Equation-of-Motion Block-Correlated Coupled Cluster Theory with up to Four-Block Correlation for Excited Electronic States of Strongly Correlated Systems

The theoretical treatment of low-lying excited states in strongly correlated (SC) systems, particularly those with multi-electron excitation character, typically requires computational methods with exponential scaling. To address this bottleneck, we develop the equation-of-motion generalized valence bond based block-correlated coupled cluster approach with up to four-block correlation (EOM-GVB-BCCC4). This method is capable of capturing low-lying excited states of SC systems with large active spaces with a polynomial <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:msup><mml:mi>N</mml:mi><mml:mn>6</mml:mn></mml:msup><mml:mo>)</mml:mo></mml:math> cost. We show that this approach provides a noticeable improvement over its lower-order truncated schemes, successfully identifying the doubly excited triplet-triplet pair state in singlet-fission candidates that were missed by its EOM-GVB-BCCC3 variant. Furthermore, the method achieves remarkably high accuracy for transition-metal complexes and organic diradicals, yielding excitation energies in excellent agreement with density matrix renormalization group (DMRG) benchmarks. These results highlight EOM-GVB-BCCC4 as a powerful method for investigating SC systems with large active spaces that are beyond the reach of conventional multireference approaches.