Influences of the substituents on the Cr=C bond in [(OC)₅Cr=C(OEt)-para-C₆H₄X] complexes: quantum Theory of Atoms in Molecules, Energy Decomposition Analysis, and Interacting Quantum Atoms

Abstract

This study was conducted to investigate the effect of various substituents on the Cr=C bond in the [(OC)₅Cr=C(OEt)-para-C₆H₄X] complexes using B3LYP*-based quantum mechanical calculations. In this respect, the study evaluates the influence of electron withdrawing and donating groups on the Cr=C bond distances and topological properties and correlates the calculated parameters with the Hammett and Brown constants for the para-substituted (σ_p and σ ⁺_p , respectively) functional groups. Also, the frontier orbital analysis was used to show the electronic structure of complexes and the percentage composition in terms of the defined groups of frontier orbitals was evaluated. To obtain insight into the physical nature of Cr=C bond bonds, we extensively used energy decomposition analysis and Bader’s Quantum Theory of Atoms-in-Molecules (QTAIM). With this aim, in addition to examining the bond critical points properties, we apply Pendás’ Interacting Quantum Atoms (IQA) scheme, which enables the rigorous and physical study of Cr=C bonds in these complexes.

Graphical abstract

Introduction

Carbenes are special classes of carbon-containing compounds that are considered as reactive intermediates in various organic transformations because of their incomplete electronic state and coordinative unsaturation. Nowadays, several stable carbenes [1,2,3] have been isolated and this field is becoming an active area of research. Carbene organometallic complexes have recently received much attention because of the possible involvement of these species in catalytic reactions [4,5,6,7]. Furthermore, these complexes have interesting bonding and reactivity characteristic and play significant roles in synthetic organic and polymer chemistry [8,9,10,11,12,13,14]. Many theoretical studies illustrated the structures and different features of these complexes [15,16,17,18,19,20]. The organometallic photochemistry of chromium(0) carbene complexes is, perhaps, one of the few metal-mediated photoreactions of general application in organic synthesis [21,22,23,24,25]. In this regard, TD-DFT and experimental study of the electronic structure of alkoxychromium(0) carbene complexes have been reported [26].

Many studies have reported the substituent effects on different physical and chemical properties. Quantum chemical investigations can afford useful relationships between the electronic and structural characteristics [27,28,29,30,31,32]. Accordingly, various computational investigations have reported substituent impact on the structural, electronic, and spectroscopic properties of organometallic complexes [17, 33,34,35,36,37,38,39,40,41,42,43,44].

Furthermore, quantitative substituent parameter scales have been found useful in clarifying the polar or steric effects of the substituent on molecular properties. For instance, the Hammett constant (σ_p) [45] and Brown constant (σ ⁺_p ) [46] described the electronic effects of substituents on the equilibrium and rate constants of a reacting molecule. It is noteworthy that the Brown’s σ ⁺_p substituent constant reflects the polar induction/resonance effects of a substituent. Thus, a positive σ ⁺_p value means that a substituent is electron-withdrawing; otherwise, it is electron-donating.

In this work, we report a computational study about the effect of substitution on the Cr=C bond in the [(OC)₅Cr=C(OEt)-para-C₆H₄X] complexes by quantum chemical calculations.

Results and discussion

Structural parameters

Figure 1 presents the structure of the studied [(OC)₅Cr=C(OEt)-para-C₆H₄X] complexes. The Cr=C_carbene bond distances in these complexes are listed in Table 1. As can be seen, longer bond distances occur in the presence of electron donating groups (EDG). This increase in bond distances is explained with II-resonance form of [(OC)₅Cr=C(OEt)-para-C₆H₄X] complexes in the presence of EDGs (Fig. 2). The relations between bond distances values with the Hammett (σ_p) and the Brown’s (σ ⁺_p ) substituent constants are:

Fig. 1

The structure of the studied [(OC)₅Cr=C(OEt)-para-C₆H₄X] complexes

Table 1 Cr-C bond distance, EDA analysis results in [(OC)₅Cr=C(OEt)-para-C₆H₄X] complexes

Fig. 2

Resonance forms of [(OC)₅Cr=C(OEt)-para-C₆H₄X] complexes in the presence of EDGs

$$\begin{aligned} r & = - 0.0363\sigma_{\text{p}} + 2.1147\quad R^{2} = 0.9539, \\ r & = - 0.0241\sigma_{\text{p}}^{ + } + 2.1098\quad R^{2} = 0.988. \\ \end{aligned}$$

Therefore, there is a good correlation between these Cr=C_carbene bond distance values and Brown’s substituent constant compared to the Hammett constant.

Molecular orbital analysis

The values of frontier orbital energies and their gap are listed in Table 2. According to the calculation results, frontier orbitals are stabilized in the presence of electron withdrawing groups (EWG) and destabilized in the presence of EDGs. The relationships between the frontier orbital energy values with the Hammett (σ_p) and the Brown’s (σ ⁺_p ) substituent constants are:

Table 2 Frontier orbital energy values, HOMO–LUMO gap, hardness (η), chemical potential (μ), electrophilicity (ω), electrodonating (ω⁻), and electroaccepting (ω⁺) powers and net electrophilicity (Δω^±) for [(OC)₅Cr=C(OEt)-para-C₆H₄X] complexes

$$\begin{aligned} E_{\text{HOMO}} & = - 0.405\sigma_{\text{p}} - 5.448\quad R^{2} = 0.9809, \\ E_{\text{HOMO}} & = - 0.2564\sigma_{\text{p}}^{ + } - 5.5033\quad R^{2} = 0.9218, \\ E_{\text{LUMO}} & = - 0.6258\sigma_{\text{p}} - 2.4117\quad R^{2} = 0.9258, \\ E_{\text{LUMO}} & = - 0.4077\sigma_{\text{p}}^{ + } - 2.5008\quad R^{2} = 0.8505. \\ \end{aligned}$$

As can be noted, there are good correlations between the HOMO energy values and Hammett substituent constants (σ_p) compared to the Brown’s (σ ⁺_p ) substituent constants. Also, there is a good correlation between frontier orbital energy, as:

$$E_{\text{HOMO}} = \, 1.6111\;E_{\text{LUMO}} + 6.3653\quad R^{2} = 0.9469.$$

This strong correlation is attributed to similar topologies of frontier orbitals in the presence of various substituents. As shown in Table 2, there are larger the HOMO–LUMO gap values in the presence of EDGs compared to EWGs.

Therefore, EWGs have the lowest LUMO energy, resulting in the smallest HOMO–LUMO gap for these studied complexes. This behavior arises from an electron-withdrawing inductive effect, which concentrates the electronic density over the substituted region of the complex. On the contrary, the largest HOMO–LUMO gap was established for EDGs due to the electron donating character of the substituent. These good correlations suggest that EWGs/EDGs influence the frontier orbital energies and the HOMO–LUMO gaps. Therefore, these correlations may be employed to calculate these parameters for other substituents for which σ_p and σ ⁺_p are known.

Frontier orbital distributions

The frontier orbital distributions of the [(OC)₅Cr=C(OEt)-C₆H₅] complex are plotted in Fig. 3. It can be seen that there is not any overlapping between atomic orbitals of chromium and C_carbene in HOMO. But, there is a π*-overlap between atomic orbitals of chromium and C_carbene in LUMO. The percentage composition in terms of the defined groups of frontier orbitals for [(OC)₅Cr=C(OEt)-para-C₆H₄X] complexes was studied to understand the character of the metal–ligand bonds and are listed in Table 3. These values show that the largest contributions of the HOMO arise from Cr(CO)₅ fragment. Moreover, the largest contribution of LUMO arises from the C(OEt)-para-C₆H₄X group.

Fig. 3

Frontier orbital plots for [(OC)₅Cr=C(OEt)-para-C₆H₅] complex

Table 3 The percentage composition in terms of the defined groups of frontier orbitals for [(OC)₅Cr=C(OEt)-para-C₆H₄X] complexes

The electron-donating (ω⁻) and electron-accepting (ω⁺) powers were defined as [47]:

$$\begin{aligned} \omega^{ - } & = \frac{{(3I + A)^{2} }}{16(I - A)} \approx \frac{{(3\varepsilon_{\text{H}} + \varepsilon_{\text{L}} )^{2} }}{{16\eta_{\text{K}} }} = \omega_{\text{K}}^{ - } , \\ \omega^{ + } & = \frac{{(I + 3A)^{2} }}{16(I - A)} \approx \frac{{(\varepsilon_{\text{H}} + 3\varepsilon_{\text{L}} )^{2} }}{{16\eta_{\text{K}} }} = \omega_{\text{K}}^{ + } . \\ \end{aligned}$$

Based on these relations, a large ω⁺ value corresponds to a better capability of charge accepting, whereas a small value of ω⁻ shows the capability to electron donating. To compare ω⁺ with −ω⁻, the following definition of net electrophilicity was proposed [48]:

$$\Delta w^{ \pm } = w^{ + } - ( - w^{ - } ) = w^{ + } + w^{ - } \approx w_{\text{K}}^{ + } - ( - w_{\text{K}}^{ - } ) = w_{\text{K}}^{ + } + w_{\text{K}}^{ - } + \Delta w_{\text{K}}^{ \pm } ,$$

where Δω^± is the electroaccepting power relative to the electrodonating power. The results show larger ω⁺ values in the presence of EWGs. Therefore, the capability of accepting charge increases in the presence of EWGs. Moreover, with the smaller values of ω⁻ in the presence of EDGs, the system is a better electron donor in the presence of EDGs.

Energy decomposition analysis (EDA)

The Cr=C chemical bond in these complexes can be regarded as a donor–acceptor orbital interaction, which is schematically illustrated in Fig. 4. The fragments [C(OEt)-para-C₆H₄X] have a doubly occupied σ-orbital, which behaves as a donor orbital, and the empty p(π) orbitals behave as acceptor orbitals.

Fig. 4

Schematic representation of the dominant orbital interactions between closed-shell metal fragments [(OC)₅Cr] and [C(OEt)-para-C₆H₄X] ligand fragment (Fischer-type carbene complexes)

We consider the Cr-C bonding situation in the complexes, which was analyzed with the EDA using the [(OC)₅Cr] and [C(OEt)-para-C₆H₄X] fragments. The results of EDA reveal that the interaction energies in the studied complexes are − 210.58 to − 204.97 kJ/mol (Table 1). In the (OC)₅Cr=C(OEt)(C₆H₅) complex, the total interaction energy between [Cr(CO)₅] and [C(OEt)(C₆H₅)] is − 208.32 kJ/mol, where the polarization energy of − 239.49 kJ/mol stabilized the adduct while the sum of the electrostatic and exchange energy destabilized the adduct by 30.38 kJ/mol. For the sake of convenience, it is customary to combine these two terms as a steric term (E_steric).

The interaction energy values reveal a stronger interaction between [(OC)₅Cr] and [C(OEt)-para-C₆H₄X] fragments in the presence of EDGs.

On the other hand, the magnitude of ΔE_polar increases in the presence of EDGs. There is a good linear relationship between these values and the Hammett constants:

$$\begin{aligned} \Delta E_{\text{polar}} & = - 13.88\sigma_{\text{p}} - \, 237.9\quad R^{2} = 0.9636, \\ \Delta E_{\text{polar}} & = - 8.6511\sigma_{\text{p}}^{ + } - \, 239.68\quad R^{2} = 0.9888. \\ \end{aligned}$$

Also, the magnitude of E_steric increases in the presence of EWGs. There is a good linear relationship between these values and the Hammett constants:

$$\begin{aligned} E_{\text{steric}} & = 16.9\sigma_{\text{p}} + \, 29.813\quad R^{2} = \, 0.9919, \\ E_{\text{steric}} & = 10.924\sigma_{\text{p}}^{ + } + \, 32.11\quad R^{2} \, = \, 0.9733. \\ \end{aligned}$$

Therefore, good correlations can be seen between the ΔE_polar and E_steric values with Brown’s (σ ⁺_p ) compared with the Hammett substituent constants (σ_p).

Topological analyses

Quantum theory of atoms-in-molecules (QTAIM) analysis

It has been proved that the QTAIM-based analysis of electron density can provide valuable information on many physical and chemical properties of molecular systems.

Electron density

The electron density values of Cr=C bonds at corresponding bond critical points (BCP) are listed in Table 4. These data show larger electron density values in the presence of EDGs. The relations between electron density values with Hammett (σ_p) and Brown’s (σ ⁺_p ) substituent constants are:

Table 4 Electron density (ρ), Laplacian of electron density (∇²ρ), the total energy density (H), Lagrangian kinetic energy (G), virial energy density (V), ELF, LOL, the overall interaction energy (E_int), and electrostatic part of the interaction energy (V_{electrostatic}) for Cr=C bonds of [(OC)₅Cr=C(OEt)-para-C₆H₄X] complexes

$$\begin{aligned} \rho & = 0.0056\sigma_{\text{p}} + \, 0.082\quad R^{2} \, = \, 0.9526, \\ \rho & = 0.0037\sigma_{\text{p}}^{ + } + \, 0.0828\quad R^{2} \, = \, 0.9887. \\ \end{aligned}$$

Therefore, there is a good correlation between these electron density values and the Brown’s substituent constant compared to the Hammett constant.

A large electron density value corresponds to shorter bonds. The results show shorter bonds in the presence of EDGs. The relation between electron density values and bond distances is:

$$\rho = - 0.153r + \, 0.4055\quad R^{2} = 0.9999.$$

Laplacian of electron density

Laplacian of electron density values of Cr=C bonds (∇²ρ) at corresponding BCP is listed in Table 4. These values are positive, likewise those for the closed-shell interactions. Although, the condition ∇²ρ > 0 and, perhaps, any other measure of charge concentration is not enough to identify chemical bonds [49].

Energy density

The energy density (H) values and its components [Lagrangian kinetic energy (G) and potential energy density (V)] of Cr=C bonds at corresponding BCP are gathered in Table 4. As can be noticed, the energy density values are negative for the shared interactions.

The positive values for Laplacian of electron density and negative values of the energy density of Cr=C bonds at corresponding BCP illustrate that the Cr=C bond has a mix of the closed shell and shared characteristic.

One can also use the ratio |V(r)|/G(r) as another useful description; |V(r)|/G(r) < 1 is the characteristic of a typical ionic interaction and |V(r)|/G(r) > 2 is defined as a “classical” covalent interaction. Taking all these criteria into consideration, the topological properties at BCP of Cr–C indicate a mixed (partially ionic and partially covalent) character of these coordination bonds because of 1 < |V(r)|/G(r) < 2 [50].

Interacting quantum atoms (IQA) approach

The mechanism of metal–ligand interactions in the studied complexes was investigated using the atomic energy partitioning method, namely interacting quantum atoms (IQA) [51,52,53,54]. This method uses the QTAIM definition of an atom, a nucleus joint with the atomic basin. The overall interaction energy and electrostatic part of the interaction energy for the Cr–C_carbene bond in [(OC)₅Cr=C(OEt)-para-C₆H₄X] complexes are presented in Table 4. These values reveal that the overall Cr–C_carbene interaction energy, E_int (Cr–C_carbene), is stabilizing for the studied complexes. The relations between overall interaction energy values with the Brown’s substituent constant and the Hammett constants are:

$$\begin{aligned} E_{\text{int}} & = - 0.0076\sigma_{\text{p}} - \, 0.1126\quad R^{2} = 0.9332, \\ E_{\text{int}} & = - 0.0053\sigma_{\text{p}}^{ + } - \, 0.1137\quad R^{2} = 0.9957. \\ \end{aligned}$$

As can be seen, there is a good correlation between these overall interaction energy values and the Brown’s substituent constant compared to the Hammett constant.

ELF analysis

We analyzed the nature of chemical bonding in Cr=C bond on the basis of electron localization function (ELF) distribution, which is indicative of concentrations of valence electron density in regions of chemical bonds.

A large ELF value corresponds to largely localized electrons, suggesting that a covalent bond, a lone pair, or inner shells of the atom are involved. Table 4 reveals larger ELF values in the presence of EWGs. The relation between ELF values and the Hammett constants is:

$${\text{ELF}} = - 0.1693r + \, 0.5817\quad R^{2} = 0.9696.$$

Moreover, the relations between ELF values with the Hammett (σ_p) and the Brown’s (σ ⁺_p ) substituent constants are:

$$\begin{aligned} {\text{ELF}} & = 0.0059\sigma_{\text{p}} + \, 0.2238\quad R^{2} = 0.8639, \\ {\text{ELF}} & = 0.0041\sigma_{\text{p}}^{ + } + \, 0.2245\quad R^{2} = 0.9592. \\ \end{aligned}$$

Therefore, there is a good correlation between ELF values and the Brown’s substituent constant compared to the Hammett constant.

LOL analysis

Localized-orbital locator (LOL) is descriptor developed for electron localization. LOL, which gives simple recognizable patterns in classic chemical bonds, has proved useful in interpreting the structures of exotic materials and the classic examples of freshman chemistry texts. LOL focuses on the topological properties of a kinetic energy density. LOL values of Cr=C bond can be interpreted similarly to ELF. Table 4 shows that the LOL values are larger in the presence of EWGs. The relation between LOL values and bond distances is:

$${\text{LOL}} = - 0.1108r + \, 0.5837\quad R^{2} = 0.9693.$$

Also, the relations between LOL values with Hammett (σ_p) and the Brown’s (σ ⁺_p ) substituent constants are:

$$\begin{aligned} {\text{LOL}} & = 0.0039\sigma_{\text{p}} + \, 0.3494\quad R^{2} = 0.863, \\ {\text{LOL}} & = 0.0027\sigma_{\text{p}}^{ + } + \, 0.3499\quad R^{2} = 0.9594. \\ \end{aligned}$$

Therefore, there is a good correlation between LOL values and the Brown’s substituent constant compared to the Hammett constant.

Conclusion

The B3LYP*-based quantum mechanical calculations performed in this study on the effect of different substituents on the Cr=C bond in the [(OC)₅Cr=C(OEt)-para-C₆H₄X] complexes revealed that:

• 1. Cr=C bond distances increased in the presence of EDGs.

• 2. In the basis of the EDA analysis, the polarization energy stabilized the adduct, while the sum of the electrostatic and exchange energy destabilized it.

• 3. The largest contribution of HOMO and LUMO arises from the Cr(CO)₅ fragment and C(OEt)-para-C₆H₄X group, respectively.

• 4. The calculated overall interaction energy for Cr–C_carbene bond was stabilizing for the studied complexes.

• 5. ELF and LOL values increased in the presence of EWGs.

• 6. Electron density, ELF, and LOL of the overall interaction energy values for the Cr–C_carbene bond in the studied complexes have good correlations with the Brown’s substituent constant compared to the Hammett constant.

Computational methods

The Gaussian 09 suite program was used for the calculations [55]. The standard 6-311G(d,p) basis set was applied for the calculations of systems including C, H, and O [56,57,58,59]. Calculations related to Cr element were performed using the element standard Def2-TZVPPD basis set [60]. Geometry was optimized using the B3LYP* method with c3=0.15 [61].

The partial population density of states (PDOS) was used to assess the information of molecular orbitals. The spectrum was convoluted using a full width at half maximum (FWHM) of 0.3 eV. These assessments plus the comprehensive analysis of the contributions of atomic orbitals to the molecular orbitals were performed using the GaussSum 3.0 software package [62].

The bonding interactions between the [(OC)₅Cr] and [C(OEt)-para-C₆H₄X] fragments were evaluated using the energy decomposition analysis (EDA) in the Multiwfn 3.3.9 software package [63]. The instantaneous interaction energy (ΔE_int) between the two fragments was calculated as:

$$\Delta E_{\text{int}} = \Delta E_{\text{polar}} + \Delta E_{\text{els}} + \Delta E_{\text{Ex}} ,$$

where E_polar is the electron density polarization term (the induction term) calculated by subtracting E (SCF last) from E (SCF 1st). E_els and E_Ex are the electrostatic interaction and the exchange repulsion terms, respectively.

The Multiwfn 3.3.9 software package was also used for the topological analysis of electron density [64]. The computations of calculation of interaction energies within the IQA approach were carried out with the AIMAll package [65].