Accelerated discoveries of new materials, molecules, and chemical reactions on a computer require low-cost methods that would enable rapid screening of chemical and configurational spaces. Lower-than-DFT computational costs have only been demonstrated in (semi-)empirical methods that are either analytical (such as reactive force fields and artificial neural networks) or are based on the tight-binding formalism. These models, however, often require large training sets and involve parameters that often lack transferability even among chemically similar species. Consequently, they only allow for knowledge interpolation, not for extrapolation.<br/><br/>We posit that a low-cost, minimally empirical, and transferable chemical bond breaking and formation model must satisfy two criteria. First, it must be exact for at least one physical system. Second, it must be derived from formally exact theories (DFT and/or configuration interaction). To this end, we reformulated a rather overlooked Anderson-Weeks-Adams-Gilbert theory of localized orbitals from 1960s in the DFT language. The derived total energy expression turns out to be equivalent to a Huckel model with variationally optimized atomic states, non-empirical Hamiltonian matrix elements, and explicit orthogonalization, electrostatic, and exchange-correlation terms. Importantly, the theory is exact in the asymptotic limit of large interatomic separations to the first order in the interatomic overlap. Uniquely, the electronegativity equalization principle emerges in the theory in a very natural way. Numerical tests for symmetric Hx polygons (2≤x≤12) of different spin multiplicities reveal superior accuracy in comparison with state-of-the-art (semi)empirical models, using only a single parameter that is eliminated in energy differences between bonded structures. Generalization of the methodology to main-group elements and polar covalent bonds is underway.

Asymptotic density functional theory ansatz for accelerated simulations of chemically interacting systems

ACS Spring 2022

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