Electronic excitations in semiconductors: Variational Green's-function approach

Ab initio green's function calculations on highly conducting polymers: Effects of electron correlation and aperiodicity

The asymptotics of the equal-time one-particle Green's function ofthe half-filled one-dimensional Hubbard model is studied at finitetemperature. We calculate its correlation length by evaluatingthe largest and the second largest eigenvalues of the QuantumTransfer Matrix (QTM). In order to allow for the genuinelyfermionic nature of the one-particle Green's function, we employthe fermionic formulation of the QTM based on the fermionicR-operator of the Hubbard model. The purely imaginary value ofthe second largest eigenvalue reflects the kF( = π/2) oscillations of the one-particle Green's function athalf-filling. By solving numerically the Bethe ansatz equationswith Trotter numbers up to N = 10240, we obtain accurate data forthe correlation length at finite temperatures down into the verylow-temperature region. The correlation length remains finiteeven at T = 0 due to the existence of the charge gap. Ournumerical data confirm Stafford and Millis' conjecture regardingan analytic expression for the correlation length at T = 0.

We have calculated the Debye-Waller factor (DWF) of Cu from a model that was used successfully in earlier calculations of anharmonicity by Cowley and Shukla. The present calculation has been carried out using quasiharmonic theory, the lowest-order (λ2) anharmonic perturbation theory, and a Green's function (GF) method which sums an infinite series of the λ2−type anharmonic terms. The static approximation ω → 0 in the cubic contribution to the self-energy of the GF, introduced in the earlier work on the DWF by Shukla and Hubschle is further justified by showing that in the high-temperature limit the exact results for the λ2 anharmonic contributions (cubic and quartic) to the Helmholtz free energy are given in this approximation. Results for the DWF are also obtained for a modified version of the Morse potential with λ2 perturbation theory (PT) and the GF method. The GF results are in excellent agreement with the experimental Mossbauer and X-ray data in the entire temperature range, 300 K  T  120...

ABSTRACTGreen's functions have been a tool to analyze important reservoir geomechanics effects like subsidence, compaction, well closure, and permeability variation. However, the classical Green's function is related to linear elastic, homogenous, and geometrically simplified media. The use of auxiliary functions that consider heterogeneous media has the potential to simplify the numerical analyses of some complex problems. This research work proposes a new approach to Green's function method based on artificial neural networks (ANNs) to consider stratified media with direct application in reservoir geomechanics. These solutions obtained through ANN have as output the normalized displacement at any point of the stratified massif due to the application of a point load inside the massif. The input data of the proposed ANN are the material properties of the media, the point load, and the point of interest. By using the developed ANN‐based Green's function together with the classical Green's function approach, it is possible to obtain individually the displacement at any point of the massif due to a pore pressure variation within the reservoir, only discretizing the reservoir boundary. This leads to a more efficient method when compared to traditional methods, such as the finite element method. For the points of interest, seafloor, and top and bottom of the reservoir, the numerical example presented was 25 times faster than the classic Green function approach on a computer with 12 threads of 2.6 GHz and 32 GB RAM. This reduction in processing time is crucial for decision‐makers to act in field applications.

In this paper, we analyze the properties of the recently proposed real-time equation-of-motion coupled-cluster (RT-EOM-CC) cumulant Green's function approach [Rehr et al., J. Chem. Phys. 152, 174113 (2020)]. We specifically focus on identifying the limitations of the original time-dependent coupled cluster (TDCC) ansatz and propose an enhanced double TDCC ansatz, ensuring the exactness in the expansion limit. In addition, we introduce a practical cluster-analysis-based approach for characterizing the peaks in the computed spectral function from the RT-EOM-CC cumulant Green's function approach, which is particularly useful for the assignments of satellite peaks when many-body effects dominate the spectra. Our preliminary numerical tests focus on reproducing, approximating, and characterizing the exact impurity Green's function of the three-site and four-site single impurity Anderson models using the RT-EOM-CC cumulant Green's function approach. The numerical tests allow us to have a direct comparison between the RT-EOM-CC cumulant Green's function approach and other Green's function approaches in the numerical exact limit.

In this paper we consider the energy levels and the polarization ratios of an impurity pair in mixed molecular crystals using the one-particle Green's function method. The off-diagonal matrix elements of the weighted density of states function for the first singlet exciton band in crystalline benzene have been obtained and applied for the splitting of the energy levels of an isotopic impurity pair. An extension of Rashba's formula for the polarization ratio of the impurity pair has been derived.

A simple but accurate and computationally efficient method for routine ab initio calculations of molecular Rydberg states is described. The method, which can be applied to Rydberg states associated with a nondegenerate ion core, consists in the self-consistent solution of an effective one-electron problem. First, the restricted Hartree-Fock problem of the ion core is solved. The orbital energies and certain two-electron Coulomb matrix elements with respect to the molecular orbital basis are then used to construct an energy-dependent many-body correction to the Hartree-Fock mean field. This correction is derived from the Dyson equation satisfied by the one-particle Green's function. The method is applied to calculate Rydberg potential-energy curves of HCO. The presented data confirm and extend recent large-scale multireference configuration-interaction calculations and help develop a detailed theoretical description of the astrophysically important dissociative recombination of a low-energy electron with HCO(+). As further illustration of the utility of the method, the first ab initio calculations of the excited states of an electron bound to the guanidinium cation [C(NH(2))(3)](+) are reported.

We consider a large system of interacting bosons with a homogeneous condensate at absolute zero temperature. By carrying out an analysis of the perturbation expansion of the one-particle Green's function and the density—density correlation function, we derive a general relationship between them.

Pseudo Jahn–Teller origin of ferroelectric instability in BaTiO3 type perovskites: The Green's function approach and beyond

A many-body theory is presented based on an electronic Hamiltonian appropriate for describing core-valence excitation processes. It is shown that the core polarization propagator satisfies a factorization theorem relating this propagator to the product of two one-particle Green's functions, namely, a core Green's function and a valence Green's function which is calculated in the field of a time-dependent core potential. A diagrammatic theory for this valence Green's function is developed. The core-valence excitation energy is decomposed into relaxation and correlation contributions up to second order. A physical interpretation of this decomposition is given and the relationship between the analytical expressions and the various diagrams is pointed out. A general order analysis of relaxation and correlation terms is performed making use of the factorization theorem. An illustrative model is presented which allows an exact diagrammatic calculation of the valence Green's function with the time-dependent core potential via the Dyson equation. The analogy between the spectral function of our model and the spectral function of x-ray emission spectra of solids is discussed.

A Green's-function method is used to study the thermodynamic properties of self-interacting massless fermions in one space dimension and one time dimension. It is shown that the exact expression can be obtained for the thermodynamic one-particle Green's function for the case where the dimensionless chemical potential $\ensuremath{\mu}=0$, which is identical with the corresponding field-theoretic Green's function. The number density is obtained as an infinite sum. It exhibits a peculiar peaked behavior as a function of momentum. The energy, however, is a continuous function of temperature.

view Abstract Citations (188) References (15) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Exact Green's function method of solar force-free magnetic-field computations with constant alpha . I. Theory and basic test cases. Chiu, Y. T. ; Hilton, H. H. Abstract Exact closed-form solutions to the solar force-free magnetic-field boundary-value problem are obtained for constant alpha in Cartesian geometry by a Green's function approach. The uniqueness of the physical problem is discussed. Application of the exact results to practical solar magnetic-field calculations is free of series truncation errors and is at least as economical as the approximate methods currently in use. Results of some test cases are presented. Publication: The Astrophysical Journal Pub Date: March 1977 DOI: 10.1086/155111 Bibcode: 1977ApJ...212..873C Keywords: Boundary Value Problems; Force-Free Magnetic Fields; Green'S Functions; Magnetic Field Configurations; Solar Corona; Solar Magnetic Field; Eigenvectors; Graphs (Charts); Lines Of Force; Singularity (Mathematics); Truncation Errors; Solar Physics full text sources ADS |

A new general method is described for obtaining SCF orbitals for electronic systems without restrictions of the symmetry of the open shells. With a Green's function method an optimal SCF operator is constructed for each state of a given configuration. The unperturbed one-particle Green's function is optimal with this operator and permits a quasiparticle interpretation. The SCF equations are derived in matrix formulation convenient for numerical applications within a limited basis set. It is shown that the SCF orbitals thus obtained satisfy the necessary conditions for the energy to be stationary. An application of the SCF method is given for the three lowest S states of the helium atom.

The valence shell photoelectron spectra of 2-chloropyridine and 3-chloropyridine have been studied both experimentally and theoretically. Synchrotron radiation has been employed to record angle resolved photoelectron spectra in the photon energy range 20-100 eV, and these have enabled anisotropy parameters and branching ratios to be derived. The experimental results have been compared with theoretical predictions obtained using the continuum multiple scattering Xα approach. This comparison shows that the anisotropy parameter associated with the nominally chlorine lone-pair orbital lying in the molecular plane is strongly affected by the atomic Cooper minimum. In contrast, the photoionization dynamics of the second lone-pair orbital, orientated perpendicular to the molecular plane, seem relatively unaffected by this atomic phenomenon. The outer valence ionization has been studied theoretically using the third-order algebraic-diagrammatic construction (ADC(3)) approximation scheme for the one-particle Green's function, the outer valence Green's function method, and the equation-of-motion (EOM) coupled cluster (CC) theory at the level of the EOM-IP-CCSD and EOM-EE-CC3 models. The convergence of the results to the complete basis set limit has been investigated. The ADC(3) method has been employed to compute the complete valence shell ionization spectra of 2-chloropyridine and 3-chloropyridine. The relaxation mechanism for ionization of the nitrogen σ-type lone-pair orbital (σN LP) has been found to be different to that for the corresponding chlorine lone-pair (σCl LP). For the σN LP orbital, π-π* excitations play the main role in the screening of the lone-pair hole. In contrast, excitations localized at the chlorine site involving the chlorine πCl LP lone-pair and the Cl 4p Rydberg orbital are the most important for the σCl LP orbital. The calculated photoelectron spectra have allowed assignments to be proposed for most of the structure observed in the experimental spectra. The theoretical work also highlights the formation of satellite states, due to the breakdown of the single particle model of ionization, in the inner valence region.

The electronic structure of organic-inorganic interfaces often features resonances originating from discrete molecular orbitals coupled to continuum lead states. An example is molecular junction, individual molecules bridging electrodes, where the shape and peak energy of such resonances dictate junction conductance, thermopower, I-V characteristics, and related transport properties. In molecular junctions where off-resonance coherent tunneling dominates transport, resonance peaks in the transmission function are often assumed to be Lorentzian functions with an energy-independent broadening parameter Γ. Here we define a new energy-dependent resonance broadening function, Γ(E), based on diagonalization of non-Hermitian matrices, which can describe resonances of a more complex, non-Lorentzian nature and can be decomposed into components associated with the left and right leads, respectively. We compute this quantity via an ab initio non-equilibrium Green's function (NEGF) approach based on density functional theory (DFT) for both symmetric and asymmetric molecular junctions, and show that our definition of Γ(E), when combined with Breit-Wigner formula, reproduces the transmission calculated from DFT-NEGF. Through a series of examples, we illustrate how this approach can shed new light on experiments and understanding of junction transport properties in terms of molecular orbitals.