back-donation from 4d orbitals of Ru to the empty σ*(P–C). In addition, we can see secondary contributions from non-covalent interactions of type CH…Cl, CH…π. The former involves charge transfer from the lone pair of chlorine to the empty σ*(C–H), whereas the latter consist of donation from σ(C–H) to the empty π* of phenyl ring. Additionally, homopolar dihydrogen close contacts CH…HC lead to the two ways charge delocalization channels σ(C–H)➔ σ*(C–H) (and vice-versa) [61,62,63,64]. They all amount to ΔEorb(4 + 5 + 6) = −14 kJ mol−1 (Fig. 8). Apart from these charge delocalization components within CH…Cl and CH…π and CH…HC interactions, one can observe, in addition, the crucial stabilization stemming from dispersion as already discussed above.

Fig. 8
figure 8

Primary deformation density contributions Δρ1, Δρ2, and Δρ3, with the corresponding orbital interaction energies ΔEorb(1–3) describing Ru–P bond in complex 1. In addition, formation of secondary non-covalent interactions of the types CH…Cl, CH…π, and CH…HC are presented (Δρ4, Δρ5, Δρ6). Blue/red contours correspond to accumulation/depletion of electron density

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An interesting question emerges at this point, namely, how the relative importance of all bonding contributions will change when going from substrates to the corresponding transition states. As an example, the most relevant deformation density contributions for the transition state 1_TS are presented in Fig. 9.

Fig. 9
figure 9

Deformation density contributions Δρ1, Δρ2, Δρ3, and Δρrest with the corresponding orbital interaction energies ΔEorb(1–3) and ΔEorb(rest) describing Ru–P bond in the transition state 1_TS. Blue/red contours correspond to accumulation/depletion of electron density

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It is clearly seen that predominantly non-covalent close contacts of the types CH…Cl and CH…π described by Δρ1–3 stabilize the transition state; it corresponds to the electronic stabilization ΔEorb(1 + 2 + 3) = −12 kJ mol−1. Interestingly, the remaining part Δρrest appears to be dominant (ΔEorb(rest) = −16 kJ mol−1) and it is also associated with the formation of CH…Cl, CH…π and CH…HC augmented further by the intra-fragment density reorganization (Fig. 9). Importantly, it is seen from Table 3 that dispersion is decisively the most important stabilizing factor (ΔEdispersion = −74 kJ mol−1) in 1_TS. Similar conclusions on the crucial role of London dispersion forces are valid when considering the remaining transition state structures (Table 3). Similarly, critical role of van der Waals forces has been recently recognized in Diels-Alder cycloadditions as nicely reviewed in Ref. [60]—the authors have also stated correctly, that, although a rational tuning of a reaction barrier through various types of non-covalent interactions (inducing pure London dispersion) is still in “….its infancy” [60], it constitutes a promising new way toward better understanding and designing of chemical reactions.

Table 3 ETS energy decomposition results (in kJ mol−1) from BLYP-D3/TZP describing bonding between the dissociating ligand and the remaining Ru-based fragment in transition states
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The changes in bonding constituents when going from the considered substrates (1–3) to the corresponding transition states are collected in Table 4. Such analysis allows for decomposition of the electronic barrier ΔE0≠ into changes in bonding contributions. It can immediately be seen that the lowest barrier noted for dissociation of the 3-bromopyridine ligand located in cis position to the NHC moiety (3cis) is related to the least unfavourable changes in both the electrostatic and orbital interactions contributions; such changes are only + 213 and + 90 kJ mol−1, respectively. Considering decoordination of 3-bromopyridine in trans position (3trans), the corresponding changes in ΔEelstat and ΔEorb values are more repulsive, + 292 and + 135 kJ mol−1, respectively, what results in the higher barrier ΔE0‡, by 25 kJ mol−1, as compared to 3cis. In both cases, a drop in Pauli term is noted; however, it is the least negative for activation of 3cis (Table 4). Variations in dispersion and distortion terms are less pronounced. As opposed, the highest barrier noted for 1 can be traced back to the most significant unfavourable changes in both the electrostatic and orbital interactions contributions which are + 501 and + 238 kJ mol−1, respectively, despite the most favourable relief in Pauli repulsion (− 629 kJ mol−1) and distortion energy term (− 43 kJ mol−1).

Table 4 Changes of ETS bonding contributions (BLYP-D3/TZP) when going from substrates (X) to the corresponding transition states (TS)
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Summarizing the above ETS-NOCV based results, one can state that in the complexes 1–3, the bond between the dissociating ligand and the Ru-based fragment is dominated by electrostatic contribution, followed by charge transfer components of σ and π symmetry. In addition, we have identified and quantified the strength of secondary interactions stemming from non-covalent contacts of type CH…Cl, CH…π, and CH…HC. Charge transfer stabilization due to such interactions is between 10 and 15 kJ mol−1, depending on the type of complex. Dispersion contribution appeared to be relatively the least important, though, it can, at absolute level, contribute as much as − 144 kJ mol−1 for complex 1. Exactly opposite situation is valid when considering the transition state structures—namely, the majority of overall stabilization originates from dispersion forces within CH…Cl, CH…π, and CH…HC contacts. It was experimentally shown that initiation rates for olefin metathesis catalysed by Grubbs complexes increase with the change of the halide ligand from Cl, through Br, to I, which was explained mainly by increase in steric bulk promoting phosphine dissociation [6]. According to the present results, stronger London dispersion interactions that stabilize the transition states is another reason for this effect.

Despite crucial role of dispersion in absolute stabilization of the transition states, we have found that the height of the electronic barriers is predominantly controlled by dominating (unfavourable) changes in electrostatic and orbital interaction contributions despite favourable relief in Pauli repulsion and geometry reorganization terms (when going from substrates to the corresponding transition states). In the case of orbital interaction constituent, electron donation from the ligand to the ruthenium centre is the most important, which is in accordance with the observed fast activation of the Grubbs-type complexes bearing ligands that exhibit weak electron donor ability, like pyridine, 3-bromopyridine, or 4-phenylpyridine [7]. Replacing the PCy3 ligand by less electron donating PPh3 also results in increasing the initiation rate [6]. Smaller ligand size might also favour dissociation because of lower dispersion component in total stabilization of a complex. These results demonstrate that any barrier of chemical transformation must originate from variations of all chemical bonding constituents and it is impossible to envision a priori which term will be of prime importance—to this end, quantum chemical analyses of bonding contributions in both substrates and transition states or even better along the entire reaction pathways (e.g. the powerful Activation Strain Model [65], the related approaches [66,67,68,69,70,71], as well as Electron Localization Function and Bonding Evolution Theory [72,73,74]) are in our view crucial for detailed understanding and more rational design of chemical reactions.

Conclusions

Activation of the Grubbs-type catalysts (H2IMes)(PCy3)(Cl)2Ru=CHPh (1), (H2IMes)(PCy3)(Cl)2Ru=CH-CH=CMe2 (2), and (H2IMes)(3-Br-py)2(Cl)2Ru=CHPh (3) has been computationally studied by exploring the reaction pathways for the phosphine and 3-bromopyridine ligands dissociation, combined with the ETS-NOCV analysis of bond energies. Formation of 14-electron propagating species from the Hoveyda-Grubbs-type initiators (H2IMes)(Cl)2Ru=CH(o-OiPrC6H4) (4), (H2IMes)(Cl)2Ru=CH(5-NO2–2-OiPrC6H3) (5), and (H2IMes)(Cl)2Ru=CH(2-OiPr-3-PhC6H3) (6) has also been considered, assuming the dissociative mechanism. Additionally, the IQA energy decomposition has been performed to describe intramolecular interactions in the Hoveyda-Grubbs complexes.

The theoretically determined activity order for the Grubbs-type catalysts, 2 ≤ 1 < < 3, is consistent with the respective initiation rates reported for these systems. Whereas the concentration of the 14-electron ruthenium alkylidene species should be much higher for the initiator 3, compared to the catalysts 1 and 2, a thermodynamic equilibrium between the complex 3 and mono(3-bromopyridine) ruthenium alkylidene species is predicted. The calculated barriers for decoordination of the isopropoxy fragment of the Hoveyda ligand are also in accordance with observed relative activities of the catalysts 4–6.

Although the solvent effects estimated for dissociation of the Grubbs-type complexes are not very significant, they may sometimes be decisive for the predictions concerning the relative activities of these catalysts. In particular, a summary correction to the dissociation energies and barriers, including both solvent simulation and BSSE, is often not negligible. In the case of the initiation step for the Hoveyda-Grubbs-type catalysts, the solvent effects are less important.

According to the ETS-NOCV results, in the Grubbs-type complexes, the bond between the dissociating ligand and the Ru-based fragment is dominated by electrostatic contribution, followed by charge delocalization components; the latter contains primary σ(Ru–P) and π(Ru–P) components together with the secondary non-covalent CH…Cl, CH…π, and CH…HC interactions. Additionally, London dispersion forces appeared to be (at absolute level) also very efficient (between ~50 and 150 kJ mol−1, depending on the catalyst). In contrary, in the case of the corresponding transition state structures, the majority of overall stabilization originates predominantly from London dispersion forces exerted by the pronounced CH…Cl, CH…π, and CH…HC interactions. The height of the electronic barriers is associated with the prevailing (unfavourable) variations in the electrostatic and orbital interaction contributions despite the favourable relief in Pauli repulsion and geometry reorganization terms (when going from substrates to the corresponding transition states). From the IQA analysis, it is found that the isopropoxy group in the Hoveyda-Grubbs-type catalysts forms numerous intra-molecular CH…Cl, CH…π, and CH…Ru interactions which can be crucial for the activity of these catalysts.