Quantum dynamics analysis

A completely different approach, in particular for fast imimolecular processes, extracts state-resolved kinetic infomiation from molecular spectra without using any fomi of time-dependent observation. This includes conventional line-shape methods, as well as the quantum-dynamical analysis of rovibrational overtone spectra [18, 33, 34 and 35]. 

Dennison coupling produces a pattern in the spectrum that is very distinctly different from the pattern of a pure nonnal modes Hamiltonian , without coupling, such as (Al.2,7 ). Then, when we look at the classical Hamiltonian corresponding to the Darling-Deimison quantum fitting Hamiltonian, we will subject it to the mathematical tool of bifiircation analysis [M]- From this, we will infer a dramatic birth in bifiircations of new natural motions of the molecule, i.e. local modes. This will be directly coimected with the distinctive quantum spectral pattern of the polyads. Some aspects of the pattern can be accounted for by the classical bifiircation analysis while others give evidence of intrinsically non-classical effects in the quantum dynamics. 

Minehardt T A, Adcock J D and Wyatt R E 1999 Quantum dynamics of overtone relaxation in 30-mode benzene a time-dependent local mode analysis for CH(v = 2) J. Chem. Phys. 110 3326-34... 

Quack M and Stohner J 1993 Femtosecond quantum dynamics of functional groups under coherent infrared multiphoton excitation as derived from the analysis of high-resolution spectra J. Rhys. Chem. 97 12 574-90... 

For the first time, the primary nitrone (formaldonitrone) generation and the comparative quantum chemical analysis of its relative stability by comparison with isomers (formaldoxime, nitrosomethane and oxaziridine) has been described (357). Both, experimental and theoretical data clearly show that the formal-donitrones, formed in the course of collision by electronic transfer, can hardly be molecularly isomerized into other [C,H3,N,0] molecules. Methods of quantum chemistry and molecular dynamics have made it possible to study the reactions of nitrone rearrangement into amides through the formation of oxaziridines (358). 

In a recent analysis carried out for a bounded open system with a classically chaotic Hamiltonian, it has been argued that the weak form of the QCT is achieved by two parallel processes (B. Greenbaum et.al., ), explaining earlier numerical results (S. Habib et.al., 1998). First, the semiclassical approximation for quantum dynamics, which breaks down for classically chaotic systems due to overwhelming nonlocal interference, is recovered as the environmental interaction filters these effects. Second, the environmental noise restricts the foliation of the unstable manifold (the set of points which approach a hyperbolic point in reverse time) allowing the semiclassical wavefunction to track this modified classical geometry. 

Further Analysis of Solutions to the Time-Independent Wave Packet Equations of Quantum Dynamics II. Scattering as a Continuous Function of Energy Using Finite, Discrete Approximate Hamiltonians. 

Because the mapping approach treats electronic and nuclear dynamics on the same dynamical footing, its classical limit can be employed to study the phase-space properties of a nonadiabatic system. With this end in mind, we adopt a onemode two-state spin-boson system (Model IVa), which is mapped on a classical system with two degrees of freedom (DoF). Studying various Poincare surfaces of section, a detailed phase-space analysis of the problem is given, showing that the model exhibits mixed classical dynamics [123]. Furthermore, a number of periodic orbits (i.e., solutions of the classical equation of motion that return to their initial conditions) of the nonadiabatic system are identified and discussed [125]. It is shown that these vibronic periodic orbits can be used to analyze the nonadiabatic quantum dynamics [126]. Finally, a three-mode model of nonadiabatic photoisomerization (Model III) is employed to demonstrate the applicability of the concept of vibronic periodic orbits to multidimensional dynamics [127]. 

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]... 

Following Fey nman s original work, several authors pmsued extensions of the effective potential idea to construct variational approximations for the quantum partition function (see, e g., Refs. 7,8). The importance of the path centroid variable in quantum activated rate processes was also explored and revealed, which gave rise to path integral quantum transition state theory and even more general approaches. The Centroid Molecular Dynamics (CMD) method for quantum dynamics simulation was also formulated. In the CMD method, the position centroid evolves classically on the efiective centroid potential. Various analysis and numerical tests for realistic systems have shown that CMD captures the main quantum effects for several processes in condensed matter such as transport phenomena. 

Thus far our examination of the quantum mechanical basis for control of many-body dynamics has proceeded under the assumption that a control field that will generate the goal we wish to achieve (e.g., maximizing the yield of a particular product of a reaction) exists. The task of the analysis is, then, to find that control field. We have not asked if there is a fundamental limit to the extent of control of quantum dynamics that is attainable that is, whether there is an analogue of the limit imposed by the second law of thermodynamics on the extent of transformation of heat into work. Nor have we examined the limitation to achievable control arising from the sensitivity of the structure of the control field to uncertainties in our knowledge of molecular properties or to fluctuations in the control field arising from the source lasers. It is these subjects that we briefly discuss in this section. 

A quantum dynamical study of the Cl- + CH3 Br 5k2 reaction has been made.78 The calculations are described in detail and the resulting value of the rate constant is in much better agreement with experiment than is that derived from statistical theory, hi related work on the same reaction, a reaction path Hamiltonian analysis of the dynamics is presented.79 The same research group has used statistical theory to calculate the rate constant for the 5n2 reaction... 

The present analysis relies on - and extends - the comprehensive theoretical study of Refs. [23,24] on the multi-state interactions in the manifold of the X — E states of Bz+. Like this recent work, it utilizes an ab initio quantum-dynamical approach. In Refs. [23,24] we have, in addition, identified strong coupling effects between the B — C and B — D electronic states, caused by additional conical intersections between their potential energy surfaces. A whole sequence of stepwise femtosecond internal conversion processes results [24]. Such sequential internal conversion processes are of general importance as is evidenced indirectly by the fluorescence and fragmentation dynamics of organic closed-shell molecules and radical cations [49,50]. It is therefore to be expected that the present approach and results may be of relevance for many other medium-sized molecular systems. 

We now briefly summarize the key results of the analysis of Refs. [50,51] for a reduced XT-CT model of the TFB F8BT heterojunction, using explicit quantum dynamical (MCTDH) calculations for a two-state model parametrized for 20-30 phonon modes. At this level of analysis, an ultrafast ( 200 fs) XT state decay is predicted, followed by coherent oscillations, see Fig. 8 (trace exact in panel (a)). Further analysis in terms of an effective-mode model and the associated HEP decomposition (see Sec. 4.2) highlights several aspects ... 

In contrast to the subsystem representation, the adiabatic basis depends on the environmental coordinates. As such, one obtains a physically intuitive description in terms of classical trajectories along Born-Oppenheimer surfaces. A variety of systems have been studied using QCL dynamics in this basis. These include the reaction rate and the kinetic isotope effect of proton transfer in a polar condensed phase solvent and a cluster [29-33], vibrational energy relaxation of a hydrogen bonded complex in a polar liquid [34], photodissociation of F2 [35], dynamical analysis of vibrational frequency shifts in a Xe fluid [36], and the spin-boson model [37,38], which is of particular importance as exact quantum results are available for comparison. 

C. M. Morales and W. H. Thompson. Mixed quantum-classical molecular dynamics analysis of the molecular-level mechanisms of vibrational frequency shifts. J.Phys. Chem. A, lll(25) 5422-5433, JUN 28 2007. 

The salient features of the dynamics of our model molecule are best exhibited with the help of Poincare sections that have already proved useful in the analysis of the double pendulum presented in Section 3.2. Fig. 4.7 shows the rpp projection of an x = 0 surface of section of a trajectory for a = 0.1, uq = 10 and E = 4 started at 0 = 0.957T, x = sin(0), y = 0, z = cos(0) and tj = 1.42. The resulting y-p Poincare section clearly shows chaotic features. This indicates that the classical dynamics of the skeleton of the model molecule is chaotic. But the most striking feature of the model molecule is its fully chaotic quantum dynamics. This is proved by Fig. 4.8, which shows the chaotic quantum fiow of the molecule on the southern hemisphere of the Bloch sphere. Fig. 4.8 was produced in the following way. First we defined the Poincar6 section by p = 0, dp/dt > 0. Then, we ran 40 trajectories in x,y,z,r],p) space for a = 0.1, Uo = 10 and E = Q starting at the 40 different initial conditions... 

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