Atom-Centered Potentials (ACPs) address a core challenge in computational chemistry: balancing computational efficiency with accuracy. ACPs are corrective potentials added to the Hamiltonian to reduce quantum chemical modeling errors, significantly improving calculated properties when used in programs like Gaussian-16.

The development workflow (see figure) begins with selecting target atoms, choosing ACP parameters, and specifying the method/basis set. A high-accuracy reference dataset (typically CCSD(T)/CBS) is then assembled for fitting. Using constrained linear least-squares optimization, we generate ACPs tailored to the chosen purpose.

Functionally, ACPs are similar to the Hubbard $U$, modifying the electronic environment. Structurally, they resemble effective core potentials (ECPs), a well-established tool in computational chemistry. The potentials have the form: $$V_\alpha = U_L(r) + \sum_{l=0}^{L-1} \left[ U_l(r) – U_L (r) \hat{P}_l \right]$$ where $\alpha$ is the atom, $U_L(r)$ is a radial potential, $U_l(r)$ is a potential associated with specific angular momentum values (s, p, d, …), and $\hat{P}_l$ are spherical harmonic projection operators. $U_L(r)$ is constructed as a sum of Gaussian functions: $$U_L(r) = r^{-2}\sum_i c_i e^{-\zeta_i r^2}$$ In the development of ACPs, we select a fixed range of values for $\zeta_i$, and use the LASSO method to perform the optimization. The formulation of ACPs enables easy integration into widely used software like Gaussian, requiring only minor input modifications and no custom coding.