# Self‐consistent Approximation To The Polarization Propagator

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### Range-separatedtime-dependentdensity-functionaltheory

which combines a density-functional approximation for the short-range response kernel and a frequency-dependent second-order Bethe-Salpeter approximation for the long-range response kernel. This approach goes beyond the adiabatic approximation usually used in linear-response TDDFT

### Non-iterative doubles corrections to the random phase and

nth-order polarization propagator approximations. [2] In the zeroth-order polarization propagator approximation, excita-tion energies are simply equal to orbital energy differences. The ﬁrst-order polarization propagator approximation is also called time-dependent Hartree Fock or the random phase approximation [a] P. A. B. Haase

### Model Order Reduction Algorithm for Estimating the Absorption

self-consistent ﬁeld theory, such as the linear response time- order polarization propagator approximation (FOPPA),14 the polarization propagator. In the

### Algebraic-diagrammatic construction propagator approach to

A propagator approach that has been used for a long time to calculate polarizabilities and other linear response functions, is the second-order polarization propagator approximation (SOPPA) [30 32].

### X-ray absorption spectra from the resonant-convergent ﬁrst

complex polarization propagator CPP approach. The CPP has been implemented in the Hartree-Fock, multiconﬁgura-tion self-consistent ﬁeld, and Kohn-Sham DFT electronic structure theory 10,11 Our methodology has been illustrated in a letter 12 , but there are several key issues that need to be addressed in

### A quotation from Peskin & Schroeder, Chapter 7: We cheated

Vacuum polarization Vacuum polarization affects the photon propagator. For this reason, vacuum polarization is sometimes called photon self energy But the photon mass remains 0 in the interacting theory. For this reason I don t like the term photon self-energy (The photon mass is 0 in all orders of perturbation theory because of

### A guide to. Feynman diagrams in the many-body problem

13 2 The two-particle Green's function propagator 228 13.3 Polarization (` density fluctuation ') propagator 230 13.4 Retarded polarization propagator and linear response 232 13.5 The collective excitation propagator 233 13.6 Plasmons and quasi plasmons 234 13.7 Expressing the two-particle propagator in terms of the scattering

### Ab Initio Full Cell GW+DMFT for Correlated Materials

of this choice, certain contributions to the polarization propagator involving interactions far from the supercell, that would require the bosonic self-consistency of EDMFT [24], are omitted. In practice, this choice means that rather than partitioning into the strictly strongest interactions (for example,inad or f shell),coupledtoa low-level

### Self-consistent approximations in relativistic plasmas

to construct self-consistent approximations to two-particle propagators that preserved the basic conservation laws. Our solution to the problem was written up in the paper Conservation laws and correlation functions1, and the concept generalized to deriving self-consistent approximations

### Chapter 10 Dyson s equation, RPA and Ladder Approximations

propagators have been replaced by clothed propagators. → Self-consistent renormalization Exact form of above not known. First solve above for bare propagator, substitute into Dyson s equation to get first approximation for clothed propagator etc. Self consistency is obtained when results stop changing.

### Thermal averaging of the indirect nuclear spin-spin coupling

Thermal averaging of the indirect nuclear spin-spin coupling constants of ammonia: The importance of the large amplitude inversion mode

### An RPA program for jellium spheres

The RPA approximation to form, the polarization propagator is 2 Coul (2L+1)e ~~TT~l~ 11RPA {i +H0~}~0. (1) VL = The exchange correlation interaction is of the Here 110 is the independent-particle polarization form of a density-dependent contact interaction

### Many Electron Theory - University of Utah

Ratner who attempted self-consistent calculations. Oddershede pushed the Second Order Polarization Propagator Approach, SOPPA, and made this a viable method for response functions such as they appear in indirect spin-spin coupling constants and other magnetic problems. Responses of higher

### First-principles calculations of long-range intermolecular

by us that the complex linear polarization propagator method provides accurate abinitioand ﬁrst-principles density functional theory values of the C6 disper-sion coeﬃcients in comparison with those reported in the literature. The selected samples for the investigation of dispersion interactions in the electronic ground

### CISS07 8/29/2007 Comprehensive treatment of correlations at

Link between sp and two-particle propagator Self-consistent Green s functions Hartree-Fock Dynamical self-energy and spectroscopic factors < 1 Self-energy using G-matrix in second order Qualitative features; missing ingredients! Excited states and G ⇔ G and excited states Conserving approximations; HF

### View Journal View Issue

conductor-like approximation (C-PCM),30 the integral-equation formalism (IEF-PCM),40 or the surface and simulated volume polarization for electrostatics [SS(V)PE] approach.41,42 2.2 Free energy Because the concept of a dielectric constant implicitly includes solventaveraging,theelectrostatic energiesinPCM theoryarefree

### Faddeev Random Phase Approximation (FRPA) Application to

Random Phase Approximation improves over TDA by including mixture between positive and negative energy excitations example: plasmon pole in polarization propagator Matthias Degroote (Ghent University) FRPA: Application to Molecules INT 2011 Spring Program 11 / 23

### Simulating X‐ray absorption spectra with complete active

propagation approaches [5 8], complex polarization propagators [9], oscillator strengths beyond the electric-dipole approximation [10 13], and so forth. In particular for transition-metal (TM) compounds X-ray spectroscopy is a frequently used technique that can provide valuable insights into

### The Effect of Substituents on Indirect Nuclear Spin-Spin

work we have used two levels of approximation to the polarization propagator: SOPPA(CCSD) [15,25] and RPA [47,48], which can also be considered as a first order polarization propagator approximation [53]. In all coupling constant calculations we have used a local version of the DALTON program

### PoS(NUFACT2014)055

proach based on a Green s function formalism. The polarization propagator is approximated by iteration of its ﬁrst-order contribution. In this way, the formalism takes into account one-particle one-hole excitations out of the correlated nuclear ground state. Within the RPA an excited nu-

### Massive Meson Fluctuation in NJL Model

Based on the self-consistent scheme beyond mean- eld approximation in the large Nc expansion, including current quark mass explicitly, a general scheme of SU(2) NJL model is developed. To ensure the quark self-energy ex-panded in the proper order ofNc, an approximate internal meson propagator is deduced, which is in order ofO(1=Nc). In our

### Nonlinear Spectroscopy of Core and Valence Excitations Using

2 Nonlinear X-Ray Spectroscopies A system of interacting electrons is described by the Hamiltonian H^ ¼ X i ^p2 i 2m i þ 1 2 X ij V^ r i r j; ð1Þ where ^p i isthe momentumof the ith electron andV^ is the Coulomb potential.

### Consequences for sp propagator in infinite systems

polarization propagator (including spin summations) Approximation known as Self-consistent formulation Note medium modification important so

### Meson mass modi cation in strange hadronic matter

baryon ground state is treated in the relativistic Hartree approximation in the nonlinear ˙-! and linear ˙-˚ model. In stable SHM, the masses of all the mesons reveal considerable reduction due to large vacuum polarization contribution from the hyperons and small density dependent e ects caused by larger binding. PACS: 21.65+f, 24.10Jv

### Institute for Advanced Study, Princeton NJ 08540 USA Lyman

In this Letter we introduce a self-consistent approximation which improves on the Nelson is determined by the propagator for the d c = dressed by the vacuum polarization bubbles. We thus

### March 24, 1981 (T/E) Model for the Generation of Leptonic

self-consistent perturbation expansion for the QED self-mass was - developed, and it was shown that a sum of graphs containing vacuum polarization loops diverges before the momenta reach infinity. This causes a singularity in the (completely renormalized) photon propagator

### CORRELATIONS IN QE(LIKE) NEUTRINO- NUCLEUS SCATTERING

CORRELATIONS IN QE(LIKE) NEUTRINO-NUCLEUS SCATTERING Natalie Jachowicz, T. Van Cuyck, R. González-Jímenez, N. Van Dessel, V. Pandey DEPARTMENT OF PHYSICS AND ASTRONOMY

### Spectroscopic factors and the physics of the single- particle

Integral equation for three-time polarization propagator from Dyson equation! Propagators are dressed according to approximation (must be self-consistent)

### Constraints on Short-Range Spin-Dependent Interactions from

orbitals; MCSCF, multiconﬁgurational self-consistent ﬁeld; SOPPA (CCSD), second-order polarization propagator with coupled-cluster singles-doubles amplitudes; FCI, full conﬁgura-tion interaction. The theoretical results are presented as a sum of four contributions, as described in the text. Reference J exptðHzÞ Conditions

### SECOND QUANTIZATION- BASED METIJODS IN QUANTUM CHEMISTRY

polarization propagator restricted Hartree-Fock random-phase approximation Rayleigh-Schrodinger perturbation theory self-consistent field superconfiguration interaction stationary point time-dependent Hartree-Fock unrestricted Hartree-Fock 1.

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Hartree-Fock approximation (Jsrgensen 1975), which is identical to the random- phase approximation (RPA) with exchange. The second-order approximation is equiv- alent to the higher RPA method of Shibuya and McKoy (1970) and the self-consistent polarisation propagator approach of Linderberg et nl (1972) both of which must

### Dalton2018.2 Dalton Program Manual

Dalton2018.2 { Dalton Program Manual K. Aidas C. Angeli, K. L. Bak, V. Bakken, R. Bast, L. Boman, O. Christiansen, R. Cimiraglia, S. Coriani, J. Cukras, P. Dahle,

### Algebraic-diagrammatic construction (ADC) propagator approach

the polarization propagator [27]. Such a propagator method, used for a long time to calculate polarizabilities and other linear response functions, is the second-order polarization propagator approximation (SOPPA) [28-30]. In particular, the SOPPA method has been

### J Schirmer and F Mertins YDOHQFHHOHFWURQH[FLWDWLRQVSHFWUD

a consistent second-order approximation (SOPPA) for the polarization propagator by making use of the so-called superoperator formalism [12]. Yeager, Jgrgensen and col- laborators [3, 13, 141 worked out a multiconfiguration RPA method (MCRPA) obtained by introducing a multiconfiguration self-consistent field (MCSCF) formulation of the

### Preface p. vii

Polarization propagator p. 316 Random Phase Approximation p. 321 RPA in finite systems and the schematic model p. 326 Energy-weighted sum rule p. 332 Excited states in atoms p. 336 Correlation energy and ring diagrams p. 340 RPA in angular momentum coupled representation p. 342 Exercises p. 346 Excited states in infinite systems p. 347

### First time combination of frozen density embedding theory

polarization propagator is a robust and accurate method for the calculation of excited states.29 Additionally, its mathematical structure is well suited to include external one-particle operators since it is based on a non-iterative ground state method, making it straight forward to include environmental models in ADC.

### Syddansk Universitet Assessment of charge-transfer

paper investigates the combination of both the long-range Multi-Conﬁguration Self-Consistent Field (MCSCF) and Second Order Polarization Propagator Approximation (SOPPA) ansätze with a short-range DFT (srDFT) description. We ﬁnd that the combinations of SOPPA or MCSCF with TD-DFT

### Self-consistent Green s function calculations of O at small

Oct 19, 2020 Eq. (2) in terms of an unperturbed propagator g0 αβ (ω). The (dressed) solution g αβ(ω) is then used to evaluate an improved self-energy, which then contains the eﬀects of fragmentation. The whole procedure is iterated until self-consistency is reached. Baym and Kadanoﬀ showed that a self-consistent solution of the above equation

### Spin polarization and chiral symmetry breaking at ﬁnite

the self consistent equations for the spin polarization and chiral condensate are solved numerically in the framework of the Hartree approximation. Numerical calculations show that in the one ﬂavor model the spin polarization is possible at ﬁnite density if the ratio G 2/G 1 is larger than O(1). We ﬁnd that the inter-