A multi-fragment real-time extension of projected density matrix embedding theory: Non-equilibrium electron dynamics in extended systems

In this work, we derive a multi-fragment real-time extension of projected density matrix embedding theory (pDMET) designed to treat non-equilibrium electron dynamics in strongly correlated systems. As in the previously developed static pDMET, real-time pDMET partitions the total system into many fragments; the coupling between each fragment and the rest of the system is treated through a compact representation of the environment in terms of a quantum bath. Real-time pDMET involves simultaneously propagating the wavefunctions for each separate fragment-bath embedding system along with an auxiliary mean-field wavefunction of the total system. The equations of motion are derived by (i) projecting the time-dependent Schrodinger equation in the fragment and bath space associated with each separate fragment and by (ii) enforcing the pDMET matching conditions between the global 1-particle reduced density matrix (1-RDM) obtained from the fragment calculations and the mean-field 1-RDM at all points in time. The accuracy of the method is benchmarked through comparisons to the time-dependent density-matrix renormalization group (TD-DMRG) and time-dependent Hartree-Fock (TDHF) theory; the methods were applied to a single-impurity Anderson model and multi-impurity Anderson models with ordered and disordered distributions of the impurities. The results demonstrate a large improvement over TDHF and rapid convergence to the exact dynamics with an increase in fragment size. Our results demonstrate that real-time pDMET is a promising and flexible method to simulate non-equilibrium electron dynamics in heterogeneous systems of large size

A real-time extension of density matrix embedding theory for non-equilibrium electron dynamics

We introduce real-time density matrix embedding theory (DMET), a dynamical quantum embedding theory for computing non-equilibrium electron dynamics in strongly correlated systems. As in the previously developed static DMET, real-time DMET partitions the system into an impurity corresponding to the region of interest coupled to the surrounding environment, which is efficiently represented by a quantum bath of the same size as the impurity. In this work, we focus on a simplified single-impurity time-dependent formulation as a first step toward a multi-impurity theory. The equations of motion of the coupled impurity and bath embedding problem are derived using the time-dependent variational principle. The accuracy of real-time DMET is compared to that of time-dependent complete active space self-consistent field (TD-CASSCF) theory and time-dependent Hartree-Fock (TDHF) theory for a variety of quantum quenches in the single impurity Anderson model (SIAM), in which the Hamiltonian is suddenly changed (quenched) to induce a non-equilibrium state. Real-time DMET shows a marked improvement over the mean-field TDHF, converging to the exact answer even in the non-trivial Kondo regime of the SIAM. However, as expected from analogous behavior in static DMET, the constrained structure of the real-time DMET wavefunction leads to a slower convergence with respect to active space size, in the single-impurity formulation, relative to TD-CASSCF. Our initial results suggest that real-time DMET provides a promising framework to simulate non-equilibrium electron dynamics in which strong electron correlation plays an important role, and lays the groundwork for future multi-impurity formulations

Direct simulation of proton-coupled electron transfer across multiple regimes

The coupled transfer of electrons and protons is a central feature of biological and molecular catalysis, yet fundamental aspects of these reactions remain poorly understood. In this study, we extend the ring polymer molecular dynamics (RPMD) method to enable direct simulation of proton-coupled electron transfer (PCET) reactions across a wide range of physically relevant regimes. In a system-bath model for symmetric, co-linear PCET in the condensed phase, RPMD trajectories reveal distinct kinetic pathways associated with sequential and concerted PCET reaction mechanisms, and it is demonstrated that concerted PCET proceeds by a solvent-gating mechanism in which the reorganization energy is mitigated by charge cancellation among the transferring particles. We further employ RPMD to study the kinetics and mechanistic features of concerted PCET reactions across multiple coupling regimes, including the fully non-adiabatic (both electronically and vibrationally non-adiabatic), partially adiabatic (electronically adiabatic, but vibrationally non-adiabatic), and fully adiabatic (both electronically and vibrationally adiabatic) limits. Comparison of RPMD with the results of PCET rate theories demonstrates the applicability of the direct simulation method over a broad range of conditions; it is particularly notable that RPMD accurately predicts the crossover in the thermal reaction rates between different coupling regimes while avoiding a priori assumptions about the PCET reaction mechanism. Finally, by utilizing the connections between RPMD rate theory and semiclassical instanton theory, we show that analysis of ring-polymer configurations in the RPMD transition path ensemble enables the a posteriori determination of the coupling regime for the PCET reaction. This analysis reveals an intriguing and distinct “transient-proton-bridge” mechanism for concerted PCET that emerges in the transition between the proton-mediated electron superexchange mechanism for fully non-adiabatic PCET and the hydrogen atom transfer mechanism for partially adiabatic PCET. Taken together, these results provide a unifying picture of the mechanisms and physical driving forces that govern PCET across a wide range of physical regimes, and they raise the possibility for PCET mechanisms that have not been previously reported

Tipping the Balance between Concerted versus Sequential Proton-Coupled Electron Transfer

We use quantized molecular dynamics simulations to investigate the competition between concerted and sequential proton-coupled electron-transfer (PCET) reaction mechanisms in inorganic catalysts. By analyzing reactive nonadiabatic PCET trajectories and computing both concerted and sequential rate constants, we characterize various molecular features that govern inorganic PCET reactions, including the solvent polarity, ligand-mediated electron–proton interactions, and intrinsic proton-transfer (PT) energy barrier. Using atomistic simulations with over 1200 atoms, we find that the symmetric iron biimidazoline system is extremely biased toward the concerted mechanism because of the strong ligand-mediated electron–proton interaction and the short PT distance. However, by investigating system-bath models in which electron–proton interactions are shielded, which are representative of ruthenium terpyridylbenzoates and iron (tetraphenylporphyrin)benzoates, we predict that a crossover between the concerted and sequential PCET mechanisms may be possible either by increasing the polarity of the solvent or by increasing the intrinsic PT energy barrier. In addition, we predict the possibility of a crossover in the PCET mechanism by directly varying the strength of the ligand-mediated electron–proton interactions. The results presented here reveal new strategies for altering the competition between the competing PCET mechanisms and design principles for controlling PCET in catalytic systems

The fate of atomic spin in atomic scattering off surfaces

We explore model electron dynamics of an atom scattering off a surface within the time-dependent complete active space self consistent field (TD-CASSCF) approximation. We focus especially on the scattering of a hydrogen atom and its resulting spin-dynamics starting from an initially spin-polarized state. Our results reveal competing electronic time-scales that are governed by the electronic structure of the surface as well as the character of the atom. The timescales and nonadiabaticity of the dynamics are reported on by the final spin-polarization of the scattered atom, which may be probed in future experiments

Cluster size convergence of the density matrix embedding theory and its dynamical cluster formulation: A study with an auxiliary-field quantum Monte Carlo solver

We investigate the cluster size convergence of the energy and observables using two forms of density matrix embedding theory (DMET): the original cluster form (CDMET) and a new formulation motivated by the dynamical cluster approximation (DCA-DMET). Both methods are applied to the half-filled one- and two-dimensional Hubbard models using a sign-problem free auxiliary-field quantum Monte Carlo impurity solver, which allows for the treatment of large impurity clusters of up to 100 sites. While CDMET is more accurate at smaller impurity cluster sizes, DCA-DMET exhibits faster asymptotic convergence towards the thermodynamic limit. We use our two formulations to produce new accurate estimates for the energy and local moment of the two-dimensional Hubbard model for U / t = 2,4,6. These results compare favorably with the best data available in the literature, and help resolve earlier uncertainties in the moment for U / t = 2

The Fate of Atomic Spin in Atomic Scattering Off Surfaces

We explore model electron dynamics of an atom scattering off a surface within the time-dependent complete active space self-consistent field (TD-CASSCF) approximation. We focus especially on the scattering of a hydrogen atom and its resulting spin dynamics starting from an initially spin-polarized state. Our results reveal competing electronic time scales that are governed by the electronic structure of the surface as well as the character of the atom. The time scales and nonadiabaticity of the dynamics are reported on by the final spin polarization of the scattered atom, which may be probed in future experiments

The Rest-Frame UV Luminosity Density of Star-Forming Galaxies at Redshifts z>3.5

We have measured the rest--frame lambda~1500 Ang comoving specific luminosity density of star--forming galaxies at redshift 3.5<z<6.5 from deep images taken with the Hubble Space Telescope (HST)and the Advanced Camera for Surveys (ACS), obtained as part of the Great Observatories Origins Deep Survey (GOODS). We used color selection criteria to construct samples of star--forming galaxies at redshifts z~4, 5 and 6, identified by the signature of the 912 Ang Lyman continuum discontinuity and Lyman-alpha forest blanketing in their rest--frame UV colors (Lyman--break galaxies). The ACS samples cover ~0.09 square degree, and are also relatively deep, reaching between 0.2 and 0.5 L_3^*, depending on the redshift, where $L_3^*$ is the characteristic UV luminosity of Lyman--break galaxies at z~3. The specific luminosity density of Lyman--break galaxies appears to be nearly constant with redshift from z~3 to z~6, although the measure at z~6 remains relatively uncertain, because it depends on the accurate estimate of the faint counts of the z~6 sample. If Lyman--break galaxies are fair tracers of the cosmic star formation activity, our results suggest that at z~6 the universe was already producing stars as vigorously as it did near its maximum several Gyr later, at 1<~z<~3. Thus, the onset of large--scale star formation in the universe is to be sought at around z~6 or higher, namely at less than ~7% of the current cosmic age.Comment: AAS LaTeX macros 4.0, 11 pages, 1 postscript figure. Accepted for publication in The Astrophysical Journal, Letter. Minor changes to the figure caption. The data and the GOODS-group papers can be found at http://www.stsci.edu/science/goods