Azaboracyclooctatetraenes reveal that the different aspects of triplet state Baird-aromaticity are nothing but different

The Baird-aromaticity of BN/CC cyclooctatetraene isosteres (azaboracyclooctatetraenes) in their lowest triplet states (T 1 ) has been explored through computations of various aromaticity indices that describe the different aspects of aromaticity (magnetic, electronic, energetic and geometric). While cyclooctatetraene ( COT ) is aromatic in its T 1 state following Baird's 4 n rule, we now reveal that the degrees of Baird-aromaticity of its BN/CC isosteres vary with aromaticity aspect considered. The thermodynamically most stable octag-onal B 4 N 4 H 8 isomer, having an alternating B and N pattern (borazocine, B 4 N 4 COT-A ), is only weakly aromatic or nonaromatic in T 1 according to energetic and electronic indices, while magnetic descriptors suggest it to have about two thirds the Baird-aromaticity of T 1 state COT ( 3 COT ). The extent of Baird-aromaticity of intermediate BN/CC isosteres also varies markedly with aromaticity aspect considered


| INTRODUCTION
][11][12] Yet, features of the magnetically induced current densities of the two molecules (a diatropic ring current in benzene while local circulations at the N atoms in borazine) can be related via a set of intermediate current densities computed for model molecules with non-integer nuclear charges in between those of C, B and N. [10] Furthermore, a recent analysis of the experimental electron density reveals an island-like electron delocalization at the N atoms, leading to only weak aromatic character, [13] in line with conclusions based on computed electronic indices. [11,14,15]Interestingly, the index of deviation from aromaticity (IDA), which measures the degree of electron density polarization, estimated borazine in S 0 to be even antiaromatic. [11]n contrast, geometric and energetic indices suggest that it still exhibits a degree of aromaticity. [7,8,12][18][19][20][21] Herein we explore if azabora[4n]annulenes in their T 1 states also exhibit extensive variations with regard to their potential Baird-aromaticity when evaluated based on the different aromaticity aspects.
The smallest member, 1,3,2,4-diazadiboretidine (Chart 1), first synthesized in the 1960s, [22][23][24] exhibits no T 1 state Baird-aromatic character, although it was noted that a D 2h symmetric transition state structure has a negative NICS value and a diatropic ring current (electronic indices, in contrast, suggested a nonaromatic character of this structure). [25]Yet, as CBD in its T 1 state has a moderate Baird-aromaticity [26][27][28] one may assume that 1,3,2,4-diazadiboretidine is not an ideal molecule for a test on Baird-aromaticity of azabora[4n]annulenes in their T 1 states.[31] Hence, we argue that borazocine (Chart 1), octahydro-1,3,5,7,2,4,6,8-tetraazatetraborocine (B 4 N 4 COT-A), also first synthesized in the 1960s, [24,32,33] is a more suitable scaffold for exploration of the potential Baird-aromaticity in azabora[4n]annulenes.The potential Hückel antiaromaticity of B 4 N 4 COT-A in S 0 and the aromaticity of the dianion have earlier been explored computationally, [34,35] and the results for the S 0 state dianion are noteworthy as they can be related to the T 1 state of the neutral species.Indeed, based on valence bond (VB) theory 3 B 4 N 4 COT-A could be more Baird-aromatic than borazine is Hückel-aromatic in S 0 because the T 1 state of B 4 N 4 COT-A requires structures with two atoms with one unpaired same-spin π-electron each (Figure 1).This requires transfer of an electron from an N atom to a B atom, and that VB-structures such as I -III make significant contributions while structures such as IV -VI contribute much less (Figure 1B).However, as becomes clear through our study, the extent of Baird-aromaticity varies extensively with aromaticity aspect considered.
Interestingly, large differences between the magnetic and energetic aromaticity aspects have earlier been observed for the 10π-electron systems (N 6 H 6 ) 2+ and C 2 N 4 H 6 as these were about as aromatic as benzene according to magnetic criteria but much less when based on electronic ones. [36]It was concluded that "[a]romatic compounds exhibit ring current induced magnetic shielding, but the reverse conclusion that ring current induced magnetic shielding identifies aromaticity is not justified." [36]Indeed, it has been shown mathematically that there is no explicit connection between a magnetically induced ring current and electron delocalization. [37] number of questions now emerge when considering BN/CC COT isosteres in their T 1 states.If there is a variation in their Baird-aromaticity with regard to the aromaticity aspect considered, can this variation be rationalized?Are there structural factors that contribute to strong Baird-aromaticity in T 1 and others that contribute to the opposite?Besides COT and two B 4 N 4 H 8 isomers (Group 1, Figure 2), all possible isomers of BNC 6 H 8 , with eight-membered rings with tricoordinate B, N and C atoms (Group 2), were investigated.We also examined a selection of B 2 N 2 C 4 H 8 isomers by which the importance of various structural features can be tested (Group 3), and one B 3 N 3 C 2 H 8 isomer which corresponds to B 4 N 4 COT-A except for one CC segment (Group 4).Through systematic study, we can conclude that the magnetic aspect of Baird-aromaticity in these molecules seldom agrees with the other aspects of Baird-aromaticity, resembling what has earlier been observed for the Hückelaromaticity in the S 0 states of (N 6 H 6 ) 2+ and C 2 N 4 H 6. [36]

| COMPUTATIONAL METHODS
Geometry optimizations were carried out with the Gaussian 16 [38] program package using different DFT functionals [39][40][41][42][43][44][45] and the 6-311G(d,p) valence triple-zeta basis set of Pople and co-workers. [46]Restricted and unrestricted Kohn-Sham DFT were used for, respectively, the closed-shell singlet ground state and the lowest ππ* triplet state.All wave functions were found to be stable, and the character of the stationary points as minima or saddle-points was checked through frequency calculations.The T 1 state geometries were optimized using either UBLYP, UB3LYP, UCAM-B3LYP, UOLYP and UωB97X-D, and the performances of these functionals were evaluated based on single-point UCCSD(T)/cc-pVTZ energies calculated at the optimized UDFT geometries.
The aromaticity analysis was based on computations at the UB3LYP/6-311G(d,p) level and applied a variety of indices and approaches: the electron density of delocalized bond (EDDB) function, [47,48] nucleus independent chemical shifts (NICS), [49,50] anisotropy of induced current density (ACID), [51] multicenter electron sharing indices (MCI), [52,53] the aromatic fluctuation index (FLU), [54] geometry-based harmonic oscillator model of aromaticity (HOMA) [55] and the isomerization stabilization energy (ISE) approach. [31,56]For HOMA the recently developed parameters for BN bonds (α = 72.03and R opt = 1.402Å) [55] have been used.[59][60] The external magnetic field was applied perpendicularly to the molecular plane.The current density maps were plotted 1 bohr above the ring plane by setting clockwise/counterclockwise circulations to represent diatropic/paratropic current densities.The bond current strengths were obtained by numerical integration of the current densities passing through a rectangle bisecting the bond center.The integration rectangle starts from the ring center and extends 5 bohr from the bond center outside the molecular ring.This rectangle spreads 5 bohr above and 5 bohr below the ring plane.Ring current strengths (J, in nA T -1 ) were calculated as the average of all bonds in the given ring.
The overarching aim of our study is to explore the T 1 state Baird-aromaticity of various BN/CC isosteres of COT using different types of indices and to determine the cause of the differences observed.We split the analysis into three sections; (i) a first comparison between COT and the two B 4 N 4 H 8 isomers in their T 1 states, followed by (ii) an analysis of the Baird-aromatic character of the T 1 states of azaboraCOTs with partial CC-to-BN exchange, and finally, (iii) a detailed exploration of the magnetically induced current densities of S 0 state borazine and selected T 1 state azaboraCOTs in order to identify causes for the difference in the aromaticity assessments from magnetic vs. electronic and energetic indices.The results discussed come from calculations with the UB3LYP functional as this DFT functional provided the best geometries when benchmarked with single-point UCCSD(T)/cc-pVTZ energies calculated at optimized UDFT T 1 state geometries (see the Supporting Information, p. 3).All azaboraCOTs investigated, except one, are planar in their T 1 states.The exception is 3 B 3 N 3 C 2 COT which adopts two different puckered conformers in T 1 .For the other azaboraCOTs, geometry optimizations always lead to fully planar conformers, i.e., only higher-energy conformers with puckered eightmembered rings were found on the T 1 potential energy surfaces (PESs).Yet, azaboraCOTs with E,Z,Z,Z configurations have puckered minima in their S 0 states, but interestingly, in T 1 they either rearrange to the planar all-Z isomers or remain puckered and of higher energy (see Supporting Information, p. 6).
3 COT versus two 3 B 4 N 4 COT isomers: In the S 0 state, B 4 N 4 COT-A exists in only one conformer, a planar D 4h symmetric structure with B-N bonds of 1.430 Å, in contrast to the highly puckered structure of two borazocines earlier determined crystallographically, which have tBu substituents at the N and either isothiocyanate or methyl substituents at the B atoms [33,61] (see Supporting Information, p. 8).Isomer B 4 N 4 COT-B in S 0 exists in two conformers, both of which puckered; one C 2 symmetric of low energy and a second with no symmetry and a relative energy of 31 kcal/mol (Table S4).In T 1 , on the other hand, both isomers adopt a planar and highly symmetric structure (Figure 3A), similar to 3 COT, yet 3 B 4 N 4 COT-B is 128.7 kcal/mol higher in energy than 3 B 4 N 4 COT-A.
Although the repulsion between electron pairs on adjacent N atoms and between holes on adjacent B atoms in character, it will not increase the Baird-aromaticity as there can be no N=N and B=B double bonds as required for the second Kekulé-type resonance structure.Another notable feature is the much higher triplet energies (E(T 1 )) of B 4 N 4 COT-A and B 4 N 4 COT-B than of COT (Table 1), a feature that indicates less aromatic stabilization in the T 1 states of the two B 4 N 4 H 8 isomers than that of 3 COT (in S 0 , the three molecules are either nonaromatic or weakly antiaromatic, see Table S5).Normal B-N single and double bond lengths are, respectively, 1.564 and 1.363 Å, [7] which means that the B-N bonds of 3 B 4 N 4 COT-A (all 1.442 Å, Figure 3A) are intermediate between single and double bonds.In 3 B 4 N 4 COT-B the B-N bonds are just slightly longer than in the more stable isomer.The geometry-based HOMA values of 3 COT, 3 B 4 N 4 COT-A and 3 B 4 N 4 COT-B are 0.944, 0.884 and 0.608, respectively, indicating a similar geometric aromaticity of 3 B 4 N 4 COT-A as of borazine in S 0 , but a more modest aromaticity of 3 B 4 N 4 COT-B.However, a caveat with the usage of HOMA for Bairdaromaticity assessments is the lack of reference bond lengths and parameters for species in electronically excited states as it was developed for the S 0 state.Therefore, as an additional geometric-energetic aromaticity indicator, we considered the lowest vibrational modes, which for each of the three molecules is an out-of-plane vibration.The energy penalty for distorting a strongly aromatic compound out of planarity is normally significant.Indeed, 3 COT has an out-of-plane vibration at 146 cm -1 while the corresponding vibrations for 3 B 4 N 4 COT-A and 3 B 4 N 4 COT-B are, respectively, 60 and 68 cm -1 .Yet, for benzene and borazine in S 0 the out-ofplane vibrations occur at much higher values of 412 and 291 cm -1 (they are also the lowest vibrations for these molecules), but when going to larger cycles there is a gradual increase in angle strain which renders the PESs for puckering (and aromaticity loss) more shallow.This becomes clear from the tropylium cation (Trp + ) and COT dication (COT 2+ ) in their Hückel-aromatic S 0 states, as these species have (much) smaller out-of-plane vibrational frequencies (222 and 35 cm -1 , respectively) than benzene.Indeed, it is interesting that 3 COT has a higher out-of-plane vibrational frequency than COT 2+ , indicating a larger energy penalty for out-of-plane deformations in the former (and a higher degree of aromaticity).Thus, it becomes apparent that 3 B 4 N 4 COT-A and 3 B 4 N 4 COT-B have slightly stronger preferences for planarity than COT 2+ which is generally considered as Hückel-aromatic.
Next, we analyzed the magnetic aromaticity aspect.The NICS(1) zz values of 3 COT, 3 B 4 N 4 COT-A and 3 B 4 N 4 COT-B are, respectively, -32.4,-19.3 and -16.3, suggesting that 3 COT is the most Baird-aromatic but that both B 4 N 4 COT isomers in their T 1 states are significantly aromatic.One may argue that the negative NICS value of B 4 N 4 COT-A stems from local circulations at the N atoms, resembling what has been observed for the cyclic (HF) 3 complex where local circulations at the three HF molecules lead to a negative NICS in the ring center (-2.94) [62] and a false "aromaticity." [63]However, the ACID plots of 3 COT, 3 B 4 N 4 COT-A and 3 B 4 N 4 COT-B reveal that all three compounds have true diatropic ring currents (Figure 3B), motivating the classification of the two B 4 N 4 H 8 isomers as Baird-aromatic based on the magnetic aspect.In contrast, borazine in S 0 has a NICS(1) zz value of merely -5.9 (Table 2), and the current density plot reveals a significantly weakened ring current and localized circulations at the three N atoms. [10]Here it should be noted that the borazocine dianion in S 0 earlier was observed to exhibit a strong diatropic ring current, [34] and with two electrons in both the HOMO and LUMO of the neutral borazocine, the Hückel aromaticity of the dianion can be related to the Bairdaromaticity of 3 B 4 N 4 COT-A having one electron in each of these two orbitals.
The isomerization stabilization energies (ISEs) of 3 COT, 3 B 4 N 4 COT-A and 3 B 4 N 4 COT-B were also calculated (Figure 3D).Whereas 3 COT is clearly Bairdaromatic with a negative ISE similar to the value earlier reported by Zhu, An and Schleyer (-15.6 kcal/mol), [31] 3 B 4 N 4 COT-A behaves as a non-aromatic species since its two ISE values are close to zero.Interestingly, the ISE values of the latter are even smaller than those of borazine in S 0 (Tables 1 and 2).The ISE values of  [64] Here, it is notable that the second ISE value of 3 B 4 N 4 COT-B is low and representative of nonaromaticity.The fourth aromaticity aspect, the electronic aspect, reinforces the interpretation of the ISE values.The FLU values of all molecules are non-zero but it is more than 200 times larger for 3 B 4 N 4 COT-A than for 3 COT, while in case of 3 B 4 N 4 COT-B it is 50 times larger than that of 3 COT.Thus, FLU indicates that the two isomers of On the other hand, 3 B 4 N 4 COT-A exhibits more extensive delocalization than borazine in S 0 where 3.44 π-electrons (57%) are delocalized over the hexagon, which gives support to the qualitative hypothesis put forth above that borazocine can be more Baird-aromatic in T 1 than borazine is Hückel-aromatic in S 0 .Still, the extent of π-electron delocalization is lower than that of 3 COT.Finally, one can also observe visually that the spin density is extensively delocalized in 3 B 4 N 4 COT-A (Figure 3C), yet slightly less so than in 3 COT if one considers plots with gradually larger spin density isovalues (Table S6).
In summary, while 3 COT indisputably Baird-aromatic according to each of the four aromaticity aspects (magnetic, geometric, energetic and electronic) this is not the case for the two 3 B 4 N 4 COT species because they are only unquestionably Baird-aromatic according to the magnetic aspect.A question is at which azaboraCOTs the split between the various aspects of T 1 state Baird-aromaticity emerge as one goes from 3 COT to 3 B 4 N 4 COT?
Intermediate azabora COTs in their T 1 states: We now successively replace two C atoms of COT with one B and one N atom (Groups 2 -4, Figure 2).All possible BNC 6 H 8 isomers with eight-membered rings ( 3 1,2-BNC 6 COT, 3 1,3-BNC 6 COT, 3 1,4-BNC 6 COT and ), and finally one 3 B 3 N 3 C 2 H 8 isomer, were examined.While there can be dative bonding in the S 0 states of 1,2-and 1,4-BNC 6 COT leading to zwitterionic resonance structures, such structures are the only closed-shell structures that can be formulated for 1,3-and 1,5-BNC 6 COT as they are mesoionic, [65][66][67] i.e., negative and positive charges must either be placed on the B and N atoms or at adjacent C atoms (Figure S2).Also, B 2 N 2 C 4 COT-F is a mesoionic compound.
Of the four BNC 6 COT isomers, 1,2-BNC 6 COT is the thermodynamically most stable in both S 0 and T 1 .The second most stable in S 0 is 1,4-BNC 6 COT at a relative energy of 29.4 kcal/mol, while this isomer is the least stable in the T 1 state 30.6 kcal/mol above 3 1,2-BNC 6 COT (Table S8).Clearly, the possibility for a direct BN π-dative bond in 1,2-BNC 6 COT is strongly stabilizing in S 0 (Figure S2), similar to the situation for the three azaborines (BNC 4 H 6 ) in S 0 where the 1,2-azaborine is the most stable isomer. [68]In contrast, the 1,3-and 1,5-BNC 6 COT isomers, being mesoionic, are markedly destabilized in this state.In T 1 , on the other hand, they are of lower relative energy than 1,4-BNC 6 COT since they can be described as composed of two polyenyl radical segments and neutral B and N atoms (Figure S2).Consequently, the E(T 1 ) of 1,3-and 1,5-BNC 6 COT are very low due to their extensive destabilization in S 0 (Tables 3 and S8).The E(T 1 ) of 1,2-and 1,4-BNC 6 COT are higher yet still much more similar to that of COT than to that of  1).Indeed, the rather low E(T 1 ) of 1,2-and 1,4-BNC 6 COT can indicate some aromatic stabilization in T 1 .
The effect of replacing two C atoms with one B and one N atom on the geometric aspect of Baird-aromaticity is interesting.Compared to both 3 COT and 3 B 4 N 4 COT, the HOMA values of the four 3 BNC 6 COT isomers are slightly lower (0.70-0.80,Table 3), yet still indicative of clear aromatic character.The CC bond lengths and the modest BLA in the hexatriene carbon segment (1.386-1.433Å, Figure S2) of 3 1,2-BNC 6 COT and in the butadiene segment of 3 1,4-BNC 6 COT (1.386 -1.419 Å) also suggest π-electron delocalization indicative of aromatic character, and so do the out-of-plane vibrational frequencies ν oop which are intermediate between those of 3 COT and 3 B 4 N 4 COT-A (Table 3).
Interestingly, the NICS(1) zz values for three of the four 3 BNC 6 COT isomers resemble the values for 3 B 4 N 4 COT-A and 3 B 4 N 4 COT-B despite that they have six C atoms and may be expected to mainly resemble 3 COT.Only one isomer, 3 1,4-BNC 6 COT, has a NICS value that tends towards that of 3 COT.Unsurprisingly, the ACID plots reveal diatropic ring currents in all four isomers in their T 1 states (Figure 4), similar as for 3 B 4 N 4 COT-A and 3 B 4 N 4 COT-B.
However, opposite to the magnetic and geometric aromaticity indicators, the electronic indices FLU, MCI and EDDB H (π) tell that the four 3 BNC 6 H 8 isomers are at most weakly aromatic when compared to 3 COT.The three electronic indices vary as to which isomer exhibits a weak aromatic character and which ones are nonaromatic.MCI indicates that 1,2-BNC 6 COT may have a weak aromatic character with an MCI value of 20% of that of 3 COT, while FLU indicates that 3 1,3-BNC 6 COT may have a modest aromatic character, although the FLU value is significantly higher than that of 3 COT (0.029 vs. 0.001).With regard to the EDDB H (π) values they are distinctly lower than that of 3 B 4 N 4 COT-A, and the percentage of delocalized π-electrons in the four 3 BNC 6 COT isomers (57 -63%) is the same or just slightly higher than that of borazine in S 0 (57%) and considerably lower than that of the Baird-aromatic 3 COT (93%).
For the ISE values, it should be stressed that we selected only ISE reactions in which the same number of bond types exist on the reactant (nonaromatic) and product (aromatic) side, as the ISE values otherwise incorporate both aromatic stabilization energies and differences in bond strengths.Thus, an H atom that migrates by a 1,3-shift must transfer between either two C atoms, two B atoms, or two N atoms.A further caveat with the ISE values is the fact that the relative energies vary significantly among the non-aromatic isomers, as these are differently able to host a triplet diradical (some nonaromatic isomers can form resonance stabilized The formally aromatic isomer of this compound adopts a strongly puckered conformation in T 1 and an ISE value is therefore not meaningful. polyenyl radical segments).Hence, the ISE values do not only describe the aromatic stabilization but also the extent of resonance stabilization in the non-aromatic isomers on the reactant side.Yet, if one considers the energy difference between the most stable non-aromatic and the most stable aromatic isomer among the 1,2-BNC 6 COT species in T 1 one gets an ISE value of -7.7 kcal/mol (Table 3), and for the 1,3-BNC 6 COT species we similarly calculate an ISE value of -7.8 kcal/mol.Since these ISE values are based on the most stable nonaromatic isomer they do not incorporate any internal destabilization within the nonaromatic isomer, and accordingly, should predominantly correspond to the lowering in energy due to aromatic stabilization when going from the nonaromatic to the aromatic isomer (for the complete list of ISE equations and relative energies see the ESI).From the ISE values calculated in this way it becomes clear that approximately half of the Baird-aromaticity has been lost when going from3 COT to three of the 3 BNC 6 COT while 3 1,4-BNC 6 COT exhibits a smaller loss.Now, returning to the question posed in the Introduction as to when (at which T 1 state azaboraCOT) the split between the magnetic versus electronic and energetic aromaticity aspects sets in, the split exists for the 3 BNC 6 COT isomers.They exhibit significantly negative NICS values and diatropic ring currents (although not as strong as for 3 COT), but the values of the electronic indices differ markedly from those of 3 COT.Among the geometric and energetic indices, HOMA and ν oop reveal values that are somewhat lower than those of 3 COT, yet still indicative of aromaticity.The ISE values, in contrast, tend towards non-aromaticity.Clearly, incorporation of just one pair of B and N atoms into the COT scaffold weakens Baird-aromaticity, which is most apparent via the electronic and energetic aromaticity aspects.
Going to the six 3 B 2 N 2 C 4 COT isomers, isomers A and F exhibit stronger magnetic aromaticity than 3 B 4 N 4 COT-A according to NICS while the opposite is the case for the other isomers.The ν oop of 3 B 2 N 2 C 4 COT-A and -F are also similar to that of 3 1,2-BNC 6 COT, and their percentage π-electron delocalization according to EDDB H (π) is high (68-69%) when compared to borazine in S 0 , and approaching that of 3 3 COT, yet, when evaluating the energetic impact of aromaticity one should also consider relative energies.The thermodynamically most stable B 2 N 2 C 4 COT isomer I U R E 4 ACID plots of 3 1,2-BNC 6 COT, 3 1,3-BNC 6 COT, level.The isodensity value is 0.03 e/Å 3 and the red arrow indicates the continuous circulation of small arrows throughout the plane of the ring.Fullscale ACID plots are given in Figures S8-S21.
in both S 0 and T 1 is B 2 N 2 C 4 COT-B (Table S9), whereas B 2 N 2 C 4 COT-F is the absolutely least stable in both states (in the T 1 state it is 64 kcal/mol above 3 B 2 N 2 C 4 COT-B).I.e., despite significant Baird-aromatic character according to magnetic and geometric indices, it is of very high energy.The E(T 1 ) of isomer A is high and intermediate between those of COT and B 4 N 4 COT-A while the E(T 1 ) of the mesoionic B 2 N 2 C 4 COT-F is minute.The other four B 2 N 2 C 4 H 8 isomers considered have higher E(T 1 ) energies, but at most slightly less than half that of B 4 N 4 COT-A.
Finally, among B 3 N 3 C 2 H 8 species, we explore only the 3 B 3 N 3 C 2 COT isomer, which has a consecutive (BN) 3 segment.This molecule can be viewed as B 4 N 4 COT-A with one BN unit exchanged to a CC unit, and as noted, we could only locate puckered conformers (a planar C s symmetric structure is a transition state for inversion between two equivalent puckered conformers and 2.2 kcal/mol higher in energy).Due to the puckered ring, the spin density is separated into two segments corresponding to separate radicals (Figure S6).Thus, 3 B 3 N 3 C 2 COT cannot be Baird-aromatic as supported by a very low electron delocalization throughout the ring, no ring current and a NICS value that suggests a lack of aromaticity (Table 3).Despite this, the geometric HOMA index (0.846) corresponds to a significant aromaticity.
Analysis of magnetically induced current densities: In this section we further explore borazine in S 0 and a selection of the azaboraCOTs which in their T 1 states have strong Baird-aromatic character according to the magnetic criteria.The total and the π-electron current density maps of borazine in S 0 and 3 B 4 N 4 COT-A are displayed in Figure 5A-D.In the case of borazine in S 0 , there are local currents around the N atoms instead of a significant global circulation.In contrast, in 3 B 4 N 4 COT-A there are significant diatropic π-electron ring currents which are uniformly distributed over the molecular ring, and the separated current densities of 3 B 4 N 4 COT-A (Figure 5E,F) clarifies that the π α -electron current density has a somewhat stronger contribution than the π β -electrons.Quantitative descriptions of the current density distributions are obtained from the integrated bond current strengths (Table 4), and the total π-electron ring current strength of 3 B 4 N 4 COT-A is three times larger than that of borazine in S 0 and $60% that of 3 COT, in line with the NICS values given above.
Interestingly, the replacement of two C atoms of 3 COT by one N and one B atom, leading to 3 1,2-BNC 6 COT and 3 1,3-BNC 6 COT, results in π-electron currents which are approximately two thirds that of 3 COT (Table 4 and Figure 6), i.e., only slightly larger than that of 3 B 4 N 4 COT-A.Thus, it is not the sheer number of B and N atoms that is decisive for the current densities but rather the connectivity between the B, C and N atoms, which is also apparent from the isomeric azabora-COTs  stronger current densities than 3 1,2-BNC 6 COT and 3 1,3-BNC 6 COT (Table 4).Clearly, the azaboraCOT with the strongest π-electron current densities is not the one with the structurally closest resemblance to 3 COT but instead the 3 B 2 N 2 C 4 COT-F with a high relative energy (64 kcal/mol) compared to the most stable isomer ( 3 B 2 N 2 C 4 COT-B).A similar finding was made earlier for azaborines (BNC 4 H 6 ) in their S 0 states where the least stable isomer (1,3-azaborine) displayed the highest aromatic character. [68]o resolve the cause of the differences in current densities, we related these to virtual transitions from the occupied to unoccupied orbitals. [69]The orbital diatropic and paratropic contributions to the total current density come from, respectively, virtual translational and rotational orbital transitions.The weight of the given orbital transition becomes more pronounced as the energy gap between the given occupied-virtual orbital pair decreases.Hence, the magnetic aspect of aromaticity does not merely reflect the electron configuration(s) that correspond to the state under consideration (here, S 0 or T 1 ) as it also involves virtual transitions to unoccupied orbitals as a means for the molecule to respond to the applied magnetic field being an external perturbation.
Borazine in S 0 belongs to the D 3h point group (Figure 7).In this point group, the in-plane translations (T x,y ) have e' symmetry, whereas the in-plane rotation (R z ) has a' 2 symmetry.Our calculations showed that π-electron currents in borazine in S 0 are dominated by the contribution of the e" level.The HOMO-LUMO (e" to e") excitation is both rotationally and translationally allowed since the product e" Â e" = a' 1 + a' 2 + e' contains the symmetries of both T x,y and R z , and this explains why the π-electron currents in borazine in S 0 are very weak.Now going to the T 1 state, the αand β-electrons are considered separately within the unrestricted formalism.COT has D 8h symmetry (Figure 8), whereby the in-plane translations (T x,y ) have e 1u symmetry and the in-plane rotation (R z ) has a 2g symmetry.For the π α -electrons the main contribution to the induced currents comes from the excitation e 2u to e 3g , since the product e 2u Â e 3g = e 1u + e 3u contains the symmetry of in-plane translations, which solely contributes to diatropic currents.Similarly, within π β -electrons the main contribution comes from the e 1g to e 2u excitation (e 1g Â e 2u = e 1u + e 3u ), also giving rise exclusively to diatropic currents.As a consequence, 3 COT displays a strong Baird-aromatic character.A further feature of the D 8h symmetry is the fact that all occupied π-orbitals except the lowest are doubly degenerate (Figure 8).Within each of those degenerate pairs, one can carry out unitary transformations, which for the nonbonding orbital pair (e 2u ), filled only with π α -electrons, implies that those MOs can be transformed between localized representations (shown in Figure 8) and delocalized representations (Figure S22).Thus, both the two π α -electrons in the α-spin orbital manifold and the two holes in the β-spin orbital manifold are perfectly delocalized, providing for a high degree of Baird-aromaticity.
Going to the D 4h symmetric 3 B 4 N 4 COT-A (Figure 3A), the in-plane translations (T x,y ) have e u symmetry and the in-plane rotation (R z ) has a 2g symmetry (Figure 9).Our numerical results show that π α -electron currents are dominated by b 2u and b 1u SOMOs, while the π β -electron currents solely come from the degenerate e g level.The π α -electron currents arise from the excitations from b 2u and b 1u to e g .These excitations contribute to diatropic currents since the products b 2u Â e g = b 1u Â e g = e u contain the symmetry of inplane translations.It is further noteworthy that our calculations showed that the π α -electron e g level solely gives a paratropic current density contribution, which, however, is very weak.This paratropic contribution comes from the transition to the virtual e g level, since the product e g Â e g = a 1g + a 2g + b 1g + b 2g contains the symmetry of the in-plane rotation (a 2g ).The π β -electron currents arise from excitations from the degenerated e g level to b 2u and b 1u which contribute to diatropic currents.On the other hand, there is a simultaneous excitation e g to e g which is rotationally allowed and reduces the overall diatropic contribution of the e g level.This can explain why π β -electron currents are weaker than that of π α -electrons.Combined, in 3 B 4 N 4 COT-A there are both translational (diatropic) and rotational (paratropic) transitions, yet the diatropic are significantly stronger and the situation tends towards that of 3 COT where there are only translational transitions.Here it is notable that strong diatropic ring currents were earlier observed for the borazocine dianion in S 0, [34,35] a species that resembles 3 B 4 N 4 COT-A as the same virtual excitations are involved in the two species, however, with two electrons in the b 2u and b 1u orbitals of the first while one π α electron in each of these orbitals of the latter.At this point, it is relevant to ask, why is the π-electron delocalization of 3 B 4 N 4 COT-A, at an orbital level, lower than that of 3 COT?In contrast to 3 COT, 3 B 4 N 4 COT-A is D 4h symmetric, and thereby the former pair of degenerate nonbonding orbitals (e 2u ) has turned into the nondegenerate b 2u and b 1u , which are localized on, respectively, the four N atoms and the four B atoms (Figure 9A).This orbital feature has direct consequences for the π-electron delocalization of 3 B 4 N 4 COT-A (and its Baird-aromaticity) as it is no any longer possible to transform between localized and delocalized representations of the highest occupied π α -orbitals.The azabora-COT 3 B 2 N 2 C 4 COT-F, which is C 2 symmetric, also has no degenerate frontier orbitals, but for this molecule the nondegenerate a u and b 3u orbitals are much closer in energy and resemble the degenerate e 2u orbital level in 3 COT (Figure S23).Taken together, with an analysis of the translational and rotational virtual transitions to which the induced current densities can be related, we can achieve an understanding of the strong ring currents in 3 B 4 N 4 COT-A and similar azaboraCOTs.These, however, are not necessarily related to the other aspects of triplet state Baird-aromaticity.

| CONCLUSIONS
From our computational analysis, it is apparent that borazocine in T 1 ( 3 B 4 N 4 COT-A) according to energetic and most electronic aromaticity descriptors is as weakly aromatic as borazine in S 0 , but when evaluated by magnetic aromaticity indices the first molecule is significantly more aromatic than the latter, as exemplified by NICS (1) zz values of -19.3 and -5.9, respectively.The symmetry properties of the orbitals of borazine in S 0 are such that they provide for both strong translational (diatropic) and rotational (paratropic) transitions.In contrast, for 3 B 4 N 4 COT-A the translational transitions are much stronger than the rotational ones, a situation that tends towards that of 3 COT where the rotational transitions are nil.These features lead to significant differences in the extent of aromaticity when evaluated with magnetic as compared to electronic or energetic aromaticity indices.
Our results point to the need to identify further molecules for which the magnetic aspect of aromaticity diverges from the electronic and energetic aspects, similar to what been observed earlier for (N 6 H 6 ) 2+ and C 2 N 4 H 6. [36] Our findings support the view that one should speak of aromaticity as two phenomena, [36,64] one response aromaticity represented by the magnetic aspect and one intrinsic aromaticity represented by the electronic, energetic and geometric aspects.Our study highlights the importance of considering as many aspects of (Baird-) aromaticity as possible when novel species with potential aromatic characters are evaluated.Besides complications related to the choice of computational method there are also challenges intrinsically related to the electronic structure of the molecules, and both must be incorporated in studies of (excited state) aromaticity and antiaromaticity effects.
Structural formula, optimized bond length (blue color) in Å and symmetry (in brackets) of 3 COT, 3 B 4 N 4 COT-A and 3 B 4 N 4 COT-B.(B) ACID plots for the eight-membered ring compounds in their T 1 states at UB3LYP/6-311G(d,p) level (full ACID plots are available in the Supporting Information, Figures S8-S21).(C) Plots of the spin densities (isovalues at 0.0004 e/Å 3 ).(D) ISE values (kcal/mol) for methyl substituted 3 COT and of H 3 N + and H 3 B -substituted 3 B 4 N 4 COT-A and 3 B 4 N 4 COT-B.
3 B 4 N 4 COT, when compared to 3 COT, are non-aromatic.Additionally, the MCI values of both 3 B 4 N 4 COT-A and 3 B 4 N 4 COT-B are only a tenth of the value of 3 COT, underlining the conclusion based on FLU of weak or no aromaticity.To further explore the delocalization, we calculated EDDB H (π) values of 3 COT, 3 B 4 N 4 COT-A and 3 B 4 N 4 COT-B.It is clear that the π-electrons of 3 COT are nearly completely delocalized with an EDDB H (π) value 7.45 (93% of eight π-electrons).For 3 B 4 N 4 COT-A and 3 B 4 N 4 COT-B, EDDB H (π) indicates that the electrons are less delocalized as 5.95 (74%) and 4.15 (52%) of the π-electrons are delocalized over the octagon.
3 B 2 N 2 C 4 COT-A and 3 B 2 N 2 C 4 COT-F.Despite two B and two N atoms, these two compounds exhibitF I G U R E 5 (A and B) Total (all electron) current density maps of, respectively, borazine in S 0 and B 4 N 4 COT-A in T 1 .(C and D) π-electron current density maps of, respectively, borazine in S 0 and B 4 N 4 COT-A in T 1 .(E and F) π-electron current density maps of B 4 N 4 COT-A dissected into, respectively, αand β-electron contributions.T A B L E 4 Ring current strengths (J, in nA T -1 ) calculated as the average of all bonds in the given ring

F I G U R E 8
Frontier orbital energy levels of 3 COT.Blue arrows represent the main translational transitions.As there are no rotational transitions, the diagram contains no red dashed arrows.The variation of energy between α and β levels is ignored.F I G U R E 9 Frontier orbital energy levels of (A) 3 B 4 N 4 COT-A and (B) 3 B 4 N 4 COT-B.Blue arrows represent the main translational transitions and red dashed arrows represent the main rotational transitions.The variation of energy between α and β levels is ignored.

Finally, 3
B 4 N 4 COT-B has D 2h symmetry (Figure 9), and in this point group the in-plane translations (T x,y ) have b 2u and b 1u symmetries, whereas the in-plane rotation (R z ) has b 3g symmetry.The induced π α -electron currents are dominated by excitations from b 3u and a u SOMOs, while π β -electron currents mainly come from the b 1g and b 2g levels.The excitations from the b 3u SOMO to b 1g and b 2g are translationally allowed (b 3u Â b 1g = b 2u and b 3u Â b 2g = b 1u ), whereas the excitation to the a u level is rotationally allowed (b 3u Â a u = b 3g ).The latter one diminishes the overall diatropic contribution of the b 3u SOMO level.The excitations from the π α -electron a u SOMO to b 1g and b 2g are translationally allowed and this orbital gives solely diatropic contribution.In the π β -system there are excitations from the b 1g SOMO to a u and b 3u , which are translationally allowed, while the excitation to b 2g level is rotationally allowed (b 1g Â b 2g = b 3g ).The excitations from the b 2g SOMO to a u and b 3u are translationally allowed (b 2g Â a u = b 2u and b 2g Â b 3u = b 1u ), while the excitation to b 1g level is rotationally allowed.The observed rotationally allowed excitations from the highest SOMO levels within the β electron stack can explain why π β -electron currents are weaker than that of π α -electrons.
complex situation as one of the values approaches that of 3 COT (-15.8 kcal/mol).This may suggest some T 1 state Baird-aromaticity, but the very high relative energy of 3 B 4 N 4 COT-B (128 kcal/mol) speaks against such an interpretation.For comparison, the aromatic archetype benzene has been found to be the lowest in energy among 198 C 6 H 6 isomers, 35 kcal/mol lower in energy than the second most stable isomer, fulvene.
a E(T 1 ) and ΔISE in kcal/mol.more T A B L E 2 Triplet energies (E(T 1 )), and S 0 state HOMA, ν oop , NICS(1) zz, ΔISE, EDDB H (π), FLU and MCI values of benzene, borazine, the tropylium cation (Trp + ) and COT dication a a E(T 1 ) and ΔISE in kcal/mol.B 4 N 4 COT-A (Table Triplet energies E(T 1 ), and the T 1 state ν oop , ΔISE, NICS(1) zz , EDDB H (π), FLU and MCI values of 1,2-BNC 6 COT, 1,3-BNC 6 COT, 1,4-BNC 6 COT, 1,5-BNC 6 COT, B 2 N 2 C 4 COT-A, B 2 N 2 C 4 COT-B, B 2 N 2 C 4 COT-C, B 2 N 2 C 4 COT-D, B 2 N 2 C 4 COT-E, B 2 N 2 C 4 COT-F and B 3 N 3 C 2 COT at UB3LYP/6-311G(d,p) level T A B L E 3 a E(T 1 ) in kcal/mol.bFrequency for the out-of-plane vibrational mode in cm -1 .cISE values in kcal/mol.dCalculated as T 1 energy differences between the most stable isomer of the nonaromatic isomers and the most stable isomer among the aromatic ones.Details on the ISE equations are given in the Supporting Information, p. 15-29.eCalculated based on single ISE reactions, one with methylene/methyl substitution at N and one at B. f3 B 3 N 3 C 2 COT is markedly puckered and has no out-of-plane vibrational mode.g B 4 N 4 COT-A.The four other COT isomers lack aromatic character.Their ISE values of the first five 3 B 2 N 2 C 4 COT isomers vary in the range -12.8 to -2.6 kcal/mol with B 2 N 2 C 4 COT-C and B 2 N 2 C 4 COT-A having some aromatic character.Unexpectedly, 3 B 2 N 2 C 4 COT-F has more negative ISE values than