Showing papers on "Random phase approximation published in 2009"
TL;DR: An adiabatic-connection fluctuation-dissipation theorem approach based on a range separation of electron-electron interactions is proposed, which corrects several shortcomings of the standard random phase approximation and is particularly well suited for describing weakly bound van der Waals systems.
Abstract: An adiabatic-connection fluctuation-dissipation theorem approach based on a range separation of electron-electron interactions is proposed. It involves a rigorous combination of short-range densityfunctional and long-range random phase approximations. This method corrects several shortcomings of the standard random phase approximation and it is particularly well suited for describing weakly bound van der Waals systems, as demonstrated on the challenging cases of the dimers Be2 and Ne2.
256 citations
TL;DR: It is shown that the inclusion of second-order screened exchange to the random phase approximation allows for an accurate description of electronic correlation in atoms and solids clearly surpassing therandom phase approximation, but not yet approaching chemical accuracy.
Abstract: We show that the inclusion of second-order screened exchange to the random phase approximation allows for an accurate description of electronic correlation in atoms and solids clearly surpassing the random phase approximation, but not yet approaching chemical accuracy. From a fundamental point of view, the method is self-correlation free for one-electron systems. From a practical point of view, the approach yields correlation energies for atoms, as well as for the jellium electron gas within a few kcal/mol of exact values, atomization energies within typically 2–3 kcal/mol of experiment, and excellent lattice constants for ionic and covalently bonded solids (0.2% error). The computational complexity is only O(N5), comparable to canonical second-order Moller–Plesset perturbation theory, which should allow for routine calculations on many systems.
240 citations
TL;DR: The one-loop polarization function of graphene has been calculated at zero temperature for arbitrary wavevector, frequency, chemical potential (doping), and band gap and is used to find the dispersion of the plasmon mode and the static screening within the random phase approximation.
Abstract: The one-loop polarization function of graphene has been calculated at zero temperature for arbitrary wavevector, frequency, chemical potential (doping), and band gap. The result is expressed in terms of elementary functions and is used to find the dispersion of the plasmon mode and the static screening within the random phase approximation. At long wavelengths the usual square root behaviour of plasmon spectra for two-dimensional (2D) systems is obtained. The presence of a small (compared to a chemical potential) gap leads to the appearance of a new undamped plasmon mode. At greater values of the gap this mode merges with the long-wavelength one, and vanishes when the Fermi level enters the gap. The screening of charged impurities at large distances differs from that in gapless graphene by slower decay of Friedel oscillations (1/r(2) instead of 1/r(3)), similarly to conventional 2D systems.
189 citations
TL;DR: This work proposes and test a simple scheme for introducing long-range RPA correlation into density functional theory and provides good thermochemical results and models van der Waals interactions accurately.
Abstract: We recently demonstrated a connection between the random phase approximation (RPA) and coupled cluster theory [G. E. Scuseria et al., J. Chem. Phys. 129, 231101 (2008)]. Based on this result, we here propose and test a simple scheme for introducing long-range RPA correlation into density functional theory. Our method provides good thermochemical results and models van der Waals interactions accurately.
175 citations
TL;DR: In this paper, a simple scheme for introducing long-range RPA correlation into density functional theory is proposed and tested, which provides good thermochemical results and models van derWaals interactions accurately.
Abstract: We recently demonstrated a connection between the random phase approximation (RPA) and coupled cluster theory [J. Chem. Phys. 129, 231101 (2008)]. Based on this result, we here propose and test a simple scheme for introducing long-range RPA correlation into density functional theory. Our method provides good thermochemical results and models van derWaals interactions accurately.
154 citations
TL;DR: In this article, the adsorption of CO on the Cu111 surface is investigated in the random phase approximation RPA as formulated within the adiabatic connection fluctuation-dissipation theorem.
Abstract: The adsorption of CO on the Cu111 surface is investigated in the random phase approximation RPA as formulated within the adiabatic connection fluctuation-dissipation theorem. The RPA adsorption energy is obtained by adding a “local exchange-correlation correction” that is extrapolated from cluster calculations of increasing size, to the Perdew-Burke-Ernzerhof PBE value for the extended system. In comparison to density-functional theory calculations with the generalized gradient functionals PBE and AM05 and the hybrid functionals PBE0 and HSE03, we find a hierarchy of improved performance from AM05/PBE to PBE0/HSE03, and from PBE0/HSE03 to RPA, both in terms of the absolute adsorption energy as well as the adsorptionenergy difference between the atop and the hollow fcc sites. In particular, the very weak atop site preference at the PBE0/HSE03 level is further stabilized by about 0.2 eV in the RPA. The mechanism behind this improvement is analyzed in terms of the GW density of states that gives a spectral representation en par with the RPA formalism for the total energy.
152 citations
TL;DR: Calculations on representative sets of hydrogen bonded, dipole-dipole, charge transfer, and weakly bound complexes show that long-range RPA provides statistical errors comparable to CCSD(T) in moderate basis sets.
Abstract: We recently presented a combination of a short-range density functional approximation with long-range random phase approximation (RPA) correlation [B. G. Janesko, T. M. Henderson, and G. E. Scuseria, J. Chem. Phys. 130, 081105 (2009)]. Here we show that this approach provides very accurate interaction energy predictions for a range of noncovalent complexes. Calculations on representative sets of hydrogen bonded, dipole-dipole, charge transfer, and weakly bound (van der Waals) complexes show that long-range RPA provides statistical errors comparable to CCSD(T) in moderate basis sets. This approach shows promise for providing accurate and computationally tractable models of noncovalent interactions in biological systems.
95 citations
TL;DR: Two semi-empirical models for the photoionization of atoms A encaged in spherical single-walled fullerenes, both neutral C n (n = 60, 240 and 540) and charged C 60 ± | z |, as well as in multiwalled Fullerene onions, C 60@C 240 and C 60 @C 240 @C 540 are detailed in this paper.
Abstract: Two semiempirical models for the photoionization of atoms A encaged in spherical single-walled fullerenes, both neutral C n ( n = 60 , 240 and 540) and charged C 60 ± | z | , as well as in multiwalled fullerenes, termed fullerene onions, C 60 @C 240 and C 60 @C 240 @C 540 are detailed. The models are based on the approximation of a carbon cage C n by a spherical attractive potential well of an adjustable radius R n , thickness Δ and depth U n 0 . The first model, termed Δ -potential model, accounts for the finite thickness Δ of the cage. The second model, termed δ -potential model, simulates the cage with the help of the Dirac δ -potential, thereby viewing the cage as being infinitesimally thin. A side by a side comparison of results obtained within the two models is performed. The models’ predictabilities are evaluated. Predicted trends in the modification of photoionization spectra of encaged atoms as well as electron correlation and relativistic effects in the atoms, compared to the free atoms, obtained both at the independent particle (Hartree-Fock and Dirac Hartree-Fock) and multiparticle nonrelativistic random phase approximation with exchange (RPAE) and relativistic random phase approximation (RRPA) approximation levels, are reviewed.
80 citations
TL;DR: In this article, a semi-analytical expression for the dynamical density?density linear response function of non-interacting massless Dirac fermions (the so-called Lindhard function) at finite temperature is presented.
Abstract: At low energies, electrons in doped graphene sheets are described by a massless Dirac fermion Hamiltonian. In this work, we present a semi-analytical expression for the dynamical density?density linear-response function of non-interacting massless Dirac fermions (the so-called 'Lindhard' function) at finite temperature. This result is crucial to describe finite-temperature screening of interacting massless Dirac fermions within the random phase approximation. In particular, we use it to make quantitative predictions for the specific heat and the compressibility of doped graphene sheets. We find that, at low temperatures, the specific heat has the usual normal-Fermi-liquid linear-in-temperature behavior, with a slope that is solely controlled by the renormalized quasiparticle velocity.
71 citations
TL;DR: The tensor terms of the Skyrme effective interaction are included in the self-consistent Hartree-Fock plus Random Phase Approximation (HF+RPA) model as discussed by the authors.
59 citations
TL;DR: In this article, a self-consistent microscopic framework for the evaluation of nuclear weak-interaction rates at finite temperature is introduced, based on Skyrme functionals, which is applied in the calculation of stellar electron-capture cross sections for selected nuclei in the iron mass group and for neutron-rich Ge isotopes.
Abstract: A fully self-consistent microscopic framework for the evaluation of nuclear weak-interaction rates at finite temperature is introduced, based on Skyrme functionals. The single-nucleon basis and the corresponding thermal occupation factors of the initial nuclear state are determined in the finite-temperature Skyrme Hartree-Fock model and charge-exchange transitions to excited states are computed using the finite-temperature random-phase approximation (RPA). Effective interactions are implemented self-consistently: Both the finite-temperature single-nucleon Hartree-Fock equations and the matrix equations of RPA are based on the same Skyrme energy density functional. Using a representative set of Skyrme functionals, the model is applied in the calculation of stellar electron-capture cross sections for selected nuclei in the iron mass group and for neutron-rich Ge isotopes.
TL;DR: In this paper, the authors used the measured occupancies of valence orbits in 76Ge and 76Se as a guideline for modification of the effective mean field energies that results in better description of these quantities.
Abstract: The measured occupancies of valence orbits in 76Ge and 76Se are used as a guideline for modification of the effective mean field energies that results in better description of these quantities. With them, in combination with the self-consistent renormalized quasiparticle random phase approximation (SRQRPA) method that ensures conservation of the mean particle number in the correlated ground state, we show that the resulting 0νββ nuclear matrix element for the 76Ge-->76Se transition is reduced by ~25% compared to the previous QRPA value, and therefore the difference between the present approach and the interacting shell model predictions becomes correspondingly smaller. Analogous modification of the mean field energies for the A=82 system also results in a reduction of 0νββ matrix element for the 82Se-->82Kr transition, making it also closer to the shell model prediction.
TL;DR: Nakatsukasa et al. as mentioned in this paper presented a computational scheme of FAM suitable for systematic investigation and showed its performance for realistic Skyrme energy functionals, and discussed the width of the giant dipole resonance in the fully self-consistent RPA calculation.
Abstract: The finite amplitude method (FAM), which we have recently proposed [T. Nakatsukasa, T. Inakura, and K. Yabana, Phys. Rev. C 76, 024318 (2007)], significantly simplifies the fully self-consistent calculation of the random-phase approximation (RPA). This article presents a computational scheme of FAM suitable for systematic investigation and shows its performance for realistic Skyrme energy functionals. We adopt the mixed representation in which the forward and backward RPA amplitudes are represented by index of hole orbitals and of the spatial grid points for the three-dimensional real space. We solve a linear algebraic problem with a sparse non-Hermitian matrix, using an iterative method. We show results of the dipole response for selected spherical and deformed nuclei. The calculated peak energies of the giant dipole resonance well agree with experiments for heavy nuclei. However, they are systematically underestimated for light nuclei. We also discuss the width of the giant dipole resonance in the fully self-consistent RPA calculation.
TL;DR: It is shown that considering only fundamental vibrational excitations for the ground electronic state provides almost converged spectra and can therefore be used as a good first approximation to simulate the absorption spectra of dimers.
Abstract: First principles calculations based on density functional theory (DFT) have been combined with the multimode vibronic theory of coupled identical monomers to simulate the absorption spectra of dimers. In comparison to our previous study [J. Guthmuller et al., J. Chem. Theory Comput. 4, 2094 (2008)], where the vibrational excitations strictly accompany the electronic excitations, the vibronic model has been generalized so that the vibronic basis set contains vibrational excitations for both the ground and the excited electronic states. As a matter of illustration, this approach has been applied to a perylenetetracarboxylic diimide dimer employing a fixed dimer geometry. The exciton coupling energy is evaluated with time dependent DFT and random phase approximation calculations and by describing the effects of the solvent with the polarizable continuum model. First, the simulated monomer absorption spectrum is found to be in excellent agreement with experiment. Then, the simulated dimer absorption spectrum presents a strong dependency on the exciton coupling energy and on the inclusion of ground state vibrational excitations in the basis set. It is further shown that considering only fundamental vibrational excitations for the ground electronic state provides almost converged spectra and can therefore be used as a good first approximation. Moreover, the comparison with experiment demonstrates that the dimer absorption spectrum can be successfully reproduced by employing the exciton coupling energy determined at the time dependent DFT level provided that the effects of the solvent are included.
TL;DR: In this article, the response of closed-shell nuclei using a renormalized interaction, derived with the Unitary Correlation Operator Method (UCOM) from the Argonne V18 potential, and a second RPA (SRPA) method was examined.
TL;DR: The renormalized one-loop theory is a coarse-grained theory of corrections to the random phase approximation (RPA) theory of composition fluctuations that predicts a shift in the critical temperature of O(N(-1/2)), which is much greater than the predicted O( N(-1)) width of the Ginzburg region.
Abstract: The renormalized one-loop theory is a coarse-grained theory of corrections to the random phase approximation (RPA) theory of composition fluctuations. We present predictions of corrections to the RPA for the structure function S(k) and to the random walk model of single-chain statics in binary homopolymer blends. We consider an apparent interaction parameter χa that is defined by applying the RPA to the small k limit of S(k). The predicted deviation of χa from its long chain limit is proportional to N−1/2, where N is the chain length. This deviation is positive (i.e., destabilizing) for weakly nonideal mixtures, with χaN≲1, but negative (stabilizing) near the critical point. The positive correction to χa for low values of χaN is a result of the fact that monomers in mixtures of shorter chains are slightly less strongly shielded from intermolecular contacts. The predicted depression in χa near the critical point is a result of long-wavelength composition fluctuations. The one-loop theory predicts a shift i...
TL;DR: In this paper, the self-consistent Relativistic Mean Field (RMF) and Random Phase approximation (RPA) were applied to axially deformed nuclei.
Abstract: Covariant density functional theory, in the framework of self-consistent Relativistic Mean Field (RMF) and Relativistic Random Phase approximation (RPA), is for the first time applied to axially deformed nuclei. The fully self-consistent RMF+RRPA equations are posed for the case of axial symmetry and non-linear energy functionals, and solved with the help of a new parallel code. Formal properties of RPA theory are studied and special care is taken in order to validate the proper decoupling of spurious modes and their influence on the physical response. Sample applications to the magnetic and electric dipole transitions in $^{20}$Ne are presented and analyzed.
TL;DR: In this paper, the effect of band gap on the ground-state properties of Dirac electrons in a doped graphene within the random phase approximation at zero temperature was studied and the conductance in the gapped graphene was shown to be smaller than gapless one.
Abstract: We study the effect of band gap on the ground-state properties of Dirac electrons in a doped graphene within the random phase approximation at zero temperature. Band gap dependence of the exchange, correlation, and ground-state energies and the compressibility are calculated. In addition, we show that the conductance in the gapped graphene is smaller than gapless one. We also calculate the band-gap dependence of charge compressibility and it decreases with increasing the band-gap values.
TL;DR: In this paper, an ab initio study of the graphene quasi-particle band structure within local density approximation (LDA) was performed and it was shown that the Fermi velocity is substantially renormalized by correlation effects and that this renormalization rapidly decreases with doping.
Abstract: We present an ab initio study of the graphene quasi-particle band structure within GW approximation. In particular we studied the renormalization of the Fermi velocityvF as function of the electrostatic doping. We show that within local density approximation (LDA) the Fermi velocity is substantially renormalized by correlation effects and that this renormalization rapidly decreases with doping. We discuss our results in the light of recent experiments on graphene and intercalate graphite.
TL;DR: In this paper, the particle-hole excitation spectrum for doped graphene is calculated from the dynamical polarizability, and the effects of electron-electron interaction are included within the random phase approximation.
Abstract: The particle-hole excitation spectrum for doped graphene is calculated from the dynamical polarizability. We study the zero and finite magnetic field cases and compare them to the standard two-dimensional electron gas. The effects of electron-electron interaction are included within the random phase approximation. From the obtained polarizability, we study the screening effects and the collective excitations (plasmon, magneto-excitons, upper-hybrid mode and linear magneto-plasmons). We stress the differences with the usual 2DEG.
TL;DR: It is shown here that reference states constructed from approximate local exchange-correlation potentials give their best results with smaller rescaling factors approximately 1, however, the tested potentials yield artifacts in some systems.
Abstract: We recently presented a combination of a short-range density functional approximation with long-range random phase approximation (RPA) correlation [B G Janesko, T M Henderson, and G E Scuseria, J Chem Phys 130, 081105 (2009)] Here we explore how this approximation’s performance is affected by the choice of reference state, ie, the orbitals and orbital energy differences entering the RPA energy expression Our previous results built the reference state using a nonlocal exchange potential Rescaling the RPA correlation energy by an empirical factor >1 gave very accurate results for a wide range of properties We show here that reference states constructed from approximate local exchange-correlation potentials give their best results with smaller rescaling factors ∼1 However, the tested potentials yield artifacts in some systems
TL;DR: In this paper, the authors evaluate the stopping and image forces on a charged particle moving parallel to a doped sheet of graphene by using the dielectric-response formalism for graphene's $\ensuremath{pi}$-electron bands in the random phase approximation (RPA).
Abstract: We evaluate the stopping and image forces on a charged particle moving parallel to a doped sheet of graphene by using the dielectric-response formalism for graphene's $\ensuremath{\pi}$-electron bands in the random phase approximation (RPA). The forces are presented as functions of the particle speed and the particle distance for a broad range of charge-carrier densities in graphene. A detailed comparison with the results from a kinetic equation model reveal the importance of interband single-particle excitations in the RPA model for high particle speeds. We also consider the effects of a finite gap between graphene and a supporting substrate, as well as the effects of a finite damping rate that is included through the use of Mermin's procedure. The damping rate is estimated from a tentative comparison of the Mermin loss function with a high-resolution reflection electron energy loss spectroscopy experiment. In the limit of low particle speeds, several analytical results are obtained for the friction coefficient that show an intricate relationship between the charge-carrier density, the damping rate, and the particle distance, which may be relevant to surface processes and electrochemistry involving graphene.
TL;DR: In this paper, a separable pairing force was introduced to reproduce the pairing properties of the Gogny force in nuclear matter, which is able to describe in relativistic Hartree-Bogoliubov (RHB) calculations the pairing property in the ground state of finite nuclei on almost the same footing as the original gogny interaction.
Abstract: We have introduced a separable pairing force, which was adjusted to reproduce the pairing properties of the Gogny force in nuclear matter. This separable pairing force is able to describe in relativistic Hartree-Bogoliubov (RHB) calculations the pairing properties in the ground state of finite nuclei on almost the same footing as the original Gogny interaction. In this work we investigate excited states using the Relativistic Quasiparticle Random-Phase Approximation (RQRPA) with the same separable pairing force. For consistency the Goldstone modes and the convergence with various cutoff parameters in this version of RQRPA are studied. The first excited 2{sup +} states for the chain of Sn isotopes with Z=50 and the chain of isotones with N=82 isotones are calculated in RQRPA together with the 3{sup -} states of Sn isotopes. By comparing our results with experimental data and with the results of the original Gogny force we find that this simple separable pairing interaction is very successful in depicting the pairing properties of vibrational excitations.
TL;DR: In this article, the authors obtained x-ray absorption near-edge structures (XANES) by solving the equation of motion for the two-particle Green's function for the electron-hole pair, the Bethe-Salpeter equation (BSE), within the all-electron full-potential linearized augmented plane wave method (FPLAPW).
Abstract: We obtain x-ray absorption near-edge structures (XANES) by solving the equation of motion for the two-particle Green's function for the electron–hole pair, the Bethe–Salpeter equation (BSE), within the all-electron full-potential linearized augmented plane wave method (FPLAPW). The excited states are calculated for the Li K-edge in the insulating solids LiF, Li2O and Li2S, and absorption spectra are compared with independent particle results using the random phase approximation (RPA), as well as supercell calculations using the core-hole approximation within density functional theory (DFT). The binding energies of strongly bound excitations are determined in the materials, and core-exciton wavefunctions are demonstrated for LiF.
TL;DR: JMP2's explicit inclusion of (approximate) like-spin correlation effects provides significant improvements over SOS-MP2 for thermochemistry, and it is shown here that both JMP2 and SOS- MP2 provide a reasonable treatment of long-range correlation when combined with a short-range exchange-correlation functional.
Abstract: We have been investigating the combination of a short-range density functional approximation with long-range random phase approximation (RPA) correlation, where the direct RPA correlation is constructed using only Coulomb (i.e., not antisymmetrized) two-electron integrals. Our group’s recently demonstrated connection between RPA and coupled cluster theory suggests investigating a related method: second-order Moller–Plesset perturbation theory correlation (MP2) constructed using only Coulomb integrals. This new “JMP2” method is related to the scaled-opposite-spin SOS-MP2 approximation [Y. Jung, R. C. Lochan, A. D. Dutoi and M. Head-Gordon, J. Chem. Phys., 2004, 121, 9793], which is also constructed using only Coulomb integrals. While JMP2 and SOS-MP2 yield identical results for closed shell systems, they have important differences for open shells. We show here that both JMP2 and SOS-MP2 provide a reasonable treatment of long-range correlation when combined with a short-range exchange–correlation functional. Remarkably, JMP2’s explicit inclusion of (approximate) like-spin correlation effects provides significant improvements over SOS-MP2 for thermochemistry.
TL;DR: In this article, a self-consistent finite-temperature RPA (random phase approximation) based on relativistic energy density functionals was used to study the multipole response of nuclei at temperatures T = 0 − 2 MeV.
TL;DR: In this article, the quasi-particle (QP) self-energy and spectral function in doped graphene were investigated when symmetry breaking of the sublattices occurs.
Abstract: Motivated by a number of recent experimental studies, we have carried out the microscopic calculation of the quasi-particle (QP) self-energy and spectral function in doped graphene when symmetry breaking of the sublattices occurs. Our systematic study is based on the many-body G0W approach that is established on the random phase approximation and on graphene's massive Dirac equation continuum model. We report extensive calculations of both the real and imaginary parts of the QP self-energy in the presence of a gap opening. We also present results for spectral function, renormalized Fermi velocity and band gap renormalization of massive Dirac fermions over a broad range of electron densities. We further show that mass generating in graphene washes out the plasmaron peak in the spectral weight.
TL;DR: In this article, relativistic mean field calculations based on a covariant density functional with density-dependent zero-range forces are used to investigate collective excitation phenomena in several spherical nuclei along the periodic table.
Abstract: Continuum relativistic random-phase approximation (CRPA) is used to investigate collective excitation phenomena in several spherical nuclei along the periodic table. We start from relativistic mean-field calculations based on a covariant density functional with density-dependent zero-range forces. From the same functional an effective interaction is obtained as the second derivative with respect to the density. This interaction is used in relativistic CRPA calculations for the investigation of isoscalar monopole, isovector dipole, and isoscalar quadrupole resonances of spherical nuclei. In particular we study the low-lying E1 strength in the vicinity of the neutron evaporation threshold. The properties of the resonances, such as centroid energies and strengths distributions are compared with results of discrete RPA calculations for the same model as well as with experimental data.
TL;DR: In this paper, a complete theoretical analysis of optical properties of calcium mono chalcogenide compounds CaX (X = O, S, Se and Te) in NaCl crystal structure is calculated using the band structure results obtained through the full potential linearized augmented plane wave (FP-LAPW) method within density functional theory.
TL;DR: In this article, the effects of collective modes on the temperature relaxation in fully ionized, weakly coupled plasmas are investigated and a coupled mode (CM) formula for the electron-ion energy transfer is derived within the random phase approximation and it is shown how it can be evaluated using standard methods.
Abstract: The effects of collective modes on the temperature relaxation in fully ionized, weakly coupled plasmas are investigated. A coupled mode (CM) formula for the electron-ion energy transfer is derived within the random phase approximation and it is shown how it can be evaluated using standard methods. The CM rates are considerably smaller than rates based on Fermi’s golden rule for some parameters and identical for others. It is shown how the CM effects are connected to the occurrence of ion acoustic modes and when they occur. Interestingly, CM effects occur also for plasmas with very high electron temperatures; a regime, where the Landau–Spitzer approach is believed to be accurate.