Introducing DDEC6 Atomic Population Analysis: Part 5. New Method to Compute Polarizabilities and Dispersion Coefficients

Polarizabilities and London dispersion forces are important to many chemical processes. Leading terms in these forces are often modeled using polarizabilities and C<sub>n</sub> (n=6, 8, 9, 10 …) dispersion coefficients. Force fields for classical atomistic simulations can be constructed using atom-in-material dispersion coefficients and polarizabilities. This article addresses the key question of how to efficiently assign these parameters to constituent atoms in a material so that properties of the whole material are better reproduced. We develop a new set of scaling laws and computational algorithms (called MCLF) to do this in an accurate and computationally efficient manner across diverse material types. We introduce a conduction limit upper bound and m-scaling to describe the different behaviors of surface and buried atoms. We validate MCLF by comparing results to high-level benchmarks for isolated neutral and charged atoms, diverse diatomic molecules, various polyatomic molecules (e.g., polyacenes, fullerenes, and small organic and inorganic molecules), and dense solids (including metallic, covalent, and ionic). MCLF provides the non-directionally screened polarizabilities required to construct force fields, the directionally-screened static polarizability tensor components and eigenvalues, and environmentally screened C<sub>6</sub> coefficients. Overall, MCLF has improved accuracy and lower computational cost than the TS-SCS method. For TS-SCS, we compared charge partitioning methods and show DDEC6 partitioning yields more accurate results than Hirshfeld partitioning. MCLF also gives approximations for C<sub>8</sub>, C<sub>9</sub>, and C<sub>10</sub> dispersion coefficients and Quantum Drude Oscillator parameters. For sufficiently large systems, our method’s required computational time and memory scale linearly with increasing system size. This is a huge improvement over the cubic computational time of direct matrix inversion. As demonstrations, we study an ice crystal containing >250,000 atoms in the unit cell and the HIV reverse transcriptase enzyme complexed with an inhibiter molecule. This method should find widespread applications to parameterize classical force fields and DFT+dispersion methods.