"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 material systems, here we bridge the gap in our understanding of these methods and examine the size-dependence of errors in RT density propagation. We analyze the performance of RT 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 the 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."

# Publications

## 2023

Ranka K, Isborn CM. Size-dependent errors in real-time electron density propagation. The Journal of Chemical Physics. 2023;158(17). doi:10.1063/5.0142515

Chen MS, Mao Y, Snider A, Gupta P, Montoya-Castillo A, Zuehlsdorff TJ, Isborn CM, Markland TE. Elucidating the Role of Hydrogen Bonding in the Optical Spectroscopy of the Solvated Green Fluorescent Protein Chromophore: Using Machine Learning to Establish the Importance of High-Level Electronic Structure. The Journal of Physical Chemistry Letters. 2023;14(29):6610–6619. doi:10.1021/acs.jpclett.3c01444

Han B, Isborn CM, Shi L. Incorporating Polarization and Charge Transfer into a Point-Charge Model for Water Using Machine Learning. The Journal of Physical Chemistry Letters. 2023;14(16):3869–3877. doi:10.1021/acs.jpclett.3c00036

## 2022

Cheng C-Y, Krainova N, Brigeman AN, Khanna A, Shedge S, Isborn C, Yuen-Zhou J, Giebink NC. Molecular polariton electroabsorption. Nature Communications. 2022;13(1):7937. doi:10.1038/s41467-022-35589-4

We investigate electroabsorption (EA) in organic semiconductor microcavities to understand whether strong light-matter coupling non-trivially alters their nonlinear optical [\$\$\\chi \ˆ\(3)\łeft(ømega,\\\\\mathrm\0,0\\\\\\right)\$\$] response. Focusing on strongly-absorbing squaraine (SQ) molecules dispersed in a wide-gap host matrix, we find that classical transfer matrix modeling accurately captures the EA response of low concentration SQ microcavities with a vacuum Rabi splitting of \$\$\hslash Ømega \approx 200\$\$meV, but fails for high concentration cavities with \$\$\hslash Ømega \approx 420\$\$meV. Rather than new physics in the ultrastrong coupling regime, however, we attribute the discrepancy at high SQ concentration to a nearly dark H-aggregate state below the SQ exciton transition, which goes undetected in the optical constant dispersion on which the transfer matrix model is based, but nonetheless interacts with and enhances the EA response of the lower polariton mode. These results indicate that strong coupling can be used to manipulate EA (and presumably other optical nonlinearities) from organic microcavities by controlling the energy of polariton modes relative to other states in the system, but it does not alter the intrinsic optical nonlinearity of the organic semiconductor inside the cavity.

Taka AA, Lu S-Y, Gowland D, Zuehlsdorff TJ, Corzo HH, Pribram-Jones A, Shi L, Hratchian HP, Isborn CM. Comparison of Linear Response Theory, Projected Initial Maximum Overlap Method, and Molecular Dynamics-Based Vibronic Spectra: The Case of Methylene Blue. Journal of Chemical Theory and Computation. 2022;18(5):3039–3051. doi:10.1021/acs.jctc.1c01127

Bhat HS, Collins K, Gupta P, Isborn CM. Dynamic Learning of Correlation Potentials for a Time-Dependent Kohn-Sham System. In: Firoozi R, Mehr N, Yel E, Antonova R, Bohg J, Schwager M, Kochenderfer M, Firoozi R, Mehr N, Yel E, et al., editors. Proceedings of The 4th Annual Learning for Dynamics and Control Conference. Vols. 168. PMLR; 2022. pp. 546–558.

We develop methods to learn the correlation potential for a time-dependent Kohn-Sham (TDKS) system in one spatial dimension. We start from a low-dimensional two-electron system for which we can numerically solve the time-dependent Schrodinger equation; this yields electron densities suitable for training models of the correlation potential. We frame the learning problem as one of optimizing a least-squares objective subject to the constraint that the dynamics obey the TDKS equation. Applying adjoints, we develop efficient methods to compute gradients and thereby learn models of the correlation potential. Our results show that it is possible to learn values of the correlation potential such that the resulting electron densities match ground truth densities. We also show how to learn correlation potential functionals with memory, demonstrating one such model that yields reasonable results for trajectories outside the training set.

Gupta P, Bhat HS, Ranka K, Isborn CM. Statistical learning for predicting density–matrix-based electron dynamics. Stat. 2022;11(1):e439. doi:https://doi.org/10.1002/sta4.439

## 2021

Shedge SV, Zuehlsdorff TJ, Khanna A, Conley S, Isborn CM. Explicit environmental and vibronic effects in simulations of linear and nonlinear optical spectroscopy. The Journal of Chemical Physics. 2021;154(8):084116. doi:10.1063/5.0038196

Dunnett AJ, Gowland D, Isborn CM, Chin AW, Zuehlsdorff TJ. Influence of non-adiabatic effects on linear absorption spectra in the condensed phase: Methylene blue. The Journal of Chemical Physics. 2021;155(14):144112. doi:10.1063/5.0062950

Han B, Isborn CM, Shi L. Determining Partial Atomic Charges for Liquid Water: Assessing Electronic Structure and Charge Models. Journal of Chemical Theory and Computation. 2021;17(2):889–901. doi:10.1021/acs.jctc.0c01102