Accurate Ab Initio Calculation of Ionization Potentials of the First-Row Transition Metals with the Configuration-Interaction Quantum Monte Carlo Technique

Accurate ionization potentials of the first-row transition-metal atoms are obtained via the initiator full configuration quantum Monte Carlo technique, performing a stochastic integration of the electronic Schrödinger equation in exponentially large Hilbert spaces, with a mean absolute error of $0.13\mathrm{kcal}/\mathrm{mol}$ (5 meV). This accuracy requires correlation of the $3p$ semicore electrons and in some cases the $3s$ manifold, along with extrapolation of the correlation energies to the complete-basis-set limit, and provides a new theoretical benchmark for the ionization potentials of these systems.

Figure 1

Schematic diagram of an allowed particle-hole excitation. On the left is shown the Hartree-Fock determinant (specifically, the Cr atom is illustrated), and on the right is an excited determinant in which the two “red” electrons have been promoted into the virtual manifold. One of these electrons is drawn from the $3p$ shell, and hence the determinant on the right would be admissible with $n_{h,3p}\ge 1$ but would be disallowed in the previous frozen-core regime. No such restriction is placed on electrons of the valence manifold.

Figure 2

Convergence in complete-basis-set limit ionization potentials for the first-row transition-metal atoms compared to their experimental values with the allowed number of $3p$ holes, $n_{h,3p}$ (upper panel), and the allowed number of $3s3p$ holes, $n_{h,3s3p}$ (lower panel). Note that the $3s3p$ results for Co and Ni are achieved with Q5 extrapolations, while TQ extrapolations suffice for the remainder.