Time-dependent quantum wave packet

Koppel [180] has performed exact time-dependent quantum wave-packet propagations for this model, the results of which are depicted in Fig. 2A. He showed that the initially excited C state decays irreversibly into the X state within 250 fs. The decay is nonexponential and exhibits a pronounced beating of the C and B state populations. This model will allow us to test mixed quantum-classical approaches for multistate systems with several conical intersections. 

To uniquely associate the unusual behavior of the collision observables with the existence of a reactive resonance, it is necessary to theoretically characterize the quantum state that gives rise to the Lorentzian profile in the partial cross sections. Using the method of SQ, it is possible to extract a Siegert state wavefunction from time-dependent quantum wave packets using the Fourier relation Eq. (28). The state obtained in this way for / = 0 is shown in Figure 3.7 this state is localized in the collinear F-H-D arrangement with three quanta of excitations in the asymmetric stretch... 

Z. Lan, W. Domcke, V. Vallet, A. L. Sobolewski and S. Mahapatra, Time-dependent quantum wave-packet description of the 1 tt[Pg.427]

D. H. Zhang, O. A. Sharafeddin, and J. Z. H. Zhang, Product state distribution in time-dependent quantum wave packet calculation with an optical potential. Chem. Phys. 167 131 (1992). 

Time-Dependent Quantum Wave-Packet Dynamics and Reduced... 

In this chapter we survey characteristic features of time-dependent quantum wave-packet dynamics on conically intersecting potential-energy (PE) surfaces. The focus will be on the fully microscopic description of nontrivial dynamical processes such as ultrafast internal conversion and photoisomerization, as well as vibrational energy redistribution and dephasing. The quantum dynamics calculations discussed in this chapter are... 

In an alternative approach, exact (numerical) time-dependent quantum wave-packet methods have been employed since the early eighties of the last century to explore the d3mamics of ob-initio-haseA models of conical intersections, see Refs. 6-8 for reviews. It has been found by these calculations that the fundamental dissipative processes of population and phase relaxation at femtosecond time scales are clearly expressed already in fewmode systems, if a directly accessible conical intersection of the PE surfaces is involved. The results strongly support the idea that conical intersections provide the microscopic mechanism for ultrafast relaxation processes in polyatomic molecules. " More recently, these calculations have been extended to describe photodissociation and photoisomerization processes associated with conical intersections. The latter are particularly relevant for our understanding of the elementary mechanisms of photochemistry. 

In the chapters of Part II of this book it has been demonstrated for a variety of examples that conical intersections can provide the mechanism for extremely fast chemical processes, e.g. photodissociation, photoisomerization and internal conversion to the electronic ground state. Time-dependent quantum wave-packet calculations have established that radiationless transitions between electronic states can take place on a time scale of the order of 10 fs, if a conical intersection is directly accessible after preparation of the wave packet in the excited state, see, e.g. Chapters 8-11 and 14 15. In view of these findings and the omnipresence of conical intersections in polyatomic molecules (cf. Chapter 6), it is now widely accepted that conical intersections are of fundamental importance for the understanding of the reaction mechanisms in photochemistry and photobiology. 

Rate constant, the statistical dynamical quantity of most interest, is indispensable to our understanding and controlling of chemical reactions at the molecular level. In particular, derivation of the rate constant for an elementary chemical reaction is of essential significance since a complex reactive process may finally have a relationship to an individual elementary reaction step. There are various theoretical methods for computing rate constants for an elementary chemical reaction, and the development of the time-dependent quantum wave packet (TDQWP) method during the past two decades has enabled this... 

The following theoretical part of the chapter (see section 8.2) presents our developed quantum theories, which are capable of computing reaction rate constants for electronically nonadiabatic reaction dynamics. These recently developed time-dependent quantum wave packet theories mainly focused on solving the Schrodinger equation for nuclei motion, leaving the more... 

Generally, we apply two methods to derive the temperature-dependent rate constants from the time-dependent quantum wave packet calculations. The first one is the method using the calculated total cross-section (or... 

In this chapter we present the time-dependent quantum wave packet approaches that can be used to compute rate constants for both nonadiabatic and adiabatic chemical reactions. The emphasis is placed on our recently developed time-dependent quantum wave packet methods for dealing with nonadiabatic processes in tri-atomic and tetra-atomic reaction systems. Quantum wave packet studies and rate constants computations of nonadiabatic reaction processes have been dynamically achieved by implementing nuclear wave packet propagation on multiple electronic states, in combination with the coupled diabatic PESs constructed from ab initio calculations. To this end, newly developed propagators are incorporated into the solution of the time-dependent Schrodinger equation in matrix formulism. Applications of the nonadiabatic time-dependent wave packet approaches and the adiabatic ones to the rate constant computations of the nonadiabatic tri-atomic F (P3/2, P1/2) + D2 (v = 0,... 

Vallet V, Lan Z, Mahapatra S, Sobolewski AL, Domcke W (2004) Time-dependent quantum wave-packet description of the no photochemistry of pyrrole. J Chem Soc Faraday Discuss 127 283... 

Vallet, V., Lan, Z. G., Mahapatra, S., Sobolewski, A. L., 8c Domcke, W. (2004). Time-dependent quantum wave-packet description of the Ttcr photochemistry of pyrrole. Faraday Discussions, 127, 283-293. 

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