The Zeroth‐Order Approximation as the Bridge Between LPE and LPED: Two Coulomb‐Based QTAIM Descriptors for Intra/Intermolecular Interaction Energies

Abstract

The local potential energy (LPE) and local potential energy density (LPED) are Coulomb‐based QTAIM descriptors that assign interaction energies directly to individual bond critical points (BCPs), circumventing the locality limitation of global energy decomposition methods. Despite sharing the same algebraic expression, they differ by a single assumption—the zeroth‐order approximation—in which LPE implicitly sets the effective BCP volume to 1 Bohr 3 , collapsing LPED into an energy directly comparable to the supramolecular interaction energy (SME). Here, we provide the first rigorous derivation of this approximation, showing that its relative error is fully determined by |∇ 2 ρ bcp |/ ρ bcp , yielding a mean of 13.38% ± 2.39% across 25 chemically diverse systems. Linear correlation analysis reveals LPED achieves R 2 = 0.9607 with SME—marginally below ρ bcp ( R 2 = 0.9701) yet substantially above VIR(bcp) ( R 2 = 0.8698), confirming that isolating the electron–nucleus attractive term enhances rather than degrades predictive performance. Quantitative benchmarking establishes clear, application‐dependent selection criteria for both descriptors.