Potential linearization

Jansen H J F and Freeman A J 1984 Total-energy full-potential linearized augmented plane-wave method for bulk solids electronic and structural properties of tungsten Phys. Rev. B 30 561-9... 

By combining the Lagrange multiplier method with the highly efficient delocalized internal coordinates, a very powerfiil algoritlun for constrained optimization has been developed [ ]. Given that delocalized internal coordinates are potentially linear combinations of all possible primitive stretches, bends and torsions in the system, cf Z-matrix coordinates which are individual primitives, it would seem very difficult to impose any constraints at all however, as... 

The most general problem should be that of a particle in a nonseparable potential, linearly coupled to an oscillator heat bath, when the dynamics of the particle in the classically accessible region is subject to friction forces due to the bath. However, this multidimensional quantum Kramers problem has not been explored as yet. 

One of the most accurate approaches to solve the LDF equations for the single slab geometry is the full-potential linearized augmented plane wave (FLAPW) method (10). Here, we highlight only the essential characteristics of this approach for further details the reader is referred to a recent review article (11). 

Wdowik, U.D., Ruebenbauer, K. Calibration of the isomer shift for the 77.34 keV transition in 197-Au using the full-potential linearized augmented plane-wave method. J. Chem. Phys. 129 (10), 104504 (2008)... 

One obvious drawback of the LDA-based band theory is that the self-interaction term in the Coulomb interaction is not completely canceled out by the approximate self-exchange term, particularly in the case of a tightly bound electron system. Next, the discrepancy is believed to be due to the DFT which is a ground-state theory, because we have to treat quasi-particle states in the calculation of CPs. To correct these drawbacks the so-called self-interaction correction (SIC) [6] and GW-approximation (GWA) [7] are introduced in the calculations of CPs and the full-potential linearized APW (FLAPW) method [8] is employed to find out the effects. No established formula is known to take into account the SIC. 

Weyrich, K.H. (1988) Full-potential linear muffin-tin-orbital method, Phys. Rev., B37, 10269-10282. 

Hamada, N. and Ohnishi, S. (1986) Self-interaction correction to the local-density approximation in the calculation of the energy band gaps of semiconductors based on the full-potential linearized augmented-plane-wave method, Phys. Rev., B34,9042-9044. 

Blaha, P., Schwarz, K., Dufek, P. et al. (1995) WIEN95 A Full Potential Linearized Augmented Plane Wave Package for Calculating Crystal Properties. Technical University, Vienna. 

The advantage of the scheme lies in possibility to cut indices with a distant dependent selection criterion, rendering the method potentially linear scaling. As a consequence, orbitals for periodic structures may be created in this way (see References [25, 26]). 

Figure 3.8 Current-potential linear sweep voltammogram and the differential reflectivity change in the hydrogen adsorption region at fixed wavelengths (a) 2.34 pm and (b) 1.93 pm. The sweep rate was 15mVs with a square wave modulation of lOmV at 8.5 Hz. From Bewick et al.

It is, however, evident that either the electrode potential linearly shifts towards more negative values, or the current decreases, with pH.48... 

FPLAPW full-potential linearized augmented plane wave... 

This paper reports the results of full-potential-linear-augmented-slater-type-orbital (FLASTO) band calculations on the early transition metal monocarbides. Using the results of these calculations we will develop a bonding model which accurately accounts for the chemical properties of these compounds. This model does not require one to determine either the direction or magnitude of charge transfer between metal and non-metal atoms. 

As mentioned earlier, the existence of surface shifted core levels has been questioned.6 Calculated results for TiC(lOO) using the full potential linearized augmented plane wave method (FLAPW) predicted6 no surface core level shift in the C Is level but a surface shift of about +0.05 eV for the Tis levels. The absence of a shift in the C Is level was attributed to a similar electrostatic potential for the surface and bulk atoms in TiC. The same result was predicted for TiN because its ionicity is close to that of TiC. This cast doubts on earlier interpretations of the surface states observed on the (100) surface of TiN and ZrN which were thought to be Tamm states (see references given in Reference 4), i.e. states pulled out of the bulk band by a shift in the surface layer potential. High resolution core level studies could possibly resolve this issue, since the presence of surface shifted C Is and N Is levels could imply an overall electrostatic shift in the surface potential, as suggested for the formation of the surface states. 

Analyte Reaction Detection Applied potential Linear range Detection limit Reference... 

Slope, standard potential, linear concentration range and limit of detection should be determined using statistic methods, using data obtained for the calibration graph E vs. pSCpt (pSCpt — -log[SCpt]). 

FP-LMTO full potential-linear muffin tin orbitals ... 

Full potential linearized-augmented-plane-wave calculations for 5d transition metals using the relativistic generalized gradient approximation... 

In the case of a linear interaction between neighboring lipid bilayers, Helfrich has demonstrated that the repulsive free energy due to confinement is inversely proportional to (7b2. While this result is strictly valid for a harmonic interaction potential (linear force), we assume that it can be extended to any interaction. We will examine later under what conditions this approximation is accurate. 

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