Wavepacket theory sections

In this section, the basic theory of molecular dynamics is presented. Starting from the BO approximation to the nuclear Schrddinger equation, the picture of nuclear dynamics is that of an evolving wavepacket. As this picture may be unusual to readers used to thinking about nuclei as classical particles, a few prototypical examples are shown. 

The initial wavepacket, described in Section III.B is intrinsically complex (in the mathematical sense). Furthermore, the solution of the time-dependent Schrodinger equation [Eq. (4.23)] also involves an intrinsically complex time evolution operator, exp(—/Ht/ ). It therefore seems reasonable to assume that aU the numerical operations involved with generating and analyzing the time-dependent wavefunction will involve complex arithmetic. It therefore comes as a surprise to realize that this is in fact not the case and that nearly all aspects of the calculation can be performed using entirely real wavefunctions and real arithmetic. The theory of the real wavepacket method described in this section has been developed by S. K. Gray and the author [133]. 

The first part of the review deals with aspects of photodissociation theory and the second, with reactive scattering theory. Three appendix sections are devoted to important technical details of photodissociation theory, namely, the detailed form of the parity-adapted body-fixed scattering wavefunction needed to analyze the asymptotic wavefunction in photodissociation theory, the definition of the initial wavepacket in photodissociation theory and its relationship to the initial bound-state wavepacket, and finally the theory of differential state-specific photo-fragmentation cross sections. Many of the details developed in these appendix sections are also relevant to the theory of reactive scattering. 

If the individual wavepacket solutions of the present theory could be superimposed, this would imply that the field vectors become multivalued at every point inside the photon beam. The individual photon fields would then have to cancel each other. This implies that the axisymmetric small-scale wavepacket solution of Section VII does not apply and cannot satisfy the basic Eqs. (l)-(8) in the case of a nearly plane (one-dimensional) and broad photon-dense beam configuration. 

We used short broadband pump pulses (spectral width 200 cm 1, pulse duration 130 fs FWHM) to excite impulsively the section of the NH absorption spectrum which includes the ffec-exciton peak and the first three satellite peaks [4], The transient absorbance change signal shows pronounced oscillations that persist up to about 15ps and contain two distinct frequency components whose temperature dependence and frequencies match perfectly with two phonon bands in the non-resonant electronic Raman spectrum of ACN [3] (Fig. 2a, b). Therefore the oscillations are assigned to the excitation of phonon wavepackets in the ground state. The corresponding excitation process is only possible if the phonon modes are coupled to the NH mode. Self trapping theory says that these are the phonon modes, which induce the self localization. 

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 the time-independent approach one has to calculate all partial cross sections before the total cross section can be evaluated. The partial photodissociation cross sections contain all the desired information and the total cross section can be considered as a less interesting by-product. In the time-dependent approach, on the other hand, one usually first calculates the absorption spectrum by means of the Fourier transformation of the autocorrelation function. The final state distributions for any energy are, in principle, contained in the wavepacket and can be extracted if desired. The time-independent theory favors the state-resolved partial cross sections whereas the time-dependent theory emphasizes the spectrum, i.e., the total absorption cross section. If the spectrum is the main observable, the time-dependent technique is certainly the method of choice. 

Figure 13. Schematic sketch of a reactive NeNePo control experiment. Control is achieved through two time- and frequency-shifted photodetachment laser pulses employing an anion excited state (M ) for intermediate wavepacket propagation. The wavepacket is finally prepared on the neutral potential energy surface in a region that corresponds to enhanced reactivity of the system. The aim of the experiment and theory is to find optimal composite pulses, based on the concept of the intermediate target outlined in Section III.A, that accomplish such a reactive activation of M . Detection is performed by ionization of the potential reaction products of MO to the cationic state (not shown in the graphic).

In Sec. 3.3 we have shown how the nuclear wavepacket d3mamics on a single electronic state can be tracked in real-time with use of the time-resolved photoelectron spectroscopy. Here in this section we extend the theory to cope with nonadiabatic d3mamics and explore how the associated wavepacket bifurcation can be observed in this spectroscopy. 

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