Independent Particle Approximation Research Articles

Classical trajectory Monte Carlo model calculations for ionization of the uracil molecule by impact of heavy ions

The ionization of the uracil molecule induced by heavy-ion impact has been investigated using the classical trajectory Monte Carlo (CTMC) method. Assuming the validity of the independent-particle model approximation, the collision problem is solved by considering the three-body dynamics of the projectile, an active electron and the molecule core. The interaction of the molecule core with the other two particles is described by a multi-center potential built from screened atomic potentials. The cross section differential with respect to the energy and angle of the electrons ejected in the ionization process has been calculated for an impact of 3.5 MeV u−1 ions. Total electron emission cross sections (TCS) are presented for () and projectiles as a function of the impact energy in the range from 10 keV u−1 to 10 MeV u−1. The dependence of the TCS on the charge state of the projectile has been investigated for 2.5 MeV u−1 () and () ions. The results of the calculations are compared with available experimental data and the predictions of other theoretical models: the first Born approximation with correct boundary conditions (CB1), the continuum-distorted-wave–eikonal-initial-state approach (CDW-EIS), and the combined classical-trajectory Monte Carlo–classical over-the-barrier model (CTMC-COB).

Sum rules for the polarization correlations in photoionization and bremsstrahlung

The polarization correlations in doubly differential cross sections are investigated for photoionization and ordinary bremsstrahlung. These correlations describe the polarization transfer between incident light and ejected photoelectrons as well as between an incoming electron beam and bremsstrahlung light, respectively. They are characterized by a set of seven real parameters ${C}_{ij}$. We show that the squares of these parameters are connected by simple ``sum rules.'' These sum rules can be applied for both one-electron systems and also for atoms, if the latter are described within the independent particle approximation. In particular, they are exact in their simplest form (i) for the photoionization of $K$-, ${L}_{I,II}$-, and ${M}_{I,II}$-atomic shells, as well as (ii) for bremsstrahlung in which the electron is scattered into ${s}_{1/2}$ or ${p}_{1/2}$ states, as in the tip (bremsstrahlung) region. Detailed calculations are performed to verify the derived identities and to discuss their possible applications for the analysis of modern photoionization and bremsstrahlung experiments. In particular, we argue that the sum rules may help to determine the entire set of (significant) polarization correlations in the case when not all ${C}_{ij}$ are available for experimental observation.

Fast and accurate predictions of covalent bonds in chemical space.

We assess the predictive accuracy of perturbation theory based estimates of changes in covalent bonding due to linear alchemical interpolations among molecules. We have investigated σ bonding to hydrogen, as well as σ and π bonding between main-group elements, occurring in small sets of iso-valence-electronic molecules with elements drawn from second to fourth rows in the p-block of the periodic table. Numerical evidence suggests that first order Taylor expansions of covalent bonding potentials can achieve high accuracy if (i) the alchemical interpolation is vertical (fixed geometry), (ii) it involves elements from the third and fourth rows of the periodic table, and (iii) an optimal reference geometry is used. This leads to near linear changes in the bonding potential, resulting in analytical predictions with chemical accuracy (∼1 kcal/mol). Second order estimates deteriorate the prediction. If initial and final molecules differ not only in composition but also in geometry, all estimates become substantially worse, with second order being slightly more accurate than first order. The independent particle approximation based second order perturbation theory performs poorly when compared to the coupled perturbed or finite difference approach. Taylor series expansions up to fourth order of the potential energy curve of highly symmetric systems indicate a finite radius of convergence, as illustrated for the alchemical stretching of H2 (+). Results are presented for (i) covalent bonds to hydrogen in 12 molecules with 8 valence electrons (CH4, NH3, H2O, HF, SiH4, PH3, H2S, HCl, GeH4, AsH3, H2Se, HBr); (ii) main-group single bonds in 9 molecules with 14 valence electrons (CH3F, CH3Cl, CH3Br, SiH3F, SiH3Cl, SiH3Br, GeH3F, GeH3Cl, GeH3Br); (iii) main-group double bonds in 9 molecules with 12 valence electrons (CH2O, CH2S, CH2Se, SiH2O, SiH2S, SiH2Se, GeH2O, GeH2S, GeH2Se); (iv) main-group triple bonds in 9 molecules with 10 valence electrons (HCN, HCP, HCAs, HSiN, HSiP, HSiAs, HGeN, HGeP, HGeAs); and (v) H2 (+) single bond with 1 electron.

Theory of x-ray absorption and linear dichroism at the Ca L23-edge of CaCO3

X-ray absorption calculations of Ca L23-edge spectra of calcium carbonate in its two main crystal phases, calcite and aragonite, are reported. The multichannel multiple scattering theory with a correlated particle-hole wave function and a partially screened core-hole potential is used. Very good agreement with experiment for both CaCO3 phases is obtained, while the independent particle approximation completely fails. For aragonite, appreciable linear dichroism is predicted in agreement with recent observations.

Quasiparticle bands and spectra ofGa2O3polymorphs

Within the framework of density functional theory and Hedin's $GW$ approximation for single-particle excitations, we present quasiparticle band structures and densities of states for two gallium oxide polymorphs: rhombohedral $\ensuremath{\alpha}\ensuremath{-}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ and monoclinic $\ensuremath{\beta}\ensuremath{-}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$. The gap problem is attacked. In addition, their electron effective mass tensors are given. Solving the Bethe-Salpeter equation we also calculate excitonic optical spectra of the two polymorphs. The treatment of excitonic effects allows for a trustable prediction of optical properties from the band gap to the ultraviolet region. In addition, for few other polymorphs we also discuss the frequency-dependent dielectric tensor within the independent-particle approximation (random phase approximation) and densities of states on density functional level. We demonstrate that apart from subtle details, the overall densities of states and optical spectra, in particular the isotropically averaged spectra, are rather similar for all polymorphs, while the electronic dielectric constants vary with the structure. For all polymorphs, complete sets of elastic constants are given.

Many-electron effects on x-ray Rayleigh scattering by highly charged He-like ions

The Rayleigh scattering of x-rays by many-electron highly charged ions is studied theoretically. The many-electron perturbation theory, based on a rigorous quantum electrodynamics approach, is developed and implemented for the case of the elastic scattering of (high-energetic) photons by helium-like ion. Using this elaborate approach, we here investigate the many-electron effects beyond the independent-particle approximation (IPA) as conventionally employed for describing the Rayleigh scattering. The total and angle-differential cross sections are evaluated for the x-ray scattering by helium-like Ni$^{26+}$, Xe$^{52+}$, and Au$^{77+}$ ions in their ground state. The obtained results show that, for high-energetic photons, the effects beyond the IPA do not exceed 2% for the scattering by a closed $K$-shell.

Performance of polarisation functionals for linear and nonlinear optical properties of bulk zinc chalcogenides ZnX (X = S, Se, and Te).

We calculated the frequency dependent macroscopic dielectric function and second-harmonic generation of cubic ZnS, ZnSe and ZnTe within time-dependent density-polarisation functional theory. The macroscopic dielectric function is calculated in a linear response framework, and second-harmonic generation in a real-time framework. The macroscopic exchange-correlation electric field that enters the time-dependent Kohn-Sham equations and accounts for long range correlation is approximated as a simple polarisation functional αP, where P is the macroscopic polarisation. Expressions for α are taken from the recent literature. The performance of the resulting approximations for the exchange-correlation electric field is analysed by comparing the theoretical spectra with experimental results and results obtained at the levels of the independent particle approximation and the random-phase approximation. For the dielectric function we also compare with state-of-the art calculations at the level of the Bethe-Salpeter equation.

Rayleigh x-ray scattering from many-electron atoms and ions

A theoretical analysis is presented for the elastic Rayleigh scattering of x-rays by many-electron atoms and ions. Special emphasis is placed on the angular distribution and linear polarization of the scattered photons for the case when the incident light is completely (linearly) polarized. Based on second-order perturbation theory and the independent particle approximation, we found that the Rayleigh angular distribution is strongly affected by the charge state and shell structure of the target ions or atoms. This effect can be observed experimentally at modern synchrotron facilities and might provide further insight into the structure of heavy atomic systems.

Defect complexes in congruentLiNbO3and their optical signatures

The structure and stability of defect clusters in ${\mathrm{LiNbO}}_{3}$, as well as their influence on the linear and nonlinear optical susceptibilities, are calculated within density functional theory (DFT) using semilocal and hybrid exchange-correlation functionals. In particular, the complexes modeling the Li shortage during the crystal growth, the Li-vacancy model and the Nb-vacancy model, are examined in detail. It is found that clustering significantly decreases the formation energies of all considered defects with respect to the dilute limit. The Li-vacancy model is energetically preferred with respect to the total formation energy, while the Nb-vacancy model has the lowest formation energy per single point defect. The independent-particle approximation based on the hybrid DFT electronic structure describes the ${\mathrm{LiNbO}}_{3}$ optical response much better than semilocal DFT. A further improvement between the calculated optical absorption and second-harmonic generation spectra with experiment is achieved if the calculations take defect complexes into account. Nb antisite polarons give rise to optical absorption within the band gap.

First-Principles Investigation of Strong Excitonic Effects in Oxygen 1s X-ray Absorption Spectra.

We calculated the oxygen 1s X-ray absorption spectra (XAS) of acetone and acetic acid molecules in vacuum by utilizing the first-principles GW+Bethe-Salpeter method with an all-electron mixed basis. The calculated excitation energies show good agreement with the available experimental data without an artificial shift. The remaining error, which is less than 1% or 2-5 eV, is a significant improvement from those of time-dependent (TD) density functional methods (5% error or 27-29 eV for TD-LDA and 2.4-2.8% error or 13-15 eV for TD-B3LYP). Our method reproduces the first and second isolated peaks and broad peaks at higher photon energies, corresponding to Rydberg excitations. We observed a failure of the one-particle picture (or independent particle approximation) from our assignment of the five lowest exciton peaks and significant excitonic or state-hybridization effects inherent in the core electron excitations.

Geometrical and optical benchmarking of copper(II) guanidine-quinoline complexes: insights from TD-DFT and many-body perturbation theory (part II).

Ground- and excited-state properties of copper(II) charge-transfer systems have been investigated starting from density-functional calculations with particular emphasis on the role of (i) the exchange and correlation functional, (ii) the basis set, (iii) solvent effects, and (iv) the treatment of dispersive interactions. Furthermore (v), the applicability of TD-DFT to excitations of copper(II) bis(chelate) charge-transfer systems is explored by performing many-body perturbation theory (GW + BSE), independent-particle approximation and ΔSCF calculations for a small model system that contains simple guanidine and imine groups. These results show that DFT and TD-DFT in particular in combination with hybrid functionals are well suited for the description of the structural and optical properties, respectively, of copper(II) bis(chelate) complexes. Furthermore, it is found an accurate theoretical geometrical description requires the use of dispersion correction with Becke-Johnson damping and triple-zeta basis sets while solvent effects are small. The hybrid functionals B3LYP and TPSSh yielded best performance. The optical description is best with B3LYP, whereby heavily mixed molecular transitions of MLCT and LLCT character are obtained which can be more easily understood using natural transition orbitals. An natural bond orbital analysis sheds light on the donor properties of the different donor functions and the intraguanidine stabilization during coordination to copper(I) and (II).

The phonon vacuum state in a Lipkin model

The action of the long-range residual force on the expectation value of observables in the nuclear ground states is evaluated by finding optimal values for the coefficients of the canonical transformation which connects the phonon vacuum state with the independent-particle ground-state using the two-level Lipkin-Meshkov-Glick (LMG) model. After estimating the improvements over the predictions of the independent-particle approximation we compare the ground and first excited states wave functions, obtained using the presented approach, with those, obtained using the conventional random phase approximation (RPA) and its extended version. The problem with overbinding of the nuclear ground state calculated using the RPA is shown to be removed if one sticks to the prescriptions of the present approach. The reason being that the latter conforms to the original variational formulation.

The Franz–Keldysh effect revisited: Electroabsorption including interband coupling and excitonic effects

We study the linear optical absorption of bulk semiconductors in the presence of a uniform and constant (dc) electric field with an approach suitable for including excitonic effects while working with many-band models. The absorption coefficient is calculated from the time evolution of the interband polarization excited by an optical pulse. We apply the formalism to a numerical calculation for GaAs using a 14-band k·p model, which allows us to properly include interband coupling, and the exchange self-energy to account for the excitonic effects due to the electron–hole interaction. The Coulomb interaction enhances the features of the absorption coefficient captured by the k·p model; the enhancement depends on the strength of the dc field and the polarization of the optical field. With respect to the polarization dependence, we find that the anisotropy described by the independent particle approximation can be modified significantly by the Coulomb interaction.

Study of electron capture and ionization in proton collisions with N2 using ab initio methods

Electron capture cross sections in collisions of protons with the nitrogen molecule are obtained with two semiclassical ab initio methods: one uses multireference configuration interaction wavefunctions while the other is based on monoelectronic wavefunctions and the independent particle approximation. The accuracy and usefulness of this last, simplified, approach is discussed in view of its applicability to study larger systems.

Divalent Rydberg atoms in optical lattices: Intensity landscape and magic trapping

We develop a theoretical understanding of trapping divalent Rydberg atoms in optical lattices. Because the size of the Rydberg electron cloud can be comparable to the scale of spatial variations of laser intensity, we pay special attention to averaging optical fields over the atomic wavefunctions. Optical potential is proportional to the ac Stark polarizability. We find that in the independent particle approximation for the valence electrons, this polarizability breaks into two contributions: the singly ionized core polarizability and the contribution from the Rydberg electron. Unlike the usually employed free electron polarizability, the Rydberg contribution depends both on laser intensity profile and the rotational symmetry of the total electronic wavefunction. We focus on the $J=0$ Rydberg states of Sr and evaluate the dynamic polarizabilities of the 5s$n$s($^1S_0$) and 5s$n$p($^3P_0$) Rydberg states. We specifically choose Sr atom for its optical lattice clock applications. We find that there are several magic wavelengths in the infrared region of the spectrum at which the differential Stark shift between the clock states (5s$^2$($^1S_0$) and 5s5p($^3P_0$)) and the $J=0$ Rydberg states, 5s$n$s($^1S_0$) and 5s$n$p($^3P_0$), vanishes. We tabulate these wavelengths as a function of the principal quantum number $n$ of the Rydberg electron. We find that because the contribution to the total polarizability from the Rydberg electron vanishes at short wavelengths, magic wavelengths below $\sim$1000 nm are ``universal" as they do not depend on the principal quantum number $n$.

Photovoltaic application of the V, Cr and Mn-doped cadmium thioindate

The CdIn2S4 spinel semiconductor is a potential photovoltaic material due to its energy band gap and absorption properties. These optoelectronic properties can be potentiality improved by the insertion of intermediate states into the energy bandgap. We explore this possibility using M=Cr, V and Mn as an impurity. We analyze with first-principles almost all substitutions of the host atoms by M at the octahedral and tetrahedral sites in the normal and inverse spinel structures. In almost all cases, the impurities introduce deeper bands into the host energy bandgap. Depending on the site substitution, these bands are full, empty or partially-full. It increases the number of possible inter-band transitions and the possible applications in optoelectronic devices. The contribution of the impurity states to these bands and the substitutional energies indicate that these impurities are energetically favorable for some sites in the host spinel. The absorption coefficients in the independent-particle approximation show that these deeper bands open additional photon absorption channels. It could therefore increase the solar-light absorption with respect to the host.

Photon absorption and photon scattering—What we do not know and why it matters

We examine some of the problems of theory and experiment that are limiting our understanding of photon absorption and photon scattering. Much of what we know and don't know is signified via simple models, whether (i) in semi-classical non-relativistic dipole radiation of the hydrogen atom, treated as two quantum particles bound in a Coulomb potential, or (ii) in full relativistic multipole radiation of an atom in independent particle approximation. Chaotic and singular features can already be recognized. The inconsistencies in a non-relativistic multipole description lead to spurious predictions for absorption and scattering, but even the full theory is not in agreement with experiment. Additionally, paradoxes associated with quantum entanglement are already present in these simple models. The more advanced approaches treating many particle interactions and field quantization lead to a more sophisticated description of states and fields and cross-sections, which can simplify to the simpler models in various sum rule approximations, by invoking limitations on experimental measurement. Advanced discussions include issues of correlations and consequences of infrared divergence. A further level of complexity is to recognize the inevitable presence of environments, whether in a cage, a solid or a plasma, with consequences of modifying isolated processes, and in the significances for coherence and decoherence, and loss of entanglement. We conclude by reviewing the current status of the agreement between theory and experiment for photon absorption and scattering.

Two-photon decay of inner-shell vacancies in heavy atoms

Based on the second-order perturbation theory, we investigate the two-photon decay of $K$-shell vacancies in heavy atoms. The many-electron transition amplitude that occurs in the theory is evaluated by means of the independent particle approximation (IPA). By using this approach, computations are performed for the decay of neutral gold and are directly compared with recent experimental data, not relying on any scaling assumptions. The obtained results confirm previously identified discrepancies between the IPA theory and the experiment for the $2s\ensuremath{\rightarrow}1s$ transition, and an apparent ``resonance'' region of the $3s\ensuremath{\rightarrow}1s$ transition, but they show a moderate agreement with the measured data for the $3d\ensuremath{\rightarrow}1s$ and $4s+4d\ensuremath{\rightarrow}1s$ cases. Moreover, with the help of the IPA we discuss the validity of the nonrelativistic scaling that was employed in the past to estimate the relative two-photon transition probabilities $P$ in heavy atoms based on calculations done for lighter elements and different decay geometries. We find, in particular, that the electric-dipole angular distribution of emitted photons holds rather well even in the high-$Z$ domain, while the assumption that the relative probability $P$ is independent of nuclear charge may result in 10--30% inaccuracy of theoretical predictions.

Quasiparticle band structure and optical properties of theα12Si-Ge superstructure from first principles

The quasi-particle band structure and dielectric function for the so-called magic sequence SiGe$_2$Si$_2$Ge$_2$SiGe$_{12}$ (or $\alpha_{12}$) structure [PRL 108, 027401 (2012)] are calculated by many-body perturbation theory (MBPT) within an ab-initio framework. On top of density functional calculations within the local density approximation (LDA) leading to a fundamental band gap of 0.23 eV, we have computed the quasi-particle band structure within the G$_0$W$_0$ approach opening the gap to 0.61 eV. Moreover, we have calculated the optical properties by solving the Bethe-Salpeter equation (BSE) for the electron-hole two-particle correlation function. When comparing the imaginary part of the dielectric function obtained at various levels of approximation, \emph{i.e.} the independent particle approximation (or random phase approximation) based on (i) the LDA or (ii) GW band structures, and (iii) the BSE including local field effects and electron-hole correlations, we observe that the important first transition is better explained with taking into account excitonic effects. Moreover, the onset transition originating from the direct transition of the magic sequence structure is also investigated.

Symmetry Breaking and Hole Localization in Multiple Core Electron Ionization

Motivated by recent opportunitites to study hollow molecules with multiple core holes offered by X-ray free electron lasers, we revisit the core-hole localization and symmetry breaking problem, now studying ionization of more than one core electron. It is shown, using a N2 molecule with one, two, three, and four core holes, for example, that in a multiconfigurational determination of the core ionization potentials employing a molecular point group with broken inversion symmetry, one particular configuration is sufficient to account for the symmetry breaking relaxation energy in an independent particle approximation in the case of one or three holes, whereas the choice of point group symmetry is unessential for two and four holes. The relaxation energy follows a quadratic dependence on the number of holes in both representations.