Magnetic Criteria of Aromaticity
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Chemical Society Reviews Magnetic Criteria of Aromaticity Journal: Chemical Society Reviews Manuscript ID: CS-TRV-02-2015-000114.R2 Article Type: Review Article Date Submitted by the Author: 10-May-2015 Complete List of Authors: Stanger, Amnon; Technion, Chemistry Gershno-Poranne, Renana; Technion, Chemistry Page 1 of 34 Chemical Society Reviews Magnetic Criteria of Aromaticity Renana Gershoni-Poranne [a] and Amnon Stanger* [a] Addresses [a] R. Gershoni-Poranne, Prof. A. Stanger Schulich Faculty of Chemistry and the Lise Meitner-Minerva Center for Computational Quantum Chemistry, Technion – Israel Institute of Technology, Haifa 32000, Israel. E-mail: [email protected] Dedication Dedicated to Prof. Yitzhak Apeloig on the occasion of his 70 th birthday. Introduction Preface: Benzene was discovered in 1825 by Faraday. The determination and understanding of its structure presented a great challenge to scientists: the compound was highly unsaturated, yet did not show any of the typical reactions of unsaturated compounds, e.g., addition of bromine. The first suggestion that the molecule is cyclic is traditionally attributed to Kekulé in his 1865 1 and 1866 2 papers, although some argue that this idea was presented earlier by Josef Loschmidt. 3 In any event, accumulating experimental evidences, mainly experiments that were conducted by Ladenburg and Wroblewsky, indicated that the proposed structure was unsatisfactory, as it did not account for there being only three disubstituted isomers of benzene instead of the expected four. It was only in 1872 that Kekulé suggested oscillating structures, in which synchronous 1,2-shifts of the three double bonds occur very rapidly. 4 It took about six decades until Erich Hückel 5-9 and Linus Pauling 10 introduced their quantum mechanical based MO and VB explanations, respectively, which introduced the concept of delocalization (of bonds and electrons). This fundamental property is vital to the topic of the present paper. When a metallic loop (containing delocalized electrons) is inserted into a magnetic field, an electric current is induced. The current in the loop induces a magnetic field that opposes the external magnetic field at the inside of the loop. Aromatic molecules contain cyclically delocalized electrons and therefore, when subjected to a magnetic field, show a ring current and a resulting induced magnetic field. However, there are some fundamental differences between the classic (loop) and quantum (molecular) phenomena. The main one, which is relevant to this paper, is the direction (sense) of the induced current and its resulting induced magnetic field. While the direction of an induced current in a loop is determined by the relative orientation of the magnetic field and the loop’s movement, the direction of the current in a molecule depends also on the type of the system. Generally, an external magnetic field 1 Chemical Society Reviews Page 2 of 34 induces a paratropic ring current (the opposite direction relative to a classic loop) in a system that contains 4n π electron, while a system containing (4n+2) π electrons shows a diatropic ring current (the same direction as a classic loop). A frontier orbitals based explanation has been offered by Fowler and collaborators. 11-13 In a nutshell, this explanation rests on the different symmetry changes that take place when, under an external magnetic field, a HOMO-LUMO transition occurs in the double-degenerated HOMO of a (4n+2) π electrons system to the doubly degenerated LUMO vs. a single HOMO to a single LUMO level in 4n π electrons systems. This, in turn, causes a different balance between the linear momenta of transition, which produce diatropic ring currents, and angular momenta of transition, which produce paratropic ring currents. A later work by Corminboeuf et al 14 studies the angular momentum of transition on NICS using CMO-NICS and suggests similar conclusions. We shall return to the consequences and support for this explanation later. Since the HOMO-LUMO gaps in 4n π electrons systems are smaller than the HOMO-LUMO gaps in (4n+2) π electrons systems it is important to note here that (a) the paratropic currents in the former are generally stronger than the diatropic currents in the latter, since transitions between energy levels are proportional to ∆E-1 between the respective levels, and (b) it is important to include configuration interactions (CI) in the calculations of the induced ring currents (and the resulting induced magnetic fields), due to the energy proximity of the empty orbitals in 4n π electrons systems. Conversely, the calculations of the induced ring currents and induced magnetic field of (4n+2) π electrons systems are much less sensitive to the inclusion of CI. Phenomenologically, it is well established that aromatic compounds exhibit diatropic ring currents under external magnetic field and antiaromatic compounds exhibit paratropic ring currents under the same conditions. The question that is raised here (and will be answered later) is whether the appearance of diatropic and paratropic ring currents under external magnetic fields is limited only to aromatic and antiaromatic compounds. In other words, is the presence of an induced ring current under an external magnetic field a sufficient or only a necessary condition to define a system as aromatic (or antiaromatic)? There are mainly four criteria for aromaticity: energy, structure, electron density based indices 15 and magnetic properties. The first two have been discussed recently 16 and in this issue of Chemical Society Reviews . The third, electron density based criteria, was reported by Solà and coworkers to be “the most accurate among those examined” in the comprehensive comparison they conducted in 2008. 17 However, all three of these criteria are beyond the scope of this article. Magnetic criteria are currently the most popular methods and include NMR chemical shifts of 1H, 3He and Li +, magnetic susceptibility anisotropy, magnetic susceptibility exaltation, Nucleus Independent Chemical Shifts (NICS), Aromatic Ring Current Shielding (ARCS) and Current Density Analysis (CDA) plots. We will focus our attention on 1H-NMR techniques and the two computational methods NICS and CDA, which are most in use today. NMR chemical shifts . The ring current model (RCM) 18 suggests that, for a (4n+2) π electrons system, the diatropic ring current will form an induced magnetic field which is opposite to the external field at the center of the current. The lines of this magnetic field are curved (see Figure 1) and outside of the ring they are in same direction as the external field. Thus, protons that are outside of the ring experience a 2 Page 3 of 34 Chemical Society Reviews downfield shift, while protons which are inside the ring experience an upfield shift. In 4n π electrons systems a paratropic ring current is induced, thus the effect on the external and internal protons is exactly the opposite. This model was challenged, 19 but a response to this challenge advocated that the model is valid. 20, 21 Thus, chemical shifts of protons can and have been used to identify aromatic and antiaromatic compounds. An extension of the use of NMR to assess aromaticity was developed mainly by R. Mitchell. 22 This and the conclusions regarding NMR as an aromaticity-determining tool are discussed below. Figure 1. Ring current and induced magnetic field in benzene. Magnetic susceptibility exaltation :23 This method is based on the empirical observation that for non- aromatic systems the experimental magnetic susceptibility can be predicted from the magnetic susceptibilities of the atoms with some correction factors. Aromatic systems show a magnetic susceptibility that is larger than the one calculated from the atoms and this difference is termed exaltation. This method was popular during the 60s-80s of the last century. Nowadays, mainly due to the difficultly of quantifying aromaticity with this method and the need for an empirical reference, together with the development of computational methods that allow a more detailed and direct study of the magnetic properties, in a qualitative and quantitative fashion, this method is rarely used. Thus, a CAS search of the topic “Magnetic susceptibility exaltation” in the last ten years yielded 51 results. None of them is an experimental measurement of the property and most of them are used as computational evidence for aromaticity of the studied compounds, mainly in comparison to other criteria of aromaticity, such as the recent demonstration by Andjelkovic et al. 24 Since the experimental measurement of magnetic susceptibility exaltation is almost non-existent and computationally there are better methods for assessing aromaticity (see below), this topic will not be further discussed here. It should be emphasized that neither aromaticity nor ring currents are measureable quantities. However, both NMR chemical shifts and diamagnetic susceptibility exaltation are experimentally measurable quantities that result from ring currents. The following two methods, current density analysis (CDA) and nucleus independent chemical shifts (NICS) are computational only. Current Density Analysis (CDA). This method visualizes the ring current via arrows. The direction of the arrows (clockwise or anticlockwise) describes the type of the current (paratropic or diatropic) while the size of the arrows indicates the strength of the current. The most popular methods for current density analysis are the Continuous Transformation of Origin of Current Density – Diamagnetic Zero (CTOCD- DZ) 25-27 also known as the ipsocentric method. 11, 12, 28 Two other CDA methods are the anisotropy of 3 Chemical Society Reviews Page 4 of 34 induced current density (ACID) 29 and gauge inlcuding magnetically induced current (GIMIC).30 The main advantage of the CDA methods is the pictorial representation of the ring current/s in the system. For example, it is easy to see that, pentalene has a global paratropic ring current and two small local paratropic currents, 31, 32 something that would be difficult (although not impossible, see below) to see with other methods.