Drude extended

Irude model thus predicts that the dispersion interaction varies as 1//. wo-dimensional Drude model can be extended to three dimensions, the result being ... 

The Drude oscillators are typically treated as isotropic on the atomic level. However, it is possible to extend the model to include atom-based anisotropic polarizability. When anisotropy is included, the harmonic self-energy of the Drude oscillators becomes... 

An important alternative to SCF is to extend the Lagrangian of the system to consider dipoles as additional dynamical degrees of freedom as discussed above for the induced dipole model. In the Drude model the additional degrees of freedom are the positions of the moving Drude particles. All Drude particles are assigned a small mass mo,i, taken from the atomic masses, m, of their parent atoms and both the motions of atoms and Drude particles (at positions r, and rdj = r, + d, ) are propagated... 

Fig. 8.6. Energy loss spectra of BaBi03 with different momentum-transfer q (in units of A ) in [100] (a), and [110] (b) directions. The zero loss is stripped by fitting as an asymmetric Lorentzian function. The energy region below 1.0 eV is extended by a Drude model.

The model was originally proposed by Paul Drude in 1902 as a simple way to describe dispersive properties of materials [108]. A quantum version of the model (including the zero-point vibrations of the oscillator) has been used in early applications to describe the dipole-dipole dispersion interactions [109-112]. A semiclassical version of the model was used more recently to describe molecular interactions [113], and electron binding [114]. The classical version has been subsequently used for ionic crystals [115-120], simple liquids [121-127], water [128-135], and ions [136-139], and in recent decades has seen widespread use in MD and MC simulations. In recent years, the Drude model was extended to interface with QM approaches in QM/MM methods [140], facilitated by the simplicity of the model in that it only includes additional charge centers. 

While initially introduced for 1,2 and 1,3 interactions, the use of Thole screening has been extended to non-bond atom pairs [138]. While this extension was initially motivated by the need to fine-tune interactions involving divalent ions, the approach is general and may be applied to any atom pair In practice, this term is applied only when the two particles approach each other closer than a specified threshold, typically 5 A. For example. Thole screening was recently used to calibrate interactions between mobile ions and nucleic acid bases during development of the Drude polarizable force field for DNA [20,151]. 

Molecular Dynamics Simulations with the Classical Drude Polarizable Model via an Extended Lagrangian Integrator... 

Lemkul, J. A., Roux, B., van der Spoel, D and MacKerell, A. D., Jr., Implementation of Extended Lagrangian Dynamics in GROMACS for Polarizable Simulations Using the Classical Drude Oscillator Model, In Press./ Comput. Chem., 2015. 36,1480-1486. 

The 1 eV absorption appears to be dominated by the free carrier intraband absorption (the Drude-like tail extending into the deep infrared). Although there may be a weak interband contribution (with a finite energy gap) as well, this is uncertain because of the strength of the metallic free carrier absorption. 

Fig. la. Schematic showing the optical field (magnetic component) at an interface which supports surface plasmons. The dielectric function in the dielectric medium is the diectric function in the metal can be approximated hy the Drude-Lorentz expression given in the upper right hand corner. Notice that the field extends much farther into the dielectric than the metal, b. The reflectivity in an ATR configuration. The 0 is the critical angle and 0gp is the angle at which the surface plasmon is excited. Reflectivity extends from zero to one. Notice that the reflectivity from s waves, i.e., those waves with their electric vector perpendicular to the plane of incidence do not excite a surface mode.. 

Keeping in mind possible caveats with respect to the interpretation of the results inferred from the extended Drude model, we find that this approach to the data analysis is extremely fruitful and provides important insights into the charge dynamics in cuprates. It is instructive to examine the behavior of the frequency-dependent scattering rate and of the effective mass within simple models. Here we restrict ourselves to one model developed... 

It is important to mention one serious deficiency of the extended Drude analysis. This formalism is based on an isotropic version of Fermi-liquid theory which is highly questionable in cuprates where the electronic structure is in fact very anisotropic in the ab-plane. One approach that addresses this problem is to first calculate the conductivity, using a proper anisotropic theory with A -dependent Fermi velocity and scattering rate 1/r, and then use the real and imaginary parts of the calculated conductivity to find the effective scattering rates l/r(co) and m. Some steps in that direction have been made by Stojkovic and Pines (1996) and Branch and Carbotte (1998). 

From an analysis of the anisotropy in the conductivity spectra of Lai g5Sro.i5Cu04, van der Marel and Kim (1995) concluded that m /mab does not exceed 5 in this compound. A larger anisotropy was inferred by Henn et al. (1996) from an analysis of ellipsometric data for Lai.s7Sro.i3Cu04. This latter analysis is based on the extended Drude model. Again one must question the applicability of this model to the c-axis response of this compound since (7 (o) at a> 0 is smaller than the minimum metallic conductivity. 

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