Introduction

Sextet divalent silylenes, with R1-S̈i-R2 formula, are of great interest because of evolving from exotic reaction intermediates to important chemical species [1,2,3,4,5]. In contrast to the carbon atom, silylenes have a low ability to form hybrid orbitals [4, 6,7,8,9] and therefore prefer the (ns)2(np)2 valence electron configurations in their divalent species. Since two electrons remain as a singlet pair in the ns orbital, they mostly prefer to exist as singlets and can interact as a Lewis acid or base. Also, the simplest silylene is S̈iH2, a singlet. The basicity of silylenes may be triggered by their nucleophilicity or proton affinity [4, 10,11,12]. As a result, they can serve as ancillary ligands in transition metal complexes in which there are synergic electron transfers between the low valent silicon atoms and transition metals such as rhodium [13]. The first heavy alkene (DS̈iCH (SiMe3)2) was reported in 1976 by Lappert [14]. Silylenes are applied in light-emitting diode (LED), electroluminescence (EL), silicon chemical vapor deposition (CVD) processes, photonics, optics, electronics, and semiconductor [15,16,17,18,19,20,21,22,23].

Electropositive Si atoms substitution can diminish ΔEs-t by lowering the energy of the triplet state [24,25,26]. Various investigations on silylenes with substituted electropositive atoms were reported [15, 27], such as Apeloig that studied the effects of electropositive substituents on ΔEs-t of silylenes [28,29,30,31].

Considering the applications of silylenes [15,16,17,18,19,20,21,22,23, 28], the purpose of the present work is to reach novel silylenes that accommodate up to six electropositive Si atoms at different possible positions (Table 1) and assess the influences of them on the geometrical parameters, stability (ΔΕs-t), the heat of hydrogenation (ΔEH), nucleophilicity (N), and electrophilicity (ω), at B3LYP/6–311++G** level of theory. Evidently, a number of them can be employed as multidentate ligands.

Table 1 Optimized bond length (Å), bond angle (∠AS̈id, ∠S̈iDE, and ∠S̈iAF /deg), and symmetry for novel singlet (1s–24s) and triplet (1t–24t) silylenes, at B3LYP/6–311++G** level
Full size table

Computational methods

Full geometry optimizations are accomplished without any symmetry constraints by means of hybrid functional B3LYP [32,33,34,35] and the standardized 6–311++G** basis set, by using the GAMESS package of programs [32, 36]. Restricted and unrestricted B3LYP density functional methods are employed for singlet and triplet states, respectively.

The nucleophilicity index, N, is defined as N = EHOMO(Nu) - EHOMO(TCNE), where TCNE is tetracyanoethylene and is chosen as the reference [37]. The global electrophilicity, ω [38], is also calculated following the expression ω = (μ2/2η), where μ is the chemical potential (μ ≈ (EHOMO + ELUMO)/2) and η is the chemical hardness (η = ELUMO − EHOMO) [39] and natural bond orbital (NBO) charges are provided, at the same level of theory [32]. Structural parameters including bond distances, bond angles, dihedral angles, and symmetries are also calculated.

Results and discussion

Silicon substitution effects on thermodynamic and structural parameters of bicyclo[2.2.1]hepta-7-silylenes are compared and contrasted, at B3LYP/6–311++G** level of theory. Special consideration is paid to their singlet (s) and triplet (t) multiplicity, geometrical parameters, relative stability (ΔΕs-t = Εt-Es), nucleophilicity (N), electrophilicity (ω), proton affinity (ΔΕPA), second-order perturbation stabilization energies (E(2)), and band gap (ΔΕHOMO-LUMO) (Tables 1, 2, 3, 4, 5, and 6). All structures appear with C1 symmetry, except silylenes 1, 4, 8, 16, 21, and 24 for showing C2 symmetries.

Table 2 Singlet–triplet energy gaps (ΔEs–t, kcal/mol) for singlet (1s–24s) and triplet (1t–24t) silylenes, at B3LYP/6–311++G** level of theory
Full size table
Table 3 Calculated second-order perturbation stabilization energies (E(2)), for the intermolecular interactions (donor/acceptor NBO) of singlet silylenes, at the B3LYP/6–311++G** level of theory
Full size table
Table 4 The highest occupied and the lowest unoccupied molecular orbital energies (EHOMO/eV, ELUMO/eV, respectively), along with band gaps (ΔEHOMO–LUMO, kcal/mol), nucleophilicity (N), chemical potential (μ), proton affinity (ΔEPA, kcal/mol), zero-point vibrational energy (ZPVE, kcal/mol), and global electrophilicity (ω) for singlet silylenes (1s-24s), at B3LYP/6–311++G** level of theory
Full size table
Table 5 NBO charges on -S̈i- for singlet (1s–24s) and triplet (1t–24t) silylenes, at B3LYP/6–311++G** level of theory
Full size table
Table 6 Calculated second-order perturbation stabilization energies (E(2)), for the intermolecular interactions (donor/acceptor NBO) and bond angle (deg) of singlet (1’s-24’s) protonated silylenes, at the B3LYP/6–311++G** level of theory
Full size table

The silylene bond lengths (A-S̈i or S̈i-D) for 1s–24s vs. 1t–24t vary in a range of 1.91 Aͦ to 2.50 Aͦ. Divalents with silicon adjacent to the silylene center have higher S̈i–Si bond lengths than S̈i–C. For instance, the S̈i–Si bond length in silylene 2s is 0.43 Å longer than S̈i–C. Interestingly, silylenes 10s and 19s have the lowest and highest bond lengths. Also, the bond lengths of singlet and triplet silylenes 8, 9, and 21 are similar (Table 1).

Divalent bond angles (∠AS̈iD) of our silylenes range from 71.62° to 102.08°. Silylene 4s with high bond lengths (A–S̈i and S̈i–D = 2.48 Å) has the lowest ∠AS̈iD (71.62°), and 21t with low bond lengths (A–S̈i and S̈i–D = 1.93 Å) has the highest ∠AS̈iD (102.08°). Triplet silylenes have wider divalent bond angles (∠AS̈iD) than their corresponding singlet states. For example, the ∠AS̈iD in silylene 6t is 4.74° wider than divalent bond angles 6s. Also, the bond angles (∠S̈iDE and ∠S̈iAF) of singlet silylenes are wider than corresponding triplets. For instance, ∠S̈iDE bond angles of 4s and 4t are 103.12° and 98.76°, respectively (Table 1).

The singlet-triplet energy gaps (∆Es-t) are employed to compare the relative stabilities at B3LYP/6–311++G** levels of theory. The calculation of ΔEs-t in substitution of silicon atoms has been useful in providing insight into how the singlet is stabilized (or destabilized) relative to the triplet and also how the geometry of the two states is affected by substitution. All calculated ΔEs-t parameters appear with positive values indicating that every singlet silylene is more stable than its corresponding triplet state. For example, singlet 2s is 23.40 kcal/mol more stable than its corresponding triplet 2t. Evidently, among silylenes (1s–24s), the most stable appears to be singlet 9s which is 39.75 kcal/mol more stable than its corresponding triplet 9t. The overall stability order of our silylenes based on their ΔEs-t values is 9 > 1 > 7 > 3 > 21 > 12 > 8 > 2 > 6 > 10 > 5 > 11 > 19 > 22 > 20 > 14 > 4 > 15 > 18 > 17 > 23 > 24 > 16 > 13 (Tables 2). This stability can be related to our imposed topology.

In the case of singlet silylene, we have β-silicon effect [40,41,42,43] that the maximum stabilization is a result of the interaction between the β-silicon and anti-bonding character of lone pair (LP*) silylene that increases the electron population of silylene center. This effect is much smaller than the back-donating ability that must be related to both the greater polarizability of the C–Si electron density and to the ability of the C–Si bond to overlap effectively with the LP* on the silylene center. So, silylenes 3, 7, 8, 9, 12, and 21 with β-silicon and σC-Si → LP*Si interactions have higher stability than others. Among them, every silylene that shows the higher level of E(2) for σC-Si → LP*Si interactions has higher stability than others. So, silylene 9 has the highest stability for two interactions (σC(A)-Si(B) and Si(C)-C(D) → LP*Si) with the highest E(2) (5.23 kcal/mol). Silylene 7 with two interactions (σC(A)-Si(B) and A(C)-Si(F) → LP*Si, E(2) = 4.36 kcal/mol) has higher stability than 3 with one σC(A)-Si(B) → LP*Si interaction (E(2) = 5.16 kcal/mol). In the same way, silylene 12 despite high E(2) (3.52 kcal/mol) has lower stability than 21. Because, silylene 12 and 21 have three and four σC(A)-Si(B) → LP*Si interactions, respectively (Table 3).

As the addition of silicon atoms, their stability decreased. For example, silylene 2 without any interactions has higher stability than 6 with σC(D)-Si(C) → LP*Si interaction (E(2) = 4.85 kcal/mol). Likewise, silylene 19 with high interactions (σSi(C)-C(D) → LP*Si, E(2) = 4.61 kcal/mol) has lower stability than 11 with σSi(A)-Si(B) → LP*Si interaction (E(2) = 3.35 kcal/mol). Silylene 10 with two interactions (σC(A)-Si(B) and C(A)-Si(F) → LP*Si, E(2) = 4.20 kcal/mol) has higher stability then 5 with σC(D)-Si(C) → LP*Si interaction (E(2) = 4.85 kcal/mol) (Table 3).

In order to characterize the substituent effect on stability data, we have compared and contrasted the zero-point vibrational energy (ZPVE) of singlet silylenes. Interestingly, the effect of successive divalent Si substituting on the calculated ZPVE shows the addition of silicon atoms decreases ZPVE. For example, silylene 23s with six silicon atoms has low stability (ΔΕs–t = 14.50 kcal/mol) and ZPVE (55.83 kcal/mol). Likewise, bicyclo[2.2.1]heptanylene (1s) without any silicon has high stability (ΔΕs–t = 33.00 kcal/mol) and ZPVE (93.71 kcal/mol) (Table 4).

The correlation coefficients of the fit between the band gaps (ΔΕHOMO–LUMO) of our silylenes with ΔEs-t and ELOMO are 0.78 and 0.84, respectively. For instance, silylene 9s has high ΔEs-t (39.75 kcal/mol), ΔΕHOMO–LUMO (76.20 kcal/mol), and ELOMO (−2.67 eV) (Fig. 1 (a and b) and Table 4). Furthermore, the direct relationship between the ΔΕs–t with μ and η are demonstrated by the correlation coefficient of the linear fit between the two values (R2 = 0.65 and 0.77, respectively). For example, silylene 1s has high stability (ΔΕs–t = 33 kcal/mol), μ (−4.20 eV), and η (3.41 eV) (Fig. 1 (c and d)).

Fig. 1
figure 1

Correlation diagrams between ΔΕHOMO–LUMO (kcal/mol) and ΔEs-t (kcal/mol) (a), ELUMO (eV) and ΔEs-t (kcal/mol) (b), μ (eV) and ΔEs-t (kcal/mol) (c), η (eV), and ΔEs-t (kcal/mol) (d), ω (eV) and ΔEs-t (kcal/mol), and ω (eV) and ΔΕHOMO–LUMO (kcal/mol) (d)

Full size image

Also, the ω appears inverse correlation with our results of ΔΕs–t and ΔΕHOMO–LUMO values (R2 = 0.86 and 0.78, respectively) (Fig. 1 (e and f)). The increasing electropositive or π-acceptor capability of the substituents decreases the population of the Si 3pz orbital leading to a high positive electrostatic potential in the lone pair region yielding higher electrophilicity of the silicon atom, thereby increasing the stability of the triplet silylene and decreasing singlet-triplet gap [44, 45]. In other words, μ is a measure of stability; therefore, as μ becomes high negative, the structure becomes less stable and easy to get an electron. For instance, 24s with the highest μ (−4.94 eV) and ω (4.94 eV) has low stability (ΔΕs–t = 14.46 kcal/mol) and band gap (ΔΕHOMO–LUMO = 56.88 kcal/mol). On the other extreme, 1s with the lowest negative μ (−54.29 eV) and ω (2.58 eV) shows high stability (ΔΕs–t = 33.00 kcal/mol) and band gap (ΔΕHOMO–LUMO = 78.87 kcal/mol) (Tables 2 and 4).

The nucleophilicity index and gas-phase proton affinity (PA) are critical factors for showing the aptitude of our silylenes for coordination to transition metal complexes. As a result, silylene 12s with rather high stability (ΔEs-t = 30.02 kcal/mol) and N (3.45 eV) has high negative ΔEPA (−223.73 kcal/mol) that can be applied as accumulated multidentate ligands (Tables 2 and 4).

The electrostatic potential (ESP) map has largely been used as a molecular descriptor of the chemical reactivity, which takes part in both electrophilic and nucleophilic reactions. For investigating, the electrostatic potential (ESP) surfaces are plotted over the optimized electronic structures of our silylenes using density functional B3LYP method with 6–311++G** basis set. The red and blue regions indicate the lowest (most negative) and highest (most positive) electrostatic potential energy values, respectively (Fig. 2) [46]. The ESP maps show that silylene center with red region has the negative potential as a nucleophilicity site.

Fig. 2
figure 2

The ESP maps of singlet (1s–24s) silylenes, at B3LYP/6–311++G** level of theory

Full size image

The NBO charges on –S̈i– were computed for the singlet and triplet states of the silylene species (Table 5). Charges on all the triplet silylenes are less than those of their corresponding singlet species. For example, atomic charges on –S̈i– of 2s and 2t are +0.6589 and + 0.4195, receptively. Due to the rather higher electronegativity of carbon than silicon atom, it is anticipated to place a higher partial positive atomic charge on its adjacent silylene (–S̈i–). In the other words, silicon atoms in singlets tend to have their nonbonding electrons in the atomic orbitals with higher s-character. Consequently, electropositive substitutions (–S̈i–) transfer charge from their corresponding S̈i–A and S̈i–D bonding orbitals with higher p-character to the partially populated s-type orbital on the silicon atom. For example, 3s with two carbons adjacent to its silylene center has a more positive atomic charge on its –S̈i– (+1.0168) than 2s which has one nitrogen (–S̈i– = +0.6589).

The gas-phase proton affinity (PA) is one of the most important thermodynamic properties that shows the importance of acid-base chemistry [47]. The ΔEPA of reactions for singlet silylenes is calculated, at B3LYP/6–311++G** levels of theory. We have employed the NBO analysis to stress the roles of intermolecular orbital interactions through second-order perturbation theory. The NBO analysis provides significant evidence for the nature of our protonated silylenes. Every interaction that stabilization of positive charge causes increased negative ΔEPA. In this regard, silylene 1s without any silicon atom at its structure has the lowest ΔEPA (−216.20 kcal/mol). Silicon atoms at A and D situations have less effect on the stability of the positive center. For instance, silylene 3s with one Si at B situation has higher ΔEPA than 4s with two Si at A and D situations because protonated silylene 3’s has higher σ(A)-(B) → LP*Si-H interaction (E(2) = 26.55 kcal/mol) than 4’s (E(2) = 0.76 kcal/mol).

Contrary to our anticipation, silylene 2s with one silicon at situation A has the rather high ΔEPA (−222.65 kcal/mol) because of high σC(E)-H(exo) → LP*Si-H interactions (33.49 kcal/mol) at 2’s (Tables 4 and 6). The silicon atoms in the B situation are better than C for stabilizing the positive center of silylene. For example, silylene 7s has higher ΔEPA than 8s (−221.05 and − 221.22 kcal/mol, respectively), because protonated silylene 7’s has higher σC(A)-Si(B) → LP*Si-H interaction (E(2) = 9.78 kcal/mol) than σC(D)-Si(C) → LP*Si-H interaction (E(2) = 8.93 kcal/mol) of 8’s. The important factor for stability of protonated silylenes is their bond angles (∠SiDC and ∠SiAB). For instance, the protonated center of 17’s has stabilized its positive charge by bending too much to one side (∠SiAB = 75.07°), so it has the highest σSi(A)-Si(B) → LP*Si-H interactions (E(2) = 53.63 kcal/mol). Likewise, silylenes 11s and 20s with high interactions and low bond angles (∠SiDC and ∠SiAB) have the highest ΔEPA (−225.21 and − 226.45 kcal/mol, respectively) (Tables 4 and 6).

Conclusions

In this research, we have studied thermodynamical and geometrical parameters of novel singlet (s) and triplet (t) forms of bicyclo[2.2.1]hepta-7-silylenes, all of which appear as minima on their potential energy surfaces at B3LYP/6–311++G** level of theory. The 2,3-disilabicyclo[2.2.1]hepta-7-silylene (9) shows the highest stability indicated by its relatively high ΔEs-t. The overall trend of ΔEs-t is 9 > 1 > 7 > 3 > 21 > 12 > 8 > 2 > 6 > 10 > 5 > 11 > 19 > 22 > 20 > 14 > 4 > 15 > 18 > 17 > 23 > 24 > 16 > 13, which appears rather similar to the trend of ΔEHOMO-LUMO and ELOMO. Silylenes 3, 7, 8, 9, 12, and 21 with β-silicon have higher stability for σC-Si → LP*Si interactions than others. So, silylene 9 has the highest stability for two σC(A)-Si(B) and Si(C)-C(D) → LP*Si interactions with the highest E(2) (5.23 kcal/mol).

The electrophilicity (ω) appears inverse correlation with our results of ΔΕs–t and ΔΕHOMO–LUMO values (R2 = 0.86 and 0.78, respectively). Silylene 1s has a high stability (ΔΕs–t = 33.00 kcal/mol), ΔEHOMO-LUMO (78.67 kcal/mol), η (3.41), and NBO charge on -S̈i- (1.001) has low ΔEPA (−216.20 kcal/mol), negative μ (−4.20 eV), and ω (2.58 eV). The interactions of donor and acceptor NBOs give a detailed assessment of ΔEPA and geometrical features of our protonated silylenes. Contrary to our anticipation, 1-silabicyclo[2.2.1]hepta-7-silylene (2s) with one silicon has the rather high ΔEPA (−222.65 kcal/mol) because of high σC(E)-H(exo) → LP*Si-H interactions (33.49 kcal/mol) at protonated silylene 2’s. Also, the 2,6-disilabicyclo[2.2.1]hepta-7-silylene (7s) has higher ΔEPA than 3,6-disilabicyclo[2.2.1]hepta-7-silylene (8s) (−221.05 and − 221.22 kcal/mol, respectively), because protonated silylene 7’s has higher σC(A)-Si(B) → LP*Si-H interaction (E(2) = 9.78 kcal/mol) than σC(D)-Si(C) → LP*Si-H interaction (E(2) = 8.93 kcal/mol) of 8’s.

The nucleophilicity index and gas-phase proton affinity (PA) are crucial factors for showing the aptitude of our silylenes for coordination to transition metal complexes. As a result, we introduce silylene 12s with rather high stability (ΔEs-t = 30.02 kcal/mol), N (3.45 eV), and negative ΔEPA (−223.73 kcal/mol) that can be applied as accumulated multidentate ligands.