CSPs

Bare die such as integrated circuits may be assembled in plastic or ceramic carriers, called chip-scale packages, whose dimensions are slightly larger than the chip. CSPs are often defined as packages that are no larger than 1.5 times the area of the die or no more than 1.2 times the width or length of the die. If the carrier is a BGA type, an alternate definition is that the solder-ball pitch be less than 1 mm. The pitch of 

The die may be attached and wire bonded or flip chip bonded to a small rigid interconnect substrate such as a ceramic or a plastic laminate, for example, bisma-leimide triazine (BT). Conventional wire bonding and overmolding processes, as in leadframe CSPs, are also used. 

This CSP type uses a flexible circuit having solder balls or metal bumps as an interconnect interposer between the chip and the next circuit board level. The bare 

Chip is attached face down and wire bonded to the interposer. A thin elastomer, sandwiched between the chip and interposer, cushions the chip and the solder-ball interconnects, relieving stresses (see Fig. 1.13). The interposer generally consists of a metallized, flexible polyimide tape on which are formed electrical connections by photolithographic processes. As a final step, the exposed wire bonds and edges of the chip are molded with epoxy. 

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Sec. 2 presents the CSP method, while an improved approach built on it (CI-CSP) is described in Sec. 3. Sec. 4 gives some examples of applications of the CSP and CI-CSP methods to the photochemical ultrafast dynamics in clusters. Directions for future progress and improvements are discussed in Sec. 5. 

The principal idea behind the CSP approach is to use input from Classical Molecular Dynamics simulations, carried out for the process of interest as a first preliminary step, in order to simplify a quantum mechanical calculation, implemented in a subsequent, second step. This takes advantage of the fact that classical dynamics offers a reasonable description of many properties of molecular systems, in particular of average quantities. More specifically, the method uses classical MD simulations in order to determine effective... 

With the above definitions, there is no additional overall phase factor to be included in (27). Eqs. (24)-(27) are the CSP approximation.Like TDSCF, CSP is a separable approximation, using a time-dependent mean potential for each degree of freedom. However, the effective potentials in CSP... 

The accuracy of the CSP approximation is, as test calculations for model. systems show, typically very similar to that of the TDSCF. The reason for this is that for atomic scale masses, the classical mean potentials are very similar to the quantum mechanical ones. CSP may deviate significantly from TDSCF in cases where, e.g., the dynamics is strongly influenced by classically forbidden regions of phase space. However, for simple tunneling cases it seems not hard to fix CSP, by running the classical trajectories slightly above the barrier. In any case, for typical systems the classical estimate for the mean potential functions works extremely well. 

It is obvious that CSP depends, as does TDSCF, on the choice of coordinates. As pointed out in Sec. 2.2, numerical convenience often limits the choice of the coordinates. CSP may, however, offer practical prospects for the choice of physically optimal modes. The deviation of the true potential from CSP separability is given by ... 

AVcorr can be evaluated readily from the classical MD simulation for any choice of coordinate system, and it may be possible to determine the modes that give the smallest AVcorr- These should be optimal CSP modes. Work along these lines is in ])rogress in our group. So far, however, the coordi-... 

In addition to wavepackets propagated along effective potentials corresponding to individual trajectories, we also propagate in CI-CSP the CSP wavefunc-tions, governed by the average potentials Vj(qj,t) of Eq. (24). The CI-CSP ansatz for the total wavepacket of the system is then as follows ... 

For separable initial states the single excitation terms can be set to zero at all times at this level of approximation. Eqs. (32),(33),(34) together with the CSP equations and with the ansatz (31) for the total wavefunction are the working equations for the approach. This form, without further extension, is valid only for short time-domains (typically, a few picoseconds at most). For large times, higher correlations, i.e. interactions between different singly and doubly excited states must be included. 

For /2(Ar)i7, an extensive CI-CSP simulation was carried out, and the results were compared with those of the simple CSP approximation. Both calculations are for the ultrafast dynamics following excitation of the I2 into the B state. We found that the CI-CSP calculation, including doubly excited configurations , is close to converged for times up to t 500 fs, when 1500 configurations are included. Fig. 2 shows co(t)p, the coefficient of the CSP term and the doubly excited terms in the full CI-CSP wavefunction,... 

It turns out that the CSP approximation dominates the full wavefunction, and is therefore almost exact till t 80 fs. This timescale is already very useful The first Rs 20 fs are sufficient to determine the photoadsorption lineshape and, as turns out, the first 80 fs are sufficient to determine the Resonance Raman spectrum of the system. Simple CSP is almost exact for these properties. As Fig. 3 shows, for later times the accuracy of the CSP decays quickly for t 500 fs in this system, the contribution of the CSP approximation to the full Cl wavefunction is almost negligible. In addition, this wavefunction is dominated not by a few specific terms of the Cl expansion, but by a whole host of configurations. The decay of the CSP approximation was found to be due to hard collisions between the iodine atoms and the surrounding wall of argons. Already the first hard collision brings a major deterioration of the CSP approximation, but also the role of the second collision can be clearly identified. As was mentioned, for t < 80 fs, the CSP... 

Fig. 1. Comparison between the CID-CSP, CSP, TDSCF, and the numerically exact autocorrelation functions.

The intensities are plotted vs. v, the final vibrational quantum number of the transition. The CSP results (which for this property are almost identical with CI-CSP) are compared with experimental results for h in a low-temperature Ar matrix. The agreement is excellent. Also shown is the comparison with gas-phase, isolated I. The solvent effect on the Raman intensities is clearly very large and qualitative. These show that CSP calculations for short timescales can be extremely useful, although for later times the method breaks down, and CTCSP should be used. 

Two methods for time-dependent quantum simulations of many-atom systems are examined in this article the CSP-based and the Cl-CSP-based algorithms. The CSP method begins with a separable approximation for... 

Fig. 2. The contribution c<, of the CSP approximation to the Cl wavefunction and the correlation coefficients d jaj/0 versus time.

The computational efficiency is a major advantage of CSP and CI-CSP, and we expect that in the forthcoming few years CSP-based methods will be extensively used as practical tools for the study of an increased range of dynamical processes in large systems. 

Cyclodextrin stationary phases utilize cyclodextrins bound to a soHd support in such a way that the cyclodextrin is free to interact with solutes in solution. These bonded phases consist of cyclodextrin molecules linked to siUca gel by specific nonhydrolytic silane linkages (5,6). This stable cyclodextrin bonded phase is sold commercially under the trade name Cyclobond (Advanced Separation Technologies, Whippany, New Jersey). The vast majority of all reported hplc separations on CD-bonded phases utilize this media which was also the first chiral stationary phase (csp) developed for use in the reversed-phase mode. 

Isomerism about a formal Csp —Csp double bond Isomensm about a formal (C—C C-aryl and C-acyl derivatives... 

Conformation about a Csp —Csp single bond (Conformation of the ring (Nitrogen inversion... 

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