Understanding proton magnetic shielding in the benzene molecule

According to the ring current model quoted in textbooks of nuclear magnetic resonance spectroscopy, the downfield chemical shifts of hydrogen nuclei in aromatic molecules is due to intense delocalized currents induced in the p-electron cloud by a magnetic field at right angles to the molecular plane. By using the Biot-Savart law, it was found that the delocalized ring currents deshield the out-of-plane component of proton shielding tensor via an essentially local mechanism taking place in the close vicinity of protons. The p ring currents over distant carbons shield the protons. p and r electrons deshield benzene protons via different mechanisms clearly observed in plots of the shielding density function defined in the text. These results provide a novel interpretation of the phenomenology and suggest that the familiar model for interpreting chemical shifts of aromatics should be revised. 2004 Published by Elsevier B.V. The ab initio model for the current densities induced in the benzene molecule by a magnetic field perpendicular to the ring plane started being developed in the early 1980s [1,2]. Accurate representations of the streamlines and modulus of the current density field are now available [3]. However, current density maps are not sufficient to understand some aspects of magnetic response of the benzene molecule. In particular, nuclear magnetic shielding of both hydrogen and carbon nuclei are not fully understood. The present note is aimed at investigating the source of deshielding of benzenic hydrogen nuclei via magnetic shielding density maps [4,5]. It was found that these maps provide powerful analytical tools for interpreting nuclear magnetic shielding [6]. Let us consider a molecule interacting with a static magnetic field with flux B, generating an electronic current density JðrÞ. The magnetic field induced at point r0 by a feedback effect is given by the Biot-Savart law [7,8], * Corresponding author. Fax: +39-059-373-543. E-mail address: [email protected] (P. Lazzeretti). 0009-2614/$ see front matter 2004 Published by Elsevier B.V. doi:10.1016/j.cplett.2004.04.022 BINDðr0Þ 1⁄4 1 c Z r r0 jr r0j JðrÞdr rðr0Þ B; ð1Þ where r is the distance of the volume element dr from the origin. The effective field acting on the point r0 is Bþ BINDðr0Þ. The second-rank dimensionless tensor rðr0Þ describes the local magnetic shielding. If r0 coincides with RI , the position of nucleus I , the nuclear magnetic shielding can be defined via radðRIÞ rIad 1⁄4 1 c abc Z dr rb RIb jr RIj Jd c ðrÞ; ð2Þ