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This paper introduces a real-time nonorthogonal multiconfigurational self-consistent field (RT-TD NOMCSCF) formalism to address systematic peak shifting errors in electronic structure methods that obscure experimental comparisons. By employing independently propagated orbital sets, the method reveals that peak shifting is influenced not only by state averaging but also by the external configurational space, leading to a more accurate recovery of transition energies. The findings establish a unified framework for nonlinear real-time electronic structure theories, enhancing the reliability of simulations for ultrafast processes.
Peak shifting in electronic structure predictions is not just a result of internal state averaging, but also a consequence of external configurational influences.
Self-consistent field real-time electronic structure methods are a powerful approach for modeling ultrafast processes but suffer from systematic errors in predicted transition energies, commonly known as peak shifting, that obscure direct comparison with experiment. Although this effect has been explored in single reference methods, a general understanding that extends to multiconfigurational methods remains unresolved. Here, we develop a real-time nonorthogonal multiconfigurational self-consistent field (RT-TD NOMCSCF) formalism in which independently propagated orbital sets generate a compact, nonorthogonal wavefunction. The approach establishes a unified framework for nonlinear real-time electronic structure theories, which we use to reveal the common origin of peak shifting across single and multireference limits. Using this framework, we demonstrate that peak shifting does not arise exclusively from the effect of state averaging over the internal space basis, but also from the accessible external configurational space. By systematically expanding the internal space with independently propagated orbital sets, RT-TD NOMCSCF suppresses this aver- aging, recovers correct transition energies, and distinguishes intrinsic peak shifting from numerical peak drifting caused by propagation errors. Thus, these developments establish nonlinear real-time electronic structure methods that enables more accurate simulations of ultrafast processes.