Coupled dipole method

V. Kerasek, O. Brzobohaty, P Zemanek, Longitudinal optical binding of several spherical particles studied by the coupled dipole method. J. Opt. A Pure Appl. Opt. 11 (2009) 034009. P.A.M. Dirac, The Principles of Quantum Mechanics, Oxford University Press, Oxford, 1958. 

In general, the study of the scattered intensity by systems where multiple scattering is non-negligible is a difficult task. In order to resolve these difficulties we have used several approximations the particle size is assumed to be much smaller than the incident wavelength, so the Rayleigh dipole approximation is used to characterize the particle scattering. For the surface case, the perfect conductor approximation (PCA) ( = -go) for the substrate is applied. In both systems, the scattered field is calculated in the far-field approximation. For the purpose of this research, these approximations do not constitute serious restrictions and facilitate the numerical calculations. For real substrates (metallic or dielectric) and/or finite size particles, the main conclusions are unaffected [9]. The scattered intensity is calculated by means of the coupled dipole method (CDM) [10] for both the volume case and the surface case. In the latter, the PCA allows us to apply the image theory [11]. 

Light scattering and extinction by a single aggregate 3.2.1. Coupled dipole method (CDM)... 

There are a number of other approaches to calculate VW interactions that are not covered here more exact expressions are given, especially, for the case of two spheres (Langbein 1970 Clayfield, Lumb, and Mackey 1971 Langbein 1974). Recently, more accurate calculations have been reported, using the coupled dipole method for nanocolloids (Kim and Kent 2009) and multipole expansions using classic electrostatics and statistical mechanics methods (Stenhammar et al. 2010) the results are compared with the classical Hamaker expression. 

Lakhtakia,A. (1992) Strong and weak forms of the method of moments and the coupled dipole method for scattering of time-harmonic electromagnetic fields, Intf Mod. Phys. C, 3, 583-603. 

Chaumet, P. C., Sentenac, A., and Rahmani, A. (2004) Coupled dipole method for scatterers with large permittivity, Phys. Rev. E, 70, 036606/1-6. 

Rahmani, A., Chaumet, P. C., and Bryant, G. W. (2002) Coupled dipole method with an exact long-wavelength limit and improved accuracy at finite frequencies. Opt. Lett, 27, 2118-2120. 

Singham, S. B., and Bohren, C. F. [1987] Light scattering by an arbitrary particle A physical reformulation of the coupled dipole method. Opt. Lett, 12,10-12. 

R. Schmehl, The coupled-dipole method for light scattering from particles on plane surfaces, Diplomarbeit, Universitat Karlsruhe (TH), Karlsruhe (1994)... 

M.A. Taubenblatt, T.K. Tran, Calculation of light scattering from particles and structures on a surface by the coupled-dipole method, J. Opt. Soc. Am. A 10, 912 (1993)... 

Thakkar and Lupinetti5 have used the coupled-cluster method in conjunction with the Douglas-Kroll relativistic Hamiltonian to obtain a very accurate value for the static dipole polarizability of the sodium atom. Their revised value for a(Na) = 162.88 0.6 au resolves a previous discrepancy between theory and experiment and when combined with an essentially exact value for lithium, establishes the ratio a(Li)/a(Na) = 1.0071 0.0037, so that, because of the... 

However, because the shape of the TD is well-calculated, it is possible to scale uniformly the TDC in such a way that Eq. (8) gives the experimental result for the transition dipole moment p P. We do this by multiplying each element in the cube by p P/(or equivalently post-processing the calculated coupling). This method does not work for forbidden transitions, of course. If TDs are calculated using time-dependent density functional theory or semiempirical methods like ESfDO [82], no scaling is necessary [83]. 

Figure 8. A summary of couplings calculated between the Bchl Qy transition and the carotenoid S2 transition for LH2. are those calculated by the TEXT method for Rps. acidophila [73], the provide a comparison with the dipole-dipole method, and V - are those calculated for Rs. molischianum using the CEO method [11],...

Dipolar hyperfine coupling of f- H The point dipole method is a common approximation for the H dipolar hfc in -position of n-electron radicals (see Fig. 2.8). The dipolar couplings can be estimated more accurately by taking account of the extension of the electron wave-function for the unpaired electron [26]. Computation of the electronic structure with evaluation of the coupling tensors from first principles in quantum chemistry programs is an alternative that is frequently used in modem applications. 

Hohm et al. have calculated the static dipole polarizability of P4 clusters using ab initio finite-field MP and coupled-cluster methods. The results have been compared with frequency-dependent measurements obtained fi-om the gas phase refi active index. 

Electric dipole polarizability, 28 Electric polarizability, 14 Electron correlation, 8, 10 Electronic virial theorem, 15 Equation of Motion coupled cluster method (EOM-CC), 38, 54 Eulero-Lagrange equation, 51... 

Kello and Sadlej have employed the Breit-Pauli Hamiltonian in all-electron relativistic calculations, which included electron correlation effects. These authors have adapted techniques, which include electron correlation effects such as the coupled cluster method or the Mpller-Plesset (MP) perturbation method, to include relativistic effects and applied them to molecules such as AgH, AuH, etc., to compute dipole moments and quadrupole moments. 

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