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Nuclear Magnetic Resonance Spectroscopy
Published in Rui Yang, Analytical Methods for Polymer Characterization, 2018
As a special case, let us discuss the proton resonance of benzene. The chemical shift of the protons in benzene is observed at 7.3 ppm, while that in ethylene is observed at 5.23 ppm. The shielding of aromatic protons as compared to olefinic protons is reduced, caused by the circulating π-electrons surrounding the entire molecule. An aromatic molecule can be visualized as a current loop, where π-electrons freely move in a circle formed by the σ framework. If these compounds are subjected to an external magnetic field, a diamagnetic ring current is induced. The secondary field resulting from this current is aligned opposite to B0. As a result, protons in the molecular plane and outside the ring are deshielded. Conversely, protons in the region above or below the plane of the ring are strongly shielded (Figure 5.8).
Structure, aromaticity and reactivity of corannulene and its analogues: a conceptual density functional theory and density functional reactivity theory study
Published in Molecular Physics, 2018
Youer Deng, Donghai Yu, Xiaofang Cao, Lianghong Liu, Chunying Rong, Tian Lu, Shubin Liu
To quantify the aromaticity propensity, several descriptors have been available in the literature from the perspective of the energetics, electron delocalisation, geometric variation and magnetic property criteria [61–66]. Here, we consider three descriptors, including, at first, the HOMA (harmonic oscillator model of aromaticity) index, which is a geometrical measurement of the equalisation of chemical bonds on an aromatic ring. Its definition is the following [67]: where n is the bond number of the considered ring, Rav is the average bond length, Ri is the bond length (all in Å), of each bond on the ring, and α is the normalisation constant (for C-C bonds α = 257.7). A HOMA value of <0, = 0 and = 1 represents antiaromatic, nonaromatic and perfect aromatic systems, respectively. The second descriptor that we considered is the aromatic fluctuation index (FLU), which describes the fluctuation of electronic charge between adjacent atoms in a given ring. Its definition is as follows [68]; , and , where Sij(A) is the overlap of the molecular orbitals i and j within the basin of atom A. The smaller the FLU value, the stronger the aromaticity. And, finally, the last index employed in our study is the nucleus-independent chemical shift (NICS) derived from the effect of aromatic ring current. It is found that a diatropic (diamagnetic) ring current is associated with aromaticity, whereas a paratropic (paramagnetic) ring current signals antiaromaticity. This difference in ring currents generates noticeable differences in NMR chemical shifts, and thus can be used to quantify aromaticity and antiaromaticity [69,70]. In formulation, NICS at the chosen point RN located at or on top of a ring can be described as the sum of partial chemical shifts arising from occupied molecular orbitals Ψk0 [71–73:] where the first and second terms on the right-hand side of Equation (19) are the diamagnetic and paramagnetic contributions, respectively, LN = rN × ∇ refers to the angular momentum operator, rN = r − RN, and r is the electron position. A more negative value of σ is an indication of a stronger aromaticity, whereas a positive σ value suggests that the ring is antiaromatic. We only consider the case of RN = 0 in this study [74]. That is, the chosen point is located at the centre of the ring to be studied and the calculated property is denoted by NICS(0) [70–72].