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A decomposition of the exact exchange-correlation potential of time-dependent density functional theory into an interaction component and a kinetic component offers a new starting point for non- adiabatic approximations. The components are expressed in terms of the exchange-correlation hole and the difference between the one-body density matrix of the interacting and Kohn-Sham systems, which must be approximated in terms of quantities accessible from the Kohn-Sham evolution. We explore several preliminary approximations, evaluate their fulfillment of known exact conditions, and test their performance on simple model systems for which available exact solutions indicate the significance of going beyond the adiabatic approximation., 16 pages, 10 figures

We explore an asymmetric two-fermion Hubbard dimer to test the accuracy of the adiabatic approximation of time-dependent density functional theory in modelling time-resolved charge transfer. We show that the model shares essential features of a ground state long-range molecule in real-space, and by applying a resonant field we show that the model also reproduces essential traits of the CT dynamics. The simplicity of the model allows us to propagate with an "adiabatically-exact" approximation, i.e. one that uses the exact ground-state exchange-correlation functional, and compare with the exact propagation. This allows us to study the impact of the time-dependent charge-transfer step feature in the exact correlation potential of real molecules on the resulting dynamics. Tuning the parameters of the dimer allows a study both of charge-transfer between open-shell fragments and between closed-shell fragments. We find that the adiabatically-exact functional is unable to properly transfer charge, even in situations where the adiabatically-exact resonance frequency is remarkably close to the exact resonance, and we analyze why., Comment: 6 figures

The present study is an effort to unveil and characterize the failure and success of real-time Time-dependent density functional theory simulated charge transfer dynamics. To this aim, we study two distinct examples found in the literature: a dramatic failure is reported in [S. Raghunathan, M. Nest, J. Chem. Theor. Comput. 7, 2492 (2011)] whereas in [C.A. Rozzi et al., Nat. Commun. 4, 1602 (2013)] the simulations show good agreement with experiments. We find that the choice of Single Slater Determinant for the Kohn Sham initial state renders the simulation of charge transfer dynamics starting in the ground state very challenging. In contrast, starting the simulation in a photo-excited state facilitates the description and we show that even a simple functional can perform well. We formulate exact conditions to be satisfied by the exchange-correlation functional in order to keep the resonances of the system constant and relate the degree of their violation to the performance of a given functional approximation. We show that even the best possible ground state approximation to the exchange-correlation density functional violates the exact conditions, resulting in inaccurate dynamics.

When running time-dependent density functional theory (TDDFT) calculations for real-time simulations of non-equilibrium dynamics, the user has a choice of initial Kohn-Sham state, and typically a Slater determinant is used. We explore the impact of this choice on the exchange-correlation potential when the physical system begins in a 50:50 superposition of the ground and first-excited state of the system. We investigate the possibility of judiciously choosing a Kohn-Sham initial state that minimizes errors when adiabatic functionals are used. We find that if the Kohn-Sham state is chosen to have a configuration matching the one that dominates the interacting state, this can be achieved for a finite time duration for some but not all such choices. When the Kohn-Sham system does not begin in a Slater determinant, we further argue that the conventional splitting of the exchange-correlation potential into exchange and correlation parts has limited value, and instead propose a decomposition into a "single-particle" contribution that we denote $v_{xc}^s$, and a remainder. The single-particle contribution can be readily computed as an explicit orbital-functional, reduces to exchange in the Slater determinant case, and offers an alternative to the adiabatic approximation as a starting point for TDDFT approximations., Comment: 11 pages, 9 Figures. submitted for special invited issue honoring Evert Jan Baerends, in Phys. Chem. Chem. Phys. (2016)

Adiabatic approximations in time-dependent density functional theory (TDDFT) will in general yield unphysical time-dependent shifts in the resonance positions of a system driven far from its ground-state. This spurious time-dependence is rationalized in [J. I. Fuks, K. Luo, E. D. Sandoval and N. T. Maitra, Phys. Rev. Lett. {\bf 114}, 183002 (2015)] in terms of the violation of an exact condition by the non-equilibrium exchange-correlation kernel of TDDFT. Here we give details on the derivation and discuss reformulations of the exact condition that apply in special cases. In its most general form, the condition states that when a system is left in an arbitrary state, in the absence of time-dependent external fields nor ionic motion, the TDDFT resonance position for a given transition is independent of the state. Special cases include the invariance of TDDFT resonances computed with respect to any reference interacting stationary state of a fixed potential, and with respect to any choice of appropriate stationary Kohn-Sham reference state. We then present several case studies, including one that utilizes the adiabatically-exact approximation, that illustrate the conditions and the impact of their violation on the accuracy of the ensuing dynamics. In particular, charge-transfer across a long-range molecule is hampered, and we show how adjusting the frequency of a driving field to match the time-dependent shift in the charge-transfer resonance frequency, results in a larger charge transfer over time., Comment: 16 pages, 10 figs

We show that an asymmetric two-fermion two-site Hubbard model illustrates the essential features of long-range charge-transfer dynamics in a real-space molecule. We apply a resonant field that transfers one fermion from one site to the other. Via constrained search we find the exact ground-state exchange-correlation functional, and use it to propagate the Kohn-Sham system, giving the first "adiabatically-exact" calculation of time-resolved charge-transfer. This propagation fails to properly transfer charge. We analyze why by comparing the exact and adiabatically-exact potentials and discuss the role of the derivative discontinuity. The implication for real-space molecules is that even the best possible adiabatic approximation, despite capturing non-local step features relevant to dissociation and charge-transfer excitations, cannot capture fully time-resolved charge-transfer dynamics.

arXiv:1211.2849, We show that whenever an electron transfers between closed-shell molecular fragments, the exact correlation potential of time-dependent density functional theory develops a step and peak structure in the bonding region. This structure has a density dependence that is nonlocal both in space and in time that even the exact adiabatic ground-state exchange–correlation functional fails to capture it. For charge-transfer between open-shell fragments, an initial step and peak vanish as the charge-transfer state is reached. The inability of usual approximations to develop these structures leads to inaccurate charge-transfer dynamics. This is illustrated by the complete lack of Rabi oscillations in the dipole moment under conditions of resonant charge transfer for an exactly solvable model system. The results transcend the model and are applicable to more realistic molecular complexes., We gratefully acknowledge financial support from the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences and Biosciences under Award DE-SC0008623 (N.T.M.) and a grant of computer time from the CUNY High Performance Computing Center under NSF Grant CNS-0855217. The European Research Council (ERC-2010-AdG-267374), Spanish: FIS2011-65702-C02-01), Grupos Consolidados (IT-319-07), and EC Projects CRONOS (280879-2) and CNS-0958379 are gratefully acknowledged. J.I.F. acknowledges support from an FPI fellowship (FIS2007-65702-C02-01).

The exact exchange-correlation (xc) potential of time-dependent density functional theory has been shown to have striking features. For example, step and peak features are generically found when the system is far from its ground-state, and these depend nonlocally on the density in space and time. We analyze the xc potential by decomposing it into kinetic and interaction potential components, and comparing each with their exact-adiabatic counterparts, for a range of dynamical situations in model one-dimensional (1D) two-electron systems. We find that often, but not always, the kinetic contri- bution is mostly responsible for these features, that are missed by the adiabatic approximation. The adiabatic approximation often makes a smaller error for the potential contribution, which we write in two parts, one being the Coulomb potential due to the time-dependent xc hole. These observations also held in non-equilibrium cases we studied where there are large features in the correlation po- tential although no step structure. In ground-state situations, step and peak structures arise in cases of static correlation, when more than one determinant is essential to describe the interacting state. We investigate the time-dependent natural orbital occupation numbers and find the corresponding relation between these and the dynamical step is more complex than for the ground-state case., Comment: 13 pages and 20 figures

We show that the exact exchange-correlation potential of time-dependent density-functional theory displays dynamical step structures that have a spatially non-local and time non-local dependence on the density. Using one-dimensional two-electron model systems, we illustrate these steps for a range of non-equilibrium dynamical situations relevant for modeling of photo-chemical/physical processes: field-free evolution of a non-stationary state, resonant local excitation, resonant complete charge-transfer, and evolution under an arbitrary field. Lack of these steps in usual approximations yield inaccurate dynamics, for example predicting faster dynamics and incomplete charge transfer., Financial support from the National Science Foundation (CHE-1152784) and a grant of computer time from the CUNY High Performance Computing Center under NSF Grants No. CNS-0855217 and No. CNS-0958379 are gratefully acknowledged. J. I. F. acknowledges support from a FPI Fellowship (FIS2007-65702-C02-01). A.R. acknowledges financial support from the European Research Council Advanced Grant DYNamo (ERC-2010-AdG-Proposal No. 267374) Spanish Grants (No. FIS2011- 65702- C02-01 and No. PIB2010US-00652), Grupos Consolidados UPV/EHU del Gobierno Vasco (IT-319-07), and the European Commission Project CRONOS (280879-2).

We present a local density approximation (LDA) for one-dimensional (1D) systems interacting via the soft-Coulomb interaction based on quantum Monte Carlo calculations. Results for the ground-state energies and ionization potentials of finite 1D systems show excellent agreement with exact calculations obtained by exploiting the mapping of an N-electron system in d dimensions onto a single electron in N×d dimensions, properly symmetrized by the Young diagrams. We conclude that 1D LDA is of the same quality as its three-dimensional (3D) counterpart, and we infer conclusions about 3D LDA. The linear and nonlinear time-dependent responses of 1D model systems using LDA, exact exchange, and the exact solution are investigated and show very good agreement in both cases, except for the well-known problem of missing double excitations. Consequently, the 3D LDA is expected to be of good quality beyond the linear response. In addition, the 1D LDA should prove useful in modeling the interaction of atoms with strong laser fields, where this specific 1D model is often used., We acknowledge funding by the Spanish MEC (Contract No. FIS2007-65702-C02-01), ACI-promciona project (Contract No. ACI2009-1036), “Grupos Consolidados UPV/EHU del Gobierno Vasco” (Contract No. IT-319-07), and the European Community through the e-I3 ETSF project (Contract No. 211956). M.A.L.M. acknowledges support from the French ANR (Contract No. ANR-08-CEXC8-008-01).

Long-range charge-transfer excitations pose a major challenge for time-dependent density-functional approximations. We show that spin-symmetry breaking offers a simple solution for molecules composed of open-shell fragments, yielding accurate excitations at large separations when the acceptor effectively contains one active electron. Unrestricted exact-exchange and self-interaction-corrected functionals are performed on one-dimensional models and on the real LiH molecule within the pseudopotential approximation to demonstrate our results., We acknowledge support from MEC (Grant No. FIS2007-65702-C02-01), ACI promociona (Grant No. ACI2009-1036), Grupos Consolidados UPV/EHU del Gobierno Vasco (Grant No. IT-319-07), the e-I3 ETSF project (Contract No. 211956), the National Science Foundation (Grant No. CHE-0647913), and the Cottrell Scholar Program of the Research Corporation for Science Advancement, as well as a grant of computer time from the CUNY High Performance Computing Center under NSF Grants No. CNS-0855217 and No. CNS-0958379.

Through the exact solution of a two-electron singlet system interacting with a monochromatic laser we prove that all adiabatic density functionals within time-dependent density-functional theory are not able to discern between resonant and nonresonant (detuned) Rabi oscillations. This is rationalized in terms of a fictitious dynamical exchange-correlation (xc) detuning of the resonance while the laser is acting. The nonlinear dynamics of the Kohn-Sham system shows the characteristic features of detuned Rabi oscillations even if the exact resonant frequency is used. We identify the source of this error in a contribution from the xc functional to the set of nonlinear equations that describes the electron dynamics in an effective two-level system. The constraint of preventing the detuning introduces a new strong condition to be satisfied by approximate xc functionals., We acknowledge support by MICINN (FIS2010-21282- C02-01), ACI-promociona (ACI2009-1036), Grupos Consolidados UPV/EHU del Gobierno Vasco (IT-319-07), the European Community through e-I3 ETSF project (Contract No. 211956), and the European Research Council Advanced Grant DYNamo (ERC-2010-AdG -Proposal No. 267374). J.I.F. acknowledges support from an FPI-fellowship (FIS2007-65702-C02-01).

El pdf del artículo es la versión pre-print: arXiv:1108.3196v1, To address the impact of electron correlations in the linear and non-linear response regimes of interacting many-electron systems exposed to time-dependent external fields, we study one-dimensional (1D) systems where the interacting problem is solved exactly by exploiting the mapping of the 1D N-electron problem onto an N-dimensional single electron problem. We analyze the performance of the recently derived 1D local density approximation as well as the exact-exchange orbital functional for those systems. We show that the interaction with an external resonant laser field shows Rabi oscillations which are detuned due to the lack of memory in adiabatic approximations. To investigate situations where static correlations play a role, we consider the time-evolution of the natural occupation numbers associated to the reduced one-body density matrix. Those studies shed light on the non-locality and time-dependence of the exchange and correlation functionals in time-dependent density and density-matrix functional theories. © 2011 Elsevier B.V. All rights reserved., We acknowledge support by MICINN (FIS2010-21282-C02-01), ACI-promociona (ACI2009-1036), “Grupos Consolidados UPV/EHU del Gobierno Vasco” (IT-319-07), and the European Community through e-I3 ETSF project (Contract No. 211956).