Electron density structural torsion

Quantum chemical topology (QCT) extracts chemical information from the electron density, ρr, and its derivatives. In this context, however, a direct Helmholtz decomposition of the gradient field of the density, ∇ρr, is uninformative because a gradient field is purely longitudinal. We introduce the density structural torsional vector (DSTV), Fρr=∇lnρrρ0×∇∇2ρr, where ρ0 is a constant positive reference density introduced to make the logarithm dimensionless; its value does not affect the resulting field. The DSTV measures the local directional noncollinearity between the relative density gradient and the spatial variation of the Laplacian of the density and is divergence-free by construction. Its associated scalar descriptors, Sr=sinθr and Sρr=ρrsinθr, where θ(r) is the local angle between the relative density gradient and the gradient of the Laplacian of the density quantify, respectively, the purely angular and density-weighted forms of this noncollinearity, with the latter emphasizing regions of appreciable electron density. Illustrative molecular calculations show that these descriptors reveal anisotropic density-curvature organization, shell structure, and bond-region features that are not immediately evident from the electron density, its gradient, or its Laplacian considered separately. Numerical examples are presented for simple diatomics, including Li2 with a non-nuclear attractor, and the water molecule. The method is proposed as a complementary electron density-derived vectorial descriptor for the real-space analysis of electronic structure.