Showing papers on "Random phase approximation published in 1998"

An efficient implementation of time-dependent density-functional theory for the calculation of excitation energies of large molecules

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.

Finite-temperature full random-phase approximation model of band gap narrowing for silicon device simulation

Abstract: An analytical model of the band gap narrowing (BGN) in silicon was derived from a non-self-consistent finite-temperature full random-phase approximation (RPA) formalism. Exchange-correlation self-energy of the free carriers and correlation energy of the carrier-dopant interaction were treated on an equal basis. The dispersive quasi-particle shift (QPS) in RPA quality was numerically calculated for a broad range of densities and temperatures. The dispersion was found to be smooth enough for the relevant energies to justify the rigid shift approximation in accordance with the non-self-consistent scheme. A pronounced temperature effect of the BGN only exists in the intermediate density range. The contribution of the ionic part of the QPS to the total BGN decreases from 1/3 at low densities to about 1/4 at very high densities. Based on the numerical results, Pade approximations in terms of carrier densities, doping, and temperature with an accuracy of 1 meV were constructed using limiting cases. The analytical expression for the ionic part had to be modified for device application to account for depletion zones. The model shows a reasonable agreement with certain photoluminescence data and good agreement with recently revised electrical measurements, in particular for p-type silicon. The change of BGN profiles in a bipolar transistor under increasing carrier injection is demonstrated.

Finite rank approximation for random phase approximation calculations with Skyrme interactions: An application to Ar isotopes

Abstract: Starting from an effective interaction of Skyrme type, a finite rank separable approximation is proposed for the residual particle-hole interaction with the aim to allow one to perform structure calculations in very large particle-hole spaces. The approximation is checked on a specific example by calculating isoscalar quadrupole and isovector dipole modes in a finite nucleus using the random phase approximation. It is found that the finite rank approximation is very accurate in the isoscalar channel and it reproduces reasonably well the isovector channel. The use of the finite rank interaction is illustrated by calculating the evolution of the dipole strength distribution along the Ar isotope chain, from $A=32$ to $A=52.$

An optimized-effective-potential method for solids with exact exchange and random-phase approximation correlation

Abstract: We present a new density-functional method which does not exploit the local density approximation (LDA). In this method, we use an exchange-correlation energy which consists of the exact exchange (EXX) energy and the correlation energy in the random-phase approximation (RPA). A static approximation is used in the evaluation of the functional derivative of the RPA correlation energy. The self-consistent results for solid Cu, Fe, Co, Ni, Si, and MnO (type-II antiferromagnets) are presented. For the transition metals Cu, Fe, Co, and Ni, it is shown that the correlation potential gives rise to a large contribution which has the opposite sign to the exchange potential. The resulting eigenvalue dispersions and the magnetic moments are very close to those of the LDA and experiments. On the other hand, the Fermi-contact parts of the hyperfine field are rather different from the LDA results, and are in better agreement with experiments. The band gap obtained for Si is larger than the LDA value by . For MnO, the density of states shows good correspondence with data obtained by x-ray photoelectron spectroscopy and bremsstrahlung isochromat spectroscopy.

Charge Fluctuations in Quantum Point Contacts and Chaotic Cavities in the Presence of Transport

Abstract: We analyze the frequency-dependent current fluctuations induced into a gate near a quantum point contact or a quantum chaotic cavity. We use a current and charge conserving, effective scattering approach in which interactions are treated in random phase approximation. The current fluctuations measured at a nearby gate, coupled capacitively to the conductor, are determined by the screened charge fluctuations of the conductor. Both the equilibrium and the non-equilibrium current noise at the gate can be expressed with the help of resistances which are related to the charge dynamics on the conductor. We evaluate these resistances for a point contact and determine their distributions for an ensemble of chaotic cavities. For a quantum point contact these resistances exhibit pronounced oscillations with the opening of new channels. For a chaotic cavity coupled to one channel point contacts the charge relaxation resistance shows a broad distribution between 1/4 and 1/2 of a resistance quantum. The non-equilibrium resistance exhibits a broad distribution between zero and 1/4 of a resistance quantum.

Systematics of the excitation energy of the 1+ scissors mode and its empirical dependence on the nuclear deformation parameter

Abstract: From the data on dipole excitations obtained in photon scattering experiments we extract and tabulate the mean values of the excitation energy of the ${1}^{+}$ scissors mode in nuclei of the mass region $130lAl200.$ The centers of gravity of the observed $M1$ strength distributions are always close to 3 MeV including several moderately deformed transitional nuclei. In particular, the data exhibit a weak dependence of the scissors mode energy on the deformation parameter. Including roughly the deformation dependence of pairing effects we could modify an earlier estimate based on a schematic random phase approximation and get a simple formula which yields qualitative agreement with the data.

Comparison of density matrix renormalization group calculations with electron-hole models of exciton binding in conjugated polymers

Abstract: By analogy with inorganic semiconductors such as GaAs or Si, electron-hole models may be expected to provide a useful description of the excited states of conjugated polymers. Here, these models are tested against density matrix renormalization group (DMRG) calculations. The DMRG method is used to generate nearly-exact descriptions of the ground state, 11Bu optical gap state, and the band gap of the Pariser-Parr-Pople (PPP) Hamiltonian of polyenes with between 2 and 40 carbon atoms. These are compared with both bare electron-hole (singles configuration interaction theory and the random phase approximation) and dressed electron-hole (second and third order Green’s function) methods. For the optical gap, only second-order Green’s function results were obtained. When an unscreened (Ohno) electron-electron interaction potential is used, the dressed electron-hole methods work well for the band gap. The difference between the band gap predicted by bare and dressed electron-hole methods increases with chain leng...

Surface energy of a bounded electron gas: Analysis of the accuracy of the local-density approximation via ab initio self-consistent-field calculations

Abstract: We report an {ital ab initio} evaluation of the surface energy of a simple metal, performed via a coupling-constant integration over the dynamical density-response function. The rapid rate of change of the electron density at the surface is treated exactly. Long-range correlations are treated self-consistently in the random-phase approximation; short-range correlations are included in time-dependent local-density-functional theory. Our results provide a numerical measure of the error introduced by the usual local-density approximation; this error is found to be small. {copyright} {ital 1998} {ital The American Physical Society}

Electronic stopping power of aluminum crystal

Abstract: {ital Ab initio} calculations of the electronic energy loss of ions moving in aluminum crystal are presented, within linear-response theory, from a realistic description of the one-electron band structure and a full treatment of the dynamical electronic response of valence electrons. For the evaluation of the density-response function we use the random-phase approximation and, also, a time-dependent extension of local-density-functional theory. We evaluate both position-dependent and random stopping powers, for a wide range of projectile velocities. Our results indicate that at low velocities band-structure effects slightly enhance the stopping power. At velocities just above the threshold velocity for plasmon excitation, the stopping power of the real solid is found to be smaller than that of jellium electrons, corrections being of about 10{percent}. This reduction can be understood from sum rule arguments. {copyright} {ital 1998} {ital The American Physical Society}

Reflection coefficient and localization length of waves in one-dimensional random media

Abstract: We develop a powerful method of exactly calculating various transport characteristics of waves in one-dimensional random media with (or without) coherent absorption or amplification. Using the method, we compute the probability densities of the reflectance and of the phase of the reflection coefficient, together with the localization length, of electromagnetic waves in sufficiently long random dielectric media. We find substantial differences between our exact results and the previous results obtained using the random phase approximation (RPA). The probability density of the phase of the reflection coefficient is highly nonuniform when either disorder or absorption (or amplification) is strong. The probability density of the reflectance when the absorption or amplification parameter is large is also quite different from the RPA result. We prove that the probability densities in the amplifying case are related to those in the absorbing case with the same magnitude of the imaginary part of the dielectric permeability by exact dual relationships. From the analysis of the average reflectance that shows a nonmonotonic dependence on the absorption or amplification parameter, we obtain a useful criterion for the applicability of the RPA. In the parameter regime where the RPA is invalid, we find that the exact localization length is substantially larger than the RPA localization length.

Dynamic exchange-correlation potentials for the electron gas in dimensionality D = 3 and D = 2

Abstract: Recent progress in the formulation of a fully dynamical local approximation to time-dependent density functional theory appeals to the longitudinal and transverse components of the exchange and correlation kernel in the linear current-density response of the homogeneous fluid at long wavelength. Both components are evaluated for the electron gas in dimensionality $D=3$ and $D=2$ by an approximate decoupling in the equation of motion for the current density, which accounts for processes of excitation of two electron-hole pairs. Each pair is treated in the random phase approximation, but the role of exchange and correlation is also examined; in addition, final-state exchange processes are included phenomenologically so as to satisfy the exactly known high-frequency behaviors of the kernel. The transverse and longitudinal spectra involve the same decay channels and are similar in shape. A two-plasmon threshold in the spectrum for two-pair excitations in $D=3$ leads to a sharp minimum in the real part of the exchange and correlation kernel at twice the plasma frequency. In $D=2$ the same mechanism leads to a broad spectral peak and to a broad minimum in the real part of the kernel, as a consequence of the dispersion law of the plasmon vanishing at long wavelength. The numerical results have been fitted to simple analytic functions.

Excitation of multipole plasmon resonances in clusters by fast electron impact

Abstract: We demonstrate that the electron energy loss spectrum in collision with metal clusters or fullerenes depends strongly on the scattering angle of the electron. This results from the fact that the excitation probability of the surface plasmon modes of different multipolarity is correlated with the scattering angle of the electron. We derive the kinematic conditions under which the plasmon excitation with the given angular momentum dominates in the cross section. We perform our treatment in the resonance plasmon approximation and also in the random phase approximation with exchange using the wavefunctions of the Hartree-Fock jellium model. We compare the predictions of these two quite different approaches for the cluster and report their qualitative agreement. Theoretical results are compared with the available experimental data for the electron-fullerene collision. Reasonable agreement between theoretical and experimental results is reported.

Continuum quasiparticle random-phase approximation description of isovector E-1 giant resonances

Abstract: Isovector $E1$ giant resonances in nonmagic nuclei are calculated by using a method which takes into account the single-particle continuum in the framework of a continuum quasiparticle random-phase approximation. A special procedure is formulated which gives the spurious dipole state at zero energy. The calculations are performed in a stable nonmagic tin isotope as well as unstable magic and nonmagic tin isotopes. The role of the single-particle continuum and the spurious dipole state is discussed. It turned out that the first ingredient has a noticeable influence on the resonance form.

Dielectric function of a two-component plasma including collisions

Abstract: A multiple-moment approach to the dielectric function of a dense nonideal plasma is treated beyond the random phase approximation including collisions in the Born approximation. Sum rules are checked, and the relation to the dc electrical conductivity is pointed out. Enlarging the number of moments used, converging results are obtained. The proposed approach is compared to a perturbation expansion of the Kubo formula.

Finite temperature nuclear response in the extended random phase approximation

Abstract: The nuclear collective response at finite temperature is investigated for the first time in the quantum framework of the small amplitude limit of the extended time-dependent Hartree-Fock approach, including a non-Markovian collision term It is shown that the collision width satisfies a secular equation By employing a Skyrme force, the isoscalar monopole, isovector dipole, and isoscalar quadrupole excitations in {sup 40}Ca are calculated and important quantum features are pointed out The collisional damping due to decay into incoherent two-particle{endash}two-hole states is small at low temperatures but increases rapidly at higher temperatures {copyright} {ital 1998} {ital The American Physical Society}

Local electric dipole strength in heavy nuclei

Abstract: We show that, within a two-group schematic random phase approximation model, a concentration of local dipole strength in the lower tail region of the electric giant dipole resonance can show up. The model is tested under more realistic circumstances for the isovector 1${}^{\ensuremath{-}}$ states in ${}^{116}$Sn.

First-order corrections to random-phase approximation GW calculations in silicon and diamond

Abstract: We report on ab initio calculations of the first-order corrections in the screened interaction W to the random-phase approximation polarizability and to the GW self-energy, using a noninteracting Green’s function, for silicon and diamond. It is found that the first-order vertex and self-consistency corrections to the polarizability largely compensate each other. This does not hold, however, for the first-order corrections to the GW gap. For silicon the compensation between the first-order vertex and self-consistency correction contributions to the gap is only about 35%, while for diamond it is even absent. The resulting gap values are significantly and systematically too large, the direct gaps for silicon and diamond being 0.4 eV and 0.7 eV larger than their GW values, respectively. The success of GW in predicting electronic properties of, e.g., silicon and diamond can therefore apparently not be understood in terms of ‘‘small’’ corrections to GW to first order in W using a noninteracting Green’s function. @S0163-1829~98!01819-0# I. INTRODUCTION One of the most successful methods of describing exchange-correlation effects in ab initio calculations is the random-phase approximation ~RPA! GW approach, where the ~irreducible! polarizability P is calculated in the RPA and the self-energy S is calculated to first order in the dynamically screened interaction W. 1,2 It is remarkable in this connection that non-self-consistent RPA GW calculations lead to quasiparticle ~QP! band gaps that are in excellent agreement with experiment in the case of a large group of semiconductors if the starting point is chosen to be the density-functional theory ~DFT! in the local-density approximation ~LDA!. Henceforth we will call this non-selfconsistent RPA GWapproach ‘‘standard GW.’’ The inherent assumption that higher-order corrections can be neglected is, however, far from obvious. The inclusion of vertex ( V) and so-called self-consistency ~SC! corrections to S and P has been studied by a number of researchers, mainly for the homogeneous electron gas. Hubbard 3 introduced the corrections to the RPA by means of a local-field factor ~not to be confused with the so-called local-field effects to be introduced later on!. In the electron gas case much effort has gone into obtaining expressions for local-field factors in the dielectric function; see, for instance, Refs. 2 and 4. DuBois, 5 whose work can be considered as an extension to the work of Gell-Mann and Brueckner, 6,7 stresses the importance of taking into account all polarizability diagrams of the same order in the Wigner-Seitz radius r s . He noticed the significant cancellation between V and SC corrections in the high-density limit. Geldart and Taylor 8 found a similar compensation for the static polarizability. They attempted to construct a local-field factor that includes SC corrections. Mahan and Sernelius, 9 using the local-field factor approach, concluded that the effects of V corrections to the bandwidth of the homogeneous electron gas nearly cancel when added to both the self-energy and the polarizability, as was already predicted by Rice. 10

Spin-flip exchange scattering of low-energy electrons in ferromagnetic iron

Abstract: We present a theory of spin-flip exchange scattering of low-energy electrons, directed at the ferromagnetic transition metals, with application to Fe. The model used employs a tight-binding description of the paramagnetic spd bands. Ferromagnetic exchange splitting of the bands is achieved by including on-site Coulomb repulsion between electrons in 3d orbitals, which is treated in a mean-field approximation. The low-energy electron interacts with the metal electrons via the Coulomb interaction, and the magnetic excitations in the metal are treated within the random-phase approximation. Both spin waves and Stoner excitations contribute to the energy loss of the low-energy electron. We show that the relative importance of these two loss mechanisms is influenced very importantly by the degree of localization of the 3d orbital. We also present results based on the use of accurate wave functions. These show that spin-wave loss peaks should be prominent features in spin-polarized electron energy-loss spectra. {copyright} {ital 1998} {ital The American Physical Society}

Structure and reactions of exotic nuclei

Abstract: Exotic nuclei far off -stability and asymmetric nuclear matter are investigated using nuclear many-body theory. Meson-nucleon coupling constants in asymmteric matter are derived from Dirac-Brueckner calculations. Their use in an effective density-dependent field theory is discussed. Finite nuclei close to the neutron drip line are described by non-relativistic nuclear structure methods. Ground and excited states are studied by continuum Hartree-Fock-Bogoliubov and quasiparticle random phase approximation theory. Pair interactions are found to be of major importance for the binding properties of two-neutron halo systems. The structure of single-nucleon halo nuclei is mainly determined by dynamical core polarization. Applications to recent data on the dipole response of and longitudinal momentum distributions from the break-up of are discussed. Break-up reactions at relativistic energies are described in a distorted wave eikonal approximation.

On the Plasma Oscillation in Superconductivity.

Abstract: The plasma mode in the superconducting state is studied within the random phase approximation It is proved that the plasma oscillation in the limit of zero momentum ( q ) is not affected by the superconductivity This statement itself has been obtained so far under some special conditions where energies of the plasma frequency and the superconducting order parameter are much different In this paper, we clarify that it holds true at all temperatures irrespective of (1) the magnitude of the plasma frequency, (2) the symmetry of the order parameter, and (3) details of the system, eg , dimensionality and the layered structure We also show that the plasma sum-rule is satisfied even in the superconducting state, which states that the spectrum of the density-density correlation function in the limit q →0 is dominated by the plasma mode only Although the phase fluctuation of the order parameter couples with the charge one, the collective phase oscillation, so-called the Carlson-Goldman mode, does not contri

Car-Parrinello Molecular Dynamics on excited state surfaces

Abstract: This paper describes a method to do ab initio molecular dynamics in electronically excited systems within the random phase approximation (RPA). Using a dynamical variational treatment of the RPA frequency, which corresponds to the electronic excitation energy of the system, we derive coupled equations of motion for the RPA amplitudes, the single particle orbitals, and the nuclear coordinates. These equations scale linearly with basis size and can be implemented with only a single holonomic constraint. Test calculations on a model two level system give exact agreement with analytical results. Furthermore, we examined the computational efficiency of the method by modeling the excited state dynamics of a one-dimensional polyene lattice. Our results indicate that the present method offers a considerable decrease in computational effort over a straight-forward configuration interaction (singles) plus gradient calculation performed at each nuclear configuration.