Open-Shell Coupled-Cluster Valence-Bond Theory Augmented with an Independent Amplitude Approximation for Three-Pair Correlations: Application to a Model Oxygen-Evolving Complex and Single Molecular Magnet

We report the failure of coupled-cluster valence-bond (CCVB) theory with two-pair configurations [J. Chem. Phys. 2009, 130, 084103 (2009)] for open-shell (OS) spin-frustrated systems where including three-pair configurations is necessary to properly describe strong spin-correlations. We extend OS-CCVB by augmenting the model with three-pair configurations within the independent amplitude approximation (IAA). The resulting new electronic structure model, OS-CCVB+i3, involves only a quadratic number of independent wavefunction parameters. It includes the recently reported closed-shell CCVB+i3 as a special case. Its cost is dominated by integral transformations and it is capable of breaking multiple bonds exactly for all systems examined so far. The strength of OS-CCVB+i3 is highlighted in realistic systems including the [CaMn$_3$O$_4$] cubane subunit of the oxygen-evolving complex and a molecular magnet with the [Cr$_9$] core unit as well as model systems such as N$_3$, V$_3$O$_3$, and P$_5$. We show that OS-CCVB+i3 is only slightly dependent on the underlying perfect-pairing reference while OS-CCVB shows a stronger dependence. We also emphasize the compactness of the OS-CCVB+i3 wavefunction compared to the heat-bath configuration interaction wavefunction, a recently introduced soft exponential-scaling approach.