Time-dependent quantum wavepacket approach

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. 

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,... 

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. 

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. 

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 ... 

In Section 4.1 we will use the time-independent continuum basis 4//(Q E,0), defined in Section 2.5, to construct the wavepacket in the excited state and to derive (4.2). Numerical methods are discussed in Section 4.2 and quantum mechanical and semiclassical approximations based on the time-dependent theory are the topic of Section 4.3. Finally, a critical comparison of the time-dependent and the time-independent approaches concludes this chapter. 

In this section we review three simple approximate time-independent methods which are specifically designed for calculating absorption spectra. Time-independent quantum scattering calculations, which can give exact results, will not be discussed. Such methods have been reviewed for instance by Nyman and Yu 2000 [81] and Althorpe and Clary 2004 [82]. In Section 6 we instead describe the time-dependent wavepacket approach, which can also give exact results. In the present section we review (i) a zero point energy model, (ii) the simple reflection principle model and (iii) the reflection principle model [3]. The accuracy of these models, which should only be applied to direct or near-direct reactions, will... 

Nenhauser, D., Baer. M., Judson, R.S. and Konri, D.J. (1990) Time-dependent (wavepacket) quantum approach to reactive scattering ibrationally resolved rcac tion probabilities for F J- H2 —i HE + H, Chem. Phys. Lett. 169, 372-379. 

Time-independent approaches to quantum dynamics can be wxriational where the wavefunction for all coordinates is expanded in some basis set and the parameters optimized. The best knowm variational implementation is perhaps the S-matrix version of Kohn s variational prineiple which was introduced by Miller and Jansen op de Haar in 1987[1]. Another time-independent approach is the so called hyperspherical coordinate method. The name is unfortunate as hyperspher-ical coordinates may also be used in other contexts, for instance in time-dependent wavepacket calculations [2]. 

K. Kulander, Collision induced dissociation in collinear H + H2 Quantum mechanical probabilities using the time-dependent wavepacket approach. J. Chem. Phys. 69 5064 (1978). 

H + H2 Quantum mechanical probabilities using the time-dependent wavepacket approach, J. Chem. Phys. 69 5064 (1978) J. C. Gray, G. A. Fraser, D. G. Truhlar, and K. C. Kulander, Quasiclassical trajectory and quantal wavepacket calculations for vibrational energy transfer at energies above the dissociation threshold,... 

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