Valence and core ionization energies of atoms and small molecules using variational Monte Carlo with explicit correlation and Slater-type basis sets

Abstract Context Reliable prediction of both valence and core ionization energies remains challenging because these processes involve different balances of electron correlation, orbital relaxation, and basis-set flexibility. In this work, we assess whether variational Monte Carlo (VMC) with explicit correlation and compact Slater-type basis sets can provide accurate ionization energies without fitting to experimental data. As expected from their greater flexibility, double-zeta (DZ) and Hartree–Fock limit (HFL) Slater-type basis sets provide better agreement with experiment than single-zeta (SZ), particularly for atomic ionizations and some molecular cases. For H 2 O, VMC/HFL achieves a mean absolute error (MAE) of 0.42 eV, comparable to 0.39 eV from CCSD-GF/TZ2P; for CO, VMC/HFL gives an MAE of 0.67 eV. Removing the polarization functions has little effect on the core ionization energies. The calculations without polarization functions yield overall mean absolute errors of 0.65 eV for H ₂ O and 0.67 eV for CO. The accuracy arises from variational optimization of the explicit-correlation parameters without fitting to experimental ionization energies, supporting VMC as a practical approach for ionization-energy estimates and for extension to larger systems. Methods Hartree–Fock wave functions with Slater-type basis sets were used as trial wave functions. For atoms, the SZ, DZ, and HFL orbital expansions were taken from the literature. For neutral molecules, Hartree–Fock calculations were performed with Gaussian 09 using Slater-type basis sets from the literature to generate the corresponding LCAO coefficients. Single valence and core ionization energies were computed with the VMC method using a nine-parameter Boys–Handy explicit correlation factor and Slater-type basis sets, with and without polarization functions. The VMC calculations and parameter optimizations were performed with computer programs developed by the authors’ research group.