Exploiting the Aromatic Chameleon Character of Fulvenes for Computational Design of Baird-Aromatic Triplet Ground State Compounds

Due to the reversal in electron counts for aromaticity and antiaromaticity in the closed-shell singlet state (normally ground state, S0) and lowest * triplet state (T1 or T0), as given by Hückel’s and Baird’s rules, respectively, fulvenes are influenced by their substituents in the opposite manner in the T1 and S0 states. This effect is caused by a reversal in the dipole moment when going from S0 to T1 as fulvenes adapt to the difference in electron counts for aromaticity in various states; they are aromatic chameleons. Thus, a substituent pattern that enhances (reduces) fulvene aromaticity in S0 reduces (enhances) aromaticity in T1, allowing for rationalizations of the triplet state energies (ET) of substituted fulvenes. Through quantum chemical calculations we now assess which substituents and

: Aromatic resonance structures influencing the S0 and T1 states of pentafulvene resulting in an "aromatic chameleon" character.
The properties of substituted fulvenes have been the subject of numerous experimental and theoretical investigations. [1,15] As a consequence of the opposite polarities of fulvenes in their S0 and T1 states exocyclic substituents have opposite effects on the aromaticities in these states, and this impacts on a series of properties. For example, exocyclic substituents that enhance the contribution of the zwitterionic resonance structure in S0 with a Hückel-aromatic 6π-electron 5MR [16] will disfavor the zwitterionic resonance structure in T1 with a Baird-aromatic 4π-electron 5MR in T1. [17] Indeed, the difference between the S0 and the T1 state aromaticity was found to correlate with ET, [18] a relationship that can be useful for the design of functional molecules with tailored ET. Interestingly, a polarity reversal was also observed when going from the S0 state to the lowest singlet excited state (S1) of substituted fulvenes, [19] and it has been found that the substituent effects of the lowest excited states of cyclopentadienes and siloles, being cross-hyperconjugated analogues of fulvenes, can be rationalized by this model as well. [18]  Now, can the ET of fulvenes be tuned to such extent that the triplet state becomes the ground state, i.e., a T0 state? Such a reversal in the order between the lowest singlet and triplet states would imply that the substituted fulvene is dominated by the resonance structure having a cationic 5MR and a negatively charged exocyclic C atom ( Figure 2).
Previously it was found that 1,2,3,4-tetrachloro-6,6-dicyanofulvene has a calculated ET of 16.0 kcal/mol, significantly lower than that of the parent fulvene (36.8 kcal/mol). [17] Since both the parent and the pentachloro substituted cyclopentadienyl cations (Cp + and CpCl5 + , respectively) have T0 states according to EPR and photoionization spectroscopy, [20][21][22] a fulvene with an electronic structure dominated by a resonance structure with a cationic 5MR is likely to have a T0 state. However, it is known from experiments that the order of the lowest two states of cyclopentadienyl cations depends strongly on the substituents; while Cp + and CpCl5 + have T0 states, [20,21] the pentaphenyl cyclopentadienyl cation has an S0 state. [18] Indeed, the finding that Cp + has a T0 state is in line with it being a non-disjoint diradical, a species with the triplet state below the open-shell singlet state. [ 23 ] Several quantum chemical studies have also shown that Cp + is aromatic in its T0 state, [7,8,11,24,25] in accordance with Baird's rule. [6] In support of this last finding, the calculated aromatic stabilization energy of Cp + in its T0 state is 20.9 -23.2 kcal/mol, [7,25,26] only slightly lower than the 22.1 -28.8 kcal/mol for the cyclopentadienyl anion (Cp -) in its S0 state. [27,28] A D5h symmetric structure observed experimentally is further in line with an aromatic character of the triplet state Cp + . [21] Recently, several larger polycyclic and macrocyclic high-spin compounds which are influenced by Baird-aromaticity in their ground states have been generated, [29,30] and a fulvalene with Baird-aromatic character in its T0 state was designed computationally. [31] In our view it should be valuable to identify small triplet ground state compounds that can be synthesized easily, or alternatively, formed in one step from readily available precursor compounds. To probe if the ET of fulvenes can be tuned to an inverted ET, we first performed quantum chemical calculations of the parent (1) and 48 disubstituted fulvenes ( Figure 3).
We probed which two positions are the most important in tuning ET; the two 6-positions (X), the 2-and 5-positions (Y), or the 3-and 4-positions (Z)? The information from the disubstituted fulvenes provides the basis for design of further substituted fulvenes with very low and inverted ET. Finally, we explored computationally if a triplet ground state fulvenium cationic species can be generated by simple addition of an appropriate additive to a readily available and stable fulvene. Indeed, the calculations show that a fulvenium dication reached by diprotonation should have a T0 state and significant Baird-aromatic character.

Figure 3:
The parent fulvene and the set of disubstituted fulvenes, having either two X, Y or Z substituents, included in the present study.

Computational Methods
Optimized geometries and energies of the substituted fulvenes of Figure 3 in S0 and T1 were obtained using the M06-2X functional. [32] The bulk of these calculations was carried out with the 6-311+G(d,p) valence triple-zeta basis set of Pople and co-workers, [33] but for a limited set of fulvenes we also used the cc-pVTZ valence triple-zeta basis set of Dunning. [34] The nature of the optimized structure (minimum or saddle point) was probed through frequency calculations at the same level. All DFT calculations were performed using Gaussian 16 revision B.01. [35] The DFT calculations of the T1 states were performed with the unrestricted Kohn-Sham formalism. To place the results of the (U)M06-2X calculations on a more firm ground we also examined the ET of a few selected fulvenes through calculations with the G4 composite method [ 36 ] and through state-avareged CASPT2 calculations with three states using the atomic natural orbital (ANO-RCC-VDZP) basis set with a contraction [C, N, O, F/3s2p1d, S/4s3p1d, H/2s1p]. [37][38][39] These latter calculations were carried out with the Molcas 8 and OpenMolcas packages. [39] With regard to aromaticity, the magnitude is normally evaluated in terms of structural, magnetic, and energetic criteria. [40,41] In analogy with the earlier study of monoand disubstituted fulvenes in their S0 states by Krygowski and co-workers, [42,14] we used three readily accessible quantitative measures of aromaticity; the nucleus independent chemical shift (NICS), [43][44][45][46] the harmonic oscillator model of aromaticity (HOMA) [47][48]49] indices, and the aromatic fluctuation index (FLU). [50] To analyze the ring-currents, ACID plots have been computed at the M06-2X/6-311+G(d,p) level. [51] NICS values, taken as the negative of the out-of-plane of component of the NMR shielding tensors, were calculated using the gauge independent atomic orbital (GIAO) method [52] at the GIAO-(U)M06-2X/6-311+G(d,p) level 1.0 Å above the ring centers (NICS(1)zz). [53] For a few fulvenes, NICS-Z scans were performed as reported by Stanger, scanning from the ring centers to 5 Å above the ring planes with increments of 0.1 Å. [54,55] HOMA is a geometry based indicator of aromaticity, and takes a value of 1.0 for a perfectly aromatic system with all bond lengths equal to an ideal value (1.388 Å for CC bonds). [47][48][49] Gradually more negative NICS values, as well as HOMA values that approach 1.0, indicate higher aromaticity of the rings.
FLU was calculated at the M06-2X/6-311+G(d,p) level of theory and was computed using delocalization indices, δ(A,B), [56] with the expression: where A0  AN and the string = { 1 , 2 , … , } contains the ordered elements according to the connectivity of the N atoms in a ring or in a chosen circuit (FLU can be calculated for any arbitrary circuit in a given molecule). V(A) is defined as: and  is a simple function to make sure that the first term is always greater or equal to 1.
The FLU index was obtained with the ESI program. [57] The delocalization indices of Eq. 1 were calculated using the overlaps between occupied molecular orbitals in the atomic basins generated by the AIMAll program. [58] The ( , ) reference value of 1.389 e used for C-C bonds in FLU calculations corresponds to the ( , ) of benzene computed at the M06-2X/6-311+G(d,p) level of theory. FLU is close to 0 in aromatic species, and differs from it in non-aromatic ones. As an indicator of Hückel (low values) or Baird (high values) aromatic character, we use the γ descriptor defined as the absolute value of the FLU/FLU ratio. [59] To compute FLU and FLUβ, the same Eq. (1) was used but now considering only the α or β molecular spin orbitals and taking the ( , ) reference value in Eq. (1) as half the reference value used for non-spin split FLU calculations.

Results and Discussion
An important first question is if the planar T1 state structures always correspond to the lowest minimum in the T1 state of substituted fulvenes or if there can be fulvenes with the optimal T1 state structures having the CX2 plane twisted perpendicularly to the plane of the five-membered ring (5MR)? To resolve this issue we examined how the lowest two triplet states (T1 and T2) vary in energy with rotation about the exocyclic C=C bond in three fulvenes ( Figure 4); the parent fulvene (1), one with high ET (2) and one with low ET (3).
We subsequently explored the substituent effects on the T1 energies of the various disubstituted fulvenes of Figure 3. Based on the information gained we design fulvenes and fulvenium dications with T0 states.

Optimal triplet state structures of fulvenes:
Previously, we revealed a good agreement between the ET of substituted fulvenes at their planar structures calculated with (U)M06-2X and those calculated with CASPT2 at (U)M06-2X geometries. [17] A maximum deviation of 4.2 kcal/mol was found, yet, to further probe the quality of the (U)M06-2X computations we now performed state-averaged CASPT2/ANO-RCC-VDZP geometry optimizations in the S0, T1 and T2 states of three fulvenes 1 -3 (X = H, F, and CN; Table 1 and Figure 4). These calculations were performed with an active space of eight electrons in eight orbitals for 1 and 2, and ten electrons in ten orbitals for 3. For the planar structures of the three fulvenes the largest difference in the T1 state energies (ET) between CASPT2 and (U)M06-2X is 2.3 kcal/mol (Table 1). Moreover, CASPT2 geometry optimization brings no substantial change in the ET because the CASPT2 geometries of the planar 3 B2 state (T1 state) resemble the corresponding UM06-2X geometries ( Figure 4).  Rotation about the exocyclic C=C double bond should be more facile in T1 than in S0 as the exocyclic CC bond is elongated upon excitation. A fulvene with the CX2 moiety oriented perpendicularly to the 5MR could even be lower in energy than the planar T1 state structure. Yet, CASPT2 calculations reveal that for each of 1 -3, the planar structures of the T1 state (1 3 B; primarily a HOMO to LUMO excitation) are more stable than the twisted ones (Table 1). On the other hand, for 1 and 2 the T2 state (1 3 A; primarily a HOMO-1 to LUMO excitation) prefers the twisted structure over the planar one, while the T2 surface is shallow for 3. At planar structures the T2 states of the three fulvenes are 18 -22 kcal/mol above the T1 states, whereas at the perpendicularly twisted structures the T1 and T2 states are isoenergetic. Accordingly, the T1 and T2 states vary as shown in Figure 5.   Table 1).

Connection between the S0-T1 aromaticity difference and ET:
The changes in aromaticity when going from S0 to T1 were determined by ∆NICS (1) Figure 6). Indeed, a linear correlation between ET and ∆NICS(1)zz,ST is found (R 2 = 0.880), also when going to fulvenes with low ET (below ~20 kcal/mol). This extends our earlier similar observation for a smaller set of 6,6-disubstituted fulvenes with higher ET. [18]  In contrast, a poor correlation is observed between ET and HOMA (R 2 = 0.523, Figure 7). Better correlations are found for the subsets of X-and Y-substituted fulvenes, particularly for the X-substituted ones (R 2 = 0.949 and 0.601, respectively, Figure S2A and S2B), whereas there is no correlation for the Z-substituted fulvenes (R 2 = 0.006, Figure   S2C). The lack of correlation for the Z-substituted fulvenes is in part due to a larger steric repulsion between the two Z substituents in the T1 state than in the S0 state, a feature that stems from a marked influence by a T1 state resonance structure with a formal double bond between the two Z-substituted carbon atoms ( Figure 1). Additionally, the lack of correlation is also related to HOMO and LUMO since these orbitals have larger lobes at C2, C5 and C6 than at C3 and C4 (Figure 8).  (Table 2). For example, when two amino groups are moved from the X to the Y positions (fulvene 6 vs. 7) the ET changes from 54.8 to 19.9 kcal/mol. Fulvenes with small ET are generally obtained with electron-donating groups (EDGs) as Y or with electron-withdrawing groups (EWGs) as X. This is consistent with their aromatic chameleon feature ( Figure 1) because with EDGs as Y the cationic charge in the 5MR of the T1 state can be delocalized onto the substituents while with EWGs as X the negative charge on the exocyclic C atom can be delocalized to these groups. In line with this, when the two amino groups are moved from the X-to the Y-positions (fulvenes 6 vs.

7)
there is a simultaneous change in aromaticity in both the S0 and T1 states; the NICS(1,S0)zz value changes by +29.2 ppm to less aromatic while the NICS(1,T1)zz value changes by -27.4 ppm to more aromatic ( Table 2). Similar differences are found in the HOMA values of the two compounds in S0 and T1, respectively.   Triplet ground state fulvenes: As noted above 2,3,4,5-tetrachloro-6,6dicyanofulvene (15) has a calculated ET of ~16 kcal/mol. [17] Using the relationship between the electronic substituent effects, the S0 and T1 aromaticities, and ET we can now design fulvenes with much smaller and even inverted ET, i.e., ET < 0 kcal/mol (fulvenes with T0 states state. In further support, calculations with the high-level G4 composite method [36] gives a   because the total spin density at the 5MR of 18, excluding the two amino groups, is 1.10 e while it is 1.58 e in the 1,3-diaminoCp + (Figure 9). Yet, by comparing the spin density plots of 18 and 1,3-diaminoCp + , one still sees a strong resemblance between the two species. With regard to the geometries the CC bond lengths of the 5MRs are rather similar in the triplet states of 18 and 1,3-diaminoCp + with the largest deviation being in one bond that differs in length by 0.03 Å (see Figure S5). Noteworthy, the 1,3-diaminocyclopentadiene moiety in the triplet ground state fulvalene of Solel and Kozuch is influenced by Baird-aromaticity, [31] and it resembles geometrically the 5MR of 18. Yet, a stark difference between 18 and 1,3-diaminoCp + is the order of the lowest singlet and triplet states because 1,3-diaminoCp + has an S0 state with ET = 28.5 kcal/mol and GT = 26.2 kcal/mol. The cause for this difference is a much stronger -conjugative interaction between the amino groups and the central Cp + ring in the singlet state of 1,3-diaminoCp + than in 18 as revealed by C-N bond lengths of 1.313 and 1.390 Å, respectively ( Figure S5). [60] Although there is a stark difference in the order of the singlet and triplet states of 18    is likely challenging. Moreover, full amino-substitution at the 5MR, which might be easier to achieve synthetically, leads to 2,3,4,5-tetraamino-6,6-dicyanofulvene (24) having an ET at M06-2X/6-311+G(d,p) level of 10.4 kcal/mol and a GT of 8.0 kcal/mol, a result from steric congestion turning the four amino groups out of conjugation with the 5MR. A different approach to generate a fulvene with a T0 state is needed. Here, we propose to increase the electron withdrawal by the EWGs (cyano groups) at the exocyclic position through protonation, and simultaneously utilize chloro substituents as EDGs at the 5MR.
With this approach one can utilize protonation at the N atoms of the cyano groups of 2,3,4,5tetrachloro-6,6-dicyanofulvene (15(H) + , 15(H)2 2+ ), a fulvene which is stable at ambient conditions and readily available. [17] Although neutral 6,6-dicyanofulvenes (DCFs) have rather low-lying triplet states, [ 61 , 62 ] 2+ in their triplet states is less apparent ( Figure   11). The ACID plot for 3 CpCl5 + is consistent with that by Sander and co-workers, who calculated a NICS(0) value of -2.4 ppm, indicating moderate aromatic character. [  (0.0215) is equally aromatic as that of CpCl5 + (0.0216), while the FLU value of 3 Cp + (0.0084) is lower, again indicating that 3 Cp + is more triplet state Baird-aromatic than 3 CpCl5 + . A similar observation is made when regarding the geometric aromaticity index HOMA ( Figure 12). An analysis shows that 3 CpCl5 + has extensive -electron donation from the Cl lone pairs into the ring, as well as delocalization of the excess spin from the ring onto the Cl atoms, leading to a weakened cyclic (Baird-aromatic) -electron delocalization within the 5MR (see Figure S4). Now, a high value of  for the five-membered ring of HOMA and FLU in the sense that 15(H2) 2+ shows a slightly more negative value (-13.8 ppm) than 18 (-12.5 ppm), both in their T0 states. at M06-2X/6-311+G(d,p) level. HOMA values given in red inside the rings.

Conclusions
We have revealed strong correlations between the changes in aromaticity of fulvene derivatives when going from the S0 to the T1 state and the corresponding energy differences