Open-shell coupled-cluster valence-bond theory augmented with an independent amplitude approximation for three-pair...

We report the failure of coupled-cluster valence-bond (CCVB) theory with two-pair configurations [D. W. Small and M. Head-Gordon, J. Chem. Phys. 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. 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 [CaMn₃O₄] cubane subunit of the oxygen-evolving complex and a molecular magnet with the [Cr₉] core unit as well as model systems such as N₃, V₃O₃, and P₅. 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.