Introduction

The chemistry of divalent compounds such as carbenes, organosilicon, etc. has fascinated a considerable attention in recent years [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]. Divalent silylenes are congeners of carbenes, but mostly seem to have the s configuration as the ground state [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]. The larger size of the valence orbitals of silicon reduces the electron–electron repulsion of the lone pair on the Si atom accordingly enlarges the split energy of electrons. Thus, a silylene energetically favors the s ground state as a stable configuration [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]. These intermediates are employed in light-emitting diode, electroluminescence, Si chemical vapor deposition procedures, optics, electronics, and semiconductors [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]. The simplest, acyclic, linear, and unsaturated silylene with H2C = Si molecular structure has been of great interest as a possible divalent intermediate in numerous organosilicon reactions. It may be established in the interstellar medium [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]. Silylidenes have been the subject of various theoretical investigations and experimental surveys [16,17,18,19,20]. The first unsaturated silylene was searched by Murrell et al. in 1977 at theoretical methods and levels [21]. The experimental findings recognized silylidene via its electronic absorption spectrum, in 1979 [22] and later its microwave spectrum [23]. Optical properties, structural parameters, rotational constants, force constants, and vibrational frequencies of silavinylidene derivatives were estimated using computational chemistry [24,25,26,27]. In 1997, laser-induced fluorescence spectroscopy and theoretical expectations were used in order to establish the ground state of this divalent species [28]. The influences of the substituted polar groups on thermodynamic stability (ΔΕs-t) were first described by Hopkinson et al. [29]. In spite of many investigations, achieving at s (ΔΕs-t > 0) vs. t ground state (ΔΕs-t < 0) for saturated and unsaturated NHCs, NHSis, and NHGes seems as a challenging issue. If the promotion energy is increased, the s ground state will be reached. If the promotion energy is decreased, the t ground state will be reached. To this end, electronic, inductive, mesomeric, and steric influences are applied to change the multiplicity of NHCs, NHSis, and NHGes [29,30,31,32,33,34]. For instance, the substituted EDGs increase the 3p-character of Si valence orbitals which leads to t configuration. Gordon identified the first t ground state silylenes [17, 18, 30]. Apeloig researched the effects of EDGs on the multiplicity of silylenes [19, 20, 31]. Considering applications of unsaturated silylenes and increasing demand for stable NHSis [34], here we have studied substituent effects of EWGs and EDGs on two “W” and “chair” orientations with silylenic centers of 1-s, 2x-s, 3x-s, and 1-t, 2x-t, and 3x-t Hammick silylenes (x = NH, PH, AsH, O, S, and Se), at DFT (Fig. 1) [35,36,37,38,39].

Fig. 1
figure 1figure 1

The optimized structures of the studied NHSis in this work

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Computational methods

Geometry optimizations are carried out without any symmetry constraint, operating the GAMESS [40, 41] program at the (U)B3LYP [42,43,44,45] and (U)M06-2X methods [46, 47] together with 6–311 +  + G** and AUG-cc-pVTZ basis sets [48,49,50,51,52,53,54,55]. All optimized structures turn out to be minima on their energy surfaces for showing no imaginary frequency. The s-t energy gap (ΔEs-t), energies of the frontier molecular orbital (FMO), band gap (ΔΕHOMO-LUMO and ΔΕSOMO-SOMO+1 for s and t species, respectively), ionization potential (IP), and electron affinity (EA) are calculated at 298.15 K and 1.00 atm [56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79]. The natural bond orbital (NBO) charges [56,57,58,59], the global reactivity descriptors [80,81,82,83], and the condensed Fukui function (CFF) are provided at the same level of theory [84, 85]. The nucleophilicity index (N) is acquired from the energy difference between EHOMO of s NHSi (or ESOMO of t NHSi) and tetracyanoethylene [80,81,82,83]. The electrophilicity index (ω = μ2/2η), chemical potential (μ = (EHOMO-ELUMO)/2), and the maximum amount of electronic charge index (ΔNmax =  − μ/\(\eta\))are obtained as well [80,81,82,83]. The CFF descriptors are calculated using the Multiwfn program via f + A = ρAN + 1 − ρAN (ρA is the electron population number of A atom and N refers to the number of electrons stable states), f + A = qAN + 1 − qAN (nucleophilic attack), f − A = qAN − qAN − 1 (electrophilic attack), and DfA = f + A − f − A (condensed dual descriptor) [84, 85]. The site is favored for a nucleophilic attack if DfA > 0 and is favored for an electrophilic attack if DfA < 0.

Results and discussion

Following the previous research works on divalent compounds [34,35,36,37,38,39], in this research the substitution effects were studied on the singlet (s) and triplet (t) silapyridine-4-ylidene fused by two furan rings. The physical prarmeters have been obtained using DFT calculations according to the previous reports [60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79].The present work covers thermodynamic, kinetic, and electronic effects of EWGs and EDGs on the scrutinized s and t NHSis vs. the first synthesized silylenes at DFT (Schemes 1) [86,87,88,89].

Scheme 1
scheme 1

The synthesized silylene by West (I-s), Denk (II-s) as well as Kira (III-s)

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Recently, different theoretical studies has been carried out on fusion of the different rings of pyridine-4-ylidene and heavier derivatives (Schemes 2).

Scheme 2
scheme 2

The reported newly divalent species in the computational chemistry

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The resulted reports reveal that heteroatom type, size of the fused ring, number of fused rings, and orientation of the substituted dopants change stability and other properties of these divalent species. Our s and t NHSis turn out to be minima for showing no negative force constant. Structural parameters including bond length (R; C—Si and Si—C) in angstrom, divalent and dihedral bond angles in degree (\(\widehat{\mathrm{A}}\) (C − Si − C) and \(\widehat{\mathrm{D}}\) (C − Si − C − X), respectively), and symmetry of silylenes are considered. Except for 3AsH-s and 3PH-s with C1 symmetry, structural optimizations of other silylenes show Cs symmetry for all s and t states. All silylenes show \(\widehat{\mathrm{D}}\cong\) 180°. In each of the three series, 1-s, 2x-s, and 3x-s silylenes show more R (about 0.020–0.040 Å) and less \(\widehat{\mathrm{A}}\) (about 10°) than their 1-t, 2x-t, and 3x-t analogous. For instance, 2O-s and 3AsH-s show R of 1.868, 1.890, 1.853, and 1.846 Å, also \(\widehat{\mathrm{A}}\) of 92.461° and 94.434°, respectively. Likewise, 2O-t and 3AsH-t show R of 1.878, 1.876, 1.864, and 1.836 Å, also \(\widehat{\mathrm{A}}\) of 102.021° and 104.150°, respectively. Our silylenes turn out as singlet ground state for showing positive ΔEs-t values [33]. In series 1, while fusion of two benzene rings thermodynamically stabilizes the corresponding silylene (ΔEs-t = 185.30 kJ/mol), in series 2 and 3, by decreasing the electronegativity and increasing the atomic radius, the ΔEs-t diminishes from 215.10 kJ/mol for EWGs to 193.66 kJ/mol for EDGs (Table 1).

Table 1 The calculated ΔΕs-t (in kJ/mol), polarity (in Debye), and polarizability (in kJ/mol) of the inspected singlet and triplet NHSis
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All silylenes show more ΔEs-t than III (138.48 kJ/mol). This is because of the higher electronegativity of EWGs which makes them a stronger π-acceptor and hence prefers the singlet over the triplet state which causes a higher ΔEs-t. In going from the most electronegative heteroatom to the least electronegative one, the ΔEs-t is decreased. More π-electron delocalization of the substituted dopantʼs free electron pair in two furan rings and a silapyridine ring makes possible more polarity and less polarizability of the s NHSis with regard to the t ones. Then again, substitution of either EWGs or EDGs groups in a zigzag (W) arrangement to the silylenic center produces less polarity. In accordance with Hoffmann et al.’s statement [89], a molecule could be known as stable if its smallest vibrational frequency is at least 100 cm−1 and it reveals an enormous FMO energy difference (here ΔEHOMO-LUMO for s states and ΔΕSOMO-SOMO+1 for t ones) [86,87,88]. Now, vibrational analysis demonstrates that the scrutinized NHSis including 1-s, 2x-s, 3x-s, 1-t, 2x-t, and 3x-t, where x = NH, PH, AsH, O, S, and Se, are real minimums revealing positive frequency, and hence positive force constant (Table 2).

Table 2 The rounded frequency (in cm−1), FMO energy (in kJ/mol), and their energy differences (ΔEHOMO−LUMO for s states and ΔΕSOMO−SOMO+1 for t ones in kJ/mol) of the inspected singlet and triplet NHSis
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While fusion of two benzene rings kinetically stabilizes the s and t states of the corresponding silylenes, 1-s (ΔEHOMO-LUMO = 364.96 kJ/mol) and 1-t (ΔΕSOMO-SOMO+1 = 290.09 kJ/mol), in two other series by decreasing the electronegativity of x dopants and increasing their atomic radius, the kinetic stability is diminished from 393.46 for EWGs to 191.61 kJ/mol for EDGs (Table 2). Hence, amid s NHSis, the most kinetic stable structures are 2NH-s and 2O-s (393.38 and 393.46 kJ/mol), and the least stable ones are 3PH-s and 3AsH-s (378.04 and 379.50 kJ/mol), correspondingly, which they are stabilized considerably more than IIIs (351.33 kJ/mol). Between t NHSis, 2NH-t and 2O-t species to some extent accomplish the abovementioned conditions by Hoffmann et al., indicating the smallest vibrational frequency of 73.42 and 73.57 cm−1 besides ΔΕSOMO-SOMO+1 of 299.92 and 277.68 kJ/mol respectively. Between t NHSis, 3AsH-t species contravene the above conditions, emerging lower vibrational frequency of 66.96 cm−1 and a lower ΔΕSOMO-SOMO+1 (191.61 kJ/mol) than that of the distinguished by Hoffmann and co-workers. The band gap of all s and t NHSis is more than III-s (ΔEHOMO-LUMO = 351.33 kJ/mol) and III-t (ΔΕSOMO-SOMO+1 = 138.32 kJ/mol). Among these synthesized silylenes, the silylenic centers of I-s and II-s molecules completely enjoy from π-conjugation of two nitrogen groups adjacent to their silylenic centers, while III-s benefits only from the hyper-conjugation effect of four SiMe3 groups. This difference significantly is influenced on stability of them. Here, the optimized NHSis similar to III silylene suffer from lack of π-donating of the neighboring nitrogen groups to silylenic centers. The highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of s NHSis is considered dissimilar to the semi occupied molecular orbital (SOMO, SOMO + 1) of t NHSis (for instance, 2O-s and 2O-t silylenes, Fig. 2).

Fig. 2
figure 2

The FMO shapes of the selected 2O-s and 2O-t silylenes

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Replacement of two EWGs in chair organizations to the silylenic center of 2O-s progresses unbroken π-conjugation by employing 3σ2 or sp2—lone pair of the divalent center and reduces HOMO energy of 1-s from −520.13 to −581.25 kJ/mol in 2O-s and hence increases stability of HOMO of 2O-s structure. Undoubtedly, conjugation of the free electron pairs on EWGs with π-electrons of the fused double bond (C = C) in the silapyridine ring of 2O-s structure, decreases LUMO energy of 1-s from −155.28 to −187.80 kJ/mol in 2O-s (Fig. 2). Moreover, conjugation of the unpaired lone pairs on EWGs with the semi-filled 3pπ-orbital of the silylenic center of 2O-t diminishes the SOMO energy of 1-t from −322.10 to −354.89 kJ/mol in 2O-t and henceforth increases the stability of SOMO in 2O-t. Furthermore, replacement of two EWGs in chair positions to the silylenic center of the 2O-t structure adjusts π-conjugation by employing the half-captured s1p1 orbital of the silylenic center and free electrons of furanʼs oxygen and hence reduces SOMO + 1 energy of 1-t from −32.00 to −77.11 kJ/mol then increases stability of SOMO + 1 in 2O-t (Fig. 2). Delocalization of free electron pairs on EDGs and oxygen heteroatoms in the silapyridine ring not only leads to low leveling of HOMO and SOMO (e.g., from −520.13 in 1-s to −538.49 kJ/mol in 3AsH-s and from −322.10 in 1-t to −330.75 kJ/mol in 3AsH-t) but also delocalization in the fused furan rings changes LUMO and SOMO + 1 energy (e.g., from −155.28 in 1-s to −158.95 kJ/mol in 3AsH-s and from −32.00 in 1-t to −139.02 kJ/mol in 3AsH-t, Fig. 3).

Fig. 3
figure 3

The FMO shapes of the selected 3AsH-s and 3AsH-t silylenes

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Interestingly, the presence of two EWGs in the fused furan rings either in the “W” or “chair” positions of the silylenic center of the s and t NHSis engages π-cross conjugation (β-SOMO + 1 in 2O-t, Fig. 2) and the resulted ring current of the silapyridine ring has more than two EDGs. The polarity and polarizability of s NHSis with the substituted EWGs are different from those of s NHSis with the substituted EDGs and even the corresponding t ones. This observation implies that besides the inductive effect of more electronegative elements, by involving lone pairs of the substituted groups and silylenic centers in mesomeric effect, and π-conjugation polarity is decreased due to the increment of ring current with respect to chair arrangement to silylenic center (Table 2). Consistent with the DOS plots, every s NHSi displays more Eg value than its corresponding t NHSi so that the most value is estimated for the substituted EWG—singlet silylenes, and the least value is calculated for the substituted EDG—triplet silylenes. For example, 4.00 eV for 2O-s vs. 2.56 eV for 2O-t (Fig. 4), also 3.94 eV for 3AsH-s vs. 1.99 eV for 3AsH-t (Fig. 5).

Fig. 4
figure 4

The density of state (DOS) plots of the selected 2O-s and 2O-t silylenes

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Fig. 5
figure 5

The DOS plots of the selected 3AsH-s and 3AsH-t silylenes

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Dissimilar to nonpolar and symmetric (achiral) molecules, the NBO charge is not commonly dispersed over the fused furan and silapyridine rings, revealing the inductive effect along with the mesomeric effect of the substituted EWGs and EDGs, respectively. For instance, we are shown the calculated NBO charges for the 2O-s, 2O-t, 3AsH-s, and 3AsH-t silylenes (Figs. 6 and 7).

Fig. 6
figure 6

The NBO charges calculated for the selected 2O-s and 2O-t silylenes

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Fig. 7
figure 7

The NBO charges calculated for the selected 3AsH-s and 3AsH-t silylenes

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Regardless of the W (zigzag) and/or chair arrangement, the positive NBO charge is dispersed over hydrogen, carbon, silylenic center, and EDGs, while the negative NBO charge is dispersed over silapyridinicʼs nitrogen, carbon, and EWGs. The dispersed NBO charge qualitatively confirms that the substituted EWGs and EDGs in the difuranosilapyridine structure either in the “W” or “chair” positions of the silylenic center stabilize not only the s NHSis but also the t ones. The negative and positive NBO charges of the s and t NHSis indicate that these sites can be attacked more easily by electrophilic and nucleophilic regents, correspondingly. The electrostatic potential (ESP) maps qualitatively confirm blue color for positive charge, red color for negative charge, the electron cloud in the middle of two rings, and the dependency of NBO charge on electronegativity of EWGs and EDGs (Fig. 8).

Fig. 8
figure 8

The ESP maps and contours of the selected 2O-t and 3AsH-t silylenes. The red and blue regions on the scale bar indicate the lowest and the highest ESP values, respectively

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For enquiry of the substituent effects of EWGs and EDGs on global reactivity of their corresponding s and t NHSis, we are calculated N, ω, μ, η, S, and ΔNmax (Table 3).

Table 3 The calculated N, ω, μ, η, S, and ΔNmax (all in kJ/mol) of the inspected singlet and triplet NHSis
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A commonly found finding is the lower N, higher ω, higher absolute value of μ, higher η, and lower S of every s NHSis than every t congener. The positive ΔNmax index exhibits the positive charge capacity of every s and t NHSi, and here all species are expected electron acceptor in organic chemistry reactions or catalysts. Certainly, the five-membered furan ring contains lower basicity than the six-membered pyridine ring and other amines. The reduced basicity is strengthened by π-delocalization of the free electron on the oxygen atom of the furan ring. In fact, the smaller bond angle of the furan ring (about 12°) than the pyridine ring enlarges the p character of the bonding sp2 orbital and the s character of the nonbonding σ orbital. Here, the higher s character of the nonbonding σ orbital of either the doped EWGs or EDGs in either W or chair positions leads to lower N and higher ω of their s and t NHSis than in 1-s and 1-t structures. The Hirshfield charges, CFFs, atomic, and global indices are calculated to predict the chemical system’s reactive sites and character. Here, the Hirshfield charges, CFFs, and Dfs for silylenic centers of the selected singlet NHSis display dissimilar trends dependent on the electronegativity, size, and topology of the substituted heteroatoms of NH, PH, AsH, O, S, and Se, either in the “W (ortho)” or “chair (para)” position of the silylenic center, in the fused rings (Table 4).

Table 4 The calculated charges, CFF, and condensed dual descriptors for silylenic center of the selected singlet NHSis
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For example, the silylenic center of the 2NH-s species shows the most nucleophilicity via the highest f − (−0.3889 e), the lowest f + (−0.1241 e), and the most positive value of Df (+ 0.2649 e) between NHSis, while the silylenic center of the 3AsH-s species shows the most electrophilicity via the lowest f − (−0.1611 e), the highest f + (−0.5044 e), and the most negative value of Df (-0.3433 e) between NHSis. Comparatively, at the level of computation, the IP and EA for benzene (a reference molecule) have been reported to be 889.69 and −66.51 kJ/mol, respectively [90]. A closed look at 1-s and the substituted NHSis (2x-s and 3x-s) shows that the electrons are more and less binded than those of benzene, respectively (Table 5).

Table 5 The calculated Ε values for neutral (N), cation (N − 1), and anion (N + 1) states (in hartree), IP = E (N − 1) − E (N) and EA = E (N + 1) − E (N) (in kJ/mol) of the selected singlet NHSis
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Interestingly, the 1-s species shows the most positive value of IP and EA (691.44 and 303.75 kJ/mol), then the 2NH-s and 3NH-s isomers show the most positive value of IP and EA (361.00 and 50.49 kJ/mol, respectively), while the 3AsH-s species shows the most negative value of EA (−170.42 kJ/mol) between NHSis. Hence, substituent effects compete with the aromaticity of NHSis because substituentsʼ interaction with the π-system decreases degree the of π-electron delocalization.

Conclusion

To reach for novel s and t NHSis, we have studied electronic effects on structural, thermodynamic, and kinetic factors of the fused dibenzo and difuranosilapyridine-4-ylidenes. To this end, three series structures (from 1-s to 3x-t; x = NH, PH, AsH, O, S, and Se) are compared and contrasted with some of the synthesized silylenes using DFT. Every s NHSi exhibits more polarity, lower polarizability, more positive frequency, and higher ΔΕHOMO-LUMO than its corresponding t NHSi; yet ΔΕHOMO-LUMO of them is more than III-s and III-t. In other words, all silylenes substituted by EWGs and EDGs display more stability than III, so that the ΔEs-t and ΔΕHOMO-LUMO ranges are changed from 193.66 and 379.50 kJ/mol for 3AsH to 215.10 and 393.46 kJ/mol for 2O-s vs. 138.48 and 351.33 kJ/mol for III-s, respectively. The ESP contour maps qualitatively confirm the distributed NBO atomic charge and determine nucleophilic and electrophilic sites. Moreover, s silylenes show lower nucleophilicity (N), higher electrophilicity (ω), chemical potential (μ), and global hardness (η) than their related t congeners. The fused furan NHSis (either s or t ones) reveal lower N and higher ω than 1-s and 1-t structures on account of the inductive effect and mesomeric effect of the EWGs and EDGs on the completed σ2 orbital and 3pπ2 orbital of their silylenic centers. Indeed, the stability and electronic properties of s and t NHSis are considerably dependent on the electronegativity and radius of the substituted groups. We hope for experimental investigations that substitute the different heteroatoms in two fused furan silapyridines either the “W” or “chair” position of the silylenic center with the purpose of stabilizing not only the s silylenes but also the t congeners. Based on the Hirshfield charge, CFF, and Df results, the silylenic center of the 2NH-s species shows the highest nucleophilicity, whereas the silylenic center of the 3AsH-s species shows the highest electrophilicity. A close look at 1-s and the substituted NHSis (2x-s and 3x-s) shows that the electrons are more and less binded than benzene.