Although the unique cyclo [18]carbon (C 18 ) realized by recent experiments has been greatly concerned, it has so far remained elusive. In contrast, its precursors C 18 -(CO) n (n = 6, 4, and 2), which can be separated stably, are of more practical significance. In this paper, the bonding character, electron delocalization, and aromaticity of the C 18 -(CO) n (n = 6, 4, and 2) with out-of-plane and in-plane dual π systems (π out and π in ) perpendicular to each other are studied by combining quantum chemical calculations and wavefunction analyses. These cyclocarbon oxides exhibit alternating long and short C-C bonds and extensive electron delocalization, and a significant diatropic induced ring current under the action of external magnetic field is therefore observed, which reveals the aromatic characteristic in the molecules. The global electron delocalization and significant influence of the number of intramolecular carbonyl (-CO) on the two sets of π conjugated systems have been focused on, and the essential reason for the distinct difference in the overall aromaticity of the molecules was also clarified. It seems that the substituent -CO groups hinders the electron delocalization of the π in system but has relatively small effect on the π out system, resulting in the molecules with less -CO group showing greater aromaticity.

Considering their remarkable chemical stability, the precursors of cyclo[18]carbon (C18), C18-(CO)n (n = 2, 4, and 6), have more practical significance than the elusive C18 ring. In the present paper, the electronic spectrum and (hyper)polarizability of the C18-(CO)n (n = 2, 4, and 6) are studied by theoretical calculations and analyses for revealing the utility of introduction of carbonyl (-CO) groups on molecular optical properties. The analysis results show that the successive introduction of -CO groups leads to red-shift of the absorption spectrum, but maximum absorption of all molecules is mainly due to the charge redistribution caused by electron transition within C18 ring. Except for the vanishing first hyperpolarizability of C18-(CO)6 results from its octupolar character, the (hyper)polarizabilities of the precursors present an ascending trend with the increase of -CO groups in the molecule, and the higher-order response properties are more sensitive to the number of -CO groups. By means of (hyper)polarizability density analysis and (hyper)polarizability contribution decomposition, the fundamental reasons for the difference of (hyper)polarizability of different molecules were systematically discussed from the perspectives of physical and structural origins, respectively. As to the frequency dispersions under the incident light, the significant optical resonances were found on the hyperpolarizability of molecules C18-(CO)n (n = 2, 4, and 6), which contrast with the fact that it has inconspicuous influences on molecular polarizability.

No abstract

The independent gradient model (IGM) originally proposed in Phys. Chem. Chem. Phys., 19, 17928 (2017) has been increasingly popular in visual analysis of intramolecular and intermolecular interactions in recent years, and it has many clear advantages over the widely employed noncovalent interaction (NCI) method, such as intrafragment and interfragment interactions can be elegantly isolated and thus separately studied, the isosurfaces are smoother and less jaggy. However, we frequently observed that there is an evident shortcoming of IGM map in graphically studying weak interactions, that is its isosurfaces are usually too bulgy; in these cases, not only the graphical effect is poor, but also the color on some areas on the isosurfaces is inappropriate and may lead to erroneous analysis conclusions. In addition, the IGM method was originally proposed based on promolecular density, which is quite crude and does not take actual electronic structure into account. In this article, we first present a detailed overview of the IGM analysis, and then propose our new variant of IGM, namely IGM based on Hirshfeld partition of molecular density (IGMH), which replaces the free-state atomic densities involved in the IGM method with the atomic densities derived by Hirshfeld partition of actual molecular electron density. This change makes IGM have more rigorous physical background. In addition, we describe some indices defined on the top of IGM or IGMH framework to quantify contributions from various atoms or atom pairs to interaction between specific fragments. A large number of application examples in this article, including molecular and periodic systems, weak and chemical bond interactions, fully demonstrate the important value of IGMH in intuitively understanding interactions in chemical systems. Comparisons also showed that the IGMH usually has markedly better graphical effect than IGM and overcomes known problems in IGM. Currently IGMH analysis has been efficiently supported in our freely available and user-friendly wavefunction analysis code Multiwfn (http://sobereva.com/multiwfn), and a detailed tutorial is presented. We hope that IGMH will become a new popular method among chemists for exploring interactions in wide variety of chemical systems.

Graphically revealing interaction regions in a chemical system enables chemists to notice the areas at a glance where significant interactions have formed, it is very helpful in studying chemical bonds, intermolecular and intramolecular interactions. Reduced density gradient (RDG) has already been widely employed in literatures to visually exhibit weak interaction regions, in fact it also has the ability of revealing chemical bonding regions. Unfortunately, RDG cannot clearly show both types of the interactions at the same time. In this paper, we propose a new real space function named interaction region indicator (IRI), which is a slight modification on RDG. We found IRI can reveal chemical bonding and weak interaction regions equally well, this brings great convenience in the study of various chemical systems as well as chemical reactions. It is noteworthy that IRI has simpler definition, lower computational cost and better graphical effect than the density overlap regions indicator (DORI), which has similar purpose to IRI. In this article IRI is also compared with atom-in-molecules (AIM) topology analysis of electron density, we demonstrated that IRI has the ability to reveal additional interactions to provide chemists a more complete picture. In addition, we put forward a variant of IRI named IRI-pi, which is dedicated to reveal interactions of pi electrons. It is found that IRI-pi can not only distinguish type of pi interactions but can also exhibit pi-interaction strength. IRI and IRI-pi have been efficiently implemented in our freely available Multiwfn wavefunction analysis code, it is expected that they will become new useful members of computational chemists' toolbox in studying chemical problems.