3.1. Stabilization of ptC
The cyclopropene molecule, [C
], 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
). 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
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
structure of C
are shown in Figure 2
. On going from ttC
, one of the
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
acceptor ligands or the removal of the lone pair of electrons to stabilize the ptC
]. Thus, in the dicationic species [C
, the electronic charge on the central carbon is expected to reduce and, hence, stabilize the system. The molecular orbitals of the [C
) clearly show the reduction in the natural electronic charge on the central carbon by delocalization.
The saturated analogue cyclopropane, C
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
]. To this end, spiropentadiene C
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
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
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
to −41.76 for ptC
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
]. In the case of ptC
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.
3.2. 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
, C, Si, Ge, N
, and As
) (Figure 1
). For example, the model cyclopropane systems can be expressed as [XC
(X = B, Al, and Ga), [XC
] (X = C, Si, and Ge), and [XC
(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, () 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.,
), 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 [XCH] (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 [XCH] (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 [XCH] (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 [XCH] spiro compounds, the ttXs were either transition states or higher order saddle points except for [GaCH] for which the ttX stationary point structure could not be obtained. For the group 13 compounds, the ptXs structures of [XCH for X = B and Ga were the minima, while, for X = Al, it was a transition state. In the other [XCH] (X = hetero-atom) spiro compounds, the ptXs structures were transition states (TSs) or higher order saddle points.
In the complementary saturated spiropentane-type [XCH] 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.
3.3. 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 (
) 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
. The potential energy profile for the stereomutation in XC
systems via ptX
TSs is given in Figure 3
a. 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
systems where X = group 13 elements, (i.e., B
, and Ga
) the ttX
s are the TSs that connect the minima ptX
s, and thus the stereomutation here is ptX
. The stereomutation barrier for X = Al
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
] were found to be higher order saddle points except for X = Al
where the ptX
is a transition state leading to stereomutation.