A new NICS-based aromaticity index; NICS-rate Siamak Noorizadeh * , Maryam Dardab Chemistry Department, College of Sciences, Shahid Chamran University, Ahvaz, Iran article info Article history: Received 24 February 2010 In final form 6 May 2010 Available online 19 May 2010 abstract The NICS-rate index is introduced as a new aromaticity indicator. The presence of a maximum/minimum in the NICS-rate curve ( DNICS Dr versus r) of a molecule indicates to aromaticity/antiaromaticity of the system. For those molecules, which show both maximum and minimum in their curves, the absolute ratio of the maximum to the minimum NICS-rates (NRR) is defined as a measure of aromaticity. Also NRR = 0.5 is found as the boundary between aromatic and nonaromatic systems. Surprisingly for those molecules in which NICS(0) cannot correctly give the aromaticities of the rings, the NICS-rate successfully predicts the aromaticities of the systems. Ó 2010 Elsevier B.V. All rights reserved. 1. Introduction Aromaticity, the property resulting from cyclic conjugation [1], is an important concept in chemistry and has been subject of de- bate since the 19th century and is still an attracting considerable interest. Since high stability, low reactivity and sustained induced ring current imply to high aromaticity, therefore this concept is one of the features controlling the stability and reactivity of unsat- urated cyclic and polycyclic compounds and has a key role in many reactions which occur in the biological systems. Theoretical inves- tigation for the origin of this concept has gained a rapid develop- ment [2–7] and two issues of Chemical Reviews were dedicated to cover this topic [8,9]. Many efforts have been made to quantify aromaticity [10–12]; but since it is not a directly observable quan- tity therefore, it is usually evaluated indirectly by measuring a property that reflects the aromatic character of the molecule. Accordingly, aromaticities are evaluated on the basis of some ener- getic, geometric, electronic and magnetic criteria. Several methods for the calculation of magnetic-based aroma- ticities are introduced [13–17]. One of the most widely used indi- ces is the Nucleus-Independent Chemical Shift (NICS), which is defined as the negative of magnetic shielding in a given point of the molecule [18]. It is shown that negative NICS value of a ring indicates to presence of an induced diatropic ring current, which is interpreted as aromaticity; whereas positive value denotes para- tropic ring current and is interpreted as antiaromaticity. This index has been used extensively to asses the aromaticity and antiaroma- ticity of many organic and inorganic compounds [19–26]. In some cases, however, using NICS value at the geometrical center of the ring (NICS(0)) may mislead or contradict other indices of aromatic- ity [27–30]. Therefore it seems that single NICS(0) value is not a very good tool for assessing whether a molecule is aromatic or not. Hence due to its conceptual imperfections, NICS has been re- fined considerably [31]. As shown by Lazzeretti [27] and Aihara [32], NICS(0) values contain important spurious contributions from the in-plane tensor components that are not related to aromaticity. Therefore NICS(1) (1 Å above/below the plane of the ring), which essentially reflects p effects, is a better indicator of the ring cur- rent. It is recalled that, at this distance the effects of the local r- bonding contributions are diminished [33,34]. It is also shown that NICS(1) zz , which is the out-of-plane zz components’ contribution of the NICS tensor 1 Å above the ring, is better correlated with the other aromaticity indices [35]. Recently Stanger [36] developed the scheme of scanning the NICS values (NICS scan) up to a certain distance from the ring center. From the scan curve it is proposed that for aromatic systems, the NICS values will pass through a min- imum; while for antiaromatic species no minimum is observed. This method is also successfully applied in some inorganic systems [37,38]. The purpose of this Letter is to introduce a new method for indi- cation of aromaticity in cyclic compounds based on the variation of NICS index at different distances from the ring center. This method, which is denoted as NICS-rate, is applied in both monocyclic and polycyclic molecular systems. 2. Computational details The geometries of the considered molecules in this study are optimized at the MP2 level with 6-311++G** basis set. Note that, this level of theory considers both correlation and dispersion ef- fects in energy calculation. Vibrational frequencies are also calcu- lated to verify that the optimized structures are local minima on the potential energy surfaces. Using the optimized structures, NICS values are calculated at the HF/6-31+G* level of theory using the GIAO method [39]. It is mentioned that the ghost atom (Bq) is a 0009-2614/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2010.05.025 * Corresponding author. Fax: +98 6113331042. E-mail address: noorizadeh_s@scu.ac.ir (S. Noorizadeh). Chemical Physics Letters 493 (2010) 376–380 Contents lists available at ScienceDirect Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett