Size-Dependent Errors in Real-Time Electron Density Propagation

17 January 2023, Version 3
This content is a preprint and has not undergone peer review at the time of posting.


Real-time (RT) electron density propagation with time-dependent density functional theory (TDDFT) or Hartree-Fock (TDHF) is one of the most popular methods to model the charge transfer in molecules and materials. However, both RT-TDHF and RT-TDDFT within the adiabatic approximation are known to produce inaccurate evolution of the electron density away from the ground state in model systems, leading to large errors in charge transfer and erroneous shifting of peaks in absorption spectra. Given the poor performance of these methods with small model systems and the widespread use of the methods with larger molecular and materials systems, here we bridge the gap in our understanding of these methods and examine the size-dependence of errors in real-time density propagation. We analyze the performance of real-time density propagation for systems of increasing size during the application of a continuous resonant field to induce Rabi-like oscillations, during charge-transfer dynamics, and for peak shifting in simulated absorption spectra. We find that the errors in the electron dynamics are indeed size dependent for these phenomena, with the largest system producing the results most aligned with those expected from linear response theory. The results suggest that although RT-TDHF and RT-TDDFT methods may produce severe errors for model systems, the errors in charge transfer and resonantly driven electron dynamics may be much less significant for more realistic, large-scale molecules and materials.


adiabatic approximation
time-dependent electron structure
real-time propagation
charge transfer

Supplementary materials

Supporting info for ”Size-Dependent Errors in Real-Time Electron Density Propagation”
Supporting information.


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