Eliminating spin-asymmetric orbital instabilities of unrestricted MRSF-TDDFT via selective Jacobi rotation

Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory (MRSF-TDDFT) has emerged as a promising linear-response framework capable of addressing multireference electronic structure, conical intersections, and doubly excited configurations while maintaining spin purity. Extending this framework to unrestricted Kohn-Sham (UKS) orbitals introduces desirable variational flexibility but also leads to spin-asymmetric orbital instabilities that degrade numerical stability and distort excitation energies. In this study, we identify the origin of these instabilities in the residual mismatch between the α and β spatial orbitals of UKS references and introduce a selective Jacobi-rotation procedure that systematically maximizes α-β orbital overlap without altering the UKS reference energy or mixing occupied and virtual spaces. Numerical tests on thymine and s-trans-butadiene demonstrate that the Jacobi-rotated orbitals eliminate anomalous orbital-overlap patterns, suppress geometry-dependent fluctuations of UMRSF-TDDFT energies, and recover smooth and physically consistent potential energy surfaces. Benchmarking against Thiel's TBE-2 set further confirms that UMRSF-TDDFT preserves the accuracy of the original MRSF-TDDFT while benefiting from improved orbital flexibility. The resulting approach restores numerical stability to the unrestricted formulation and broadens the applicability of MRSF-TDDFT to systems requiring enhanced spin polarization or exhibiting strong multiconfigurational character.