Geometry and magnetic structure variation in manganese-oxide clusters determined by a self-consistent, LCAO method*

\textit{Ab initio} simulations are used to study the variation in geometry and magnetic structure in Mn$_{x}$O$_{y}$ ($x=$3,4; $y=$1,2) clusters. The groundstate wavefunctions for clusters with different magnetic coupling (ferromagnetic, ferrimagnetic and antiferromagnetic) are modeled with linear combinations of atomic orbitals (LCAOs). Self-consistent energies for different spin isomers are calculated by constraining the magnetic moments of Mn atoms constituting each basis AO. The ferrimagnetic and antiferromagnetic ground-state structures of Mn$_{x}$O$_{y}$ are 0.16--1.20 eV lower in energy than their ferromagnetic isomers. The presence of oxygen thus stabilizes low-spin isomers relative to the preferred high-spin ordering of bare Mn$_{3}$ and Mn$_{4}$. Each cluster has a preferred overall magnetic moment, and no evidence is seen of competing states with different spin multiplicities. However, non-degenerate isomags (clusters that possess the same spin multiplicity but different arrangements of local moments) do contribute to peak broadening observed in negative-ion photoelectron spectra. Proper accounting for all possible isomags is shown to be critical for accurate comparison with experimental spectra.