Independent gradient model based on Hirshfeld partition: A new method for visual study of interactions in chemical systems

TLDR

The independent gradient model (IGM) is widely used for visualizing molecular interactions, but its promolecular basis and often bulgy, poorly colored isosurfaces limit accurate depiction of weak interactions. This work introduces IGMH, an IGM variant that replaces free‑state atomic densities with Hirshfeld‑partitioned molecular densities, aiming to provide a more accurate and broadly useful interaction analysis tool. IGMH derives its more rigorous physical foundation by using Hirshfeld‑partitioned atomic densities instead of promolecular densities. Extensive applications to molecular and periodic systems demonstrate that IGMH yields clearer, more accurate interaction maps than IGM, and the method is now available in the Multiwfn wave‑function analysis package.

Abstract

The powerful independent gradient model (IGM) method has been increasingly popular in visual analysis of intramolecular and intermolecular interactions in recent years. 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 propose an improvement version 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. 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 supported in our wavefunction analysis code Multiwfn (http://sobereva.com/multiwfn). We hope that IGMH will become a new useful method among chemists for exploring interactions in wide variety of chemical systems.