Introduction

Silylenes (R2Si:) as one of the heavier analogs of carbenes (R2C:) are key intermediates in numerous thermal and photochemical reactions of organosilicon compounds [1, 2]. Contrary to carbon, silicon has low ability to form hybrid orbitals and a typical silicon prefers (3s)2(3p)2 valence electronic configuration which leads to the carbene-like singlet ground state [1, 2]. This is due to the difference in geometrical sizes of the ns and np orbitals when n > 2. While methylene (H2C:) has a triplet ground state with a ΔES–T of − 37.6 kJ/mol, the ground state of silylene (H2Si:) is a singlet that lies 79–96 kJ/mol lower than its corresponding triplet state. Silylenes show ambiphilic character because of the presence of an occupied s-orbital and vacant p-orbital that makes silylenes react either as an electrophile or nucleophile. Henceforth, in a silylene, two electrons occupy 3s orbital leading to a singlet ground state (Fig. 1).

Fig. 1
figure 1

Possible electronic configurations and orbitals of singlet and triplet silylenes

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There are many ways to enhance the nucleophilicity of silylenes such as using a Lewis base [3]. The σ-donation ability and high nucleophilicity of silylenes [4, 5] make them promising compounds in H-abstraction reactions, dimerization, and transition metal bridging ligands [6, 7]. While a broad assortment of N-heterocyclic silylene-transition metal complexes [8,9,10,11] and acyclic silylene ligands [12, 13] have been reported, the carbocyclic silylene ligands are less considered [14]. To suggest a sufficient stable silylene for isolation, the thermodynamic and kinetic characterization of the reactive vacant p-orbital is essential (the lone pair is inert by reason of its high s-character) [15, 16]. The synthesis of the first stable five-membered cyclic silylene I (Scheme 1) in 1994 by Denk et al. was indebted to both the electron donating from the adjacent nitrogens (thermodynamic stabilization) and the steric hindrance provided by t-Bu groups (kinetic stabilization) [17]. Consequently, silylenes II–VI were synthesized (Scheme 2) [18,19,20,21,22].

scheme 1
scheme 2

In our previous works, one of us studied carbenic derivatives of 1H containing α-cyclopropylcyclonona-3,5,7-trienylidenes which are substituted with ά-NMe, PMe, O, S, CH2, cyclopropyl, and CMe2 groups (1Xά) (Scheme 3) [23,24,25].

scheme 3

Interestingly, 1H appears as a transition state 17.1 kJ/mol less stable than its substituted analogous as the global minima [23,24,25]. These studies called for further quantitative investigations on the stabilizing effects of other hetero atoms, such as halogens. Up-to-date, nothing has been done to study the substituent effect on the largest non-planar unsaturated cyclic silylenes with C8H6X4Si: molecular formula, 2X (where X = H, F, Cl, Br, and I) via experimental and theoretical methods (Fig. 2). Here, a brief comparison is also made among these results with those of some stable synthesized silylenes I, V, and VII (Scheme 4) [18,19,20,21,22].

Fig. 2
figure 2figure 2

The optimized singlet carbene (1H-S) and singlet silylenes (2H-S, 2F-S, 2Cl-S, 2Br-S, 2I-S) are compared and contrasted to their corresponding triplet states (1H-T, 2H-T, 2F-T, 2Cl-T, 2Br-T, 2I-T) along with their corresponding symmetries, at B3LYP/AUG-cc-pVTZ level

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scheme 4

Results and discussion

Following our quest for stable cyclic compounds bearing divalent group 14 atoms, here, density functional theory (DFT) calculations are employed to form a systematic investigation on the effects of halogen substitutions on the atomic charge distribution, thermodynamic stability as a measure of ΔES–T, polarity, polarizability, kinetic stability as a measure of ΔEHOMO–LUMO, and NBO analysis of scrutinized species (Fig. 2). In each series of calculations, the results are made through comparison to the parent carbene 1H. To verify the validity of widely accepted B3LYP method for the optimizations and energy computations, all molecules are re-optimized with more accurate but time-consuming M06-2X method. The differences among the results obtained from the two methods are not significant. Henceforth, the remaining calculations are concentrated on B3LYP.

Substituent effects on charge, ΔE S–T, and polarity

Owing to the intrinsic properties of scrutinized silylenes, their triplet structures show less atomic charge distribution on Si:, C2 (Cα), C9 (Cαʹ) than those of their corresponding singlet states, at B3LYP/AUG-cc-pVTZ (Table 1).

Table 1 The NBO atomic charge distribution on divalent, carbene-like atom (D), C2 (Cα), C9 (Cαʹ), X1, and X2 atoms calculated for unsubstituted singlet, and triplet carbenes (1H-S, and 1H-T) and their corresponding tetrahalosilylenic analogous (2H-S, 2H-T, 2F-S, 2F-T, 2Cl-S, 2Cl-T, 2Br-S, 2Br-T, 2I-S, and 2I-T, respectively), at (U)B3LYP/AUG-cc-pVTZ level
figure a
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Replacement of the carbene (in our previous work) [23,24,25] with silylene in the present research leads to an increase in the p-character of C–Si compared to C–C bond [26]. In the present study, a decrease in the C–D–C angle; D being the divalent, carbene-like atom (Â/degree) is observed from 121.19o for C-D-C angle (‘D’ refers to the ‘divalent’ atom) in 1H–S carbene to 97.06o for the corresponding C–Si–C in 2H–S silylene (Table S1). Substituting of the carbene with silylene leads to an increase in the bond lengths X2C–Si: compared to X2C–C: bond. Also, X–C2 (Cα), and X–C9 (Cαʹ) bond lengths seem linearly proportional to the size of the substitution element (X = H, F, Cl, Br, and I). The T structures show larger C9–Si–C2 or Cαʹ–Si–Cα angles and less Si–C2 (Cα), Si–C9 (Cαʹ) bond lengths than those of their corresponding S states, at B3LYP/LANL2DZ-6-311 + G* level (Table S1).

Substitution of CH2–C:–CH2 with CH2–Si:–CH2 in 1H alters its status from an unstable transition state to rather stable minimum for showing no negative force constant (Table 2).

Table 2 The calculated total energy (Etot), ΔES-T, spin contamination parameter < S2 > , zero-point (ZP) correction, ZP vibrational energy (ZPVE) and dipole moment (μ) for studied carbene, and silylenes vs. the synthesized silylenes I, V, and VII (Scheme 4)
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Replacement of α,αʹ-CH2 with CF2, CCl2, CBr2, and CI2 in 2H alter their status from an unstable triplet transition state to rather stable singlet minima (Table 2). These singlet silylenes emerge as ground states, showing more stability than their corresponding triplet states. The overall stability order of the calculated and synthesized silylenes (I, V, and VII) based on their ΔES–T values is: VII > I > 2Br> 2Cl> 2I> V > 2F > 2H. Beyond such a high stability lays the mesomeric effects of non-planar cyclic 2Br–S, 2Cl–S, and 2I–S compared to VII-S, and I–S which are cyclic, planar, continuously conjugated and obeys Hückel rule of 4n + 2 (Fig. 3).

Fig. 3
figure 3

Substituent effects of halogen atoms on singlet silacyclonona-3,5,7-trienylidenes

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Moreover, 2Br-S, 2Cl-S, and 2I-S show the higher stability than V-S. The larger the substituents (—SiMe3) have the smaller stabilizing effect on carbene-like atom than the Cl, Br, and I heteroatoms. It was found that B3LYP is the most efficient method to use in performing calculations of carbene-like atoms [23,24,25]. In Table 2, it can be seen that after full optimization of scrutinized species, the spin contamination parameters < S2 > for singlet closed shell states are zero, while the spin eigenvalues are relatively closer together for diradical triplet states (more than 2.00), indicating that those wave functions were contaminated with higher spin states. Fascinatingly, our triplet parent carbene shows higher S2 than its corresponding silylenic analogous, and the S2 value for triplet silylenes increases as a function of the ring size and size of substituted group VII-T < I-T < V-T < 2H-T < 2F-T < 2Cl-T < 2Br-T < 2I-T and it increases as the steric effect increases.

The zero-point (ZP) correction and zero-point vibrational energy (ZPVE) decrease in going from singlet silylenes to their corresponding triplet states, and in going from 2H to 2I. In contrast, the stability of the synthesized species decreases in going from the cyclic-saturated V to cyclic-unsaturated diaminosilylenes I, and VII, respectively, that both become more stable in the presence of heteroatoms.

We have probed changes of enthalpy (ΔHS–T) and Gibbs free energy (ΔGS–T) which confirm the higher stability of singlet silylenes (Table S2). As anticipated, ΔHS–T and ΔGS–T trends for silylenes appear the same as that of ΔES-T, at B3LYP/LANL2DZ-6-311 ++G** level: VII > I > 2Br> 2Cl> 2I> V > 2F > 2H. Simultaneously, among our silylenes, 2Br-S and 2Br-T exhibit the highest changes of enthalpy (ΔHS–T = 170.63 kJ/mol) and free energy (ΔGS–T = 165.61 kJ/mol) (Table S2). These results are consistent with their relatively high stability difference (ΔES–T = 172.42 kJ/mol), and NBO charge distribution on Si, C2 (Cα), C9 (Cαʹ) atoms.

Paired electrons on divalent centers lead to higher dipole moments (μ) in singlet structures (1H-S‒ 2I-S, and V-S) than their corresponding triplet states (1H-T‒ 2I-T, and V-T) where the non-bonding electrons of Si atom in singlet states are paired and located in the σ-orbital which is orthogonal to π-system. While, lower μ values of I-S and VII-S with respect to their corresponding triplets and studied singlets (1H-S–2I-S) show that the non-bonding electrons of divalent silicon in formers are paired in the π-orbital which participate to ring current of π-system. Also, an increase of μ (in Debye) is observed from 2.18 in 1H-S and 1.75 in 2H-S to 6.30 in 2F-S vs. 0.43 in 1H-T, 0.57 in 2H-T, and 4.00 Debye in 2F-T (Table 2). Evidently, polarity for singlets increases as electronegativity of substitutions increases and polarizabilities (αxx, αyy, αzz, and < α>) increase as a function of the substitution size of halogen and carbene-like atoms, and it decreases as μ increases. Our triplet carbene-like atoms show higher αxx, αyy, αzz, and < α > than their corresponding singlet structures. For instance, 2I-T (218.82 a.u.) displays a higher polarizability than 2I-S (206.44 a.u.) compared to parent triplet and singlet carbenes (107.79, and 106.32 a.u., respectively) (Table S3).

Substituent effects on heat of hydrogenation of HOMO-LUMO gap, MEP map, reactivity, and NBO analysis

It is well known that the HOMO–LUMO energy gap is associated with the chemical stability to electronic excitation; the larger ΔEHOMO–LUMO, the more chemically stable compound. Moreover, the trend of kinetic stability based on ΔEHOMO–LUMO is: VII > I > 2Br> 2Cl> 2I> V > 2F > 2H > 1H, and leads to the stability enhancing against electronic excitations (Table 3).

Table 3 The calculated frontier molecular orbital energy (EHOMO, ELUMO), and ΔEHOMO-LUMO for the scrutinized structures compared to the synthesized silylenes I, V, and VII (Scheme 4), at B3LYP/LANL2DZ-6-311 ++G** level
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This means that the electron in 2Br is tighter to excite from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO) than in the synthesized silylene V (412.61 vs. 351.33 kJ/mol). As anticipated, this trend is the same as that of ΔHS–T, ΔGS–T, and ΔES–T.

Molecular electrostatic potential (MEP) map is a useful feature to examine the reactivity given that an approaching electrophile will be drawn into negative areas (the electron distribution in where effect is dominant). The importance of MEP lies in the fact that it simultaneously displays molecular size, shape as well as positive, negative, and neutral electrostatic potential regions in terms of color grading, and is very useful in research of molecular structure with its physiochemical property relationship [27]. Interestingly, the MEP maps are consistent with their point groups, atomic charge distribution on carbene-like atoms, C2 (Cα), C9 (Cαʹ), substitution atoms, and polarities (Fig. 2 and S1). For instance, the most positive charge is predicted for 2Br-S with the highest blue-colored cloud on its silicon atom. Simultaneously, the most negative charge is demonstrated for 2Br-S with the highest red colored electron cloud on its C2 (Cα), C9 (Cαʹ) atoms. In this study, every S and T speciesshows the highest difference between size, shape, along with positive and negative electrostatic potential regions in terms of color grading, because of having the highest difference between its substitution effects and polarizability (Fig. S1 and Table S3). The MEP map can also be utilized to define the nature of a molecule chemical bond and the electronegativity difference is a central causal factor in this definition. When silicon, hydrogen, and/or halogen atoms with carbon atom are to form bond, their bond will be expected to be polar covalent. Since hydrogen, halogen, and carbon atoms have higher electronegativity than silicon atom, the former will share the binding electrons with Si, but the binding electrons will be pulled closer to the more electronegative atoms, forming dipoles within the carbene-like containing molecule. We expect these bonds to be polar covalent (partly ionic), because the difference in electronegativity is between 0.4 eV and 2.0 eV on Pauling’s scale.

As said previously, the extremely high reactivity of a silylene is due to its unoccupied 3pπ orbital, since six valence electrons are less than the eight electrons needed by the octet rule, and its lone pair is predicted to be inert owing to its high s-character [28]. Henceforth, to classify the reactivity of scrutinized silylenes, their nucleophilicity index (N), global electrophilicity (ω), chemical potential (μ), global hardness (η), electronegativity (χ), global softness (S), and maximum electronic charge (ΔNmax) are evaluated using appropriate indices (Table S4). N values show conspicuous correlations with the corresponding MEP maps for calculated silylenes (Table S4 and Fig. S1). These are consistent with the energy along with pictorial sizes of the frontier molecular orbitals (Fig. S2). The 2F-S has the highest absolute values of EHOMO and ELUMO. Due to the intrinsic properties of fluorine atom, 2F-S has the lowest N, the highest ω as well as the highest χ, while its unsubstituted silylenic and carbenic analogous (2H-S and 1H-S) show an inverse relationship. 1H-S, and 2H-S silylenes show higher N than the synthesized silylenes I, V, and VII. Our halogenated silylenes show higher ωthan the synthesized silylenes I, V, and VII. Also, 1H-S is the most reactive carbene-like species, as dictated by the maximum N, minimum, along with maximum S. Interestingly, 2Br-S is the least reactive structure with the maximum and all calculated silylenes have more η and less S than the synthesized silylene V (Table S4). All calculated and synthesized species have positive values of ΔNmax with the range of 0.65–1.12 eV (for the synthesized silylene I and 2F-S, respectively), and, hence, act as electron acceptors from their environment.

To clarify the role of substituent effect in stability of silylenes, one may refer to the second-order interactions of donor (Lewis-type) and acceptor (non-Lewis-type) NBO orbitals that point to the extent of substituent effect in silylenes. NBO analysis is originally recognized as a way of quantifying resonance structure contributions to molecules and is carried out by surveying all probable interactions between electron donor and electron acceptor NBO orbitals, along with estimating their energetic importance of second-order perturbation theory [29,30,31,32]. Therefore, some of valence data including occupancy, directionality, and hybridization resulting of NBO calculation on stable 2Br-S silylene, at B3LYP/6-311 ++G**, are given in Table 4.

Table 4 The bond orbital, occupancy, coefficients, and hybrids corresponding to the intramolecular bonds in stable 2Br-S species, at B3LYP/LANL2DZ-6-311 ++G** level
figure b
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The intermolecular interaction is formed by the orbital overlap between C-Si, C–Br, and the corresponding anti-bonding orbital which results in an intermolecular charge transfer (ICT) from a Lewis valence orbital as donor, with a decreasing of its occupancy, to a non-Lewis orbital as acceptor. The first two columns of this table give the type of orbital and occupancy among 1.92854 and 1.99571 electrons. Analysis of occupancy number provides useful information about the formation of singlet and/or triplet silylenes. For instance, σC13-Br18 and σC14-Br17 bonding orbitals with the highest occupancies 1.99571 and 1.99459 electrons have 50.00% C13 and 50.13% C14 characters in a sp5.23 and sp4.81 hybrids and have 50.00% Br18 and 49.87% Br17 characters in a sp6.83 and sp7.57 hybrids, respectively. The sp5.23 hybrid on C13 has 16.06% s-character and 83.94% p-character, while the sp6.83 hybrid on Br18 has 12.77% s-character and 87.23% p-character, respectively with polarization coefficient of 0.7071. The magnitude of this coefficient indicates the significance of the two hybrids in bond formation. While, σC13-Si15, and σC14-Si15 bonding orbitals show that their silicon centers have a lesser percentage of NBOs (19.10 and 19.23%, respectively) and give a lesser polarization coefficients (0.4371 and 0.4385, respectively) than the other bonding bonds, because silicon atom has a lower electronegativity than bromine and carbon atoms (1.90 vs. 2.96 and 2.55). Also, occupancy number for lone pair on Si (1.92854) of 2Br-S shows high s-character (77.98%) indicating the paired electrons in s-orbital. The calculated second-order interaction energies (E(2)) among the orbital’s donors–acceptor in stable 2Br-S silylene are shown in Table S4. Overall, donation of σCα-Br including σC13-Br18, σC13-Br19, σC14-Br16, and σC14-Br17 to LP*Si (3pπ Si) through positive hyperconjugation on one side and donation of lone pairs on bromine atom to unoccupied orbital of silicon center via mesomeric effect on the other side are totally more than donation of lone pairs on silicon center (σ2Si) to the anti-bonding orbitals of σ*Cα-Br (that is LPSi15 → σ*C13-Br19, LPSi15 → σ*C14-Br17, LPSi15 → σ*C14-Br16, and LPSi15 → σ*C13-Br18) through negative hyperconjugation (Table S5 and Fig. 4).

Fig. 4
figure 4

Positive vs. negative hyperconjugations and their corresponding perturbation orbital diagrams for 2Br-S species

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Clearly, higher interaction among σCα-Br as donor and 3pπ Si as acceptor via positive hyperconjugation on one side and so effective interaction between LPBr as donor with 3pπ Si as acceptor through mesomeric effect on the other side leads to the elongation of the acceptor. All these intramolecular interactions confirm the higher stability and lower reactivity for singlet tetrabromosilylene compared to other species.

Substituent effects on isodesmic reactions

On the basis of the Hoffmann, Schleyer, and Schaefer’s statement, a stable species must be resistant to fragmentation, isomerization, etc. [33]. In this study, applying the appropriate isodesmic reactions, we show in detail how the substituent affects on singlet (S) and/or triplet (T) states’ stabilities of our divalent molecules, individually. In a theoretical survey on triplet carbenes, Nemirowski and Schreiner stated that the classical π-donor/σ-acceptor substituents such as amino simultaneously stabilizes singlet and destabilizes triplet state [34]. Previously, we revealed that in contradiction of their claim, amino substituents stabilize not only the singlet but also the triplet states [23,24,25]. Here, using five proposed isodesmic reactions (Scheme 5 and Table 5), we test our previous suggestion for the case of tetrahalosilylenes, at (U)M06-2X/6-311 ++G**.

scheme 5
Table 5 The substituent effects on singlet and triplet silylenes (ΔE1 to ΔE5, in kJ/mol) via isodesmic reactions 1–5 (see Scheme 5), at (U)M06-2X/6-311 ++G**
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Isodesmic reaction#1 shows the dehydrogenation of scrutinized silanes by singlet (1H-S) and/or triplet (1H-T) reference non-planar carbenes. This reaction describes that the energy change is associated with an exothermic reaction that increases its exothermicity on going from fluorine to bromine and making the 2H-S silylene as the least stable singlet species (ΔE1 = − 142.75 kJ/mol), and the 2H-T silylene as the most stable triplet species (ΔE1 = − 25.16 kJ/mol). Accordingly, the highest stability is demonstrated by 2Br-S (ΔE1 = − 200.43 kJ/mol), and the lowest stability is recognized by 2Br-T (ΔE1 = + 9.53 kJ/mol). Obviously, every S silylene appears more stable than its corresponding T state for showing a higher ΔE1. In isodesmic reaction#2, heat of dehydrogenation (ΔE2) is approximated for S and/or T carbene-like atoms using the parent planar conjugated singlet \( (\text{1}_{\text{H - S}} *) \) and/or triplet \( \text{1}_{\text{H - T}} * \) carbenes to examine the mesomeric effects of halogen atoms, along with hyperconjugation effect on stability of silylenes. The higher is the ΔE2 value, the more is the stability of silylenes. Based on heat of dehydrogenation in this exothermic reaction, the highest stabilization is encountered for 2Br-S by − 302.01 kJ/mol followed by 2Cl-S (− 291.56 kJ/mol), 2I-S (− 280.98 kJ/mol), 2F-S (− 271.87 kJ/mol), to 2H-S (− 262.30 kJ/mol) decreases for the corresponding triplet ones. Also, we estimate relative stability for the studied species employing the 1H-S* and/or 1H-T* planar carbenes and non-planar allene \( (1_{\text{H}} **) \) as the references in third isodesmic reaction [35,36,37,38]. This reaction indicates that the hyperconjugation of hydrogen atoms has a 333.90 kJ/mol stabilizing effect on 1H-S and 341.92 kJ/mol on its triplet state (1H-T). Isodesmic reaction#3 shows that the dehydrogenation is coupled with endothermic reaction which decreases going from planar conjugated 1H-*S and/or 1H-*T carbene to its corresponding non-planar analogous and increases going from every S state to its corresponding T state. In isodesmic reaction#4, we estimate relative stability for our scrutinized silylenes using the planar conjugated 1H-*S and/or 1H-*T carbene and singlet and/or triplet methylene (:CH2). The results are very different to those obtained from heat of dehydrogenation of Rxn 1–3, indicating stabilization of S carbenes and S silylenes by about 6.3–8.4 kJ/mol more than their corresponding T carbenes and T silylenes, and so carbenes are less stabilized than silylenes. Fascinatingly, the π-donor/σ-acceptor halogen groups stabilize both S and T silylenes. This is related to the higher electronegativity of halogen atoms which makes them as stronger σ-acceptors and henceforth prefers S over T state. Furthermore, on account of the higher electronegativity the π-donating of halogen atoms in S silylenes is higher than that of T analogous. Hydrogen groups stabilize both 1H-S and 1H-T carbenes (Table S6). Also, relative stability of 2H-S and 2H-T silylenes (Table S6) is more than twice of 1H-S and 1H-T carbenes. The lower electronegativity of silicon than carbon atom and the lower electronegativity of iodine than other halogen atoms lead to higher stability of 2I-T silylene than 1H-T carbene (ΔE4 = − 467.78 vs. − 200.51 kJ/mol). Consequently, isodesmic reaction#5 shows the dehydrogenation of substituted silanes by 2H-S and 2H-T reference silylenes and so the lowest stability is shown by 2Br-T (ΔE5 = 56.89 kJ/mol, See Rxn 5 in Scheme 5 and Table 5).

Conclusion

In this survey, we have compared and contrasted thermodynamical, geometrical, and kinetical parameters of nine-membered cyclic carbene and its halogenated silylenes including singlet states (1H-S–2I-S) and triplets (1H-T–2I-T). Except for reference carbene (1H) which emerges one imaginary vibrational frequency, all of silylenes show real vibrational frequency and appear as boat-shaped minima on their potential energy surfaces, at DFT. The 2Br-S shows the highest stability indicated by the highest ΔES–T, ΔHS–T, and ΔGS–T. From a thermodynamic point of view, all calculated ΔES–T, ΔHS–T, and ΔGS–T parameters appear with positive values, indicating that every singlet silylene is more stable than its corresponding triplet state. Evidently, among calculated singlet silylenes (2H-S‒2I-S), the most stable species appears to be 2Br-S which is 172.43 kJ/mol more stable than its corresponding triplet 2Br-T. The overall trend of ΔES–T, ΔHS–T, and ΔGS–T is: 2H < 2F< 2I< 2Cl< 2Br. From a kinetic viewpoint, 2Br-S shows the highest value of ΔEHOMO–LUMO (412.61 kJ/mol) which is higher than that of calculated for the parent form of Kira’s synthesized silylene (351.79 kJ/mol). Respecting the σ-donor characteristic of the stable silylenes, the highest nucleophilicity, the highest HOMO energy, and the lowest electrophilicity is calculated for unsubstituted silylene (2H-S) via hyperconjugation effect. These factors make it theoretically more susceptible for attacking an electrophile. Contrary to our expectation, 2H-S not only does not turn out to be electrophilic, but also because of its intrinsic angle strain, boat-like structure and hyperconjugation effect turn out as the most nucleophilic character among singlet silylenes. We have employed the NBO analysis to stress the roles of intermolecular donor and acceptor interactions through the second-order perturbation theory. As above the geometrical parameters such as bond length, bond angle, and symmetry compared and contrasted for our silylenes, S silylenes show higher Si–C bond lengths and lower bond angles than their corresponding T states. This is attributed to the intramolecular orbital interactions, particularly the interaction of paired electrons on divalent Si atom with σCα-Br* and the interaction of σCα-Br with 3pπ Si orbitals of the molecules. This analysis indicates that there is a negative hyperconjugation between σ2-bonding orbital of silicon with anti-bonding orbital of carbon-bromine in α,αʹ-positions of 2Br-S species which leads to stability of it, and compensating for the mesomeric effect of bromine. Isodesmic reactions are used to assess the effects of substitution on the stability of silylenes. Commonly, it is found that α,αʹ-tetrahalo groups stabilize both singlet and triplet states of our studied silylenes with a more considerable effect on the singlet. Based on heat of dehydrogenation in exothermic isodesmic reaction, the highest stabilization is encountered for 2Br-S followed by 2Cl-S, 2I-S, 2F-S, to 2H-S and decreases for substituted triplet ones. Both singlet and triplet silylenes become differently more stable in the presence of halogen atoms with a more considerable effect on the singlet. Theoretical conclusions are waiting for experimental testing and verifications.

Computational methods

Geometry optimizations of scrutinized silylenes are carried out with the GAMESS program package [39, 40], at the B3LYP [41,42,43,44,45], and M06 [46] methods, with standard triple-zeta 6-311 + G* Pople basis set [47, 48], which is constructive for the explanation of diffuse functions [48, 49], is employed for C, Si, H, F, Cl, and Br atoms, while the valence double-zeta LANL2DZ basis set with effective core potential (ECP) of Hay and Wadt is used for I atom [50]. Dynamics are studied at different methods and levels of accuracy with the DFT outcome expected to provide the more accurate structural and energetic results. For more accurate energetic data, single point calculations are performed at the B3LYP/AUG-cc-pVTZ//B3LYP/6-311 + G* [52], and M06-2X/AUG-cc-pVDZ//M06-2X/6-311 + G* levels. Triplet states are computed using unrestricted broken spin-symmetry UB3LYP and UM06-2X methods at the same levels. The vibrational frequency computations are applied to characterize the nature of stationary points as minimum (NIMAG = 0), or transition state (NIMAG = 1), at B3LYP/6-311 ++G**//B3LYP/6–311 + G* [51, 52]. The natural bond orbital (NBO) population analysis is calculated at B3LYP/LANL2DZ-6-311 ++G** and UB3LYP/LANL2DZ-6-311 ++G** for singlet and triplet states, respectively [53,54,55,56]. Also, reactivity is estimated using the same level. Hence, the nucleophilicity index (N) is calculated as N = EHOMO(Nu)−EHOMO(TCNE), where tetracyanoethylene (TCNE) is preferred as Ref. [57,58,59,60,61,62]. In this scale, the nucleophilicity index for TCNE is N = 0.0 eV, presenting the lowest HOMO energy in a long series of organic molecules already considered. This choice allowed us conveniently to handle a nucleophilicity scale of positive values. The capacity of the N index describing the nucleophilic behavior of organic molecules was tested in the context of the analysis of the nucleophilic behavior of a series of captodative ethylenes [57,58,59,60,61,62]. The global electrophilicity (ω) is computed as ω = (μ2/2η) [57,58,59,60,61,62], where μ is the chemical potential (μ = (EHOMO + ELUMO)/2) and η is the chemical hardness (η = (ELUMO−EHOMO)/2) [57,58,59,60,61,62]. Furthermore, χ is the absolute electronegativity (χ = – μ) is used to predict the electron transfer direction when the substituted species are formed, S is the global softness (S = 1/2η), and ΔNmax is the maximum electronic charge (ΔNmax = – μ/η) [57,58,59,60,61,62]. The molecular electrostatic potential (MEP) maps are anticipated at B3LYP/AUG-cc-pVTZ.