Time-dependent potentials effective potential

Petersilka, M., Gossmann, U. J., Gross, E. K. U., 1998, Time Dependent Optimized Effective Potential in the Linear Response Regime in Electronic Density Functional Theory. Recent Progress and New Directions, Dobson, J. F., Vignale, G., Das, M. P. (eds.), Plenum Press, New York. 

Time-dependent optimized effective potential in the linear response regime, M. Petersilka, U.J. Gossmann, and E.K.U. Gross, in Electronic Density Functional Theory Recent Progress and New Directions, eds. J.F. Dobson, G. Vignale, and M.P. Das (Plenum, NY, 1998). 

In this chapter, we discuss some new developments in TDDFT beyond the linear response regime for accurate and efficient nonperturbative treatment of multiphoton dynamics and very-high-order nonlinear optical processes of atomic and molecular systems in intense and superintense laser fields. In Section 2, we briefly describe the time-dependent optimized effective potential (OEP) method and its simplified version, i.e., the time-dependent Krieger-Li-Iafrate (KLI) approximation, along with self-interaction correction (SIC). In Section 3, we present the TDDFT approaches and the time-dependent generalized pseudospectral (TDGPS) methods for the accurate treatment of multiphoton processes in diatomic and triatomic molecules. In Section 4, we describe the Floquet formulation of TDDFT. This is followed by a conclusion in Section 5. Atomic units will be used throughout this chapter. 

Time-Dependent Optimized Effective Potential. Unfortunately, when trying to write v c as an explicit functional of the density, one encounters some... 

Xu, X. Mei, H. Wang, S. Zhou, Q. Wang, G. et ah A study of common discovery dosing formulation components and their potential for causing time-dependent matrix effects in high-performance liquid chromatography tandem mass... 

X, Xn, H. Mei, S. Wang, Q. Zhon, G. Wang, L. Broske, A. Pena, and W. A. Korfmacher, A stndy of common discovery dosing formnlation components and their potential for cansing time-dependent matrix effects in high-performance liqnid chromatography tandem mass spectrometry assays. Rapid Commun. Mass Spectrom. 19 (2005), 2643-2650. 

In Fe(II)-dichromate titrations, Winter and Moyer observed a time dependence of the potential after the end point. When potential readings were taken soon after each addition, an asymmetrical titration curve was observed, but when a time interval of 10 to 15 min was allowed after each addition, the curve approached the theoretical shape. We have noted that automatically recorded titration curves for the Fe(II)-dichromate titration show a considerably smaller potential jump than manually observed curves, the difference being due to lower potentials after the end point. But curves plotted with 15 s of waiting for each point differed only slightly from curves plotted with 150 s of waiting. Ross and Shain also studied the drift in potential of platinum electrodes with time and noted hysteresis effects in recorded potentiometric titration curves. These effects, due to oxidation and reduction of the platinum surface, are discussed below. 

The equations of motion used to describe the trajectory of an ion in a linear quadmpole (Equation [6.12], Section 6.4.2) are strictly valid only well inside the rod assembly, well removed from the entrance and exit. At each of these ends the ideal quadmpole field (Equation [6.11]) terminates abmptly, but in any real device is affected not only by the RF and DC potentials applied to the rods but also by the potentials applied to nearby ion optical elements (lenses etc.). Moreover, the field lines created by the potentials applied to the rods spill out for some distance outside the theoretical boundaries. These curved fringe fields (Section 6.4.2a) distort the ideal quadmpole field such that the ion motions in the x- and y-directions that are independent of one another in the main quadmpole field (Equation [6.11]) become coupled as a consequence of mixing radial and axial potentials, i.e. the electrical force exerted on an ion in the z-direction can be a function of the time dependent potentials applied in the X- and y-directions (but now curved in three-dimensions), and vice versa. These effects of fringe fields are important in the following discussion. 

Exercise 2.7 Show that in the static case the vector potential A can be chosen to be divergence free, i.e. V T = 0, without effect on the magnetic induction. Secondly, investigate what consequences this choice has for time-dependent potentials and fields. 

Rg. 7 Dependence of the transfer time on the effective potential bias for the migration of a hydrogen impurity in the vicinity of a palladium(lll) surface, The transfer times exhibit a power law dependence on the strength of the non-adiabatic couplings, as measured by Reproduced from ref. 127 with permission from the PCCP Owner Societies,... 

Morf, W.E., E. Pretsch, and N.F. de Rooij. 2009. Memory effects of ion-selective electrodes Theory and computer simulation of the time-dependent potential response to multiple sample changes. J. Electroanal. Chem. 633 137-145. 

At a frequency of 5 Hz the burst-time depended on the potential of the rectangular wave. When the largest potential was set at +0.8 V, the negative potential was closely related to the time for cell-burst. For example, when the modulation was set at 0.8 V and -0.4 V, a very long time (144 s) was required for the cell-burst. However, when the two potentials were 0.8 V and -0.8 V, the cell-burst occurred within 4 s. On the other hand, a less remarkable effect of the potential application on HeLa cells was observed when the positive potential was changed. By keeping the negative potential at -0.8 V, the burst-time was 45 s at a positive potential of 0.4 V. The increase of the positive potential caused the decrease in the burst time. 

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