Topic

# Random phase approximation

About: Random phase approximation is a(n) research topic. Over the lifetime, 4202 publication(s) have been published within this topic receiving 83067 citation(s).

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Abstract: Time-dependent density-functional (TDDFT) methods are applied within the adiabatic approximation to a series of molecules including C70. Our implementation provides an efficient approach for treating frequency-dependent response properties and electronic excitation spectra of large molecules. We also present a new algorithm for the diagonalization of large non-Hermitian matrices which is needed for hybrid functionals and is also faster than the widely used Davidson algorithm when employed for the Hermitian case appearing in excited energy calculations. Results for a few selected molecules using local, gradient-corrected, and hybrid functionals are discussed. We find that for molecules with low lying excited states TDDFT constitutes a considerable improvement over Hartree–Fock based methods (like the random phase approximation) which require comparable computational effort.

4,274 citations

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General Electric

^{1}Abstract: Reflectance data are presented for Si, Ge, GaP, GaAs, InAs, and InSb in the range of photon energies between 1.5 and 25 eV. The real and imaginary parts of the dielectric constant and the function describing the energy loss of fast electrons traversing the materials are deduced from the Kramers-Kronig relations. The results can be described in terms of interband transitions and plasma oscillations. A theory based on the frequency-dependent dielectric constant in the random phase approximation is presented and used to analyze these data above 12 eV, where the oscillator strengths coupling the valence and conduction bands are practically exhausted. The theory predicts and the experiments confirm essentially free electron-like behavior before the onset of $d$-band excitations and a plasma frequency modified from that of free electrons due to oscillator strength coupling between valence and $d$ bands and $d$-band screening effects. These complications are absent in Si. The energy loss functions obtained from optical and characteristic energy loss experiments are also found to be in good agreement. Arguments for interpreting structure in the reflectance curves above 16 eV in terms of $d$-band excitations are given.

1,739 citations

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Abstract: The self-consistent field method in which a many-electron system is described by a time-dependent interaction of a single electron with a self-consistent electromagnetic field is shown to be equivalent for many purposes to the treatment given by Sawada and Brout. Starting with the correct many-electron Hamiltonian, it is found, when the approximations characteristic of the Sawada-Brout scheme are made, that the equation of motion for the pair creation operators is the same as that for the one-particle density matrix in the self-consistent field framework. These approximations are seen to correspond to (1) factorization of the two-particle density matrix, and (2) linearization with respect to off-diagonal components of the one-particle density matrix. The complex, frequency-dependent dielectric constant is obtained straight-forwardly from the self-consistent field approach both for a free-electron gas and a real solid. It is found to be the same as that obtained by Nozi\'eres and Pines in the random phase approximation. The resulting plasma dispersion relation for the solid in the limit of long wavelengths is discussed.

890 citations

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Abstract: The polarization of graphene is calculated exactly within the random phase approximation for arbitrary frequency, wavevector and doping. At finite doping, the static susceptibility saturates to a constant value for low momenta. At q = 2kF it has a discontinuity only in the second derivative. In the presence of a charged impurity this results in Friedel oscillations which decay with the same power law as the Thomas–Fermi contribution, the latter being always dominant. The spin density oscillations in the presence of a magnetic impurity are also calculated. The dynamical polarization for low q and arbitrary ω is employed to calculate the dispersion relation and the decay rate of plasmons and acoustic phonons as a function of doping. The low screening of graphene, combined with the absence of a gap, leads to a significant stiffening of the longitudinal acoustic lattice vibrations.

886 citations

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Abstract: We report the implementation of time‐dependent density‐functional response theory (TD‐DFRT) for molecules using the time‐dependent local density approximation (TDLDA). This adds exchange and correlation response terms to our previous work which used the density‐functional theory (DFT) random phase approximation (RPA) [M. E. Casida, C. Jamorski, F. Bohr, J. Guan, and D. R. Salahub, in Theoretical and Computational Modeling of NLO and Electronic Materials, edited by S. P. Karna and A. T. Yeates (ACS, Washington, D.C., in press)], and provides the first practical, molecular DFT code capable of treating frequency‐dependent response properties and electronic excitation spectra based on a formally rigorous approach. The essentials of the method are described, and results for the dynamic mean dipole polarizability and the first eight excitation energies of N2 are found to be in good agreement with experiment and with results from other ab initio methods.

821 citations