Atom-Centered Potentials for Fast and Accurate Electronic Energies at the Complete Basis Set Limit

Quantum chemistry calculations often face a trade-off between computational cost and accuracy: Reaching the complete basis set (CBS) limit for accurate electronic energies typically requires prohibitively expensive calculations. This thesis addresses this long-standing cost–accuracy challenge by developing atom-centered potentials (ACPs) that enable fast yet accurate electronic energy predictions at the CBS limit. ACPs are auxiliary one-electron potentials added to the Hamiltonian that improve the energy or energetic property obtained with a low-cost, smallbasis method so that it reproduces the results of a high-accuracy method. In this work, ACPs are trained to accurately recover absolute Hartree–Fock (HF) and second-order Møller–Plesset (MP2) energies at the CBS level using only double-ζ basis set calculations. A diverse training set of 3302 molecular structures (spanning ten elements and up to 70 atoms) was compiled to optimize the ACP parameters, and two independent test sets were used to evaluate the generality of the ACP corrections. The ACP parameters were determined via regularized linear regression (LASSO) to prevent overfitting while ensuring physically meaningful corrections. Key results demonstrate that the ACP approach dramatically reduces basis set incompleteness errors by orders of magnitude. For example, an ACP-corrected HF method (ACPHF) achieved mean absolute errors of only 0.3 kcal/mol relative to HF/CBS energies. We also obtained MP2/CBS energies through a composite scheme (ACPComp) with an average mean absolute error of 0.5 kcal/mol. This composite ACP method retains accuracy across small and large molecules and significantly enhances computational efficiency, speeding up MP2/CBS calculations by over three orders of magnitude.