Introduction

Carbenes, well-known names to chemists, are neutral divalent species having six electron carbon atoms with two unshared electrons. Classical carbenes are inherently unstable and considered as highly reactive transient intermediates in chemical reactions [1]. As carbene carbon has six electrons, it is assumed to be an electrophilic species, but the increasing number of papers‚ have shown that the philicity of these compounds is strikingly dependent on substituents attached to the carbene carbon; for example, (CH3O)2C: and (Me2N)2C: are both nucleophilic in character [2, 3]. This property may be attributed to 2p–2p π bonding of “vacant” carbenic p orbital of these carbenes with electron pairs of the adjacent Me2N and CH3O groups.

One category of carbenes is N-heterocyclic carbenes (NHC), the representative stable and bottled species of which is 1,3-di(adamantyl)imidazol-2-ylidene, first reported by Arduengo et al. 26 years ago; its stability benefits from factors such as electronic, aromatic, and spatial, owing its viability to the mesomeric effects on nitrogen atoms [4]. Several different parameters have been suggested to measure the stability of NHCs; these include: the energy gap between singlet and triplet states (ΔES–T), the energy of hydrogenation (ΔEHyd), the energy of isodesmic reaction (ΔEiso), and finally the energy difference between HOMO and LUMO levels (ΔEH–L).The first three parameters refer to thermodynamic stability and the last one shows kinetic stability of NHCs. Furthermore, these species have received much attention from scientists, publishing books, and articles [5,6,7,8,9,10,11,12,13,14,15]. Due to their σ donating and π-accepting ability, NHCs can act as excellent ligands in organometallic compounds. In addition, various applications have been found for them, such as polymerization reaction and medicinal uses [16,17,18,19,20]. Su and Chuang predicted that using NHCs skeleton would stabilize triplet ground state of vinylidenes [21]. As a result, reactivity, as well as philicity and stability of these carbenes, are highly important.

As concerns philicity, there are different approaches for obtaining philicity; some of them are summarized in Fig. 1 [22, 23]. The philicity of some carbenes in their singlet ground state was experimentally determined for the first time by insightful studies of Moss and co-workers in 1980 based on the kinetic model of cyclopropanation reaction of some alkenes with carbenes [2, 24]. Therefore, empirical index “mCXY” (carbene selectivity index) was born which covered electrophilic, nucleophilic, and ambiphilic carbenes. Equation (1) correlates this empirical index to the resonance (\(\sigma_{R}^{ + }\)) and inductive (\(\sigma_{I}\)) substituent constants of X and Y in carbene CXY:

$$m_{CXY} = - 1.10\mathop \sum \limits_{X,Y} \sigma_{R}^{ + } + 0.53\mathop \sum \limits_{X,Y} \sigma_{I} - 0.31.$$
(1)
Fig. 1
figure 1

Ways to get philicity at a glance

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For mCXY values lower than 1.5 the corresponding carbenes are categorized as electrophilic; while nucleophilic ones have values greater than 2.2 mCXY, and ambiphilic carbenes have mCXY in between.

Another approach to obtain philicity is based on frontier molecular orbital (FMO) theory that Moss correlated it with mCXY. Therefore, the differential orbital energy of lowest unoccupied molecular orbital (LUMO) and highest occupied molecular orbital (HOMO) of carbenes and alkenes is used in 1,3-dipolar cycloadditions. If the ΔεE = εLUMOcarbine − εHOMOalkene is smaller than the ΔεN = εLUMOalkene − εHOMOcarbene, the corresponding carbene is considered to be an electrophile; the inverse ordering of differential energies makes the carbene to be a nucleophile. An ambiphilic carbene reacts rapidly with both electron-rich and electron-poor alkenes. In this method, with a superficial glance, the philicity of a carbene can be predicted quantitatively and quickly.

In another method, philicity is correlated to ionization potential (IP) and electron affinity (EA). Sander and co-workers have used these parameters and two dimensional scales for evaluating philicity of singlet carbenes as well as triplet ones [3]. Adiabatic ionization potential and adiabatic electron affinity values can be experimentally measured by negative ion photoelectron spectroscopy (NIPES) [25,26,27]. These data may then be compared with the calculated ones to assess the theoretical methods. An advantage of Sander’s method is that EA and IP can be calculated for any carbene and does not depend (as does mCXY) on specific set of alkenes or carbenes.

Another attractive scale is the theoretical global electrophilicity, ω, defined recently by Parr et al. [28]:

$$\omega = \mu^{2} /2\eta ,$$
(2)

where µ is the electronic chemical potential and η is the chemical hardness. Perez in her paper compared ω of carbenes with their empirical mCXY and found a good agreement between the theoretical and experimental philicity of the investigated species [29]. Global electrophilicity index and mCXY have an inverse order with respect to each other, i.e., a large amount of ω means a high electrophilicity. Based on Perez considerations, nucleophilic carbenes have ω values lower than 1 eV, electrophilic ones showing ω values between 1.21 and 2.40 eV (MeCF and phCCN, respectively), while for the case where ω ≈ 1 eV the carbenes are characterized as ambiphilic.

Recently, local electrophilicity (ωc) and ω of the Group 15 analogues of NHCs have been studied and it was concluded that the “ene” center of these analogues is ambiphilic [30]. It was also found that ligation properties of these compounds would be affected dramatically by the nature of the substituents.

Empirical Hammett correlation is another method for determining philicity of CXY against a series of ring-substituted styrenes by drawing logkX/kH of the addition reaction versus σ constants [31, 32]. However, a question arises as whether this method could determine philicity of carbenes. The answer is affirmative; but how?

If the Hammett ρ value is negative, positive charge will develop on alkene carbon. Therefore, electron-releasing groups lower the energy of the transition state and stabilize it. As a result CF2 will have an electrophilic character. A positive ρ value shows that a negative charge develops during the addition reaction, mitigated by electron withdrawing phenyl-moiety substituents, leading to the acceleration of the reaction; for example, benzocyclobutenylidene [33] and bicyclo[3.2.1]octa-2,6-dien-4-ylidene [34] are known to be nucleophilic with ρ values + 1.57 and + 0.25, respectively. In the case of ambiphilic carbenes, one encounters a broken Hammett plot at σ = 0.0. This means that the reaction mechanism changes during the reaction affected by substituents.

The above discussion on importance of predicting philicity and stability of carbenes, prompted us to evaluate substitution effect on these properties for 1,3-disubstituted imidazol-2-ylidenes (1) and 1,3-diarylimidazol-2-ylidenes (2) and make a comparison between the obtained parameters (Scheme 1).

scheme 1

Results and discussion

As the nature of substituent has a remarkable effect on philicity and stability, we decided to evaluate these effect for 1,3-diarylimidazol-2-ylidenes and 1,3-disubstituted imidazol-2-ylidenes; for philicity the following three approaches were considered: adiabatic IP and EA scales, ω and differential orbital energy. For stability of NHCs, ΔES–T, ΔEHyd, ΔEiso, and ΔEH–L were computed using DFT method.

1,3-Disubstituted imidazol-2-ylidenes (1)

The electron donating substituents lead to small IP and the lowest and negative EA values of the titled carbenes (Table 1). For the substituent CH3 (with positive inductive effect, + I), the corresponding carbene has the most nucleophilic character with EA = − 0.51 eV and IP = 7.74 eV which may be attributed to its σ-electron donating properties and the positive hyperconjugation of CH3 (these data agree with those reported by Sander [3]). For substituents NH2, OCH3, OH (with − I and the positive resonance effect, + R) and also H, we encounter close nucleophilicities (EA = − 0.43, IP = 8.09; EA = − 0.46, IP = 8.35; EA = − 0.47, IP = 8.83; and EA = − 0.46, IP = 8.21 eV, respectively). In the case of halogenated species when X = Br, we encounter the highest value of EA (2.37 eV) and low IP (8.51 eV), while EA for X = F, drops to 1.82 eV showing a decrease in carbene electrophilicity. The IP increases from 8.51 eV for X = Br to 9.65 eV for X = F, from which one can guess that the corresponding carbene of the latter substituent is both less electrophilic and less nucleophilic with respect to the former. The substituent NO2 (with EA = 1.84 eV and IP = 9.92 eV of the corresponding carbene), induces the same philicity as for X = F, which is in accordance with electron withdrawing character of these substituents. Therefore, as Sander has stated, calculated EA and IP values make it possible to identify three classes of carbenes, i.e., (1) strongly nucleophilic carbenes at the bottom right part of the diagram exhibit a small or negative EA and a low IP (1d). (2) For X = NO2 the carbene has the highest EA and IP, being extremely electrophilic with no nucleophilicity. (3) Carbenes such as 1h with a high EA and low IP, it is predicted to have a small singlet–triplet energy gap and hence a triplet ground state (Fig. 2).

Table 1 DFT parameters, philicity values of 1,3-disubstituted imidazol-2-ylidene 1
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Fig. 2
figure 2

Calculated IP and EA of NHC 1 at the B3LYP/6-311++G** basis set

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Notably, the order of ω for electron donating groups is as follows \({\text{CH}}_{3} < {\text{NH}}_{2} \cong {\text{H}} \le {\text{OCH}}_{3} < {\text{OH}}\) indicating that inductive effect is significant (Table 1). Kassaee has reported ω = 0.83 eV for X = CH3 by calculating µ and η from the following equations [37]:

$$\mu \approx (E_{\text{HOMO}} + E_{\text{LUMO}}) /2,$$
(3)
$$\eta \approx E_{\text{LUMO}} - E_{\text{HOMO}} .$$
(4)

This value agrees with our value (ω = 0.82 eV) obtained from EHOMO = − 5.89 eV, ELUMO = − 0.22 eV. On the other hand, halogenated species have almost the same ω values. The NO2 substituent leads to high ω value because of its σ and π-withdrawing character. Species with high ω values have high µ (around 5.42 eV) and high ΔNmax (around 0.71 e).

The philicity of singlet state of these carbenes was determined with the aid of differential orbital energy. When ΔεE value is always bigger than the ΔεN value, substituted carbenes are nucleophilic in character; electrophilic carbenes have the inverse ordering of differential orbital energies. If ΔεE for alkenes having electron withdrawing substitution is bigger than ΔεN and also when ΔεE for electron donating substitution on the alkene is smaller than ΔεN the carbene will be considered as ambiphile.

In this regard, interaction of these singlet carbenes with several alkenes was studied (Table 2). When X = CH3 the carbene is suggested to be nucleophile, which is in agreement with the previously mentioned scales. For X = NH2 the carbene is suggested to have nucleophilic character upon addition reaction with most alkenes; however, toward (CH3)2C=C(CH3)2 it would be predicted to behave as electrophilic if it occurred. In the case of NO2 substituent, ΔεE is always smaller than ΔεN, and therefore, so the corresponding carbene has electrophilic character. Carbenes having halogen and CHO substituents act as ambiphilic toward alkenes.

Table 2 Differential orbital energies for carbene/alkene addition 1,3-disubstituted imidazol-2-ylidene 1
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Stability of carbenes can be assessed by ΔES–T, ΔEHyd, ΔEiso, and ΔEH–L. Singlet–triplet energy gap is of special importance due to its great influence in the course of carbene reactions. A great ΔES–T indicates that singlet state is more stable than triplet state and vice versa. As a result, the highest stability is exhibited by 1d (351.5 kJ/mol) (Table 3).

Table 3 Thermodynamic stability factors in kJ/mol and ΔEH–L in eV of carbenes 1
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Heat of hydrogenation can be judged by reaction 1 (Scheme 2). This parameter is negative for all investigated carbenes; the smaller the magnitude of ΔEHyd the more stable the carbene. Accordingly 1d is the most stable and 1k is the least stable of investigated carbene.

scheme 2

Another suitable and economic way of assessing the stability of singlet carbenes is endothermicity of isodesmic reaction 2 (Scheme 3); the higher ΔEiso, the higher the stability. Therefore, carbene 1d with ΔEiso = 460.99 kJ/mol has the highest stability. The higher stability of CH3 substituted carbene with respect to those carbenes with NH2, OH, and OCH3 substituents may be attributed to the + I effect and the positive hyperconjugation of CH3. As stated by Nyulàszi, the synthesis of those carbenes with ΔEiso larger than 377 kJ/mol would be feasible [38]. Accordingly, only those carbenes with electron donating substituents have ΔEiso > 377 kJ/mol. Therefore, 1a–1e is included in this category.

scheme 3

Kinetic stability can be assessed by the energy difference between HOMO and LUMO orbitals (ΔEH–L) [39]. The greater difference will result in a more stable carbene; OH and F substituted carbenes with largest ΔEH–L values (6.7 eV for both) are the most stable ones, and Br substituted carbene (ΔEH–L = 3.9 eV) is the least stable species.

The selected geometrical parameters of singlet and triplet states of these carbenes are summarized in Table S1 of the Supplementary Material.

1,3-Diarylimidazol-2-ylidenes (2)

First, the EA and IP of studied carbenes vary between − 0.38 to 2.02 and 6.53–8.42 eV, respectively (Table 4). Comparing the EA values for halogen substituted species (F: − 0.01 eV, Cl: 0.24 eV, Br: 0.29 eV) shows that for fluorine the corresponding carbene is much less electrophilic in character. The IP parameters, however, cannot be taken as a basis of carbene philicity for F, Cl and Br, since there is no significant difference between their IP values. CH3O and NH2 substituted carbenes with negative, small and close values of EA (− 0.38 and − 0.20 eV, respectively) are more efficient in reducing EA than halogens analogues indicating high nucleophilicity of their corresponding carbenes. The EA and IP values for X = NO2 substituted carbene (2.02 and 8.42 eV, respectively) are the highest, showing that such species are the most electrophilic of the studied carbenes. The results obtained from IP values for CH3O, NH2 and NO2 substituents are consistent with those of EA values. The compilation of the calculated EA and IP values of these carbenes can be seen in Fig. 3.

Table 4 DFT parameters, philicity values of 1,3-diarylimidazol-2-ylidene 2
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Fig. 3
figure 3

Calculated IP and EA of NHC 2 at the B3LYP/6-311++G** basis set

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The values of electrophilicity index of nucleophilic 1,3-diarylimidazol-2-ylidenes (2) range from 1.48 eV for X = CH3O group to 1.70 eV for X = OH (Table 4). High π-electron-releasing and low σ-withdrawing effect of X = CH3O and X = NH2 (ω = 1.49 eV, µ = − 3.16 eV) make the corresponding carbenes to be the most nucleophilic of these NHCs (2); electrophilic carbenes, show higher ω values from 3.13 eV for X = CHO to 4.25 eV for X = NO2. It should be noted that for X = NO2 the carbene is predicted to be the most electrophilic species, displaying the highest µ and ΔNmax values (− 5.22 eV and 0.81 e, respectively). Inspection of ω values of halogenated species indicates that these carbenes have almost similar philicity index with ΔNmax values around 0.50 e.

Differential orbital energy predicts that NH2 substituted 1,3-diarylimidazol-2-ylidene acts as a nucleophile because ΔεN is always smaller than ΔεE (Table 5). When X = H, F, Cl, Br, CN, and CHO the corresponding carbenes may behave as ambiphile. The carbene with NO2 as substituent has electrophilic character toward all indicated alkenes.

Table 5 Differential orbital energies for carbene/alkene addition 1,3-diarylimidazol-2-ylidene 2
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Ignoring some deviations, carbenes 2 with π-donating groups have the great ΔES–T, and therefore, the high-stability (Table 6). The NH2 substituted carbene 2a with the highest values of ΔEiso and ΔEHyd (445.39 and − 99.87 kJ/mol, respectively) is the most stable of all these species.

Table 6 Thermodynamic stability factors in kJ/mol and ΔEH–L in eV of carbenes 2
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In this series, 2b and 2f (ΔEH–L = 5.3 eV) are the most kinetically stable carbenes and 2k, in all aspects, has both the lowest thermodynamic and kinetic stability.

The selected geometrical parameters of singlet and triplet states of these carbenes are given in Table S2 of the Supplementary Material.

Conclusion

If one desires to compare the nucleophilicity and stability of carbene species 1 and 2, he/she will find that in the case of NHCs 1, the carbene 1d has the highest nucleophilicity and thermodynamic stability considering all calculated scales, which may be attributed to the +I effect and the positive hyperconjugation of CH3; in addition, 1k has the highest electrophilicity in these carbenes. As regards carbenes series 2, 2a (due to its + R) has the highest nucleophilicity and thermodynamic stability, and 2k has the highest electrophilicity and the least stability.

As has been stated by Nyulàszi, the synthesis of those carbenes with ΔEiso greater than 377 kJ/mol would be feasible. Accordingly, all investigated aryl substituted carbenes may be prepared in laboratory. This feasibility may also be pertained only to those carbenes of series 1 with electron donating substituents having ΔEiso > 377 kJ/mol. In all NHCs 2, (with electron donating or electron withdrawing groups) resonance is established. Nucleophilicities of carbenes 2, to some extent, are greater than those of carbenes 1, probably due to the presence of phenyl-moiety.

Theoretical and computational details

Density functional theory was used to fully optimize all molecules and calculate single point energy of neutral, anion and cation of carbenes without any symmetry constraint at B3LYP level of theory with 6-311++G** basis set using Spartan’ 10 program [35]. All the structures of 1,3-disubstituted imidazol-2-ylidene were determined to be at their minimum by applying real frequency calculations. Chemical potential µ, chemical hardness η, and the additional electronic charge ΔNmax were obtained using the following equations [28]:

$$\mu = - \,(IP + EA)/2,$$
(5)
$$\eta = IP - EA,$$
(6)
$$\Delta N_{\hbox{max} } = - \,\frac{\mu }{\eta }.$$
(7)

It should be noted that tetracyanoethylene was chosen as the reference for calculating nucleophilicity, \(N = E_{{{\text{HOMO}}({\text{Nu}})}} - E_{{{\text{HOMO}}({\text{TCNE}})}}\) [40].