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We will cover briefly the time-dependent density functional theory approach, extended to include pairing correlations, to induced fission of 238 U(n,f), 241,243 Pu, and 238 Np, and also results on scission neutrons and a number of very nontrivial aspects of induced fission.
Here, we present the theory, implementation, and benchmarking of a real-time time-dependent density functional theory (RT-TDDFT) module within the RMG code, designed to simulate the electronic response of molecular systems to external perturbations. Our method offers insights into nonequilibrium dynamics and excited states across a diverse range of systems, from small organic molecules to large metallic nanoparticles. Benchmarking results demonstrate excellent agreement with established TDDFT implementations and showcase the superior stability of our time integration algorithm, enabling long-term simulations with minimal energy drift. The scalability and efficiency of RMG on massively parallel architectures allow for simulations of complex systems, such as plasmonic nanoparticles with thousands of atoms. Future extensions, including nuclear and spin dynamics, will broaden the applicability of this RT-TDDFT implementation, providing a powerful toolset for studies of photoactive materials, nanoscale devices, and other systems where real-time electronic dynamics is essential.
The number and properties of the neutrons and photons emitted in nuclear fission are directly related to the excitation energy of the fission fragments when they are formed at scission. Though not observable experimentally because of the extremely short timescales, the excitation energy of fission fragments can be predicted by microscopic theory based on time-dependent density functional theory (TDDFT). Initial results on the value of the total kinetic energy of fission reactions were very promising, but could not probe all possible fragmentations. Here, in this work, we perform large-scale TDDFT calculations in 240 Pu enabled by the development of a new TDDFT solver. We obtain TDDFT trajectories covering nearly all possible fragmentations. We find that the total kinetic energy is close to experimental values only for the most likely fission while it is severely underestimated at both small and large asymmetries. This conclusion seems rather independent of the parametrization of the energy functional, both in its particle-hole and particle-particle channels.
X-ray Thomson scattering (XRTS) constitutes an essential technique for diagnosing material properties under extreme conditions, such as high pressures and intense laser heating. Time-dependent density functional theory (TDDFT) is one of the most accurate available ab initio methods for modeling XRTS spectra, as well as a host of other dynamic material properties. However, strong thermal excitations, along with the need to account for variations in temperature and density as well as the finite size of the detector significantly increase the computational cost of TDDFT simulations compared to ambient conditions. In this work, we present a broadly applicable method for optimizing and enhancing the efficiency of TDDFT calculations. Our approach is based on a one-to-one mapping between the dynamic structure factor and the imaginary time density–density correlation function, which naturally emerges in Feynman’s path integral formulation of quantum many-body theory. Specifically, we combine rigorous convergence tests in the imaginary time domain with a constraints-based attenuation of narrow-band fluctuations to improve the efficiency of TDDFT modeling without the introduction of any significant bias. As a result, we can report a speed-up by up to an order of magnitude, thus substantially reducing the burden of computational cost required for XRTS analysis.
This project focussed on two aspects of computational modeling with a view toward application for photovoltaic design: (i) increased reliability of exchange-correlation functionals in time-dependent density functional theory (TDDFT) (a method of choice of the calculation of electronic spectra and dynamics), especially for time-resolved non-perturbative dynamics, and (ii) the development of a practical but rigorously-based method for coupling electronic and nuclear motion via the exact-factorization (EF) approach (a relatively new framework for developing approximations).
In nuclei with an odd nucleon number the nonvanishing spin number density is the source of a pseudomagnetic field, which favors the splitting of the nucleon Cooper pairs. Such a pseudomagnetic field is generated always in the dynamics of any nucleus, but its effects on Cooper pairs are significantly enhanced in the dynamic evolution of nuclei with an odd number of nucleons. We present for the first time a microscopic study of the induced fission of the odd neutron compound nuclei 239 U, 241,243 Pu, and the odd proton, odd neutron compound nucleus 238 Np, performed within the time-dependent density functional theory extended to superfluid fermion systems, without any simplifying assumptions, with controlled numerical approximations, and for a very large number of initial conditions. Because of the presence of the unpaired odd nucleon(s), the time-reversal symmetry of the fission compound nucleus is spontaneously broken, an aspect routinely neglected in the most advanced microscopic approaches of the past. The emerging fission fragment properties are quite similar to the properties of fission fragments of neighboring even-even nuclei. The time from saddle-to-scission is often significantly longer in odd-odd or odd-mass nuclei than for even-even nuclei, since systems with unpaired nucleons are easier to excite and the potential energy surfaces of these nuclei have more structure, often resembling a very complicated obstacle course, rather than a more direct evolution of the nuclear shape from the top of the outer fission barrier to the scission configuration. The Pauli blocking approximation, often invoked in the literature, expected to inhibit the fission of nuclei with unpaired nucleons, is surprisingly strongly violated during the fission dynamics.
Accurate hydrodynamic modeling for laser-direct-drive (LDD) inertial-confinement-fusion (ICF) relies on precise calculations of the electron thermal conduction in all target materials. The nonlocal stopping range of electrons in ICF plasmas directly influences thermal conduction; yet, no first principles model exists for the electron mean free path in the conduction-zone regime. This work utilized time-dependent stochastic density-functional theory (TD-sDFT) to calculate the electron stopping power in deuterium-tritium (DT) plasmas at (ρ, T) conditions relevant to the conduction zone and the compressed shell in ICF. Using a combination of our TD-sDFT data and already established analytical models, we developed and trained an artificial neural network to create a global model for the nonlocal electron deposition range, λ E . We compared our machine-learning (ML) based model for λ E to the currently-used modified-Lee-More model in LDD radiation-hydrodynamic codes, such as lilac, and saw an overall decrease in the deposition range. To understand the effects of λ E on LDD ICF implosion dynamics, we implemented the ML-based model into lilac; specifically, we looked at designs consistent with a current experiment on the OMEGA laser and for a newly designed LDD-ICF target for the future OMEGA-Next facility. In both cases, we saw an overall drop in predicted ablation pressure, peak areal density, and neutron yield due to the reduced thermal conduction (smaller λ E ) in DT plasmas. Comparisons with the experiment on OMEGA are also made.
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While the variational principle for excited-state energies leads to a route to obtaining excited-state densities from time-dependent density functional theory, relatively little attention has been paid to the quality of the resulting densities in real space obtained with different exchange-correlation functional approximations or how nonadiabatic approximations developed for energies of states of double-excitation character perform for their densities. Here we derive an expression directly in real space for the excited-state density, which includes the case of nonadiabatic kernels and consequently is able, for the first time, to yield densities of states of double-excitation character. Under some well-defined simplifications, we compare the performance of the local-density approximation and exact-exchange approximation, which are in a sense at the opposite extremes of the fundamental functional approximations, on local and charge-transfer excitations in one-dimensional model systems and show that the dressed Time-Dependent Density Functional Theory (TDDFT) approach gives good densities of double excitations.
We propose a framework to learn the time-dependent Hartree–Fock (TDHF) inter-electronic potential of a molecule from its electron density dynamics. Although the entire TDHF Hamiltonian, including the inter-electronic potential, can be computed from first principles, we use this problem as a testbed to develop strategies that can be applied to learn a priori unknown terms that arise in other methods/approaches to quantum dynamics, e.g., emerging problems such as learning exchange–correlation potentials for time-dependent density functional theory. We develop, train, and test three models of the TDHF inter-electronic potential, each parameterized by a four-index tensor of size up to 60 × 60 × 60 × 60. Two of the models preserve Hermitian symmetry, while one model preserves an eight-fold permutation symmetry that implies Hermitian symmetry. Across seven different molecular systems, we find that accounting for the deeper eight-fold symmetry leads to the best-performing model across three metrics: training efficiency, test set predictive power, and direct comparison of true and learned inter-electronic potentials. All three models, when trained on ensembles of field-free trajectories, generate accurate electron dynamics predictions even in a field-on regime that lies outside the training set. To enable our models to scale to large molecular systems, we derive expressions for Jacobian-vector products that enable iterative, matrix-free training.
Rhenium disulfide (ReS 2 ), a prototypical 2D semiconductor with an anisotropic 1T′ structure due to the pronounced Peierls distortion, has demonstrated great potential for polarization-dependent optoelectronics and photonics. Here, we report an ultrafast phase transition occurring within 1 ps, accompanied by a one-dimensional Peierls-distortion relaxation in 1T′−ReS 2 revealed with combined 4D electron microscopy and time-dependent density functional theory calculations. Upon femtosecond laser pulse excitation, the Re-Re dimerization morphology rapidly transforms from a diamond cluster to zigzag chains and persists for several nanoseconds. Here, this ultrafast Peierls-distortion relaxation is further verified by transient changes in optical anisotropy via polarization-dependent transient absorption spectroscopy. Time-dependent density functional theory calculations attribute this novel phase transition to strong correlation between Peierls distortion and impulsive photoexcited carrier doping, predicting a transient band-gap collapse. This Letter opens up an exciting avenue for ultrafast control of Peierls-distortion-induced anisotropy and the metal-insulator transition in 1T′−ReS 2 .
Computation of optical properties using conventional time-dependent density functional theory (TD-DFT) is time-consuming and memory-intensive. In this study, we investigate the accuracy and efficiency of the density functional tight binding (DFTB) framework with newly optimized Slater–Koster (SK) parameters for modeling the structural, electronic properties, and absorption spectra of silver and gold nanoclusters and their alloys. Our investigation of the ground state (GS) properties demonstrates that the newly developed GS-SK parameters enable DFTB to closely approximate DFT-calculated bond lengths for octahedron, tetrahedron, icosahedra, and truncated octahedron with sizes Ag n /Au n (n = 19, 20, 38, 55), nanoclusters and Ag 20 /Au 20 nanoalloys, with a maximum deviation of approximately 0.15 Å. Formation energy results indicate that the GS-SK parameters can closely estimate changes in formation energies with alloy composition, and the comparison of electronic structures for Ag 20 , Au 20 , and AgAu alloy nanoclusters using the DFTB approximation reveals good agreement in the projected density of states (DOS) profiles and energy levels. A second set of SK parameters, ES-SK, has been developed to describe excited state (ES) properties, including the absorption spectra of silver octahedron Ag 19 , tetrahedral Ag n (n = 20, 56, 84), truncated octahedron Ag 38 , and icosahedra Ag 55 closed-shell clusters and their gold and alloy counterparts over a broad range of alloy compositions. This parametrization uses TD-DFTB calculations and fine-tunes the d and p eigenvalues by comparing them to reference absorption spectra from first-principles TD-DFT. This enables the generation of absorption spectra that closely match the reference spectra when plasmon excitation is dominant, as demonstrated by studying the plasmonic properties of icosahedral Ag n and Au n (n = 309 and 561) nanoparticles. This includes the rapid loss in plasmon quality when Au partially replaces Ag in alloy clusters. Furthermore, these results provide a foundation for addressing computational bottlenecks in plasmonics and with new prospects for applications in the quantum plasmonics for bimetallic alloys.
We investigate the electronic properties of an exemplar transition metal impurity in an insulator, with the goal of accurately describing strongly correlated defect states. Here, we consider iron in aluminum nitride, a material of interest for hybrid quantum technologies, and we carry out calculations with quantum embedding methods, density matrix embedding theory (DMET) and quantum defect embedding theory (QDET), and with spin-flip time-dependent density functional theory (TDDFT). We show that both DMET and QDET accurately describe the ground state and low-lying excited states of the defect and that TDDFT yields photoluminescence spectra in agreement with experiments. In addition, we provide a detailed discussion of the convergence of our results as a function of the active space used in the embedding methods, thus defining a protocol to obtain converged data directly comparable with experiments.
We have developed a density functional tight-binding model for hydrocarbon excited state dynamics by referencing to high-level electronic structure theory and incorporating a many-body repulsive energy. We then validate our model against n-octane geometry optimizations, bond dissociation scans, and vibrational frequencies. Our model is approximately 10 3 times more efficient than hybrid time-dependent density functional theory calculations with comparable accuracy. In conclusion, our efforts enable longer timescale excited state simulations of photochemistry and scattering of incident radiation.
We calculate the gradients of Boys diabatic state energies and couplings when the electronic vector space is generated by configuration interaction singles. Our approach follows the Lagrangian approach of Paz and Glover (rather than direct differentiation of the adiabatic-to-diabatic approaches that have been published previously). The result is that we achieve a dramatic increase in savings over previous approaches, and the present approach should be immediately useful to scientists focused on electronic relaxation, especially chemists studying electron transfer who wish to go beyond the Condon approximation. Here, a future extension to time-dependent density functional theory in the Tamm–Dancoff approximation is clear.
The overarching goal of this project was to develop computer tools for predicting how electrons move in molecules and solids at the attosecond (billionth-of-a-billionth of a second) time scale, during and after interaction with intense and/or high energy laser light. An associated goal was to also determine how X-ray spectroscopy could be used as a probe of these dynamics. The project resulted in multiple methodology developments that allow for these processes to be simulated from first-principles, most notably the use of small bulk-mimicking clusters to model solids and fixes for a deficiency in a commonly used method (time-dependent density functional theory). Additionally, the simulations showed that X-ray absorption peaks can be directly related to the electron density above the absorbing atom, and can thus be used as an intuitive probe of "where the electrons are" at a given time in the system. Collectively, these tools and results expected to be valuable for predicting and interpreting future attosecond experiments, especially for X-ray pump/probe studies at free-electron laser facilities.
Ab initio quantum-chemical methods that perform well for computing the electronic ground state are not straightforwardly transferable to electronically excited states, particularly in large molecular systems. Wave function theory offers high accuracy, but is often prohibitively expensive. Methods based on time-dependent density functional theory (TD-DFT) are crucially sensitive to the chosen exchange-correlation functional (XCF) parameterization, and system-specific tuning protocols were therefore proposed to address the method's robustness. Methods based on the variational relaxation of the excited-state electron density showcased promising results for the calculation of charge-transfer excitations, but the complex shape of the electronic hypersurface makes convergence to a specific excited state much more difficult than for the ground state when standard variational techniques are applied. We address the latter aspect by providing suitable initial guesses, which we obtain by two separate constrained algorithms. Combined with the squared-gradient minimization algorithm for all-electrons relaxation in a freeze-and-release scheme (FRZ-SGM), we demonstrate that orbital-optimized density functional theory (OO-DFT) calculations can reliably converge to the charge-transfer states of interest even for large molecular systems. We test the FRZ-SGM method on a phenothiazine-anthraquinone CT excitation in a supramolecular Pd(II) coordination cage complex as a function of the cage conformation. This compound has been studied experimentally prior to our work. We compare this freeze-and-release scheme to two XCF reparameterizations, which were recently proposed as low-cost TD-DFT-based alternatives to variational methods. Two dye-semiconductor complexes, which were previously investigated in the context of photovoltaic applications, serve as a second example to investigate the convergence and stability of the FRZ-SGM approach. Our results demonstrate that FRZ-SGM provides reliable convergence for charge-transfer excited states and avoids variational collapse to lower-lying electronic states, whereas time-dependent DFT calculations with an adequate tuning procedure for the range-separation parameter provide a computationally efficient initial estimate of the corresponding energies, with a computational cost comparable to that of configuration-interaction singles (CIS) calculations.
Thomson scattering spectra measure the response of plasma particles to incident radiation. In warm dense matter, which is opaque to visible light, x-ray Thomson scattering (XRTS) enables a detailed probe of the electron distribution and has been used as a diagnostic for electron temperature, density, and plasma ionization. In this work, we examine the sensitivities of inelastic XRTS signatures to modeling details, including the dynamic collision frequency and the electronic density of states. Applying verified Monte Carlo inversion methods to dynamic structure factors obtained from time-dependent density functional theory, we assess the utility of XRTS signals as a way to inform the dynamic collision frequency, especially its direct-current limit, which is directly related to the electrical conductivity.