  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.
