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Approximation random phase

The structure factor S(Q) of an incompressible non-ideal mixture of two polymers with an enthalpy of mixing x has been derived by deGennes [3] within the random phase approximation (RPA) according to [Pg.16]

The RPA is a mean field approximation that neglects contributions from thermal composition fluctuations and that assumes the chain conformations to be unperturbed Gaussian chains. The last assumption becomes visible from the Debye form factor in the first two terms, which for Vp, = are in accordance with Eq. 7, while the third term involves the FH interaction parameter. [Pg.16]

The inverse structure factor at Q = 0 is a susceptibility and is related to the Gibbs free energy of mixing AG according to [Pg.16]

Equation 10 is a general result based on the fluctuation-dissipation theorem [3,4,9]. So the susceptibility can independently be evaluated from AG which in the case of the mean field FH theory leads to a similar result as the RPA, [Pg.16]

For small Q ( 1/Kg) the structure factor in Eq. 9 can be expanded in Zimm approximation according to [Pg.16]

The central problem of the sum-over-states perturbation theory lies in the evaluation of the energy resolvant which includes the inverse of excitation energies and transition moments of the one-electron operators [Pg.249]

The amplitudes (SK) and (TK) are determined from the coupled sets of linear RPA equations [Pg.250]

The above equations can be combined to yield the inverse energy relations [Pg.251]

The elements of the inverse matrix (A — B) 1, which will be required later, can be obtained by diagonalisation of the Hermitian matrix (A — B) [Pg.251]

When the one-electron operators are spin free, only the spin-singlet configuration functions contribute and hence the matrix elements to be evaluated are [Pg.251]


Keller G 1986 Random-phase-approximation study of the response function describing optical second-harmonic generation from a metal selvedge Rhys. Rev. B 33 990-1009... [Pg.1301]

A second method is to use a perturbation theory expansion. This is formulated as a sum-over-states algorithm (SOS). This can be done for correlated wave functions and has only a modest CPU time requirement. The random-phase approximation is a time-dependent extension of this method. [Pg.258]

RPA, and CPHF. Time-dependent Hartree-Fock (TDFIF) is the Flartree-Fock approximation for the time-dependent Schrodinger equation. CPFIF stands for coupled perturbed Flartree-Fock. The random-phase approximation (RPA) is also an equivalent formulation. There have also been time-dependent MCSCF formulations using the time-dependent gauge invariant approach (TDGI) that is equivalent to multiconfiguration RPA. All of the time-dependent methods go to the static calculation results in the v = 0 limit. [Pg.259]

RPA (random-phase approximation) ah initio method used for computing nonlinear optical properties... [Pg.368]

The simplest polarization propagator corresponds to choosing an HF reference and including only the h2 operator, known as the Random Phase Approximation (RPA). For the static case oj = 0) the resulting equations are identical to those obtained from a Time-Dependent Hartree-Fock (TDHF) analysis or Coupled Hartree-Fock approach, discussed in Section 10.5. [Pg.259]

Coupled Hartree-Fock values within the Random Phase approximation... [Pg.95]

Figure 4 Conduction band levels and excitation levels of infinite periodic hydrogen chains by using different approximations of the polarization propagator. The left part refers to the crystalline orbital energy differences, namely, the Hartree-Fock excitation energies the right part refers to the random phase approximation results obtained by using 41 k-points in half the first Brillouin zone. Figure 4 Conduction band levels and excitation levels of infinite periodic hydrogen chains by using different approximations of the polarization propagator. The left part refers to the crystalline orbital energy differences, namely, the Hartree-Fock excitation energies the right part refers to the random phase approximation results obtained by using 41 k-points in half the first Brillouin zone.
In the random phase approximation, the transition amplitude from state 0) to l) for any one electron operator O may be written as... [Pg.179]

In this contribution, we have shown that the Bethe sum rule, like the Thomas-Reiche-Kuhn sum rule, is satisfied exactly in the random phase approximation for a complete basis. Thus, in calculations that are related to the generalized oscillator strengths of a system, the Bethe sum rule may be used as an indicator of completeness of the basis set, much as the Thomas-Reiche-Kuhn... [Pg.190]

Lohse et al. have summarized the results of recent work in this area [21]. The focus of the work is obtaining the interaction parameter x of the Hory-Huggins-Stavermann equation for the free energy of mixing per unit volume for a polymer blend. For two polymers to be miscible, the interaction parameter has to be very small, of the order of 0.01. The interaction density coefficient X = ( y/y)R7 , a more relevant term, is directly measured by SANS using random phase approximation study. It may be related to the square of the Hildebrand solubility parameter (d) difference which is an established criterion for polymer-polymer miscibility ... [Pg.301]

Saue and Jensen used linear response theory within the random phase approximation (RPA) at the Dirac level to obtain static and dynamic dipole polarizabilities for Cu2, Ag2 and Au2 [167]. The isotropic static dipole polarizability shows a similar anomaly compared with atomic gold, that is, Saue and Jensen obtained (nonrelativ-istic values in parentheses) 14.2 for Cu2 (15.1 A ), 17.3 A for Ag2 (20.5 A ), and 12.1 A for Au2 (20.2 A ). They also pointed out that relativistic and nonrelativistic dispersion curves do not resemble one another for Auz [167]. We briefly mention that Au2 is metastable at 5 eV with respect to 2 Au with a barrier to dissociation of 0.3 eV [168, 169]. [Pg.198]

Petke JD, Maggiora GM, Christoffersen RE (1992) Ab-initio configuration interaction and random phase approximation caclulations of the excited singlet and triplet states of uracil and cytosine. J Phys Chem 96 6992... [Pg.332]

Using the random phase approximation (RPA), the coherent scattering intensity Icoh(Q, t) of a polymer blend/solvent or a diblock copolymer/solvent system can... [Pg.120]

In the random phase approximation (RPA), that is, when the dephasing is rapid in the timescale under consideration, we have... [Pg.58]

In order to calculate in the framework of Random Phase Approximation the intensity 1(6) of scattering at angle 6 of the incident radiation with wavelength X. recourse should be made to the formula [31]... [Pg.164]

Eqs. (9),(11) the condition eq. (12) in the random phase approximation (RPA) formalism leads to a self-consistency relation between the symmetry potential and the Landau parameter F [26] ... [Pg.105]

In the self-consistent field linear response method [25,46,48] also known as random phase approximation (RPA) [49] or first order polarization propagator approximation [25,46], which is equivalent to the coupled Hartree-Fock theory [50], the reference state is approximated by the Hartree-Fock self-consistent field wavefunction < scf) and the set of operators /i j consists of single excitation and de-excitation operators with respect to orbital rotation operators [51],... [Pg.474]

Diblock copolymers represent an important and interesting class of polymeric materials, and are being studied at present by quite a large number of research groups. Most of the scientific interest has been devoted to static properties and to the identification of the relevant parameters controlhng thermodynamic properties and thus morphologies [257-260]. All these studies have allowed for improvements to the random phase approximation (RPA) theory first developed by Leibler [261]. In particular, the role of the concentration fluctuations, which occur and accompany the order-disorder transition, is studied [262,263]. [Pg.162]


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Phase approximation

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