Which NICS Aromaticity Index for Planar Rings in Triplet State Is Best? Hongchao Sun, Ke An, Jun Zhu* State Key Laboratory of Physical Chemistry Solid Surface and Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, Fujian 361005, China Abstract The concept of aromaticity is of fundamental importance in organic chemistry. Comparing to the aromaticity in the ground state, the excited aromaticity is much less developed. As isomerization stabilization energy (ISE) methods have been employed to evaluate aromaticity both in ground and excited states, also nucleus-independent chemical shift (NICS) values have been widely used to evaluate the ground state aromaticity, we have estimated ISE values of a set of conjugated cyclics against four NICS values (NICS(0)iso, NICS(0)zz, NICS(1)iso, NICS(1)zz) in the lowest triplet (T1) state. Our results demonstrate that NICS(1)zz is still better than NICS (0)zz in T1 state, which is consistent with previous researches. Thus we give a systematically study of the T1 aromaticity via different NICS values. INTRODUCTION Aromaticity, one of the most important concepts in organic chemistry, has attracted a great many people both experimentally and theoretically.1 As it is a virtual property, no one can assign an exact meaning to it.2,3 However, due to aromatic molecules have special features, it can be evaluated through structural,1 electronic, energetic,4 magnetic5 and reactivity6 criteria. Before nucleus-independent chemical shifts (NICS) was proposed, several magnetic criteria had been developed, such as exalted magnetic susceptibilities (Λ), 7 Li+ NMR chemical shifts, 8 , 9 3He NMR chemical shifts.10 Besides, there is another well-known criterion, Hückel 4n + 2 rule, 11 which is defined as a cyclic(planar) system containing 4n + 2 -electron is aromatic, on the contrary if it has 4n -electron then it is antiaromatic. This criterion is efficient in the ground state and has been widely accepted. Wilson12 confirmed that Hückel’s rule could be used to assess the stability of chelate compounds, Winstein13 explained the generation of homoaromaticity through it, Breslow14 identified that cyclopropenyl anions were antiaromatic. Dewar,15 Schleyer16,17,18 also enriched and consummated Hückel’s rule. Though ground state aromaticity has been deeply studied, reports on excited state aromaticity are fairly scarce. 19 In 1972, Baird20 found that 4n rings are aromatic and 4n + 2 rings antiaromatic in the lowest excited states. This new criterion is called Baird’s rule, which is contrary to Hückel’s rule. Schleyer affirmed triplet aromaticity in 4n π-electron annulenes from geometric, energetic and magnetic aspects. 21 Karadakov provided theoretical evidence to Baird’s rule, his research suggested that benzene in T1 state is antiaromatic, and cyclobutadiene is aromatic.22 Later, his computational evaluations proved the aromaticity of lowest triplet-state cyclooctatetraene from a magnetic point of view.23 Fowler supported Baird’s rule by visualizing induced ring currents in open-shell π systems.24 Ottosson25 also found that cyclopentadienyl cation(in this reference, conclusions part--original molecule is cylopentadienyl anion, but I think it should be cyclopentadienyl cation), cyclohepentrienyl anion and cyclooctatetraene were aromatic in T1 state, T1 state still means ππ* excited state. Several years later, Ottosson26 verified that the aromaticity of annulenyl-substituted olefins closely related to these compounds’ different energies. Poater and Solà analyzed the electron delocalization and aromaticity of low-lying excited states in cyclobutadiene and cyclooctatetraene, showing that they are aromatic in T1 excited states, it is in agreement with Baird’s rule.27 In 1996, NICS was proposed by Schleyer. 28 This magnetic criterion could evaluate aromaticity and antiaromaticity of a wide range of molecules, and it needn’t references. What’s more, it usually correlates well with other criteria. Heine29 then reported that NICSzz was a good measure for [n]annulenes, especially NICS(1)zz and NICS(1)zz. Carpenetti and Mills30 used NICS(1)zz to measure the antiaromaticity of indenyl and fluorenyl cationic systems, and it was consistent with the results via 1H NMR chemical shifts. Laali31 proved that NICS(1)zz was also a more reliable probe than NICS(1) when computed in janusenes. In 2006, Schleyer32 reported that NICS (0)zz was the best and the most reliable aromaticity index among selected NICS indices according to the best correlation with aromatic stabilization energy (ASE). Furthermore, Mills 33 justified that NICS(1)zz was an accurate reflection of local aromaticity, which was also sustained by the excellent linear relationship with magnetic susceptibility exaltation and indirectly validated by the excellent correlations between experimental shifts and 13 C NMR chemical shifts calculated by density functional theory (DFT) at B3LYP/6-311+g(d,p) level. Palusiak34 verified that NICS(1)zz of phenylic rings had the best linear regression versus total electron energies among NICS(0)iso, NICS(1)iso and NICS(1)zz, which might be served as a standard measure to estimate the aromaticity or antiaromaticity. Ebrahimi35 used NICS(1)zz to detect the ring aromaticity changes on complexation, which was supported by the excellent correlation of the electron density changes at the ring center against the changes of NICS(1)zz. While NICS values are widely used as an evaluation of aromaticity and antiaromaticity for molecules in ground state, few reports on the aromaticity of excited molecules are recognized in this way. Our group have made a series of research on the aromaticity of diverse monocyclic planar compounds in T1 state, such as silabenzenes,36 osmapentalenes,37 their NICS indices shown that NICS was a reliable criterion to evaluate their aromaticity. Formerly, our group38,39 also employed methyl-methylene (ISEI) and indene-isoindene isomerization stabilization energy (ISEII) methods , which were applied to evaluate aromaticity by Schleyer40 in the ground state, to identify the aromatic character in T1 state and both energies had good relationships with the NICS(T1; 1)zz values. METHDOLOGY All molecular geometries were optimized using Density Functional Theory at B3LYP/6-311++G(d,p) level, the ISE values were pure electronic energies without correction, NICS values were also calculated at B3LYP/6-311++G(d,p) level. Grey41 reported that curvature of molecular surfaces could influence the NICS values remarkably. One of the features of a aromaticity compound is that it usually has a planar structure, therefore we only selected the planar molecules in T1 state to continue our study (Table S1), they have no multi-atom substituents. Additionally, these chosen compounds should also present excitations between π orbitals. The selected compounds were listed in Figure 1. Figure 1 Five-membered rings in this study RESULTS AND DISSCUSSION Originally we tried to use ASE and NICS to evaluate aromaticity of five-membered rings in T1 state. ASE values were calculated by equation S142, but under such condition cyclopentadiene wasn’t stable, one C-C bond broke down ( Figure S1). Consequently, we have to use other energetic methods. As our previous work had confirmed that ISE were reliable methods, so we use methane-methene (ISEI, eq 1) and indene-isoindene stabilization energy (ISEII, eq 2) to evaluate these compounds’ aromaticity. Their values are listed in Table S2. NICS(1) values are calculated 1 Å above the planar ring centers while NICS(0) values are calculated at the ring centers. NICS(0) values are more prone to be influenced by CH and CC bonds.33 Properly it can explain why many NICS(0) values are positive. Generally, strongly negative NICS indices values indicate aromaticity while strongly positive ones mean antiaromaticity. 43 Based on Baird’s rule, species 2-13 ought to be aromatic, meanwhile NICS indices and ISE values of these compounds are negative, it agrees with Baird’s rule. Negative NICS indices and ISE values of species 2, 3, 13 indicate their good aromaticity, their aromaticity decrease as their aromatic number increase. As their radiuses increase, their conjugation weaken, and so do the ISE values. Besides charge and bond-length equalization contribute to the stability of cyclopentadiene cation. But, not all NICS indies agree well with Baird’s rule. The small NICS indices and ISE values, except abnormal NICS(0)zz, indicate cyclopentadiene and 1H-pyrrol-1-ium are nonaromatic compound. Their ISEI values are positive, ISEII values negative, their ISEI and ISEII values are contrary, this deviation is acceptable and can be negligible because they are small values. Positive values of 2-phosphafuran indicate that it’s antiaromatic in T1 state, which is consistent with Baird’s rule. Its ISEII value is much larger than ISEI value, maybe it is the reason that species 15d is more stable than 15b in T1 state. The statistical square of correlation coefficient show that ISE correlate well with NICS(1) indices, especially ISE versus NICS(1)zz, and ISEI correlates a little better than ISEII with NICS(1)zz. Though the performance of NICS(0)zz is not bad, many NICS(0)zz values of these species are positive, so NICS(0)zz is a suspectable index. The bad performances of NICS(0)iso show that there is no correlation between ISE and NICS(0)iso at all. Then we can draw such a conclusion that NICS(1)zz still is a reliable magnetic tensor to evaluate aromaticity of planar five-membered rings in T1 state. Figure 2 ISEI vs NICS indices in T1 state Figure 3 ISEII vs NICS indices in T1 state Figure 4 ΔSpin vs NICS indices in T1 state What’s more, we tried to evaluate their aromaticity according to their spin densities (ΔSpin = |Spinmax| - |Spinmin|, Table S3). In figure 3, it shows that NICS(1)iso correlated best with ΔSpin. Though, its correlation-ships were not good, but to some extent they did correlate with each other. Only species 15 is a 4n + 2 π-electron system, in this compound, spin densities are mainly distributed among carbon atoms and phosphorus atom, the spin density of oxygen atom is negligible, and the value of phosphorus spin density is the largest one, it shows that in T1 state, carbon atoms and phosphorus atom are excited while oxygen atom doesn’t be affected. The distribution of spin densities shows that phosphorus atom conjugates well with carbon atoms. carbon, silicon, germanium are elements from Group IVA elements of the periodic table of elements, species 2, 3, 13 contain these elements, their properties should be familiar. But species 2, the spin density is equalized among all the carbon atoms, leading to the value of ΔSpin value is zero, which is much lower than any other ones; species 3 and 13, the p orbitals of silicon and germanium atom still overlap well with those p orbitals of adjacent carbon atoms, it can be verified by their familiar spin densities distribution, in consequence, their NICS(1) values are nearly the same. As for the other species, spin densities are mainly distributed among four conjugated carbon atoms, especially adjacent carbon atoms of hetero atoms. The hetero atoms adopting sp2 hybrid orbitals have high spin densities than those adopting sp3 hybrid orbitals, because they have no vacant p orbitals, they participate in delocalization through σ bonds44 except for species 7. As beryllium atom accepts hydrogen anion, its electron density is high enough, although it has a vacant p orbital it can’t accept extra electron, so its ΔSpin value is very large. 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