Quantum wavepacket dynamics

A further model Hamiltonian that is tailored for the treatment of non-adiabatic systems is the vibronic coupling (VC) model of Koppel et al. [65]. This provides an analytic expression for PES coupled by non-adiabatic effects, which can be fitted to ab initio calculations using only a few data points. As a result, it is a useful tool in the description of photochemical systems. It is also very useful in the development of dynamics methods, as it provides realistic global surfaces that can be used both for exact quantum wavepacket dynamics and more approximate methods. 

In this section we show with full quantum wavepacket dynamics on coupled ab initio potential energy surfaces how a conical intersection can be transformed into an avoided crossing at the geometry of the conical intersection by externally breaking its symmetry, the idea developed in Sec. 5.3.3. The population transfer through the conical intersection in NO2 can be significantly suppressed using a phase-controlled far-infrared pulse. 

To investigate possible detection of the history of sequential transitions between electronic states by a pulse train with time-resolved femtosecond photoelectron spectroscopy, we compute the quantum wavepacket dynamics of the LiH system. The LiH system is suited for our purpose of studying time evolution of electronic interaction in that (1) the lowest excited state... 

To avoid unnecessary complexity and confusion, we here study an illustrative two-state nonadiabatic quantum wavepacket dynamics, the adiabatic potential functions of which are drawn in Fig. 6.17. 

Thus this book describes the recent theories of chemical dynamics beyond the Born-Oppenheimer framework from a fundamental perspective of quantum wavepacket dynamics. To formulate these issues on a clear theoretical basis and to develop the novel theories beyond the Born-Oppenheimer approximation, however, we should first learn a basic classical and quantum nuclear dynamics on an adiabatic (the Born-Oppenheimer) potential energy surface. So we learn much from the classic theories of nonadiabatic transition such as the Landau-Zener theory and its variants. 

Marquardt R, Quack M, Stohner J and Sutcliffe E 1986 Quantum-mechanical wavepacket dynamics of the CH group in the symmetric top XgCH compounds using effective Hamiltonians from high-resolution spectroscopy J. Chem. Soc., Faraday Trans. 2 82 1173-87... 

Full quantum wavepacket studies on large molecules are impossible. This is not only due to the scaling of the method (exponential with the number of degrees of freedom), but also due to the difficulties of obtaining accurate functions of the coupled PES, which are required as analytic functions. Direct dynamics studies of photochemical systems bypass this latter problem by calculating the PES on-the-fly as it is required, and only where it is required. This is an exciting new field, which requires a synthesis of two existing branches of theoretical chemistry—electronic structure theory (quantum chemistiy) and mixed nuclear dynamics methods (quantum-semiclassical). 

One can also ask about the relationship of the FMS method, as opposed to AIMS, with other wavepacket and semiclassical nonadiabatic dynamics methods. We first compare FMS to previous methods in cases where there is no spawning, and then proceed to compare with previous methods for nonadiabatic dynamics. We stress that we have always allowed for spawning in our applications of the method, and indeed the whole point of the FMS method is to address problems where localized nuclear quantum mechanical effects are important. Nevertheless, it is useful to place the method in context by asking how it relates to previous methods in the absence of its adaptive basis set character. There have been many attempts to use Gaussian basis functions in wavepacket dynamics, and we cannot mention all of these. Instead, we limit ourselves to those methods that we feel are most closely related to FMS, with apologies to those that are not included. A nice review that covers some of the... 

Heller, E. J. (1991), Wavepacket Dynamics and Quantum Chaology, in Chaos and Quantum Physics, M.-J. Giannoni et al. (Eds.) Elsevier. 

Figure 14. (a) Potential-energy surfaces, with a trajectory showing the coherent vibrational motion as the diatom separates from the I atom. Two snapshots of the wavepacket motion (quantum molecular dynamics calculations) are shown for the same reaction at / = 0 and t = 600 fs. (b) Femtosecond dynamics of barrier reactions, IHgl system. Experimental observations of the vibrational (femtosecond) and rotational (picosecond) motions for the barrier (saddle-point transition state) descent, [IHgl] - Hgl(vib, rot) + I, are shown. The vibrational coherence in the reaction trajectories (oscillations) is observed in both polarizations of FTS. The rotational orientation can be seen in the decay of FTS spectra (parallel) and buildup of FTS (perpendicular) as the Hgl rotates during bond breakage (bottom). 

Long progressions of feature states in the two Franck-Condon active vibrational modes (CC stretch and /rani-bend) contain information about wavepacket dynamics in a two dimensional configuration space. Each feature state actually corresponds to a polyad, which is specified by three approximately conserved vibrational quantum numbers (the polyad quantum numbers nslretch, "resonance, and /total, [ r, res,fl)> and every symmetry accessible polyad is initially illuminated by exactly one a priori known Franck-Condon bright state. 

In Fig. 2 we compare results using e = 0.4 for the two mixed quantum-classical methods outlined in this chapter with exact results obtained from MCTDH wavepacket dynamics calculations. To make a reliable comparison the approximate finite temperature calculations were performed at very low temperatures (/ = 25), though a product of ground state wave functions for the independent harmonic oscillator modes could have been used to make the initial conditions identical to those used in the MCTDH calculations. 

The Study of Dynamically Averaged Vibrational Spectroscopy of Atmospherically Relevant Clusters Using Ab Initio Molecular Dynamics in Conjunction with Quantum Wavepackets... 

The ab initio atom-centered density matrix propagation (ADMP) and the quantum wavepacket ab initio molecular dynamics (QWAIMD) computational methods are briefly described. Studies on vibrational and electronic properties obtained utilizing these methods are highlighted. 

This article is organized as follows. In Section 2 ab initio molecular dynamics methods are described. Specifically, in Section 2.1 we discuss the extended Lagrangian atom-centered density matrix (ADMP) technique for simultaneous dynamics of electrons and nuclei in large clusters, and in Section 2.2 we discuss the quantum wavepacket ab initio molecular dynamics (QWAIMD) method. Simulations conducted and new insights obtained from using these approaches are discussed in Section 3 and the concluding remarks are given in Section 4. 

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