mmh00 | ACSJCA | JCA10.0.1465/W Unicode | research.3f (R3.6.i11:4432 | 2.0 alpha 39) 2015/07/15 14:30:00 | PROD-JCAVA | rq_7107511 | 9/24/2016 09:54:07 | 18 | JCA-DEFAULT Article pubs.acs.org/joc 1 Quantitative Assessment of Aromaticity and Antiaromaticity 2 Utilizing Vibrational Spectroscopy 3 Dani Setiawan, Elfi Kraka, and Dieter Cremer* 4 Computational and Theoretical Chemistry Group (CATCO), Department of Chemistry, Southern Methodist University, 3215 Daniel 5 Ave., Dallas, Texas 75275-0314, United States 6 *S Supporting Information 7 ABSTRACT: Vibrational frequencies can be measured and calculated with 8 high precision. Therefore, they are excellent tools for analyzing the electronic 9 structure of a molecule. In this connection, the properties of the local 10 vibrational modes of a molecule are best suited. A new procedure is described, 11 which utilizes local CC stretching force constants to derive an aromaticity 12 index (AI) that quantitatively determines the degree of π-delocalization in a 13 cyclic conjugated system. Using Kekulébenzene as a suitable reference, the 14 AIs of 30 mono- and polycyclic conjugated hydrocarbons are calculated. The 15 AI turns out to describe π-delocalization in a balanced way by correctly 16 describing local aromatic units, peripheral, and all-bond delocalization. When 17 comparing the AI with the harmonic oscillator model of AI, the latter is found 18 to exaggerate the antiaromaticity of true and potential 4n π-systems or to 19 wrongly describe local aromaticity. This is a result of a failure of the Badger 20 relationship (the shorter bond is always the stronger bond), which is only a 21 rule and therefore cannot be expected to lead to an accurate description of the bond strength via the bond length. The AI 22 confirms Clar’s rule of disjoint benzene units in many cases, but corrects it in those cases where peripheral π-delocalization leads 23 to higher stability. [5]-, [6]-, [7]-Circulene and Kekulene are found to be aromatic systems with varying degree of delocalization. 24 Properties of the local vibrational modes provide an accurate description of π-delocalization and an accurate AI. 37−40 1. INTRODUCTION tion pattern of polycyclic aromatic hydrocarbons (PHAs). 50 Other topological descriptions use double-bond equivalents 51 25 Aromaticity and antiaromaticity are important concepts in 41 42−45 (DBEs), chemical graph theory (CGT), multicenter 52 26 chemistry as they help to explain physical and chemical − 46 π 1 8 indices such as the ring center index Iring, the multicenter 53 27 properties of cyclic -conjugated compounds. Essential to 31,47−49 ̈ ’ π 9,10 index MCI, or the electron localization−delocalization 54 28 these concepts are Huckel s4n + 2 and 4n -electron rules, 50,51 matrix (LDM). 55 29 which associate a simple count of π-electrons with the stability More advanced approaches have used thermochemical 56 30 and reactivity of the π-system in question. During the last 80 properties (Figure 1) such as the molecular energy (enthalpy) 57 31 years since the formulation of the Hückel rules, the concepts of to define a resonance or aromatic stabilization (aromatization) 58 32 aromaticity and antiaromaticity have been probed with regard energy ASE and relating this energy to the thermodynamic 59 33 to almost every molecular property. A multitude of methods 52−57 fi stability of a conjugated system. Similarly, the topological 60 34 and procedures has been developed to de ne and measure the 44 resonance energy (TREs), the bond resonance energy 61 35 degree of aromaticity in polyaromatic hydrocarbons (PHA)s, 53,58 56 11−18 fl (BRE), the superaromatic stabilization energy (SSE), 62 36 their heteroatomic analogues, to estimate the in uence of 54 ff 19−24 the energy decomposition analysis, or bond centered group 63 37 substituent e ects on aromaticity, and to determine the 59 25−30 ff π 38 degree of aromaticity in nonplanar compounds. The additivity schemes have been used to quantify the e ects of - 64 65 39 performance of the different approaches has been tested and delocalization. 31−33 40 compared. Alternatively, one can use the molecular geometry (Figure 1) 66 41 Hückel’s original description of aromaticity was based on the to determine the degree of bond equilibration under the impact 67 π 11,75,76 f1 42 π of -delocalization. Especially popular were the harmonic 68 topology (see Figure 1) of the net of -bonds in a molecule and 60 43 is the basis of molecular orbital (MO) descriptions of oscillator model HOMA, the reformulated HOMA 69 34,35 36 61,62 44 ’ (rHOMA), the electron delocalization-based HOMA 70 (anti)aromatic systems. Clar s sextet rule is another 63 64 45 π (HOMED), its extension HOMHED for heteroatoms, 71 example for the simple use of the topological features of a - 30,77−80 46 system. It requires a maximum number of disjoint aromatic and the various applications of the HOMA approaches. 72 47 benzene units and a minimum number of localized double 48 bonds in a benzenoide hydrocarbon and has provided Received: July 22, 2016 49 astonishingly reliable predictions as to the preferred delocaliza- © XXXX American Chemical Society A DOI: 10.1021/acs.joc.6b01761 J. Org. Chem. XXXX, XXX, XXX−XXX The Journal of Organic Chemistry Article − Figure 1. Overview over the various (anti)aromaticity descriptors used: DBE, double bond equivalent;41 CGT, chemical graph theory;42 45 MCI, − multicenter index;31,47 49 LDM, electron localization−delocalization matrix;50,51 HOMA(R), original harmonic oscillator model of aromaticity based on bond lengths R;60 rHOMA, reformulated HOMA;61,62 HOMED, electron delocalization-based HOMA,63 HOMHED, HOMED for heteroatoms;64 ASE, aromatic stabilization energy;57,65 BRE, bond resonance energy;53,58 TRE, topological resonance energy;44 SSE, superaromatic stabilization energy;56 EDA, energy decomposition analysis;54 NICS, nucleus-independent chemical shift;22,25,66,67 Δg, average gyromagnetic factor;68 p-PDI, para-delocalization index;69 FLU, aromatic fluctuation index;70 D3BIA, density and degeneracy-based index of aromaticity;71 CTED, corrected total electron density;72 HOMA(ρ), HOMA based on the electron density ρ at the bond critical point;73,74 AI(vib), aromaticity index based on the molecular vibrations. 73 Of course, bond lengths always depend on strain, exchange derivation of bond orders and π-ellipticities for cyclic π-systems 101 94−97 74 repulsion, core polarization, and other effects and often fail to has to be mentioned in this connection. More recently, 102 75 function as reliable bond strength and/or delocalization one has developed delocalization indices such as the para- 103 81−85 69 98 76 parameters. Therefore, HOMA indices should always be delocalization index (PDI), thesourcefunction, the 104 70 77 compared with other measures of electron delocalization. aromatic fluctuation index (FLU), the corrected total electron 105 72 78 The magnetic properties( Figure 1) of (anti)aromatic density (CTED) index, the density- and degeneracy-based 106 71 79 molecule are better suited to describe delocalization phenom- index of aromaticity (D3BIA), the anisotropy of the π- 107 99 80 ena, e.g., with the help of the diamagnetic susceptibility electron density distribution, or the analysis of the electron 108 86 100 81 exaltation Δχ, the NMR chemical shifts, their nucleus- density in terms of electron localization and delocalization. 109 82 independent analogues NICS (nucleus-independent chemical In addition, one has extended the HOMA approach to the 110 22,25,66,67 1,87,88 ρ 83 shift), diatropic and paratropic ring currents, the electron density in form of HOMA( b) by replacing distance R 111 24 73,74 84 polygonal current model, or the average g-factor of a by the electron density at the bond critical point. 112 85 hydrogen atom placed above a π-system as suitable magnetic Although electron density-based delocalization descriptors 113 68 86 probe. One could argue that the magnetic properties of a have added to the understanding of (anti)aromaticity, a simple 114 87 molecule are sufficiently detailed and so sensitive that any measure of the intrinsic bond strength, which can be used to 115 88 (anti)aromatic delocalization can be directly detected. How- quantify the degree of π-delocalization, is difficult to obtain 116 89 ever, magnetic properties are also affected by local anisotropies from the local electron density properties without considering 117 90 and can reflect σ−, and core-contributions, which one actually the electron distribution in the total bond region. Cremer and 118 101 91 wants to separate from the π-delocalization effects. It is well- Gauss have shown that the covalent part of the intrinsic 119 92 known that the NICS values exaggerate the aromatic character strength of a bond can only be obtained by integrating over the 120 93 of large ring systems and have problem transition-metal electron density in the zero-flux surface between two bonded 121 89 94 clusters/complexes and that indirect spin−spin coupling atoms. These authors also pointed out that only by 122 13 13 95 constants J( C C) only provide reliable measures of π- simultaneously evaluating the ionic (polar) part of the intrinsic 123 90−92 96 delocalization in some well-defined cases. bond strength, a reasonable account of the bond strength can 124 97 If π-delocalization dominates the electronic structure, the be given. This clearly shows that it is not possible to obtain 125 98 electron density distribution (Figure 1) can be used to develop exact information about the intrinsic bond strength and π- 126 99 indicators for (anti)aromaticity, as has been amply done within delocalization by determining the electron density at singular 127 93 100 the framework of Bader’s virial partitioning analysis.