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Machine learning a molecular Hamiltonian for predicting electron dynamics

Journal Article · · International Journal of Dynamics and Control
 [1];  [2];  [2]
  1. Univ. of California, Merced, CA (United States); University of California Merced
  2. Univ. of California, Merced, CA (United States)
+ Show Author Affiliations
We develop a computational method to learn a molecular Hamiltonian matrix from matrix-valued time series of the electron density. As we demonstrate for three small molecules, the resulting Hamiltonians can be used for electron density evolution, producing highly accurate results even when propagating 1,000 time steps beyond the training data. As a more rigorous test, we use the learned Hamiltonians to simulate electron dynamics in the presence of an applied electric field, extrapolating to a problem that is beyond the field-free training data. We find that the resulting electron dynamics predicted by our learned Hamiltonian are in close quantitative agreement with the ground truth. Our method relies on combining a reduced-dimensional, linear statistical model of the Hamiltonian with a time-discretization of the quantum Liouville equation within time-dependent Hartree Fock theory. In conclusion, we train the model using a least-squares solver, avoiding numerous, CPU-intensive optimization steps. For both field-free and field-on problems, we quantify training and propagation errors, highlighting areas for future development.
Research Organization:
Univ. of California, Merced, CA (United States)
Sponsoring Organization:
NSF; USDOE Office of Science (SC), Basic Energy Sciences (BES)
Grant/Contract Number:
SC0020203
OSTI ID:
1773846
Journal Information:
International Journal of Dynamics and Control, Journal Name: International Journal of Dynamics and Control Journal Issue: 4 Vol. 8; ISSN 2195-268X
Publisher:
Springer NatureCopyright Statement
Country of Publication:
United States
Language:
English

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