Can Baird’s and Clar’s Rules Combined Explain Triplet State Energies of Polycyclic Conjugated Hydrocarbons with Fused 4n- and (4n+2)-Rings?

Compounds that can be labeled as “aromatic chameleons” are -conjugated compounds that are able to adjust their π-electron distributions so as to comply with the different rules of aromaticity in different electronic states. We used quantum chemical calculations to explore how the fusion of benzene rings onto aromatic chameleonic units represented by biphenylene, dibenzocyclooctatetraene, and dibenzo[a,e]pentalene modifies the first triplet excited states (T1) of the compounds. Decreases in T1 energies are observed when going from isomers with linear connectivity of the fused benzene rings to those with cisor trans-bent connectivities. The T1 energies decreased down to those of the parent (isolated) 4nπ-electron units. Simultaneously, we observe an increased influence of triplet state aromaticity of the central 4n ring as given by Baird’s rule and evidenced by geometric, magnetic and electron density based aromaticity indices (HOMA, NICS-XY, ACID, and FLU). Due to an influence of triplet state aromaticity in the central 4nπ-electron units the most stabilized compounds retain the triplet excitation in Baird -quartets or octets, enabling the outer benzene rings to adapt closed-shell singlet Clar -sextet character. Interestingly, the T1 energies go down as the total number of aromatic cycles within a molecule in the T1 state increases.


Introduction
π-Conjugated compounds comprised of fused (4n+2)-and 4n-electron cycles, such as biphenylene and [N]phenylenes, are interesting for applications in organic and molecular electronics. 1-3 Yet, they are also of fundamental importance as their study sheds light on the limits of aromaticity and antiaromaticity, and ultimately on chemical bonding. [4][5][6][7][8] In their electronic ground states (S0), these compounds display properties that are intermediate between those of aromatic and antiaromatic systems, i.e., they display partial aromaticity. 9 But how do these compounds behave in their first electronically excited states, and can their properties be understood in qualitative terms? Such qualitative understanding should facilitate the identification of new compounds with useful properties for applications.
Antiaromatic compounds generally have small HOMO-LUMO energy gaps (HOMO-LUMO), low-lying triplet states, and lower excitation energies than aromatic ones. 10 The triplet state aromatic character of [4n]annulenes was first analyzed by Baird in 1972, 11 and he concluded that [4n]annulenes switch from being antiaromatic in S0 to aromatic in their lowest ππ* excited triplet (T1) states. The opposite applies for [4n+2]annulenes which become antiaromatic in their T1 states. 12 Later it has been shown that [4n]annulenes are also aromatic in their lowest singlet excited (S1) states. 13, 14 We have earlier argued that Baird's rule can be used as a back-of-an-envelope tool for rationalization of the fundamental properties of various classes of π-conjugated molecules. 15 Indeed, we found that certain hydrocarbon compounds which we described as "aromatic chameleons" are able to adjust their electronic structure so as to comply with Hückel's 4n+2 rule for aromaticity in the S0 state and Baird's 4n rule for aromaticity in the T1 and S1 states. 15,16 Fulvenes were identified as one class of aromatic chameleon compounds as they can be influenced by resonance structures in which the -electron pair of the exocyclic C=C bond is pushed in or out of the ring ( Figure 1A), allowing them to adjust the -electron count in the ring from the Hückel-aromatic 4n+2 to the Baird-aromatic 4n. Biphenylene could tentatively also be considered as an aromatic chameleon ( Figure 1B) because in the S0 state it can be influenced by a resonance structure with two 6-electron benzene rings while in the T1 state it can be described by four different Baird-aromatic resonance structures; one with a 12electron biradical perimeter (T1-I), two equivalent ones with 8-electron circuits (T1-III and T1-III'), and one with a central 4-electron cycle (T1-II). Yet, biphenylene in its S0 state can also be labeled as Hückel-antiaromatic, and previous computational studies indicated that biphenylene in this state has localized C-C bonding and some antiaromatic character in the 12π-electron perimeter. 17 The identification of new molecular motifs possessing useful properties for organic electronics applications is a growing area of molecular design. Significant focus is placed on polycyclic aromatic hydrocarbons (PAHs), even though certain of these compounds are of low stability. Elongating linear acenes is one way to decrease the HOMO-LUMO, but it is challenging because already pentacene is reported to dimerize and to be oxidized at ambient conditions. 18 Pentacene and longer series of acenes can be stabilized through substitution, 19,20 or through incorporation of heteroatoms or non-hexagonal carbocycles within the framework. 21 , 22 Another design strategy to compounds with low-lying excited states and interesting optical properties is to introduce (formally) antiaromatic 4n-electron units such as the pentalene unit. 23 π-Conjugated dinaphthoindacene isomers and diphenanthroindacene analogues were synthesized recently and reported to show less negative redox potential as a consequence of increasing paratropicity of the antiaromatic central unit. 24 Hence these kinds of molecular scaffolds could be potential candidates for organic semi-conductors.
We now investigated compounds with fused [4n+2]-and [4n]-conjugated circuits but with overall 4nπ-electron perimeters, and we test if the T1 state properties can be rationalized by usage of Baird's rule combined with Clar's rule. When applied to a PAH, the latter rule tells that the resonance structure which has the largest number of disjoint aromatic π-sextets is more important than the resonance structures with a smaller number of Clar -sextets. 25,26 Additionally, the isomer among a series of PAH isomers that can host the largest number of disjoint aromatic π-sextets (cf. benzene rings) is the thermodynamically most stable one.
Previously, it has been reported that bent PAHs are more stable than their linear isomers in the S0 state because they can host more Clar π-sextets, e.g., phenanthrene hosts two -sextets when compared to one for anthracene. 27,28 Moreover, a linear correlation between the relative isomer energies (thermodynamic stability) 29 and excitation energies 30 with the number of Clar π-sextets was reported for a series of heptabenzenoid isomers. Clar's rule can also be extended to heterocyclic systems as it has been shown that Clar structures exist in boron nitride (BN) analogues of PAHs. 31 If a compound has both (4n+2)-and 4n-electron rings we hypothesize that the isomer with the lowest energy in the T1 state is that isomer which allows for the largest number of aromatic rings, i.e., disjoint triplet diradical Baird-aromatic 4n-electron rings (Baird quartets or -octets) plus disjoint singlet closed-shell Hückel-aromatic -sextet rings (Clar sextets). If Baird's rule can be used together with Clar's rule and influence the relative isomer energies in the T1 state, then the different connectivity of various isomers should also have an impact on the T1 state energies (E(T1)). Thus, by regarding the triplet state aromaticity one could potentially rationalize the first excited state energies, something which is less straightforward based on the shapes of HOMO and LUMO and HOMO-LUMO. For this purpose, three central 4n-electron cycles (cyclobutadiene (CBD), cyclooctatetraene (COT), and pentalene (PEN)) were considered (Figure 2), and we examine our working hypothesis that Clar's and Baird's rules can be used in combination. We particularly address the scope and limitations of the hypothesis; for which compounds does it work and for which ones not?
Although the present study is fundamental in character it shows on a direction for rational tuning of the E(T1) and HOMO-LUMO that should be useful for design of novel compounds for organic electronics.

Computational methods
The Gaussian 09 program package, revision D.01, is applied for the bulk of the quantum chemical calculations. 32 The geometry optimizations were carried out at the B3LYP level 33 employing the 6-311G(d,p) 34 (1) 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, thus taking the values: The delocalization index (DI) between atoms A and B, ( , ), is obtained by the double integration of the exchange-correlation density ( (⃗⃗⃗⃗ , ⃗⃗⃗⃗ )) over the space occupied by atoms A and B: 45 For single-determinant wavefunctions (including density functional approaches), δ(A,B) is expressed as: The sums run over all the occupied molecular spin-orbitals ( good results. 49 To compute FLU and FLUβ., the same Eq. (1) was used but now considering only the α or β MSOs and taking the ( , ) reference value in Eq. (1) as half the reference value used for non-spin split FLU calculations.

Results and Discussion
The

Potential nonpolar "aromatic chameleon" compounds:
The central ring a in the class A compounds can be viewed as a 4π-electron CBD ring, or alternatively, as the four-membered ring in [4]radialene. The first compound in this series, biphenylene (A1), 17,50 was suggested above to have an "aromatic chameleon" feature ( Figure 1). 12 Yet, is this labeling in accordance with computational results? For A1 in the S0 state (A1(S0)) the NICS-XY profile in Figure 4A shows that the NICSπzz values are 9.5 ppm for the a ring and merely -7.6 ppm for the b rings (in the center of each ring), suggesting that the latter rings are weakly aromatic (the corresponding NICSπzz values for CBD and benzene in their S0 states are 18.3 and -17.6 ppm, respectively, at the (U)B3LYP/6-311+G(d,p) level, given in the Figure S9). The NICS-XY-scan of A1(S0) is the same as the previously reported one. 36 The ACID plot of A1(S0) ( Figure S19) shows that ring a has a strong paramagnetic ring-current while the b rings are only weakly aromatic. However, the corresponding FLU values are 0.0441 and 0.0052 (Table   1), and with a near-zero value for the b rings this suggests a substantial aromaticity in these rings contrasting the findings from NICS and ACID. The FLU value along the perimeter (0.0147) indicates that the π-electron delocalization is not particularly efficient along this path and that the most effective π-delocalization is locally in the six-membered rings (6-MRs).   In the ACID plot for A1(T1) the diamagnetic ring-current along the perimeter is apparent ( Figure 4). The FLU values of the CBD and benzene rings are 0.0382 and 0.0169 (Table 1), respectively, revealing that when going from the S0 to the T1 state, the antiaromatic character of CBD decreases somewhat whereas the aromaticity of the 6-MR is significantly reduced.
Due to its symmetry, A1(T1) has four possible electronic circuits for 4n-electron delocalization ( Figure 1); one global along the perimeter (FLUbab' = 0.0082; for comparison, FLU in T1 antiaromatic benzene is 0.0238), two semi-global which involves the CBD ring and one benzene ring (FLUab = 0.0157), and one local corresponding to the CBD ring (FLUa = 0.0382), respectively. The FLUbab' is the lowest, meaning that T1 state π-electron delocalization occurs most efficiently along the perimeter. Moreover, the γbab' value of 1.00 (Table 1) of the perimeter circuit indicates Baird aromatic character, and consequently, that resonance structure T1-I (Figure 1) best describes A1(T1). Interestingly, the DIs explain why FLUbab' decreases and FLUb increases significantly from the S0 to the T1 state. In short, the local circuit in the 6-MRs is blocked in the T1 state and the circuit through the perimeter is activated (see SI for a more detailed analysis). Finally, the changes in aromaticity when going from the S0 to the T1 state are also apparent in the geometries. In the T1 state the HOMA(peri) value increases by 0.5 so that the perimeter of A1(T1) can be described as an aromatic cycle.
Simultaneously, the HOMA of the a ring (-0.401) is still representative of antiaromaticity. In this context, it should be noted that a previous study using HOMA found the parent cyclobutadiene in its T1 state to be only weakly aromatic having a HOMA values of only 0.30. 51 Similar observations have been made in studies based on ELF as well as spin current density analysis. 52,53 The ISE value of CBD(T1) is 0.8 kcal/mol higher than that of COT(T1), however, Zhu and co-workers reported that the ISE values for small annulenes such as CBD are not reliable. 54 The various aromaticity measures applied to B1 and C1 in their S0 and T1 states also reveal aromatic chameleon features. Compound B1(S0) is non-planar making NICS-XY not useful, and for this reason we instead carried out a NICS-scan perpendicular to one of the b rings, 39 revealing that these are strongly aromatic (NICS(1.7)zz is -14.6 ppm, see the Figure S10). The  (Table 1) In conclusion, all three species A1 -C1 are influenced by Hückel-aromaticity in S0 and by Baird-aromaticity in T1, and can accordingly be labeled as aromatic chameleons. Now, having identified the tendency of these compounds to redistribute their electron density when going from S0 to T1, and to act as aromatic chameleons, how does this change upon benzannelation?
Such additional benzannelation may impede the ability of the electronic structure readjustment in the T1 state, but it may also depend on the connectivity (vide infra), and on the size of the central 4n-electron unit. An effect on the connectivity is indeed observed in the relaxed T1 state energies as seen next.

T1 energies and HOMO-LUMO energy gaps:
When going from linear to bent connectivities within a group of isomeric A3, B3 and C3 compounds, the E(T1) energies in general decrease (Table 2 and Figure 6A). Among these three isomer classes the A3 isomers show the largest variation while the B3 isomers show the smallest. Noteworthy, no significant differences in E(T1) between cis and trans configurations are observed; for A3 and C3 the cis-and transisomers have similar E(T1) while it is 0.08 eV lower for cis-B3BB than for trans-B3BB.
When going from A1 and C1 to A4BBBB and C4BBBB, respectively, one sees that the E(T1) of classes A and C decrease successively, approaching those of CBD (0.23 eV) and PEN (0.34 eV), respectively. Yet, for class B such a gradual decrease is not observed as the E(T1) of B4BBBB is far from that of COT (0.67 eV). The reason is likely that B4BBBB(T1) is unable to attain a planar conformation due to gradually larger steric congestion between the H atoms of the central COT ring and those at the four outer benzene rings when approaching planarity. Indeed, the E(T1) of B4BBBB is even larger than those of the two B3BB isomers.
A further interesting finding is that E(T1) for the linear compounds within class A for the shortest few members go up; for A1, A2L and A3LL the E(T1) increases from 1.92 eV, to 2.22 and 2.75 eV, respectively, while for A4LLLL it is lowered to 1.70 eV. This initial increase in E(T1) followed by a decrease is difficult to rationalize as there is no dominating factor stabilizing the S0 state for the shorter compounds and destabilizing this state for the A4LLLL, or alternatively, influencing the T1 state in the opposite sense. The variations in the E(T1) for the A1, A2L, A3LL and A4LLLL is rather the results of a series of counteracting effects (see section 2 in SI). One sees a tendency for a similar increase in class B as E(T1) goes up by 0.66 eV when going from B1 to B2L but it then decreases for B3LL. However, for class C the linear compounds ranging from C1 to C4LLLL have E(T1) within 1.30 -1.43 eV.  In the S0 state the cis-and trans-A3BB isomers are 12.5 kcal/mol (~0.54 eV) higher in energy than A3LL (Figure 7). On the other hand, in the T1 state it is the opposite because now the two A3BB isomers are 26.8 -26.9 kcal/mol (~1.2 eV) more stable than A3LL, a finding that resembles the situation between phenanthrene and anthracene in their S0 states, as well as that between various heptabenzenoid isomers (vide supra). 27 Noteworthy, the closest H···H distances in cis-A3BB in the S0 and T1 states are 2.227 and 2.213 Å, respectively, and the compound is planar in both states, indicating that differences in relative isomer energies is not caused by non-bonded H···H repulsions in the S0 state.
As seen in Table 2 the decrease in E(T1) when going from A3LL to cis-and trans-A3BB is ~1.7 eV (~39 kcal/mol), and Figure 7 thus shows that this decrease to 69% is due to thermodynamic stabilization in the T1 state and to 31% due to destabilization in the S0 state.
Interestingly, the energy difference between A3LL(T1) and A3BB(T1) is more than twice that In the S0 states of the A3 isomers the shapes of the NICS-XY-scans show more diatropic ringcurrents for rings c than rings b while there is a local paratropic current for the central CBD unit (ring a) (see Figure S13 and S15). Moreover, when going from the linear connectivity in  are the most efficient circuits for π-delocalization (Table 3) The ACID plot of A2B(T1) clearly shows one Baird π-octet and one Clar -sextet (see Figure   S25). However, the ACID plot of cis-A3BB(T1) does not support the presence of a Baird πoctet because the ring-current of the Baird π-octet is counteracted upon by the two adjacent Clar -sextets.  In this context, one can regard A4BBBB (Figure 10), a compound which could exhibit a particularly pronounced T1 state stabilization and aromaticity since it is analogous to tetrabenzanthracene, i.e., the fully benzenoid isomer among the heptabenzenoid PAHs.
Compound A4BBBB has an E(T1) of 0.62 eV (Table 1), i.e., 1.08 eV lower than that of A4LLLL. Indeed, the NICS-XY-scan and the ACID plot reveal a global current along the perimeter, and additionally, localized currents in the -sextets of the c rings as well as the quartet of the a ring ( Figure 10). This gives support for the interpretation that A4BBBB(T1) to some extent has four Hückel-aromatic -sextets and one Baird-aromatic -quartet. The view is in line with the calculated spin density as the spin is mostly localized to the central CBD unit ( Figure 10D). However, FLU gives a different description as it indicates local Hückelaromaticity in the c rings (FLUc = 0.0043, γc = 0.12) as well as semi-global (FLUcbc' = 0.0098, γcbc' = 0.27) and global (FLUperimeter = 0.0083, γperimeter = 0.39) circuits efficient for πdelocalization. According to FLU, the perimeter has the highest Baird-aromatic character.
Finally, the HOMA values in the T1 state suggest strong aromaticity in the c rings (0.844) and reasonably strong along the perimeter (0.708). In contrast, the a ring is non-aromatic (0.082) according to HOMA and this also applies to the b rings (0.155). Yet, the situation resembles that of T1 state CBD which was considered based on HOMA to have weaker T1 aromaticity. 51  bending. There is a significant difference in E(T1) between B2L and B2B (0.73 eV), but as one goes to the B3 isomers one finds that E(T1) only depends weakly on connectivity (Table 2 and Figure 6A). Moreover, for ΔHOMO-LUMO there is no variation among the B3 isomers with several different ring-currents; one that moves along the perimeter but also local diamagnetic ring-currents inside the c and a rings. The B3 and C3 isomers with bent connectivities are 17.0 and 7.3 kcal/mol more stable in their T1 states than the corresponding linear isomers (see SI), which is smaller than found for the A3 isomers (vide supra). However, these gains are now more clearly consequences of the existence of three local aromatic cycles in the bent isomers; two Clar -sextets in the c rings and one Baird-aromatic π-octet. Yet, the reason for the smaller gains in energy in T1 when going from 3LL to 3BB isomers for class B and C than for class A seems connected to the varying gains of closed-shell Hückel-aromaticity in the c rings in the different compound classes. When going from A3LL to A3LB there is a significant lowering in the NICS(1.7)zz from -3.1 to -15.3 ppm but when going from C3LL to C3LB the lowering is more modest from -13.4 to -16.9 ppm in rings c (see Figure S15). In the S0 state the relative isomer energies when going from the fully linear 3LL isomers to the doubly bent 3BB increase by 0.9 and 7.8 kcal/mol in the B3 and C3 classes, respectively (see Figure S5).
For the class C3 isomers, similar as for class A3 isomers, the NICS-XY-scan in the T1 states show an overall increase in the aromaticity when going from linear to cis/trans connectivity, and this is the case for both the c and c' rings and the central aa' (PEN) moiety ( Figure 12).
Interestingly, the two c rings in C3LL are significantly more aromatic according to NICS-XYscans than the corresponding rings in A3LL (see Figure S15). The ACID plots in the T1 state display diatropic ring-currents in all C3 compounds, yet, a weak ring-current in the central pentalene is found in the cis-and trans-C3BB ( Figure 11). With regard to C4BBBB it is, in contrast to B4BBBB, completely planar in both its S0 and T1 states (see Figures S80 and S82). The fully benzannelated C4BBBB(T1) (Figure 13) shows similar properties as A4BBBB(T1), but it is particularly noteworthy that the most diamagnetic units in the T1 state are the a rings according to NICS-XY-scan. Hence, it has five aromatic cycles; four disjoint closed-shell Clar -sextets and one disjoint triplet biradical Baird -octet.
The ACID plot in the T1 state reveals diamagnetic ring-currents along the 32π-electron perimeter along with some diamagnetic ring-currents in the benzene rings and the central pentalene unit. Similar as for A4BBBB(T1), the spin-densities of B4BBBB(T1) and C4BBBB(T1) are mostly localized to the central 8-electron moieties (see Figure S99 and Figure 13D, respectively).
Specifically, the highest localization is found in the inner benzene ring (FLUb = 0.0233 -0.0241) while the two outer benzene rings (FLUc = 0.0036 -0.0043) are more Hückelaromatic. The phenanthrene moiety has also two semi-global circuits, the naphthalene unit

Previous experimental findings on analogous compounds: Some of the compounds which
we discuss in our study were previously synthesized and they showed interesting electronic properties. When going from the linear to the cis-and trans-connectivities in dinaphthoindacene isomers (Figure 14), red-shifted absorptions in the UV-Vis spectra are observed. This is in agreement with our observation that cis/trans connectivity has significant influence on the triplet energies. It is reported that the double bond character of the fused CC bond between the arene and the central indacene/pentalene unit is important in controlling the antiaromaticity of the central unit. 24,56 Above we show that the magnetic properties of (NICS scans and ACID plots) central 4n rings are changed drastically when going from S0 to the T1 states as an influence of T1 aromaticity. However, the antiaromaticity of the pentalene core can be tuned by changing the degree of aromaticity of the peripheral rings attached to the pentalene unit. 57 Moreover, red-shifts in the UV-Vis spectra of Class A3 compounds were also observed when going from the linear to the cis/trans bent connectivities. [58][59][60] While, Cava and co-workers and Barton separately reported that the cis/trans isomers of Class A3 compounds are only stable in the dark, 61 , 62 a later study by Lohman showed that the cis/trans A3 compounds are photostable. 63 The light sensitivity of class A3 compounds can tentatively be related to lower T1 aromaticity of the cyclobutadiene as a central unit. The electronic properties of class B compounds, B1, B3LL, and B4LLLL are enhanced upon increased conjugation, and they are reported to have interesting applications as photoresponsive columnar liquid crystal materials. 64 Among the C3 isomers, C3LL and cis-as well as trans-C3BB are synthesized previously and C3LL could be useful for organic heterojunction photovoltaic cells. 65 Finally, it is argued that a conjugated polyaromatic hydrocarbon is stable towards oxidation if E(T1) of the polyaromatic hydrocarbon is smaller than the E(T1) of oxygen. 66 In all three series of compounds, the E(T1) are decreasing as a function of connectivity, which should lead to a gain in stability.

Conclusions
Our present study illustrates the use of Baird's rule as a back-of-an-envelope tool for rationalization of excited state properties of -conjugated hydrocarbons, and ultimately, for the design of molecules with targeted optical properties. We also show that Clar's rule, if connected to Baird's rule, can be extended to the T1 state of fully benzenoid hydrocarbons provided that a central benzene unit is replaced by either a 4-electron CBD ring or an 8electron COT or PEN unit. In the T1 states, these units take the character of local triplet state Baird-aromatic units, leaving the other rings relatively undisturbed. The optoelectronic properties of π-conjugated hydrocarbons can therefore be modulated by the insertion of 4nelectron antiaromatic units. When comparing several different isomeric compounds having a central 4n-electron unit, the isomer that is most stable is the one that allows for the largest number of Clar -sextets and Baird -quartet/octets combined. The lowest triplet energy is observed for the C4BBBB isomer containing five aromatic cycles, four disjoint Clar -sextets and one disjoint Baird -octet. Thus, using Baird's rule on triplet state (anti)aromaticity together with Clar's rule one can rationalize the triplet state energies of a range of compounds with potential applicability in organic electronics.