Efficient Grouped-Bath Ansatz for Spin–Flip Nonorthogonal Configuration Interaction in Transition-Metal Charge-Transfer Complexes

We introduce a novel grouped-bath ansatz that approximates the spin-flip nonorthogonal configuration interaction (SF-NOCI) ansatz, named SF-GNOCI, which significantly reduces computational cost while preserving accuracy. SF-NOCI, originally developed by Mayhall et al., is a robust and nearly "black-box" electronic structure theory well suited for studying charge-transfer phenomena. It captures orbital relaxation effects for all configurations within the active space, providing a balanced correlation among charge transfer and other states. However, including these relaxation effects for all configurations results in a sharp increase in computational cost, especially for the large active spaces commonly encountered in transition metal complexes. To overcome this challenge, we grouped configurations based on the number of electrons associated with each atom. Configurations within each group share a common set of bath orbitals, significantly reducing computational overhead. We demonstrate the performance of SF-GNOCI through benchmark calculations on two systems: the avoided crossing of the lowest singlet states in LiF dissociation and the low-lying charge transfer states of [Fe(SCH₃)₄]^2-/1-. Our results show that SF-GNOCI achieves accuracy comparable to standard SF-NOCI while reducing computational cost by a factor of 10 for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>F</mml:mi><mml:mi>e</mml:mi></mml:mrow><mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mrow><mml:mi>S</mml:mi><mml:mi>C</mml:mi><mml:mi>H</mml:mi></mml:mrow><mml:mn>3</mml:mn></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mn>4</mml:mn></mml:msub><mml:mo>]</mml:mo></mml:mrow><mml:mrow><mml:mn>2</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msup></mml:math> and 15 for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mi>F</mml:mi><mml:mi>e</mml:mi></mml:mrow><mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mrow><mml:mi>S</mml:mi><mml:mi>C</mml:mi><mml:mi>H</mml:mi></mml:mrow><mml:mn>3</mml:mn></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mn>4</mml:mn></mml:msub><mml:mo>]</mml:mo></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>-</mml:mo></mml:mrow></mml:msup></mml:math>. We believe that the SF-GNOCI ansatz is a promising reference state for efficiently describing charge transfer phenomena in transition metal complexes.