Random Phase Approximation With Exchange Research Articles

Photoionization cross-sections of valence ns and np (n = 2,3) atomic shells in soft x-ray region

Theoretical photoionization cross-sections for average of configuration terms of valence ns- and np- shells of atoms C, N, O, F, Ne, Si, P, S, Cl and Ar are calculated with account for intrachannel and interchannel interactions for the energy region from threshold to 400 eV. The many-electron effects were accounted for within the framework of RPAE (random phase approximation with exchange) method, which is extended for average terms of unfilled shells. Calculations demonstrate for open-shell atoms similar effects as that were known for noble gas atoms Ne and Ar, namely a strong decrease of photoionization cross-sections of ns- subshell due to the interaction of transitions ns→εp and np→εd.

All-order correlation of single excitons in nanocrystals using ak·penvelope-function approach: Application to lead halide perovskites

We discuss a variety of many-body approaches, within effective-mass and $\mathbf{k}\cdot\mathbf{p}$ envelope-function formalisms, for calculating correlated single excitons in semiconductor nanocrystals (NCs) to all orders in the electron-hole Coulomb interaction. These approaches are applied to NCs of the lead-halide perovskite CsPbBr$_{3}$, which typically present excitons in intermediate confinement with physical observables often strongly renormalized by correlation (e.g., radiative decay rate enhanced by a factor of about 7 relative to a mean-field approach, for a NC of edge length 11 nm). The many-body methods considered include the particle-hole Bethe-Salpeter equation, configuration interaction with single excitations, and the random-phase approximation with exchange (RPAE), which are shown to be closely related to each other but to treat $\mathbf{k}\cdot\mathbf{p}$ corrections differently, with RPAE being the most complete method. The methods are applied to calculate the correlation energy, the radiative lifetime, and the long-range Coulomb contribution to the fine structure of the ground-state exciton. In the limit of large NC sizes, the numerical results are shown to agree well with analytical results for this limit, where these are known. Correlated excited states of the single exciton are used to calculate the one-photon absorption cross section; the shape of the resulting cross-section curve (versus laser wavelength) at threshold and up to an excitation energy of about 1 eV is in good agreement with experimental cross sections. The equations for the methods are explicitly adapted to spherical symmetry (involving radial integrals and angular factors) and in this form permit a rapid computation for systems in intermediate confinement.

Random phase approximation with exchange for an accurate description of crystalline polymorphism

We determine the correlation energy of BN, SiO$_2$ and ice polymorphs employing a recently developed RPAx (random phase approximation with exchange) approach. The RPAx provides larger and more accurate polarizabilities as compared to the RPA, and captures effects of anisotropy. In turn, the correlation energy, defined as an integral over the density-density response function, gives improved binding energies without the need for error cancellation. Here, we demonstrate that these features are crucial for predicting the relative energies between low- and high-pressure polymorphs of different coordination number as, e.g., between $\alpha$-quartz and stishovite in SiO$_2$, or layered and cubic BN. Furthermore, a reliable (H$_2$O)$_2$ potential energy surface is obtained, necessary for describing the various phases of ice. The RPAx gives results comparable to other high-level methods such as coupled cluster and quantum Monte Carlo, also in cases where the RPA breaks down. Although higher computational cost than RPA we observe a faster convergence with respect to the number of eigenvalues in the response function.

Nondipole Effects in Time Delay of Photoelectrons from Atoms, Negative Ions, and Endohedrals

In this Letter, we investigate the non-dipole effects in time delay of photoelectrons emitted by multi-electron atoms, negative ions, and respective endohedrals. We present the necessary general formulas in the frame of the random phase approximation with exchange (RPAE) applied to atoms, negative ions, and properly adjusted to endohedrals. We concentrate on low photon energy region, where non-dipole effects are very small in the cross-sections but become observable in angular distributions. We not only derive the formulas for non-dipole effects in time delay, but perform corresponding numeric calculations. We demonstrate how the non-dipole corrections can be isolated in experiment. Concrete calculations are performed for noble gas atoms Ar and Xe, isoelectronic to them negative ions Cl- and I- and endohedrals Ar(Cl-)C60 and Xe(I-)@C60. We found that the forward-backward photoelectron time delay differences give direct information on non-dipole effects. They proved to be quite measurable and prominently affected by the presence of the fullerenes shell.

Time Delay of Photoionization by Endohedrals

In this Letter, we investigate the time delay of photoelectrons by fullerenes shell in endohedrals. We present general formulas in the frame of the random phase approximation with exchange (RPAE) applied to endohedrals A@CN that consist of an atom A located inside of a fullerenes shell constructed of N carbon atoms C. We calculate the time delay of electrons that leave the inner atom A in course of A@CN photoionization. Our aim is to clarify the role that is played by CN shell. As concrete examples of A we have considered Ne, Fr, Kr and Xe, and as fullerene we consider C60. The presence of the C60 shell manifests itself in powerful oscillations of the time delay of an electron that is ionized from a given subshell nl by a photon with energy. Calculations are performed for outer, subvalent and d-subshells.

Photoionization of endohedrals: complete semi-phenomenological approach

SynopsisWe developed a semi-phenomenological approach that permits to calculate the photoionization cross section of an endohedral A@CN. We take, along with the static pseudopotential of atom A and fullerene CN also the static and dynamic polarization of A and CN by the incoming photons and outgoing electrons. The approach is general and applicable to any spherically-symmetric endohedrals. Concrete results are obtained for Ar@C60 and Xe@C60. We take into account the multi-electron correlations in the frame of the random phase approximation with exchange (RPAE).

Intershell correlations in endohedral atoms

We have calculated partial contributions of different endohedral and atomic subshells to the total dipole sum rule in the frame of the random phase approximation with exchange (RPAE) and found that they are essentially different from the numbers of electrons in respective subshells. This difference manifests the strength of the intershell interaction. We present concrete results of calculations for endohedrals, composed of fullerene C60 and all noble gases He, Ne, Ar, Kr, and Xe thus forming respectively He@C60, Ne@C60, Ar@C60, Kr@C60, and Xe@C60. For comparison, we obtained similar results for isolated noble gas atoms. The deviation from number of electrons in outer subshells proved to be much bigger in endohedrals than in isolated atoms thus demonstrating considerably stronger intershell correlations there.

Photoionization of Endohedrals with Account of Fullerenes Polarization

We have calculated photoionization cross-section of endohedral atoms A@CN. We took into account the polarizability of the fullerene electron shell CN that modifies the incoming photon beam and the one-electron wave functions of the caged atom A. We employ simplified versions of both static and dynamic polarization. The properly modified one-electron wave functions became a starting point of the account of the multi-electron correlations in the frame of the random phase approximation with exchange (RPAE). We treat atomic and fullerenes polarization that act upon photoelectron similarly, substituting them by static polarization potential. The photon beam polarizes the fullerene. This effect is accounted for introducing a polarization factor. As concrete objects, we have considered Ar and Xe atoms inside fullerene C60. Inclusion of polarization prominently increases the photoionization cross-section mainly close to the threshold.

Beyond the random phase approximation with a local exchange vertex

With the aim of constructing an electronic structure approach that systematically goes beyond the GW and random phase approximation (RPA) we introduce a vertex correction based on the exact-exchange (EXX) potential of time-dependent density functional theory. The EXX vertex function is constrained to be local but is expected to capture similar physics as the Hartree-Fock vertex. With the EXX vertex we then consistently unify different beyond-RPA approaches such as the various re-summations of RPA with exchange (RPAx) and the second order screened exchange (SOSEX) approximation. The theoretical analysis is supported by numerical studies on the hydrogen dimer and the electron gas, and we discuss the importance of including the vertex correction in both the screened interaction and the self energy. Finally, we give details on our implementation within the plane-wave pseudo potential framework and demonstrate the excellent performance of the different RPAx methods in describing the energetics of hydrogen and van der Waals bonds.

Simulation of angular-resolved RABBITT measurements in noble-gas atoms

We simulate angular resolved RABBITT (Reconstruction of Attosecond Beating By Interference of Two-photon Transitions) measurements on valence shells of noble gas atoms (Ne, Ar, Kr, and Xe). Our non-perturbative numerical simulation is based on solution of the time-dependent Schr\"odinger equation for a target atom driven by an ionizing XUV and dressing IR fields. From these simulations we extract the angular dependent magnitude and phase of the RABBITT oscillations and deduce the corresponding angular anisotropy {\beta} parameter and Wigner time delay ${\tau}_W$ for the single XUV photon absorption which initiates the RABBITT process. Said {\beta} and ${\tau}_W$ parameters are compared with calculations in the random phase approximation with exchange (RPAE) which includes inter-shell correlation. This comparison is used to test various effective potentials employed in the one-electron TDSE. In lighter atoms (Ne and Ar), several effective potentials are found to provide accurate simulation of RABBITT measurements for a wide range of photon energies up to 100 eV above the valence shell threshold. In heavier atoms (Kr and Xe), the onset of strong correlation with the d-shell restricts the validity of the single active electron approximation to several tens of eV above the valence shell threshold.

Molecular bonding with the RPAx: From weak dispersion forces to strong correlation

In a recent paper [Phys. Rev. B 90, 125150 (2014)], we showed that the random phase approximation with exchange (RPAx) gives accurate total energies for a diverse set of systems including the high and low density regime of the homogeneous electron gas, the ${\mathrm{N}}_{2}$ molecule, and the ${\mathrm{H}}_{2}$ molecule at dissociation. In this paper, we present results for the van der Waals bonded ${\mathrm{Ar}}_{2}$ and ${\mathrm{Kr}}_{2}$ dimers and demonstrate that the RPAx gives superior dispersion forces as compared to the RPA. We then show that this improved description is crucial for the bond formation of the ${\mathrm{Mg}}_{2}$ molecule. In addition, the RPAx performs better for the ${\mathrm{Be}}_{2}$ dissociation curve at large nuclear separation but, similar to the RPA, fails around equilibrium due to the build up of a large repulsion hump. For the strongly correlated LiH molecule at dissociation we have also calculated the RPAx potential and find that the correlation peak at the bond midpoint is overestimated as compared to the RPA and the exact result. The step feature is missing and hence the delocalization error is comparable to the RPA. This is further illustrated by a smooth energy versus fractional charge curve and a poor description of the LiH dipole moment at dissociation.

Inner-shell photodetachment from a Si− negative ion: strong effect of many-electron correlations

The first theoretical investigation of the inner-shell single-photodetachment from the Si− (1s22s22p63s23p3 4So) negative ion is presented. The partial and total cross sections, the photoelectron phaseshifts, and the parameters of angular anisotropy are calculated in the framework of the many-body theory for L-shell photodetachment from Si− ion in the experimentally accessible range of photon energies (7.5–14 Ry). Comparison is made between the calculations of the response of the ionic many-electron system Si− to an electromagnetic field at the different levels of approximation: the ‘frozen-field’ random phase approximation with exchange (RPAE), and the static relaxation approximation. The optimal analysis is made when the dynamic relaxation and polarization are included within the Dyson equation method (DEM) simultaneously with the RPAE corrections (the RPAE&DEM approach). It is predicted that the photoexcitation to a resonance state of complex ‘shape-Feschbach’ nature in the open p-shell reveals itself as a prominent resonance structure in the photodetachment cross sections in the energy range of the 2s and 2p inner shell thresholds similar to that in 1s inner-shell photodetachment from C− (2006 J. Phys. B: At. Mol. Opt. Phys. 39 1379). The photodetachment dynamical characteristics clearly demonstrate the significance of all the considered many-electron correlations within the RPAE&DEM approach, however the total photodetachment cross section is dominated by a strong resonance peak just after the 2s threshold. Dynamical relaxation (screening) is identified as a decisive factor in the formation of this resonance.

Length and velocity form calculations of generalized oscillator strengths of dipole, quadrupole and monopole excitations of argon

The quadrupole, monopole and dipole generalized oscillator strengths (GOSs) as a function of momentum transfer are respectively calculated for these 3p6 → 3p5 (4p, 5p, 6p) and 3p6 → 3p5 (4s, 5s, 6s) transitions. Configuration interaction (CI) and random phase approximation with exchange (RPAE) methods are used in the determination of these GOS, in the length and velocity forms. The code of Hibbert has been used to generate the wavefunctions from which a partial of argon GOSs are been computed. The present work has reduced the gap between the absolute values of the theoretical calculations of GOSs and those of the experimental results of Zhu et al for the quadrupole excitations to 3p5 (4p, 5p). The profile of our quadrupole GOS 3p6 → 3p55p transition agrees well with the experimental result of Zhu. The best agreement (0.7%) is observed between the (length) first maximum position and the experimental one for the quadrupole GOS 3p6 → 3p54p transition. The present velocity GOS minimum position for the dipole excitation in 3p6 → 3p54s and the calculated velocity GOS maximum position of the monopole 3p6 → 3p54p transition are in good agreement with the experimental observations (differences of 1.82% and 3.08%, respectively). Correlation effects decrease with increasing of the excited state principal quantum number and have no great influence on the extrema positions.

Interelectron correlations in photoionization of outer shells near inner shell thresholds

SynopsisWe have studied the role of virtual excitations of inner shells upon outer shell photoionization. The calculations were performed in the frames of the Random Phase Approximation with Exchange (RPAE) and its generalized version GRPAE that take into account variation of the atomic field due to electron elimination and the inner vacancies decay. We apply both analytic approximation and numeric computations. The results are presented for 3p electrons in Ar and for 4d-electrons in Pd near inner shells thresholds. The effect considered proved to be quite noticeable.

On the additivity of scattering phases in collisions of electrons on endohedrals

SynopsisIt is demonstrated that an inner atom, either Ne or Ar, qualitatively affects the electron scattering phases upon an endohedral, in spite of the fact that the fullerene consists of 60 carbon atoms, while the atom staffed inside is only one. Calculations are performed in the one-electron Hartree-Fock (HF) and random phase approximation with exchange (RPAE) for the inner atom while the fullerenes shell is substituted by static potential without and with the polarization potential. The total endohedral scattering phase is a sum of atomic, Ne or Ar, and fullerenes C60 phases, contrary to the intuitive assumption that the total phases on C60 and Ne@C60 or Ar@C60 has to be the same.

Van der Waals coefficients for positronium interactions with atoms

The random-phase approximation with exchange (RPAE) is used with a $B$-spline basis to compute dynamic dipole polarizabilities of noble-gas atoms and several other closed-shell atoms (Be, Mg, Ca, Zn, Sr, Cd, and Ba). From these, values of the van der Waals ${C}_{6}$ constants for positronium interactions with these atoms are determined and compared with existing data. After correcting the RPAE polarizabilities to fit the most accurate static polarizability data, our best predictions of ${C}_{6}$ for Ps--noble-gas pairs are expected to be accurate to within 1%, and to within a few percent for the alkaline-earth metals. We also used accurate dynamic dipole polarizabilities from the literature to compute the ${C}_{6}$ coefficients for the alkali-metal atoms. Implications of increased ${C}_{6}$ values for Ps scattering from more polarizable atoms are discussed.

Low-energy positronium scattering from noble-gas atoms

Synopsisvan der Waals C6 coefficients are calculated ab initio for positronium interactions with noble-gas atoms using the random-phase approximation with exchange (RPAE). These are scaled slightly to create our best predictions. Comparisons are made with existing configuration interaction and semi-empirical data.

On the behavior of scattering phases in collisions of electrons with multiatomic objects

We have studied the energy dependence of several first scattering phases with multiatomic object. As concrete examples representing the general trends endohedrals Ne@C60 and Ar@C60 are considered. It appeared that the presence of an inner atom, either Ne or Ar, qualitatively affects the scattering phases, in spite of the fact that the fullerene consists of 60 carbon atoms, while the atom staffed inside is only one. Calculations are performed in the one-electron Hartree-Fock (HF) and random phase approximation with exchange (RPAE) for the inner atom while the fullerenes shell is substituted by static potential without and with the polarization potential. It appeared that the total endohedral scattering phase is simply a sum of atomic, Ne or Ar, and fullerenes C60 phases, contrary to the intuitive assumption that the total phases on C60 and Ne@C60 or Ar@C60 has to be the same.

Many-particle correlations in microscopic electron–hole droplets

Many-particle effects in two-component systems composed of two types of oppositely charged fermions are studied. The influence of mass ratio of the particles on physical properties of microscopic electron–hole droplets is investigated. We offer a theoretical model describing a quantum-mechanical system of a finite number of electron–hole pairs coupled by Coulomb interaction. The model is based on the Hartree–Fock approximation and the Random Phase Approximation with Exchange (RPAE). Within our theoretical approach we exclude center-of-mass motion from the spectrum of excited states of the system. Using our model we calculate the binding energies, static dipole polarizabilities and photoabsorption cross sections for the systems containing different numbers of particles with various ratios of electron and hole masses.

Electron correlation methods based on the random phase approximation

In the past decade, the random phase approximation (RPA) has emerged as a promising post-Kohn–Sham method to treat electron correlation in molecules, surfaces, and solids. In this review, we explain how RPA arises naturally as a zero-order approximation from the adiabatic connection and the fluctuation-dissipation theorem in a density functional context. This is contrasted to RPA with exchange (RPAX) in a post-Hartree–Fock context. In both methods, RPA and RPAX, the correlation energy may be expressed as a sum over zero-point energies of harmonic oscillators representing collective electronic excitations, consistent with the physical picture originally proposed by Bohm and Pines. The extra factor 1/2 in the RPAX case is rigorously derived. Approaches beyond RPA are briefly summarized. We also review computational strategies implementing RPA. The combination of auxiliary expansions and imaginary frequency integration methods has lead to recent progress in this field, making RPA calculations affordable for systems with over 100 atoms. Finally, we summarize benchmark applications of RPA to various molecular and solid-state properties, including relative energies of conformers, reaction energies involving weak and covalent interactions, diatomic potential energy curves, ionization potentials and electron affinities, surface adsorption energies, bulk cohesive energies and lattice constants. RPA barrier heights for an extended benchmark set are presented. RPA is an order of magnitude more accurate than semi-local functionals such as B3LYP for non-covalent interactions rivaling the best empirically parametrized methods. Larger but systematic errors are observed for processes that do not conserve the number of electron pairs, such as atomization and ionization.