Dynamics short-time

Stratt R M and Cho M 1994 The short-time dynamics of solvation J. Chem. Phys. 100 6700-8... 

Colloidal particles experience kicks from the surrounding atoms or molecules of the solvent. This leads to Brownian dynamics in colloidal suspensions (Fig. 14). The study of dynamics is challenging as, of course, first the equilibrium of the system has to be understood. One often knows the short-time dynamics that govern the system and is interested in long-time properties. 

Short-time Brownian motion was simulated and compared with experiments [108]. The structural evolution and dynamics [109] and the translational and bond-orientational order [110] were simulated with Brownian dynamics (BD) for dense binary colloidal mixtures. The short-time dynamics was investigated through the velocity autocorrelation function [111] and an algebraic decay of velocity fluctuation in a confined liquid was found [112]. Dissipative particle dynamics [113] is an attempt to bridge the gap between atomistic and mesoscopic simulation. Colloidal adsorption was simulated with BD [114]. The hydrodynamic forces, usually friction forces, are found to be able to enhance the self-diffusion of colloidal particles [115]. A novel MC approach to the dynamics of fluids was proposed in Ref. 116. Spinodal decomposition [117] in binary fluids was simulated. BD simulations for hard spherocylinders in the isotropic [118] and in the nematic phase [119] were done. A two-site Yukawa system [120] was studied with... 

Roe, R.-/. MD Simulation S tudy of Glass Transition and Short Time Dynamics in Polymer Liquids. VoL 116, pp. 111-114. 

The theoretical approach described before dealt with the short-time dynamic response of the star molecules. However, in the case of completely labelled stars [148] it was found that the line shape of the Zimm model provides a good description of the NSE spectra not only in the short-time regime (t < 5 ns), but also on longer time scales. 

Kalampounias, A. G., Yannopoulos, S. N., Steffen, W., Kirillova, L. I., Kirillov, S. A., Short-time dynamics of glass-forming liquids Phenyl salicylate (salol) in bulk liquid, dilute solution, and confining geometries, J. Chem. Phys., 118, 8340-8349 (2003). 

Figure 19 Mean square monomer displacements using the CRC model of PB at three temperatures compared with the monomer displacement in an FRC version of the polymer model. Also indicated is the Rouse-like regime with the subdiffusive t0 61 power law entered after the caging regime (CRC at low T) or after the short time dynamics (FRC and CRC at 353 K).

In the interval between 198 K and 253 K, the form of the structural relaxation does not change114 as is evidenced by the success of the time-temperature superposition shown in Figure 21. One can also see from this figure that an additional regime intervenes between the short-time dynamics (first 10% of the decay at the lowest temperatures) and the structural relaxation (last 80% of the decay). We will identify this regime as the MCT (3-regime... 

In the examples smdied so far, the photoinduced short-time dynamics of a molecular system has been governed by a few high-frequency intramolecular vibrational modes that strongly couple to the electronic transition, a situation that... 

Finally, we consider the performance of the MFT method for nonadiabatic dynamics induced by avoided crossings of the respective potential energy surfaces. We start with the discussion of the one-mode model. Model IVa, describing ultrafast intramolecular electron transfer. The comparison of the MFT method (dashed line) with the quantum-mechanical results (full line) shown in Fig. 5 demonstrates that the MFT method gives a rather good description of the short-time dynamics (up to 50 fs) for this model. For longer times, however, the dynamics is reproduced only qualitatively. Also shown is the time evolution of the diabatic electronic coherence which, too, is... 

Finally, we consider Model V by describing two examples of outer-sphere electron-transfer in solution. Figures 7 and 8 display results for the diabatic electronic population for Models Va and Vb, respectively. Similar to the mean-field trajectory calculations, for Model Va the SH results are in excellent agreement with the quantum calculations, while for Model Vb the SH method only is able to describe the short-time dynamics. As for the three-mode Model IVb discussed above, the SH calculations in particular predict an incorrect long-time limit for the diabatic population. The origin of this problem will be discussed in more detail in Section VI in the context of the mapping formulation. 

Figure 32. Vibronic periodic orbits of a coupled electronic two-state system with a single vibrational mode (Model IVa). All orbits are displayed as a function of the nuclear position x and the electronic population N, where N = Aidia (left) and N = (right), respectively. As a further illustration, the three shortest orbits have been drawn as curves in between the diabatic potentials Vi and V2 (left) as well as in between the corresponding adiabatic potentials Wi and W2 (right). The shaded Gaussians schematically indicate that orbits A and C are responsible for the short-time dynamics following impulsive excitation of V2 at (xo,po) = (3,0), while orbit B and its symmetric partner determine the short-time dynamics after excitation of Vi at (xo,po) = (3, —2.45).

To perform a PO analysis of nonadiabatic quantum dynamics, we employ a quasi-classical approximation that expresses time-dependent quantities of a vibronically coupled system in terms of the vibronic POs of the system [123]. Considering the quasi-classical expression (16) for the time-dependent expectation value of an observable A, this approximation assumes that the integrable islands in phase space represent the most significant contributions to the dynamics of the observables considered [236]. As a consequence, the short-time dynamics of the system is determined by its shortest POs and can be approximated by a time average over these orbits. Denoting the A th PO with period 7 by qk t),Pk t) we obtain [123]... 

The results obtained for the three-mode Model IVb are depicted in Fig. 45. As was found for the semiclassical mapping approach, the spin-coherent state propagators can only reproduce the short-time dynamics for the electronic population. The autocorrelation function, on the other hand, is reproduced at least qualitatively correctly by the semiclassical spin-coherent state propagator. 

An early application of this type of analysis was to decompose Pio/v( ) into its rotational, translational and their cross-correlation subspectra. It was shown through this decomposition that electrostatic solvation spectra for dipole and charge perturbations are dominated by rotational dynamics. More generally, it was shown how the range and symmetry of AP and molecular properties such as masses and moments of inertia are related to the relative contributions of rotational and translational degrees of freedom to SD. INM analysis has also proved useful in comparing the molecular mechaitisms contributing to short-time dynamics observed in different experiments,such as SD, optical Kerr ef-... 

Messina et al. [25] test the time-dependent Hartree reduced representation with a simple two-degree-of-freedom model consisting of the h vibration coupled to a one-harmonic-oscillator bath. The objective function is a minimum-uncertainty wavepacket on the B state potential curve of I2. Figure 12, which displays a typical result, shows that this approximate representation gives a rather good account of the short-time dynamics of the system. 

W. H. Miller Yes, the calculation is especially efficient because only short-time dynamics is required to determine the net reactive flux (while much longer time dynamics would be required to determine state-to-state reaction probabilities). 

For the H + H2 —H2 + H reaction, for example, the reactive flux requires time evolution of only -25 fs. The requirement of only short-time dynamics does indeed suggest the utility of a variety of approximations, such as the time-dependent self-consistent field approximation. 

In Eq. (98), Cq represents the free inertial motion of the tagged particle, Cs contains its full motion, C describes the complete disconnected motion of the surrounding fluid, and Co describes the short-time dynamics of this disconnected motion of the fluid. The T-matrix in Eq. (98) is given by [9]... 

Note that in deriving the contribution from the density fluctuation to the total viscosity, terms of order t2 has not been taken out. In the initial argument of separation of time scale, it was stated that contributions from terms up to order t2 should be included only in the binary term (>yf), and the collective contribution term was expected to start as f4. Thus to take out all the contributions of order t2 from Eq. (196), the short-time dynamics has to be taken out from the propagator as has been done in case of friction. This is achieved by taking out the short-time dynamics from (F(q,t)/S(q))2. Thus the corrected expression for rjspp can now be written as... 

---