Stereomutation in Tetracoordinate Centers via Stabilization of Planar Tetracoordinated Systems

: The quest for stabilizing planar forms of tetracoordinate carbon started ﬁve decades ago and intends to achieve interconversion between [ R ]- and [ S ]-stereoisomers without breaking covalent bonds. Several strategies are successful in making the planar tetracoordinate form a minimum on its potential energy surface. However, the ﬁrst examples of systems where stereomutation is possible were reported only recently. In this study, the possibility of neutral and dications of simple hydrocarbons (cyclopentane, cyclopentene, spiropentane, and spiropentadiene) and their counterparts with the central carbon atom replaced by elements from groups 13, 14, and 15 are explored using ab initio MP2 calculations. The energy difference between the tetrahedral and planar forms decreases from row II to row III or IV substituents. Additionally, aromaticity involving the delocalization of the lone pair on the central atom appears to help in further stabilizing the planar form compared to the tetrahedral form, especially for the row II substituents. We identiﬁed 11 systems where the tetrahedral state is a minimum on the potential energy surface, and the planar form is a transition state corresponding to stereomutation. Interestingly, the planar structures of three systems were found to be minimum, and the corresponding tetrahedral states were transition states. The energy proﬁles corresponding to such transitions involving both planar and tetrahedral states without the breaking of covalent bonds were examined. The systems showcased in this study and research in this direction are expected to realize molecules that experimentally exhibit stereomutation.


Introduction
The paradigm of the tetrahedral structure of tetracoordinated carbon centers (ttC) is powerful and uncontested [1,2]. However, designing molecules with unusual planar tetracoordinated carbon centers (ptC) has been an interesting area of research for about five decades. The availability of a lone pair of electrons on the central planar tetracoordinate carbon and electron deficient 3 centered-2 electron (3c-2e) bonds makes the system unstable. Hence, different approaches to stabilize the ptC have been used, and several molecules containing ptC have been reported [3].
The utilization of σ-donor and π-acceptor substituents helps in the stabilization of ptC by accepting the unfavorable electron density on the sp 2 hybridized C-atom and providing σ electron density to the electron deficient 3c-2e bonds, respectively [3,4]. The removal of the lone pair of electrons leading to the formation of a dicationic species also has been shown as a viable technique to stabilize the ptC center. Moreover, the implementation of small rings to the tetracoordinated C center-hence, making the system sterically rigidhas been a promising strategy for the stabilization of ptC [5][6][7].
Multiple efforts towards stabilizing the planar state, so that it can act as a transition state for the stereomutation process, have been futile. Monkhorst showed that the streomutation barrier (interconversion between stereoisomers without bond breaking) via a planar state is much higher as compared to the energy required for C-C bond breaking [46], which signifies the difficulty of the problem. Since then, scientists have attempted to attain a thermally accessible ptC for stereomutation. However, less results have been achieved as, for systems with stable ptC, the ttC was found to be a higher order saddle point or vice-versa.
Recently, Raghunathan et. al reported the first possible stereomutation via a thermally accessible ptX [47]. They used high level ab initio calculations, Born-Oppenheimer molecular dynamics studies using DFT, and classical dynamics to study the thermodynamic and kinetic factors corresponding to stereomutation. Moreover, they identified systems where both tetrahedral and planar forms are minima on their potential energy surface, and located a transition state that connects these two forms. The whole process happens without the breaking of any covalent bonds involving the central tetracoordinate atom.
In this paper, we endeavor to stabilize possible ptX's by exploiting the electronic and steric factors. A set of four model systems (C 3 H 4 , C 3 H 6 , C 5 H 4 , and C 5 H 8 ) were considered in this study. The model systems C 3 H 4 and C 5 H 4 were previously studied by Schleyer and co-workers [48]. The central C-atom was substituted by possible valence isoelectronic elements from group 13, 14, and 15 in order to isolate stable ptX's ( Figure 1). We used ab initio MP2 calculations to carefully design and showcase possible stereomutations in multiple systems.

Methods
Two classes of systems were considered in the present study to investigate the stability of a planar tetracoordinated system (ptX): (i) three-membered cyclic-and (ii) spiro[2,2]-type analogues ( Figure 1). The tetrahedral-tetracoordinated and the planar-tetracoordinated geometries (ttX and ptX) for the various systems were optimized at the MP2/cc-pVTZ level of theory [49,50]. The stationary points on the potential energy surface (PES) were characterized using frequency calculations at the same level. The transition states associated with the stereomutation process were connected to the respective minimum energy structures using the intrinsic reaction coordinate (IRC) analysis.
Higher-order saddle points were characterized as nth-order saddle points based on the number of imaginary frequencies obtained in the normal mode analysis. To examine the possible role of aromaticity in stabilizing planar states, the nuclear independent chemical shift (NICS) [51] values were calculated for ptC systems at the MP2/cc-pVTZ level of theory. A ghost atom was placed at the geometric center of the rings to calculate the isotropic magnetic shielding.
A negative NICS value indicates that the system is aromatic while a positive value is obtained for antiaromatic systems. NICS values have been shown to provide insights on the extent of aromatic stabilization in different classes of molecules. All the calculations were performed using the Gaussian16 software package [52]. The relative energies of the stationary points with respect to the tetrahedral structures, the number of imaginary frequencies (n im ), and important geometrical parameters for all the molecular systems investigated are given in Table 1, which are discussed in detail in the following sections. The relative energies of the stationary points with zero point energy correction are given in the Supplementary Materials. Table 1. Relative energies (∆E in kcal/mol), number of imaginary frequencies (n im ), geometric parameters (C-X bond lengths in Å) of the neutral and dicationic species of cyclopropene, spiropentadiene, cyclopropane, and spiropentane along with the skeletally substituted derivatives calculated at the MP2/cc-pVTZ level of theory. The relative energies reported here do not include zero-point energies.

Four Valence Electrons
Two Valence Electrons ttX ptX ttX ptX

Stabilization of ptC
The cyclopropene molecule, [C 3 H 4 ], in its tetrahedral form, is undoubtedly a minimum on the PES. However, the corresponding planar structure is a third-order saddle point and is ∼117 kcal/mol higher is energy as compared to the ttC (Table 1). In Table 1, a positive relative energy value of the planar form indicates destabilization compared to the tetrahedral form, and a negative value indicates that the planar form is more stable as compared to its tetrahedral counterpart. Previous studies attempted to stabilize this by using different strategies.
Just by removing two electrons (the lone pair on the central carbon), the ptC for the dicationic species [C 3 H 4 ] 2+ was found to be a minimum on the PES [48]. This phenomenon is understandable from the change in the electronic structure of the system. The molecular orbitals of the ttC and ptC structure of C 3 H 4 are shown in Figure 2. On going from ttC to ptC, one of the σ CC bond MOs is converted to a lone pair orbital, and this leaves only six electrons for four covalent bonds making the system unstable.
As explained in the introduction, one can expect the presence of π acceptor ligands or the removal of the lone pair of electrons to stabilize the ptC compounds [3]. Thus, in the dicationic species [C 3 H 4 ] 2+ , the electronic charge on the central carbon is expected to reduce and, hence, stabilize the system. The molecular orbitals of the [C 3 H 4 ] 2+ (Figure 2) clearly show the reduction in the natural electronic charge on the central carbon by delocalization.
The saturated analogue cyclopropane, C 3 H 6 also shows a similar trend. The ttC is a minimum, whereas the ptC is a second-order saddle point on the PES with an energy of ∼111 kcal/mol ( Table 1). The planar form of the dicationic counterpart of cyclopropane could not be optimized at the current level of theory, whereas the ttC is a second order saddle point on the PES.
Introducing mechanical strain by the formation of a cage-like structures around the central carbon have been shown to be effective in the stabilization of ptC [53][54][55][56]. To this end, spiropentadiene C 5 H 4 and its saturated analogue were then considered in the present study. The ptC geometry of the spiropentadiene was found to be a fourth-order saddle point on the PES as compared to the ttC minima. However, the energy difference between the planar and tetrahedral form was now reduced to ∼92.7 kcal/mol as compared to ∼117.4 kcal/mol in the case of cyclopropene (Table 1).
However, in the dicationic species of spiropentadiene, the ptC was found to be a minimum on the PES while the tetrahedral structure a higher order saddle point. The ptC was stabilized by ∼20 kcal/mol as compared to the ttC spiropentadiene. Similar to cyclopropane, the saturated ttC spiropentane was found to be a minimum whereas the ptC, which was a higher order saddle point. However, the removal of two electrons from spiropentane i.e., [C 5 H 4 ] 2+ led to the stabilization of the ptC, which is a minimum on the PES (Table 1). A comparison of the unsaturated and the saturated systems investigated above reveals that the stabilization of the ptC in the dications is due to the reduction of the electronic charge on the central carbon facilitated by electron delocalization in the rings. Moreover, the cyclopropene and spiropentadiene dications are cyclic conjugated systems with 4n + 2 π electrons with n = 0 and can be considered aromatic. From Figure 2, the possible aromatic stabilization of the dicationic species is reflected in the nature of the HOMO orbital. This resembles very closely the HOMO of the classic cyclopropyl cation system.
A similar effect is also observed in the planar form of the dicationic spiropentene molecule. Such an aromatic stabilization is deemed to be responsible for the extra stabilization of the planar as compared to the tetrahedral state upon removal of two electrons from cyclopentene. This is further examined by using NICS calculations. The computed NICS values at the geometric centers of the rings change from 11.28 for the ptC C 5 H 4 to −41.76 for ptC [C 5 H 4 ] 2+ clearly indicating the aromatic nature of the systems. The negative NICS value pointing to the aromatic nature of planar tetracoordinated systems have also been reported in literature [38,44,57]. In the case of ptC [C 3 H 4 ] 2+ system, the NICS value was found to be −45.96. The planar form of a neutral cyclopropene system leads to elongated CC bonds (∼1.83 Å) possibly due to anti-aromatic destabilization. Further investigations have concentrated on the effect of skeletal substitutions by atoms/ions isoelectronic to carbon to examine how this modulates the difference between the planar and tetrahedral forms, and to identify possible molecular models that exhibit stereomutation.

Heteroatom Substitution for the Stabilization of ptX
To identify stable model ptC systems, the central C-atoms of the saturated and unsaturated analogues of cyclopropane and spiropentane were substituted with different valence isoelectronic (four valence electrons) heteroatoms from Group 13, 14, and 15 (X = B − , Al − , Ga − , C, Si, Ge, N + , P + , and As + ) (Figure 1). For example, the model cyclopropane systems can be expressed as [XC 2 H 6 ] − (X = B, Al, and Ga), [XC 2 H 6 ] (X = C, Si, and Ge), and [XC 2 H 6 ] + (X = N, P, and As).
As seen above in the saturated and unsaturated analogues of cyclopropane and spiropentane molecules, here, as well the ttX geometries were found to be minima on the PES. However, the ptX geometries were either a transition state or a higher order saddle point. It was observed that on going down the group, the relative energies of the ptXs, ∆E (E ttX − E ptX ) decreased (B − → Al − , C → Si, N + → P + ) and then increased (Al − → Ga − , Si → Ge, P + → As + ) following a trend similar to their electronegativities.
The X-C bond length decreases when moving along a period and increases down the group (e.g. r B-C > r C-C > r N-C and r B-C < r Al-C < r Ga-C ), consistent with the change in the atomic radii, and the bond lengths indicate that the skeletal substitutions do not destabilize the three membered rings. The Wiberg bond index (WBI) [58] was also calculated for the different skeletally substituted systems (see Supplementary Materials). The WBI for most of the system indicates the presence of a stable X-C bond. However, in some systems, the bond index was found to be very low.
As noted above, the stabilization of the ptX can be achieved by reducing the electronic charge on the central atom (X). To this end, the electronic structure of the saturated and unsaturated analogues of cyclopropane and spiropentane derivatives with two valence electrons on the central atom were investigated. The ptX [XC 2 H 4 ] 2+ (X belongs to group 13 and 14, i.e., B − , Al − , Ga − , Si, and Ge) structures were found to a minima on the PES and their corresponding ttX were higher order saddle points. For X= B − and Ga − , the ttX structures could not be stabilized.
In contrast, the ptXs in [XC 2 H 4 ] 2+ (X = N + , P + , and As + ) were transition states with eigen vectors (for the imaginary frequency) corresponding to the X-C bond stretches that will lead to ring opening, which is not interesting in the context of this study. In the saturated analogues [XC 2 H 6 ] 2+ (X = B − , Al − , and Ga − ) the ptXs were minima on the PES, whereas the ttXs were transition states corresponding to stereomutation. However, in the group 14 and 15 analogues, both the ttX and ptX structures were unstable.
In the hetero-atom centered [XC 4 H 4 ] 2+ spiro compounds, the ttXs were either transition states or higher order saddle points except for [GaC 4 H 4 ] + for which the ttX stationary point structure could not be obtained. For the group 13 compounds, the ptXs structures of [XC 4 H 4 ] 2+ for X = B − and Ga − were the minima, while, for X = Al − , it was a transition state. In the other [XC 4 H 4 ] 2+ ( X = hetero-atom) spiro compounds, the ptXs structures were transition states (TSs) or higher order saddle points.
In the complementary saturated spiropentane-type [XC 4 H 8 ] 2+ systems, the ttXs were high energy saddle points, except for X = B − and N + where the ttX structures could not be optimized. In addition, the ptX geometries were also found to be transition states or higher order saddle points on the PES. This indicates the possibility of multiple systems where the tetrahedral state is a minimum and it can rotate around the central atom to go to an equivalent tetrahedral form via a planar transition state. Similarly, there are systems where the planar form is a minimum, and it can be converted to an identical planar form via the corresponding tetrahedral transition state. These aspects are addressed in the following section.

Stereomutation in Model Systems
To investigate possible stereomutation in the above systems, molecules where the ptX is a transition state connecting two isoenergic ttX minima or vice versa were considered. The IRC calculations were done to follow the normal mode corresponding to the transition state on either sides to connect to the respective minima.
The angle between the planes (φ) formed by the two three-membered rings were followed to account for the stereomutation event as it changes from 90°to 0°going from ttX to ptX. The potential energy profile for the stereomutation in XC 2 H 4 systems via ptX TSs is given in Figure 3a. The barriers for stereomutation were found to be 29.0, 49.5, 59.6, 75.2, and 80.6 kcal/mol for X = Al − , Si, Ge, P + , and As + , respectively. The stereomutation barrier increases on moving along a period and on going down the group.
In the saturated [XC 2 H 6 ] 2+ systems where X = group 13 elements, (i.e., B − , Al − , and Ga − ) the ttXs are the TSs that connect the minima ptXs, and thus the stereomutation here is ptX → ttX → ptX. The stereomutation barrier for X = Al − and Ga − is lower than X = B − . In addition, the spiropentene analogues were found to show similar features. The ptX were found to be a transition state whereas the ttX were minima on the PES. Moreover, the stereomutation barrier increases on moving down the group and along the period (Figure 4). In contrast, the saturated spiropentane i.e., ptX [XC 4 H 8 ] were found to be higher order saddle points except for X = Al − where the ptX is a transition state leading to stereomutation.

Conclusions
Five decades of research have resulted in significant progress in understanding the factors that stabilize the planar form of tetracoordinated centers, and some have been experimentally realized. The original objective of work in this area was to achieve stereomutation where the interconversion between [R]-and [S]-isomers of tetracoordinate tetrahedral centers via a planar state could be observed. Most of the molecular models proposed until recently effectively stabilize the planar state compared to the tetrahedral state. However, in these models, the tetrahedral state is destabilized or is a higher order saddle point precluding the possibility of stereomutation.
In the present study, we explored the possibility of stereomutation in simple systems containing a central tetracoordinate center isoelectronic to carbon. We demonstrated that the combination of introducing a three-membered ring, enabling aromatic stabilization, and heteroatom substitution is a viable strategy to modulate the energy difference between the planar and tetrahedral states of tetracoordinate systems. Aromaticity, assessed by molecular orbitals and NICS calculations, appears to stabilize the dicationic planar forms in the parent hydrocarbons. Introducing skeletal substitutions to the central carbon by isoelectronic species from rows III and IV of the periodic table effectively stabilizes the planar state. However, the effect of aromaticity is not crucial in this case.
We successfully demonstrated the identification of systems where stereomutation about a stereocenter is possible via a planar transition state without any bond dissociation. We hope that further work in this direction by improving the model systems and incorporating asymmetry in the central atom will result in the experimental realization of elusive systems.

Conflicts of Interest:
The authors declare no conflict of interest.

Abbreviations
The following abbreviations are used in this manuscript: ttC tetrahedral tetracoordinated carbon ptC planar tetracoordinated carbon ttX tetrahedral tetracoordinated system with X as the substituent ptX planar tetracoordinated system with X as the substituent PES potential energy surface IRC intrinsic reaction coordinate NICS nuclear independent chemical shift TS transition state