Pentacoordinate Carbon Atoms in a Ferrocene Dication Derivative—[Fe(Si₂-η⁵-C₅H₂)₂]²⁺

Abstract

Pentacoordinate carbon atoms are theoretically predicted here in a ferrocene dication derivative in the eclipsed-(1; $C_{2v}$), gauche-(2; $C_2$) and staggered-[Fe(Si${}_2$-${\eta }^5$-C${}_5$H${}_2$)${}_2$]${}^{2+}$(3; $C_{2h}$) forms for the first time. Energetically, the relative energy gaps for 2 and 3 range from −3.06 to 16.74 and −2.78 to 40.34 kJ mol${}^{-1}$, respectively, when compared to the singlet electronic state of 1 at different levels. The planar tetracoordinate carbon (ptC) atom in the ligand Si${}_2$C${}_5$H${}_2$ becomes a pentacoordinate carbon upon complexation. The ligand with a ptC atom was predicted to be both a thermodynamically and kinetically stable molecule by some of us in our earlier theoretical works. Natural bond orbital and adaptive natural density partitioning analyses confirm the pentacoordinate nature of carbon in these three complexes (1–3). Although they are hypothetical at the moment, they support the idea of “hypercoordinate metallocenes” within organometallic chemistry. Moreover, ab initio molecular dynamics simulations carried out at 298 K temperature for 2000 fs suggest that these molecules are kinetically stable.

1. Introduction

Ferrocene, Fe(${\eta }^5$-C${}_5$H${}_5$)${}_2$, is an important molecule that has been used over the last seven decades [1,2,3,4]. It opened a new avenue called organometallic chemistry, which has been continuously growing since 1951 [5,6,7,8,9]. Here, using Si${}_2$C${}_5$H${}_2$ as a ligand instead of cyclopentadienyl anion (C${}_5$H${}_5^{-}$), three ferrocene derivative dication structures are theoretically identified—eclipsed-(1; $C_{2v}$), gauche-(2; $C_2$), and staggered-[Fe(Si${}_2$-${\eta }^5$-C${}_5$H${}_2$)${}_2$]${}^{2+}$(3; $C_{2h}$)—that shows hypercoordinate nature (pentacoordination) to its one of the ligand carbon atoms (see Figure 1). Before complexation, the bare ligand contains a planar tetracoordinate carbon (ptC) atom [10,11,12,13,14,15,16]. In the last five decades, many molecules containing ptC atom have been theoretically predicted [17,18,19,20,21,22,23,24,25,26,27,28,29,30] because of the pioneering theoretical work of Hoffmann [10,31] and Schleyer [11,32], and some are experimentally realized [33,34,35,36,37]. All the structures (1–3) exhibit two pentacoordinate carbon atoms, each upon forming a complex with Fe${}^{2+}$. Carbon showing hypercoordinate behavior—either penta or hexa—is rare but not very new to chemists [38,39,40,41,42]. Non-planar pentacoordination to carbon has already been well established in systems such as CH${}_5^{+}$[38,43], CLi${}_5$[44], C(CH${}_3$)${}_5^{+}$ [45], [(Ph${}_3$PAu)${}_5$C]${}^{+}$[46], and Si${}_2$(CH${}_3$)${}_7^{+}$ [47]. Likewise, non-planar hexacoordination to carbon has been proven in CLi${}_6$ [44,48], [(Ph${}_3$PAu)${}_6$C]${}^{2+}$ [49], and C${}_6$(CH${}_3$)${}_6^{2+}$ [50,51]. Carbon atom having heptacoordination is theoretically predicted in CH${}_7^{3+}$ [52], [CTi${}_7$]${}^{2+}$ [53], and also in trophylium trication, C${}_7$H${}_7^{3+}$ [54]. The octacoordination of carbon atom was also theoretically established in carborane clusters [55] and CBe${}_8$H${}_{12}$ [56]. Through [Fe(Si${}_2$-${\eta }^5$-C${}_5$H${}_2$)${}_2$]${}^{2+}$, our aim is to open a new avenue within organometallic chemistry called “hypercoordinated metallocenes containing five bonds to carbon” [57,58,59,60].

Various isomers of Si${}_2$C${}_5$H${}_2$ have been theoretically identified by some of us in an earlier theoretical work and it was concluded that the molecule with a ptC atom, 2,7-disilatricyclo[4.1.0.0${}^{1,3}$]hept-2,4,6-trien-2,7-diyl, is the most stable structure thermodynamically [27]. The global minimum geometry of Si${}_2$C${}_5$H${}_2$ has been theoretically verified elsewhere through search algorithms [61]. The kinetic stability of the thermodynamically most stable isomer through appropriate dissociation pathways has been analyzed in detail recently [62]. It was proven theoretically that the global minimum isomer of Si${}_2$C${}_5$H${}_2$ with a ptC atom is not only thermodynamically stable but also kinetically stable [62]. Thus, in this work, new complexes using Si${}_2$C${}_5$H${}_2$ as a ligand with Fe(II) are theoretically characterized here. Optimized structures of eclipsed-, gauche-, and staggered-[Fe(Si${}_2$-${\eta }^5$-C${}_5$H${}_2$)${}_2$]${}^{2+}$obtained at the $\omega$B97X-D/def2-TZVP level of theory are shown in Figure 1a, Figure 1c, and Figure 1e, respectively. Like ferrocene, the oxidation state of Fe in all three different forms (1, 2, and 3) is +2 (i.e., Fe(II) [Ar] 3d${}^6$). However, the ligands (Si${}_2$C${}_5$H${}_2$) are neutral here with 6π electrons each. Nevertheless, these complexes do attain the 18-electron configuration or to put it in simpler terms, they do follow the effective atomic number (EAN) rule (EAN = 36; 24 electrons from Fe(II) and 12π electrons from the ligands) and attain the electron configuration of Kr.

2. Computational Details

All geometry optimization and frequency calculations were carried out using def2-TZVP basis sets [63]. Various density functionals were used such as B3LYP [64], TPSSh [65], M06-L [66], and $\omega$B97X-D [67]. Calculations were also carried out with empirical dispersion corrections (D3) [68] with Becke–Johnson damping (BJ) [69,70] (i.e., B3LYP-D3BJ, TPSSh-D3BJ) to observe the geometrical changes due to dispersion (van der Waals) interactions. Natural bond orbital analyses were conducted using $\omega$B97X-D functional to obtain the natural atomic charges and Wiberg bond indices (WBIs) [71]. Ab initio molecular dynamics (AIMD) simulations using the atom-centered density matrix propagation (ADMP) [72] method were also carried out to check the kinetic stability of these complexes. All calculations were carried out using the Gaussian program package [73].

3. Results and Discussion

The zero-point vibrational energy (ZPVE) corrected-relative energies and Gibbs free energies obtained for 1–3 at different levels for the singlet and quintet electronic states are shown in

Table 1. ZPVE-corrected relative energies ($\Delta E_0$) and thermally corrected Gibbs energies ($\Delta G_{298.15}$) of 2 and 3 relative to the singlet electronic state of 1 (${}^1{A}_1$) using def2-TZVP basis set ${}^a$.

	1 (Eclipsed)		2 (Gauche)				3 (Staggered)
	Quintet b		Singlet		Quintet		Singlet		Quintet
Functional	$\Delta {\mathit{E}}_{\mathbf{0}}$	$\Delta {\mathit{G}}_{\mathbf{298.15}}$	$\Delta {\mathit{E}}_{\mathbf{0}}$	$\Delta {\mathit{G}}_{\mathbf{298.15}}$	$\Delta {\mathit{E}}_{\mathbf{0}}$	$\Delta {\mathit{G}}_{\mathbf{298.15}}$	$\Delta {\mathit{E}}_{\mathbf{0}}$	$\Delta {\mathit{G}}_{\mathbf{298.15}}$	$\Delta {\mathit{E}}_{\mathbf{0}}$	$\Delta {\mathit{G}}_{\mathbf{298.15}}$
B3LYP	−29.14	−39.04	−2.34	−3.16	−36.36	−51.01	−2.47	−4.59	−39.25	−54.01
B3LYP-D3BJ	−7.90	−19.59	2.44	1.38	−13.04	−30.40	8.24	5.51	−2.91	−22.72
M06-L	94.58	82.77	16.74	16.75	88.72	73.84	40.34	37.89	85.93	69.80
TPSSh	95.60	82.17	13.30	12.57	89.24	72.20	30.78	28.14	86.90	69.16
TPSSh-D3BJ	118.33	108.34	13.54	13.53	113.96	95.88	32.29	31.16	112.57	93.01
$\omega$B97X-D	0.31	−4.17	−3.06	2.04	−5.11	−13.61	−2.78	−1.21	−7.82	−15.63

^a All values are in kJ mol⁻¹. ^b Transition state or second-order saddle-point at this level.

. It is noted here that calculations were carried out for the triplet electronic states of these complexes. However, they turned out to be lying above singlets and quartets and thus for brevity they are given in the supporting information (see Table S3 for details). Bonding pattern obtained for eclipsed conformer (1) through AdNDP analysis is shown in Figure 2.

3.1. Energetics

As far as relative stability is concerned among the three, different DFT functionals gave us different results (see Table 1). The quintet electronic state of the staggered (3) form is the most stable at the $\omega$B97X-D/def2-TZVP level. However, with the same def2-TZVP basis set, functionals such as M06-L, TPSSh, and TPSSh-D3BJ predict that the singlet electronic state of the eclipsed form (1) is the most stable. With the popular functional B3LYP, though we obtain the quintet of 3 as the most stable, adding empirical dispersion corrections on top of B3LYP (i.e, B3LYP-D3BJ) changes the result yet again because at the B3LYP-D3BJ/def2-TZVP level, the quintet of gauche-form (2) is the most stable. Like ferrocene, the relative energy gap (∼4 kJ mol${}^{-1}$) between staggered and eclipsed forms is quite small [8]. In the parent molecule, as per gas-phase calculations, the staggered form is a saddle-point (transition state) and the eclipsed form is a minimum [74]. In the derivatives studied here, all the three different forms in their singlet ground electronic state are minima at all levels. The quintet electronic states of staggered (3) and gauche (2) conformers are also minima whereas the eclipsed (1) conformer of quintet either turns out to be a transition-state or a second-order saddle-point at different levels. Our main motivation in this study is to analyze the bonding scenario and thus we leave this discussion with a caveat that various DFT functionals including the popular B3LYP underestimate the barrier-heights [75,76].

3.2. Bonding

Let us analyze the bonding scenario in these cations (1–3) as each isomer contains two pentacoordinate carbon atoms. The C-C bond length in 1 ($C_{2v}$) range from 1.42 to 1.47 Å (see Figure 1a), whereas in 2 ($C_2$) and 3 ($C_{2h}$) it varies from 1.41 to 1.46 Å (see Figure 1c,e). Compared to ferrocene [77], where the mean C-C bond length is equal to 1.431 Å, these bond lengths are slightly varied, which is reasonable due to the ionic character (dication) in these complexes apart from the presence of silicon atoms. Likewise, the Fe-C bond length in 1 range from 2.07 to 2.10 Å, whereas in 2 and 3 it varies from 2.07 to 2.11 Å and 2.07 to 2.12 Å, respectively. In ferrocene, the mean Fe-C bond length is equal to 2.059 Å and here they are slightly longer. The Si-C bond length connected to the pentacoordinate carbon is 1.98 Å in 1, 1.97 and 1.99 Å in 2, and 1.99 Å in 3, which reflects its single bond characteristics whereas the Si-C bond on the sides are shorter with a bond length of 1.79 Å in all the three forms. In principle, the isolated Si${}_2$C${}_5$H${}_2$ ligand almost behaves like a cyclopentadienyl anion (C${}_5$H${}_5^{-}$), with a slight exception that the former contains a 3center-2electron (3c-2e) $\sigma$ bond (see Figure 2) around the Si-C-Si region [61,62]. This is evidently seen even when it makes complexation with Fe(II).

3.3. Wiberg Bond Indices

The presence of pentacoordinate carbon atoms could be further justified with the WBIs calculated for 1, 2, and 3, in Figure 1b, Figure 1d, and Figure 1f, respectively. In all cases, the WBI values for Fe-C are in the range of 0.39 to 0.42. This indicates that they are indeed single bonds. The hypercoordinate C-Si WBI values in 1 and 3 are 0.40 and 0.38, respectively, whereas for 2 we obtained two values due to reduced symmetry and they are 0.37 and 0.41, respectively. All these values also reflect the single bond characteristics of these bonds. The Si-C WBI values in 1 to 3 are in the range of 0.71 to 0.70 showing single bond characteristics. WBI values for all C-C bond lengths are greater than one, which indicates resonance stabilization plus double bond characteristics. On the basis of these values, one could certainly conclude that the central carbon atoms are hypercoordinate (penta) in all the three forms. It is emphasized here that each hypercoordinate carbon obeys the octet-rule as the total WBI for each pentacoordinate carbon is 3.62 for 1 and 2, whereas it is 3.61 for 3. However, some of the bonds (Si-C and C-Fe) are electron-deficient bonds with fewer than two electrons as mentioned elsewhere in the example of C(CH${}_3$)${}_5^{+}$ [45].

3.4. AdNDP Analysis

To clarify the chemical bonding pattern further in these complexes, we carried out adaptive natural density partitioning (AdNDP) analysis [78,79] using the Multiwfn [80] program. For brevity, only the bonding patterns of the eclipsed conformer alone are shown here. In total, 66 valence electrons 1 are taken into account. Seven lone-pairs (LPs), four 2c-2e C-H bonds, ten 2c-2e C-C bonds, four 2c-2e C-Si bonds, two 3c-2e Si-C-Si $\sigma$ bonds, and six 19c-2e $d\pi$-$p\pi$ are shown in Figure 2. Among them, the latter are more important as they support the pentacoordinate nature of the central carbon atom. Though 1–3 are hypothetical examples at the moment, theoretically, these complexes support the idea of “hypercoordinate metallocenes” within organometallic chemistry.

3.5. MD Simulations

To verify the kinetic stability of the ferrocene derivatives (1–3), we have carried out ab initio molecular dynamics simulations using ADMP method [72]. These simulations are done at 298 K temperature and 1 atm pressure for 2000 fs time. For brevity, the time evolution of total energy for the eclipsed isomer 1 computed at the $\omega$B97XD/def2-TZVP level for 2000 fs time scale is shown in Figure 3. Similar plots for isomers 2 and 3 are shown in the supporting information. To clearly depict the alteration of the structure over the 2000 fs of time, snapshots at 400 fs interval have been added. Considering the low-energy gap among the three different forms, it is not surprising to see that the structure rotates quite freely and at the time of 1200 fs itself, one could notice a structure that is very close to the gauche-form (2). However, none of the structures broke altogether, which indicates that all these three different forms of [Fe(Si${}_2$-${\eta }^5$-C${}_5$H${}_2$)${}_2$]${}^{2+}$are kinetically stable.

4. Conclusions

In conclusion, three ferrocene derivatives (1–3) are theoretically identified here using DFT at different levels. All of them contain two pentacoordinate carbon atoms. NBO and AdNDP analyses confirm that they are indeed pentacoordinate carbons. Ab initio MD simulations carried out at 298 K temperature for 2000 fs assert that they are kinetically stable molecules. For each pentacoordinate carbon, one 3c-2e Si-C-Si $\sigma$-bond (total two for each molecule) and three 19c-2e $d\pi$-$p\pi$-bonds (total six for each molecule) exist and they follow the existing pattern of (2$\sigma$ + 6$\pi$)-dual aromaticity, which is a well-established pattern in ptC and hypercoordinate carbon molecules. Since the ligand here (Si${}_2$C${}_5$H${}_2$) contains a ptC atom before complexation, these results are surprising. Theoretically, this new class of molecules could be termed “hypercoordinate metallocenes”.