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تسجيل مستخدم جديدCollapse of the Electron Gas to Two Dimensions in Density Functional Theory
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Local and semilocal density-functional approximations for the exchange-correlation energy fail badly in the zero-thickness limit of a quasi-two-dimensional electron gas, where the density variation is rapid almost everywhere. Here we show that a fully nonlocal fifth-rung functional, the inhomogeneous Singwi-Tosi-Land-Sjolander (STLS) approach, which employs both occupied and unoccupied Kohn-Sham orbitals, recovers the true two-dimensional STLS limit and appears to be remarkably accurate for any thickness of the slab (and thus for the dimensional crossover). We also show that this good behavior is only partly due to the use of the full exact exchange energy.
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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 g
as (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.
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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.
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