Quantum time dependent

In the adiabatic bend approximation (ABA) for the same reaction,18 the three radial coordinates are explicitly treated while an adiabatic approximation was used for the three angles. These reduced dimensional studies are dynamically approximate in nature, but nevertheless can provide important information characterizing polyatomic reactions, and they have been reviewed extensively by Clary,19 and Bowman and Schatz.20 However, quantitative determination of reaction probabilities, cross-sections and thermal reaction rates, and their relation to the internal states of the reactants would require explicit treatment of five or the full six degrees-of-freedom in these four-atom reactions, which TI methods could not handle. Other approximate quantum approaches such as the negative imaginary potential method16,21 and mixed classical and quantum time-dependent method have also been used.22... 

The quantum time-dependent diffusion coefficient D(t) = Cvv(tr) dt1 is an odd function of time given by ... 

The quantum time-dependent diffusion coefficient for t > 0 thus appears as the sum of the classical time-dependent diffusion coefficient (A 7"/t ) (1 — which from now on we shall denote as Dcl(f), and of a supplementary contribution due to quantum effects, which can be shown to be always positive. 

Figure 3. In the short-memory limit (rac —> oo), the quantum time-dependent diffusion coefficient DP - 00 piotte(j as a function of yt for several different bath temperatures on both sides of Tc (full lines) yrth = 0.25(T — 2TC, classical regime) yt — 0.5 (T = Tc, crossover) yrth = 1 (T = Tc/2, quantum regime) yt = +oo (T = 0). The corresponding curves for the classical diffusion coefficient Dcl( ) are plotted in dotted lines in the same figure.

Figure 4. Quantum time-dependent diffusion coefficient D c yj(t) plotted as a function of T/Tc for several different values of yt yt — 0.5 yt = 1 yt — 5 classical limit (y1).

Quantum Time-Dependent Perturbation Theory Analysis... 

Quantum Time-Dependent Perturbation Theory Analysis of State-to-State Energy Transfer... 

Zhang, Y Straub, J. E., Direct evidence for mode-specific vibrational energy relaxation from quantum time-dependent perturbation theory. 11. The and v, modes of iron... 

A new text that provides a relatively broad view of quantum mechanics in chemistry ranging from electron correlation to time-dependent processes and scattering. 

The central equation of (non-relativistic) quantum mechanics, governing an isolated atom or molecule, is the time-dependent Schrodinger equation (TDSE) ... 

Tannor D J 2001 Introduction to Quantum Mechanics A Time Dependent Perspective (Mill Valley, CA University Science Books)... 

A comprehensive discussion of wavepackets, classical-quantum correspondence, optical spectroscopy, coherent control and reactive scattering from a unified, time dependent perspective. 

Makri N 1999 Time dependent quantum methods for large systems Ann. Rev. Phys. Chem. 50 167... 

The foundations of the modem tireory of elementary gas-phase reactions lie in the time-dependent molecular quantum dynamics and molecular scattering theory, which provides the link between time-dependent quantum dynamics and chemical kinetics (see also chapter A3.11). A brief outline of the steps hr the development is as follows [27],... 

Balint-Kurti G G, Dixon R N and Marston C C 1992 Grid methods for solving the Schrodinger equation and time-dependent quantum dynamics of molecular photofragmentation and reactive scattering processes/of. Rev. Phys. Chem. 11 317—44... 

Leforestier C et ak 1991 Time-dependent quantum mechanical methods for molecular dynamics J. Comput. Phys. 94 59-80... 

As reactants transfonn to products in a chemical reaction, reactant bonds are broken and refomied for the products. Different theoretical models are used to describe this process ranging from time-dependent classical or quantum dynamics [1,2], in which the motions of individual atoms are propagated, to models based on the postidates of statistical mechanics [3], The validity of the latter models depends on whether statistical mechanical treatments represent the actual nature of the atomic motions during the chemical reaction. Such a statistical mechanical description has been widely used in imimolecular kinetics [4] and appears to be an accurate model for many reactions. It is particularly instructive to discuss statistical models for unimolecular reactions, since the model may be fomuilated at the elementary microcanonical level and then averaged to obtain the canonical model. 

Quantum mechanically, the time dependence of the initially prepared state of A is given by its wavefimc /("f), which may be detennined from the equation of motion... 

Time-dependent quantum mechanical calcnlations have also been perfomied to study the HCO resonance states [90,91]. The resonance energies, linewidths and quantum number assigmnents detemiined from these calcnlations are in excellent agreement with the experimental results. 

In time-dependent quantum mechanics, vibrational motion may be described as the motion of the wave packet... 

I i i(q,01 in configuration space, e.g. as defined by the possible values of the position coordinates q. This motion is given by the time evolution of the wave fiinction i(q,t), defined as die projection ( q r(t)) of the time-dependent quantum state i i(t)) on configuration space. Since the quantum state is a complete description of the system, the wave packet defining the probability density can be viewed as the quantum mechanical counterpart of the classical distribution F(q- i t), p - P t)). The time dependence is obtained by solution of the time-dependent Schrodinger equation... 

As in classical mechanics, the outcome of time-dependent quantum dynamics and, in particular, the occurrence of IVR in polyatomic molecules, depends both on the Flamiltonian and the initial conditions, i.e. the initial quantum mechanical state I /(tQ)). We focus here on the time-dependent aspects of IVR, and in this case such initial conditions always correspond to the preparation, at a time of superposition states of molecular (spectroscopic) eigenstates involving at least two distinct vibrational energy levels. Strictly, IVR occurs if these levels involve at least two distinct... 

Figure A3.13.10. Time-dependent probability density of the isolated CH clnomophore in CHF. Initially, tlie system is in a Fenni mode with six quanta of stretching and zero of bending motion. The evolution occurs within the multiplet with chromophore quantum number A = 6 = A + 1 = 7). Representations are given...

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 1992 Time dependent intramolecular quantum dynamics from high resolution spectroscopy and laser chemistry Time Dependent Quantum Molecular Dynamics Experiment and Theory. Proc. NATO ARW 019/92 (NATO ASI Ser. Vol 299) ed J Broeckhove and L Lathouwers (New York Plenum) pp 293-310... 

Quack M, Stohner J and Sutcliffe E 1985 Time-dependent quantum dynamics of the picosecond... 

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]. 

Peskin U, Miller W H and Ediund A 1995 Quantum time evolution in time-dependent fields and time-independent reactive-scattering calculations via an efficient Fourier grid preconditioner J. Chem. Phys. 103 10 030... 

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