Time-dependent quantum wavepacket

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 spectral quantization (SQ), it is possible to extract a Seigert state wavefunction from time-dependent quantum wavepackets using the Fourier relation Eq. (21). The state obtained in this way for J = 0 is shown in Fig. 7 this state is localized in the collinear F — H — D arrangement with 3-quanta of excitation in the asymmetric stretch mode, and 0-quanta of excitation in the bend and symmetric stretch modes. If the state pictured in Fig. 7 is used as an initial (prepared) state in a wavepacket calculation, one observes pure... 

Abstract. This paper presents an overview of the time-dependent quantum wavepacket approach to chemical reaction dynamics. After a brief review of some early works, the paper gives an up-to-date account of the recent development of computational methodologies in time-dependent quantum dynamics. The presentation of the paper focuses on the development of accurate or numerically exact time-dependent methods and their specific applications to tetraatomic reactions. After summarizing the current state-of-the-art time-dependent wavepacket approach, a perspective on future (development is provided. 

Similar transient signals were obtained from time-dependent quantum mechanical calculations performed by Meier and Engel, which well reproduce the observed behavior [49]. They show that for different laser field strengths the electronic states involved in the multiphoton ionization (MPI) are differently populated in Rabi-type processes. In Fig. 13 the population in the neutral electronic states is calculated during interaction of the molecule with 60-fs pulses at 618 nm. For lower intensities the A state is preferentially populated by the pump pulse, and the A state wavepacket dominates the transient Na2+ signal. However, for the higher intensities used in the... 

It is informative to study the same problem in the time-dependent, quantum mechanical approach (Heller 1978a, 1981a,b). We start with the (unnormalized) wavepacket at t — 0,... 

Recently, in this laboratory, we have applied time-dependent quantum mechanics-wavepacket dynamics to several bona fide time-domain spectroscopies. Specifically, we have formulated time-dependent theories of coherent-pulse-seque nee-induced control of photochemical reaction, picosecond CARS spectroscopy, and photon echoes. These processes all involve multiple pulse sequences in which the pulses are short or comparable in time scale to the... 

Time-domain spectroscopies entail a major shift in emphasis from traditional spectroscopies, since the experimenter can control, in principle, the duration, shape, and sequence of pulses. One may say that traditional, CW spectroscopy, is passive—the experimenter attempts to study static properties of a particular molecule. Coherent pulse experiments are active in that, given a set of molecular properties (which may in fact be known from various spectroscopies), one tries to arrange for a desired chemical product, or to design a pulse sequence that will probe new molecular properties. The time-dependent quantum mechanics-wavepacket dynamics approach developed here is a natural framework for formulating and interpreting new multiple pulse experiments. Femtosecond experiments yield to a particularly simple interpretation within our approach. 

Hankel, M., Balint-Kurti, G.G. and Gray, S.K. (2003) Sine wavepackets A new form of wavepacket for time-dependent quantum mechanical reactive scattering calculations Int. J. Quant. Chem. 92, 205-211. 

Chapter 3 treats nuclear motions on the adiabatic potential energy surfaces (PES). One of the most powerful and simplest means to study chemical dynamics is the so-called ab initio molecular dynamics (or the first principle dynamics), in which nuclear motion is described in terms of the Newtonian d3mamics on an ab initio PES. Next, we review some of the representative time-dependent quantum theory for nuclear wavepackets such as the multiconfigurational time-dependent Hartree approach. Then, we show how such nuclear wavepacket d3mamics of femtosecond time scale can be directly observed with pump>-probe photoelectron spectroscopy. 

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

The time-dependent Schrddinger equation governs the evolution of a quantum mechanical system from an initial wavepacket. In the case of a semiclassical simulation, this wavepacket must be translated into a set of initial positions and momenta for the pseudoparticles. What the initial wavepacket is depends on the process being studied. This may either be a physically defined situation, such as a molecular beam experiment in which the paiticles are defined in particular quantum states moving relative to one another, or a theoretically defined situation suitable for a mechanistic study of the type what would happen if. .. 

The picture here is of uncoupled Gaussian functions roaming over the PES, driven by classical mechanics. The coefficients then add the quantum mechanics, building up the nuclear wavepacket from the Gaussian basis set. This makes the treatment of non-adiabatic effects simple, as the coefficients are driven by the Hamiltonian matrices, and these elements couple basis functions on different surfaces, allowing hansfer of population between the states. As a variational principle was used to derive these equations, the coefficients describe the time dependence of the wavepacket as accurately as possible using the given... 

An overview of the time-dependent wavepacket propagation approach for four-atom reactions together with the construction of ab initio potential energy surfaces sufficiently accurate for quantum dynamics calculations has been presented. Today, we are able to perform the full-dimensional (six degrees-of-freedom) quantum dynamics calculations for four-atom reactions. With the most accurate YZCL2 surface for the benchmark four-atom reaction H2 + OH <-> H+H2O and its isotopic analogs, we were able to show the following ... 

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