scholarly journals Linear response approach to the calculation of the effective interaction parameters in theLDA+Umethod

2005 ◽  
Vol 71 (3) ◽  
Author(s):  
Matteo Cococcioni ◽  
Stefano de Gironcoli
Keyword(s):  
Linear Response ◽  
Effective Interaction ◽  
Interaction Parameters

Two- and three-body effective electrostatic interactions in odd configurations of the iron group

1982 ◽  
Vol 60 (9) ◽  
pp. 1223-1236
Author(s):  
C. Roth
Keyword(s):  
Electrostatic Interactions ◽  
Effective Interaction ◽  
Interaction Parameters ◽  
Iron Group ◽  
Effective Interactions ◽  
A Value ◽  
Three Body ◽  
Independent Parameters

Expressions for the two- and three-body effective interactions in the configurations l″ and l″l′ were obtained, and then specialized for the case of the odd configurations in the iron group with l having a value of 2 and l′ a value of 1.There are four independent effective interaction parameters for the configuration d″. For the configuration d″p it was shown that there are 2 independent parameters for the two-body effective interactions, and 11 independent parameters for the three-body effective interactions.The results are being utilized in general investigtions for the odd configurations (3d + 4s)″4p in the iron group, and subsequently for the odd configurations in the palladium and platinum groups.

scholarly journals Coupling of Charge Regulation and Conformational Equilibria in Linear Weak Polyelectrolytes: Treatment of Long-Range Interactions via Effective Short-Ranged and pH-Dependent Interaction Parameters

Polymers ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 811 ◽  
Author(s):  
Pablo Blanco ◽  
Sergio Madurga ◽  
Francesc Mas ◽  
Josep Garcés
Keyword(s):  
Long Range ◽  
Ph Dependence ◽  
Effective Interaction ◽  
Interaction Parameters ◽  
Computational Time ◽  
Physical Parameters ◽  
Wide Range ◽  
Conformational Equilibria ◽  
Ph Dependent ◽  
Weak Polyelectrolytes

The classical Rotational Isomeric State (RIS) model, originally proposed by Flory, has been used to rationalize a wide range of physicochemical properties of neutral polymers. However, many weak polyelectrolytes of interest are able to regulate their charge depending on the conformational state of the bonds. Recently, it has been shown that the RIS model can be coupled with the Site Binding (SB) model, for which the ionizable sites can adopt two states: protonated or deprotonated. The resulting combined scheme, the SBRIS model, allows for analyzing ionization and conformational equilibria on the same foot. In the present work, this approach is extended to include pH-dependent electrostatic Long-Range (LR) interactions, ubiquitous in weak polyelectrolytes at moderate and low ionic strengths. With this aim, the original LR interactions are taken into account by defining effective Short-Range (SR) and pH-dependent parameters, such as effective microscopic protonation constants and rotational bond energies. The new parameters are systematically calculated using variational methods. The machinery of statistical mechanics for SR interactions, including the powerful and fast transfer matrix methods, can then be applied. The resulting technique, which we will refer to as the Local Effective Interaction Parameters (LEIP) method, is illustrated with a minimal model of a flexible linear polyelectrolyte containing only one type of rotating bond. LEIP reproduces very well the pH dependence of the degree of protonation and bond probabilities obtained by semi-grand canonical Monte Carlo simulations, where LR interactions are explicitly taken into account. The reduction in the computational time in several orders of magnitude suggests that the LEIP technique could be useful in a range of areas involving linear weak polyelectrolytes, allowing direct fitting of the relevant physical parameters to the experimental quantities.

scholarly journals Calculation of the effective interaction parameter in theLDA+Umethod by a linear response approach forFe(OH)2

2009 ◽  
Vol 80 (15) ◽  
Author(s):  
Mansoureh Pashangpour ◽  
Amir Abbas Sabouri-Dodaran ◽  
Khadijeh Imani ◽  
Nasser Nafari
Keyword(s):  
Interaction Parameter ◽  
Linear Response ◽  
Effective Interaction

TOWARD A RIGOROUS THEORY OF THE SCREENED ELECTRON-ELECTRON INTERACTIONS IN METALS

1991 ◽  
Vol 05 (18) ◽  
pp. 2951-2972 ◽  
Author(s):  
HUA CHEN ◽  
DANIEL C. MATTIS
Keyword(s):  
Free Energy ◽  
Spin Density ◽  
Correlation Functions ◽  
Linear Response ◽  
Effective Interaction ◽  
Linear Response Theory ◽  
Density Correlation ◽  
Hubbard Interaction ◽  
Zero Range ◽  
New Formula

A microscopic formula for the effective two-body interaction between electrons or holes in an ideal metal is derived within the linear response theory. Both the zero-range Hubbard interaction U0 and the long-range Coulomb interaction, denoted by ΔV(q), are included. The effective interaction, which is necessarily spin-dependent, is expressed in terms of the exact charge and spin density-density correlation functions and of their higher order mixtures. These correlation functions are analyzed diagrammatically. Attention is paid to clarifying the different roles played by U0 and ΔV(q). We also display the corresponding new formula for the free energy. Comparison is made with previous theories.

scholarly journals LINEAR RESPONSE IN INFINITE NUCLEAR MATTER AS A TOOL TO REVEAL FINITE SIZE INSTABILITIES

2012 ◽  
Vol 21 (05) ◽  
pp. 1250040 ◽  
Author(s):  
A. PASTORE ◽  
K. BENNACEUR ◽  
D. DAVESNE ◽  
J. MEYER
Keyword(s):  
Experimental Data ◽  
Nuclear Matter ◽  
Linear Response ◽  
Effective Interaction ◽  
Finite Size ◽  
Effective Interactions ◽  
Zero Range ◽  
Analytical Expressions ◽  
Range Force ◽  
Rotating Nuclei

Nuclear effective interactions are often modeled by simple analytical expressions such as the Skyrme zero-range force. This effective interaction depends on a limited number of parameters that are usually fitted using experimental data obtained from doubly magic nuclei. It was recently shown that many Skyrme functionals lead to the appearance of instabilities, in particular when symmetries are broken, for example unphysical polarization of odd–even or rotating nuclei. In this paper, we show how the formalism of the linear response in infinite nuclear matter can be used to predict and avoid the regions of parameters that are responsible for these unphysical instabilities.

scholarly journals Coupling of Charge Regulation and Conformational Equilibria in Linear Weak Polyelectrolytes: Treatment of Long Range Interactions via Effective Short-Ranged and pH-Dependent Interaction Parameters

2018 ◽  
Author(s):  
Pablo M. Blanco ◽  
Sergio Madurga ◽  
Francesc Mas ◽  
Josep L. Garcés
Keyword(s):  
Long Range ◽  
Ph Dependence ◽  
Effective Interaction ◽  
Interaction Parameters ◽  
Computational Time ◽  
Charge Regulation ◽  
Wide Range ◽  
Conformational Equilibria ◽  
Ph Dependent ◽  
Weak Polyelectrolytes

The classical Rotational Isomeric State (RIS) model, originally proposed by Flory, has been used to rationalize a wide range of physicochemical properties of neutral polymers. However, many weak polyelectrolytes of interest are able to regulate their charge depending on the conformational state of the bonds. Recently, it has been shown that the RIS model can be coupled with the Site Binding (SB) model, for which the ionizable sites can adopt two states: protonated or deprotonated. The resulting combined scheme, the SBRIS model, allows to analyse ionization and conformational equilibria on the same foot. In the present work this approach is extended to include pH-dependent electrostatic Long Range (LR) interactions, ubiquitous in weak polyelectrolytes at moderate and low ionic strengths. With this aim the original LR interactions are taken into account by defining effective Short Range (SR) and pH-dependent parameters, such as effective microscopic protonation constants and rotational bond energies. The new parameters are systematically calculated using variational methods. The machinery of statistical mechanics for SR interactions, including the powerful and fast transfer matrix methods, can then be applied. The resulting technique, to which we will refer as Local Effective Interaction Parameters (LEIP) method, is illustrated with a minimal model of a flexible linear polyelectrolyte containing only one type of rotating bonds. LEIP reproduces very well the pH dependence of the degree of protonation and bond probabilities obtained by semi-grand canonical Monte Carlo simulations, where LR interactions are taken explicitly into account. The reduction in the computational time in several orders of magnitude suggests that the LEIP technique could be useful in a range of areas involving linear weak polyelectrolytes, allowing direct fitting of the relevant physical parameters to the experimental quantities.

Photographic Equidensitometry of High Voltage Electron Images of Thick Noncrystalline Materials

1972 ◽  
Vol 30 ◽  
pp. 594-595
Author(s):  
Keinosuke Kobayashi
Keyword(s):  
High Voltage ◽  
Linear Response ◽  
Thickness Distribution ◽  
Contour Map ◽  
Mass Thickness ◽  
Voltage Electron ◽  
High Voltage Electron ◽  
Homogeneous Particle ◽  
Photographic Emulsions ◽  
Logarithmic Relation

Equidensitometry as developed by E. Lau and W. Krug has been little used in the analysis of ordinary electron photomicrographs, yet its application to the high voltage electron images proves merits of this procedure. Proper sets (families) of equidensities as shown in the next page are able to reveal the contour map of mass thickness distribution in thick noncrystalline specimens. The change in density of the electron micrograph is directly related to the mass thickness of corresponding area in the specimen, because of the linear response of photographic emulsions to electrons and the logarithmic relation between electron opacity and mass thickness of amorphous object.This linearity is verified by equidensitometry of a spherical solid object as shown in Fig. 1a. The object is a large (1 μ) homogeneous particle of polystyrene. Fig. 1b is a composite print of three equidensities of the 1st order prepared from Fig. 1a.

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