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Register a new userIncluding nonlocality in exchange-correlation kernel from time-dependent current density functional theory: Application to the stopping power of electron liquids
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We develop a scheme for building the scalar exchange-correlation (xc) kernel of time-dependent density functional theory (TDDFT) from the tensorial kernel of time-dependent {em current} density functional theory (TDCDFT) and the Kohn-Sham current density response function. Resorting to the local approximation to the kernel of TDCDFT results in a nonlocal approximation to the kernel of TDDFT, which is free of the contradictions that plague the standard local density approximation (LDA) to TDDFT. As an application of this general scheme, we calculate the dynamical xc contribution to the stopping power of electron liquids for slow ions to find that our results are in considerably better agreement with experiment than those obtained using TDDFT in the conventional LDA.
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Based on the time-dependent density-functional theory, we have derived a rigorous formula for the stopping power of an {it interacting} electron gas for ions in the limit of low projectile velocities. If dynamical correlation between electrons is not taken into account, this formula recovers the corresponding stopping power of {it noninteracting} electrons in an effective Kohn-Sham potential. The correlation effect, specifically the excitonic one in electron-hole pair excitations, however, is found to considerably enhance the stopping power for intermediately charged ions, bringing our theory into good agreement with experiment.
Due to the strongly nonlocal nature of $f_{xc}({bf r},{bf r},omega)$ the {em scalar} exchange and correlation (xc) kernel of the time-dependent density-functional theory (TDDFT), the formula for Q the friction coefficient of an interacting electron gas (EG) for ions tends to give a too large value of Q for heavy ions in the medium- and low-density EG, if we adopt the local-density approximation (LDA) to $f_{xc}({bf r},{bf r},omega)$, even though the formula itself is formally exact. We have rectified this unfavorable feature by reformulating the formula for Q in terms of the {em tensorial} xc kernel of the time dependent current-density functional theory, to which the LDA can be applied without intrinsic difficulty. Our numerical results find themselves in a considerably better agreement with the experimental stopping power of Al and Au for slow ions than those previously obtained within the LDA to the TDDFT.
In spin-density-functional theory for noncollinear magnetic materials, the Kohn-Sham system features exchange-correlation (xc) scalar potentials and magnetic fields. The significance of the xc magnetic fields is not very well explored; in particular, they can give rise to local torques on the magnetization, which are absent in standard local and semilocal approximations. We obtain exact benchmark solutions for two electrons on four-site extended Hubbard lattices over a wide range of interaction strengths, and compare exact xc potentials and magnetic fields with approximations obtained from orbital-dependent xc functionals. The xc magnetic fields turn out to play an increasingly important role as systems becomes more and more correlated and the electrons begin to localize; the effects of the xc torques, however, remain relatively minor. The approximate xc functionals perform overall quite well, but tend to favor symmetry-broken solutions for strong interactions.
The dynamical, long-wavelength longitudinal and transverse exchange-correlation potentials for a homogeneous electron gas are evaluated in a microscopic model based on an approximate decoupling of the equation of motion for the current-current response function. The transverse spectrum turns out to be very similar to the longitudinal one. We obtain evidence for a strong spectral structure near twice the plasma frequency due to a two-plasmon threshold for two-pair excitations, which may be observable in inelastic scattering experiments. Our results give the entire input needed to implement the Time-Dependent Current Density Functional Theory scheme recently developed by G. Vignale and W. Kohn [Phys. Rev. Lett. 77, 2037 (1996)] and are fitted to analytic functions to facilitate such applications.
Time-dependent density-functional theory (TDDFT) is a computationally efficient first-principles approach for calculating optical spectra in insulators and semiconductors, including excitonic effects. We show how exciton wave functions can be obtained from TDDFT via the Kohn-Sham transition density matrix, both in the frequency-dependent linear-response regime and in real-time propagation. The method is illustrated using one-dimensional model solids. In particular, we show that our approach provides insight into the formation and dissociation of excitons in real time. This opens the door to time-resolved studies of exciton dynamics in materials by means of real-time TDDFT.
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