Wave packet calculations

FIdthmann H, Beck C, Schinke R, Woywod C and Domcke W 1997 Photodissociation of ozone in the Chappuis band. II. Time-dependent wave packet calculations and interpretation of diffuse vibrational... 

We now illustrate the utility of Eq. (27) in relating the RWP dynamics based on the arccosine mapping, Eq. (16), to the usual time-dependent Schrodinger equation dynamics, Eq. (1). We carried out three-dimensional (total angular momentum 7 = 0) wave packet calculations for the... 

Six-dimensional, numerically accurate four-atom wave packet calculations were pioneered by Zhang and Zhang [17] and Neuhauser [18]. While numerous details of the present RWP implementation differ from these earlier approaches, it should be noted that many of the general ideas remain the same. In applications, finite-sized grids and basis sets are introduced to describe the wave packet, and... 

Gray and Wozny [101, 102] later disclosed the role of quantum interference in the vibrational predissociation of He Cl2(B, v, n = 0) and Ne Cl2(B, v, = 0) using three-dimensional wave packet calculations. Their results revealed that the high / tail for the VP product distribution of Ne Cl2(B, v ) was consistent with the final-state interactions during predissociation of the complex, while the node at in the He Cl2(B, v )Av = — 1 rotational distribution could only be accounted for through interference effects. They also implemented this model in calculations of the VP from the T-shaped He I C1(B, v = 3, n = 0) intermolecular level forming He+ I C1(B, v = 2) products [101]. The calculated I C1(B, v = 2,/) product state distribution remarkably resembles the distribution obtained by our group, open circles in Fig. 12(b). 

Times in Wave Packet Calculations on Scattering with Resonances A Hybrid Approach Involving the Lanczos Method. 

L.B. Madsen, L.A.A. Nikolopoulos, T.K. Kjeldsen, J. Fernandez, Extracting continuum information from I (l) in time-dependent wave-packet calculations, Phys. Rev. A 76 (2007) 063407. 

The reliability of high-dimensional quantum calculations based on ab initio potential energy surfaces is also demonstrated in Fig. 6, where the sticking probability of H2/Cu(l 0 0) obtained by sixdimensional wave packet calculations [32] is compared to experimental results derived from an analysis of adsorption and desorption experiments [27]. The measured experimental sticking probabilities and, via the principle of detailed balance, also desorption distributions had been fitted to the following analytical form of the vibrationally resolved sticking probability as a function of the kinetic energy ... 

These low-dimensional wave packet calculations have provided a qualitative explanation for the bimodality found experimentally in the velocity distribution of desorbing molecules [126]. The specific shape of the excited state PES leads to a bifurcation of the wave function in the excited state. The two parts of the wave function desorb with different mean velocities thus reproducing the bimodality. 

D. Chasman, R. J. Silbey, and M. Eisenberg, Chem. Phys. Lett., 175, 633 (1990). Massively Parallel Time-Dependent Wave-Packet Calculations in a Classically Chaotic Potential. 

Again, different PSD s result from different initial wave packets. Equation (56) can be used not only in wave packet calculations, but also, after simple modifications, in any other iterative scheme. One has to ensure, however, that the observation point R = i oo lies outside the interaction region and outside the region of non-zero absorbing potential. 

As has been mentioned above, a new method for the treatment of the dynamics of mixed classical quantum system has been recently suggested by Jung-wirth and Gerber [50,51]. The method uses the classically based separable potential (CSP) approximation, in which classically molecular dynamics simulations are used to determine an effective time-dependent separable potential for each mode, then followed by quantum wave packet calculations using these potentials. The CSP scheme starts with "sampling" the initial quantum state of the system by a set of classical coordinates and momenta which serve as initial values for MD simulations. For each set j (j=l,2,...,n) of initial conditions a classical trajectory [q (t), q 2(t),..., q N(t)] is generated, and a separable time-dependent effective potential V (qj, t) is then constructed for each mode i (i=l,2,...,N) in the following way ... 

Ghappuis band. II. Time-dependent wave packet calculations and interpretation of diffuse vibrational... 

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). 

Recently, there has been a renewed interest in the de Broglie-Bohm formulation of quantum mechanics as a numerical tool to perform multidimensional wave packet calculations [13-15]. It has also been used to visualize the motion of quantum mechanical wave packets by trajectories and to study the transition from quantum mechanics to classical mechanics [16-18]. Carlsen and Goscinski [16], for instance, have studied fractional and full revivals of circular Rydberg wave packets in the hydrogen atoms using this formulation. 

In early theoretical studies the photodissociation of CH3I was treated as an effective two-mode system with CH3 considered as one particle. As with ICN, a new era began with ab initio calculations performed by Morokuma and coworkers on a reasonably high level of electronic structure theory. These authors determined six- and nine-dimensional adiabatic and diabatic PESs, which were used in classical surface hopping trajectory calculations. Hammerich et al. performed large-scale five-dimensional wave packet calculations using these PESs. As concluded by Eppink and Parker One caveat of the ab initio surfaces is that they do not successfully reproduce the experimental absorption spectrum, which peaks to the red side of and is broader than the spectrum predicted by the theoretical treatments.. .. Furthermore, the predicted I quantum yields of the most... 

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. 

Derivation of Rate Constants from Quantum Wave Packet Calculation... 

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