Elastic scattering of low-energy electrons from molecular hydrogen.
Elastic scattering cross section of low energy electrons calculated by continuum Hartree-Fock equations
Taylor, H. S.↗
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Scalable learning of potentials to predict time-dependent Hartree–Fock dynamics
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.
97 MATHEMATICS AND COMPUTING↗
Electron-impact excitation of carbon and silicon in the distorted-wave approximation
The 3P to 1D electron-impact excitation cross section within the ground configuration of both neutral carbon and silicon is calculated in the distorted-wave approximation of the two-state Hartree-Fock coupled equations. An essential element of the present treatment is that orthogonality to core orbitals is not assumed in deriving equations for the scattering orbitals. A local adiabatic polarization potential is also added to the distorted-wave equations. Both elements are necessary in getting good agreement with close-coupling results for carbon to low impacting energies. The agreement is sufficiently good that predictions for silicon should be accurate to within a factor of 2.
Pindzola, M. S.↗
Applications of time-dependent perturbation theory.
Atomic and molecular time-dependent quantum- mechanical perturbation theory with differential equation formulation within Hartree-Fock approximation
TIME DEPENDENCY↗
Theoretical study of atomic and molecular gases and their reactions in the upper atmosphere Summary report, 1 May - 31 Oct. 1965
Wave functions and total energy of energy states of diatomic molecules - Hartree-Fock calculation
Diatomic molecule↗
Microscopic Modeling of Intersubband Optical Processes in Type II Semiconductor Quantum Wells: Linear Absorption
Linear absorption spectra arising from intersubband transitions in semiconductor quantum well heterostructures are analyzed using quantum kinetic theory by treating correlations to the first order within Hartree-Fock approximation. The resulting intersubband semiconductor Bloch equations take into account extrinsic dephasing contributions, carrier-longitudinal optical phonon interaction and carrier-interface roughness interaction which is considered with Ando s theory. As input for resonance lineshape calculation, a spurious-states-free 8-band kp Hamiltonian is used, in conjunction with the envelop function approximation, to compute self-consistently the energy subband structure of electrons in type II InAs/AlSb single quantum well structures. We demonstrate the interplay of nonparabolicity and many-body effects in the mid-infrared frequency range for such heterostructures.
Li, Jian-Zhong↗
Microscopic Modeling of Intersubband Resonances in InAs/AlSb Quantum Wells
Linear absorption spectra from intersubband resonance in InAs/AlSb quantum wells are analyzed theoretically using the intersubband semiconductor Bloch equation approach. Our model goes beyond the Hartree-Fock approximation and treats particle-particle correlations under the second Born approximation. Electron-electron and -LO phonon scatterings from such a treatment describe intrinsic line broadening to the intersubband resonance. Electron subbands are determined self-consistently with a spurious-state-free 8-band k.p Hamiltonian under the envelope function approximation. To compare with experimental measurements, we also included line broadening due to electron-interface roughness scattering. Excellent agreement was achieved for temperature-dependent absorption spectra in the mid-infrared frequency range, after taking into careful account the interplay of material parameters, nonparabolicity in bandstructure, and many-body effects.
Li, Jian-Zhong↗
Many-Body Effects in Quantum-Well Intersubband Transitions
Intersubband polarization couples to collective excitations of the interacting electron gas confined in a semiconductor quantum well (Qw) structure. Such excitations include correlated pair excitations (repellons) and intersubband plasmons (ISPs). The oscillator strength of intersubband transitions (ISBTs) strongly varies with QW parameters and electron density because of this coupling. We have developed a set of kinetic equations, termed the intersubband semiconductor Bloch equations (ISBEs), from density matrix theory with the Hartree-Fock approximation, that enables a consistent description of these many-body effects. Using the ISBEs for a two-conduction-subband model, various many-body effects in intersubband transitions are studied in this work. We find interesting spectral changes of intersubband absorption coefficient due to interplay of the Fermi-edge singularity, subband renormalization, intersubband plasmon oscillation, and nonparabolicity of bandstructure. Our results uncover a new perspective for ISBTs and indicate the necessity of proper many-body theoretical treatment in order for modeling and prediction of ISBT line shape.
Li, Jian-Zhong↗
Nonlinear Optimal Control of Electron Dynamics Within Hartree-Fock Theory
Consider the problem of determining the optimal applied electric field to drive a molecule from an initial state to a desired target state. For even moderately sized molecules, solving this problem directly using the exact equations of motion—the time-dependent Schrödinger equation (TDSE)—is numerically intractable. Here, we present a solution of this problem within time-dependent Hartree-Fock (TDHF) theory, a mean field approximation of the TDSE. Optimality is defined in terms of minimizing the total control effort while maximizing the overlap between desired and achieved target states. We frame this problem as an optimization problem constrained by the nonlinear TDHF equations; we solve it using trust region optimization with gradients computed via a custom-built adjoint state method. For three molecular systems, we show that with very small neural network parametrizations of the control, our method yields solutions that achieve desired targets within acceptable constraints and tolerances.
97 MATHEMATICS AND COMPUTING↗
A Hydrodynamic Theory for Spatially Inhomogeneous Semiconductor Lasers: Microscopic Approach
Starting from the microscopic semiconductor Bloch equations (SBEs) including the Boltzmann transport terms in the distribution function equations for electrons and holes, we derived a closed set of diffusion equations for carrier densities and temperatures with self-consistent coupling to Maxwell's equation and to an effective optical polarization equation. The coherent many-body effects are included within the screened Hartree-Fock approximation, while scatterings are treated within the second Born approximation including both the in- and out-scatterings. Microscopic expressions for electron-hole (e-h) and carrier-LO (c-LO) phonon scatterings are directly used to derive the momentum and energy relaxation rates. These rates expressed as functions of temperatures and densities lead to microscopic expressions for self- and mutual-diffusion coefficients in the coupled density-temperature diffusion equations. Approximations for reducing the general two-component description of the electron-hole plasma (EHP) to a single-component one are discussed. In particular, we show that a special single-component reduction is possible when e-h scattering dominates over c-LO phonon scattering. The ambipolar diffusion approximation is also discussed and we show that the ambipolar diffusion coefficients are independent of e-h scattering, even though the diffusion coefficients of individual components depend sensitively on the e-h scattering rates. Our discussions lead to new perspectives into the roles played in the single-component reduction by the electron-hole correlation in momentum space induced by scatterings and the electron-hole correlation in real space via internal static electrical field. Finally, the theory is completed by coupling the diffusion equations to the lattice temperature equation and to the effective optical polarization which in turn couples to the laser field.
Li, Jianzhong↗
Microscopic Foundation and Simulation of Coupled Carrier-Temperature Diffusions in Semiconductor Lasers
A typical semiconductor-based optoelectronic device, such as a diode laser, consists of three subsystems: an optical field, an electron-hole plasma (EHP), and a host crystal lattice. The physics of such a device involves the interplay of optical, electrical and thermal processes. A proper description of such a device requires that all three processes are treated on equal footing and in a self-consistent fashion. Furthermore, since a semiconductor laser has intrinsic spatial inhomogeneity, such a self-consistency naturally leads to a set of partial differential equations in space and time. There is a significant lacking of research interest and results on the transport aspects of optical devices in the literature with only a few exceptions. Even the most important carrier diffusion coefficient has not been properly derived and studied so far for optically excited plasma, while most of the work adopted results from electronics community where heavily doped semiconductors with mainly one type of carriers are dealt with. The corresponding transport equation for plasma energy or temperature has received even less attention. In this talk we describe our recent results on such a self-consistent derivation of temperature and carrier-density diffusion equations coupled with the lasing process. Starting from the microscopic semiconductor Bloch equations (SBEs) including the Boltzmann transport terms in the distribution function equations for electrons and holes, we derived a closed set of diffusion equations for carrier densities and temperatures with self-consistent coupling to Maxwell's equation and to an effective optical polarization equation. The coherent many-body effects are included within the screened Hartree-Fock approximation, while scatterings are treated within the second Born approximation including both the in- and out-scatterings. Microscopic expressions for electron-hole (e-h) and carrier-LO (c-LO) phonon scatterings are directly used to derive the momentum and energy relaxation rates. These rates expressed as functions of temperatures and densities lead to microscopic expressions for self- and mutual-diffusion coefficients in the coupled density-temperature diffusion equations. Approximations for reducing the general two-component description of the electron-hole plasma (EHP) to a single-component one are discussed. In particular, we show that a special single-component reduction is possible when e-h scattering dominates over c-LO phonon scattering. The ambipolar diffusion approximation is also discussed and we show that the ambipolar diffusion coefficients are independent of e-h scattering, even though the diffusion coefficients of individual components depend sensitively on the e-h scattering rates. Our discussions lead to new perspectives into the roles played in the single-component reduction by the electron-hole correlation in momentum space induced by scatterings and the electron-hole correlation in real space via internal static electrical field. Finally, the theory is completed by coupling the diffusion equations to the lattice temperature equation and to the effective optical polarization which in turn couples to the laser field. The equations derived above are implemented in various limiting cases to a typical diode laser to study the consequences of nonlinear diffusion and the cross diffusion terms on laser behavior, especially the dynamic behavior of a diode laser under modulation. Detailed results will be presented by comparing with the standard rate equation results.
Li, J.↗
Quasiparticle random-phase approximation calculations for M 1 transitions with the noniterative finite-amplitude method and application to neutron radiative capture cross sections
Here, we derive the equations of quasiparticle random-phase approximation (QRPA) based on the finite amplitude method with the Hartree-Fock+Bardeen–Cooper–Schrieffer (HF+BCS) single-particle states, and calculate the magnetic dipole (M1) transition for deformed gadolinium isotopes. Our QRPA calculation shows both large spin-flip transitions in the 5 to 10 MeV excitation energy and the low energy orbital transition that would correspond to the M1 scissors mode observed in nuclear experiments. Then, we calculate neutron capture reactions based on the statistical Hauser-Feshbach theory with the photoabsorption cross sections of even-even nuclei given by QRPA. We find that the capture cross section is enhanced due to the contribution from the low energy M1 transition although the calculated capture cross section still underestimates the experimental data. This issue in the calculated capture cross section could be improved by uncertainties of the low energy E1 transition neglected in our QRPA calculation.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Collective Excitations in InAs Well Intersubband Transitions
Intersubband transitions in semiconductor quantum well are studied using a density matrix theory that goes beyond the Hartree-Fock approximation by including the full second order electron-electron scattering terms in the polarization equation for the first time. Even though the spectral features remain qualitatively similar to the results obtained with dephasing rate approximation, significant quantitative changes result from such a more detailed treatment of dephasing. More specifically, we show how the interplay of the two fundamental collective excitations, the Fermi-edge singularity and the intersubband plasmon, leads to significant changes in lineshape as the electron density varies.
Li, Jian-Zhong↗
Noniterative solutions of integral equations for scattering. I - Single channels
Scattering matrix noniterative integral solutions applied to singlet and triplet s-wave Hartree-Fock phase shifts for electron-H-atom scattering
Kouri, D. J.↗
Finite-size effects in periodic coupled cluster calculations
Here, we provide the first rigorous study of the finite-size error in the simplest and representative coupled cluster theory, namely the coupled cluster doubles (CCD) theory, for gapped periodic systems. Given exact Hartree-Fock orbitals and their corresponding orbital energies, we demonstrate that the correlation energy obtained from the approximate CCD method, after a finite number of fixed-point iterations over the amplitude equation, exhibits a finite-size error scaling as $\mathcal{O}(N^{-\frac{1}{3}}_k)$. Here $N_k$ is the number of discretization points in the Brillouin zone and characterizes the system size. Under additional assumptions ensuring the convergence of the fixed-point iterations, we demonstrate that the CCD correlation energy also exhibits a finite-size error scaling as $\mathcal{O}(N^{-\frac{1}{3}}_k)$. Our analysis shows that the dominant error lies in the coupled cluster amplitude calculation, and the convergence of the finite-size error in energy calculation can be boosted to $\mathcal{O}(N^{-1}_k)$ with accurate amplitudes. This also provides the first proof of the scaling of the finite-size error in the third order Møller-Plesset perturbation theory (MP3) for periodic systems.
97 MATHEMATICS AND COMPUTING↗
Stochastic and mixed density functional theory within the projector augmented wave formalism for simulation of warm dense matter
Stochastic density functional theory (DFT) and mixed stochastic-deterministic DFT are burgeoning approaches for the calculation of the equation of state and transport properties in materials under extreme conditions. In the intermediate warm dense matter regime, a state between correlated condensed matter and kinetic plasma, electrons can range from being highly localized around nuclei to delocalized over the whole simulation cell. The plane-wave basis pseudopotential approach is thus the typical tool of choice for modeling such systems at the DFT level. Unfortunately, stochastic DFT methods scale as the square of the maximum plane-wave energy in this basis. To reduce the effect of this scaling and improve the overall description of the electrons within the pseudopotential approximation, we present stochastic and mixed DFT approaches developed and implemented within the projector augmented wave formalism. In conclusion, we compare results between the different DFT approaches for both single-point and molecular dynamics trajectories and present calculations of self-diffusion coefficients of solid density carbon from 1 to 50 eV.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Uncertainty quantification for neutrino opacities in core-collapse supernovae and neutron star mergers
We perform an extensive study of the correlations between the neutrino-nucleon inverse mean free paths (IMFPs) and the underlying equation of states (EoSs). Strong interaction uncertainties in the neutrino mean free path are investigated in different density regimes. The nucleon effective mass, the nucleon chemical potentials, and the residual interactions in the medium play an important role in determining neutrino-nucleon interactions in a density-dependent manner. Here we study how the above quantities are constrained by an EoS consistent with (i) nuclear mass measurements, (ii) proton-proton scattering phase shifts, and (iii) neutron star observations. We then study the uncertainties of both the charged current and the neutral current neutrino-nucleon inverse mean free paths due to the variation of these quantities, using the Hartree-Fock+random phase approximation method. Finally, we calculate the Pearson correlation coefficients between (i) the EoS-based quantities and the EoS-based quantities; (ii) the EoS-based quantities and the IMFPs; (iii) the IMFPs and the IMFPs. We find a strong impact of residual interactions on neutrino opacity in the spin and spin-isospin channels, which are not well constrained by current nuclear modelings.
79 ASTRONOMY AND ASTROPHYSICS↗
The form of spin orbitals for open-shell restricted Hartree-Fock reference functions
A new set of spin orbitals is proposed for single-reference correlation procedures based on an open-shell restricted Hartree-Fock (RHF) reference function. The spatial parts of the new spin orbitals are from an open-shell RHF calculation. These spin orbitals form a complete, orthonormal set. The RHF single determinant based on these spin orbitals is an S sub 2 eigenfunction, but a linear combination of S sub z eigenfunctions. The advantage of these spin orbitals is that equations for perturbation theory or coupled-cluster theory are symmetric in the spin indices and hence the number of independent parameters to be determined is dramatically reduced.
Jayatilaka, Dylan↗