Time-dependent quantum-mechanical

Leforestier C et ak 1991 Time-dependent quantum mechanical methods for molecular dynamics J. Comput. Phys. 94 59-80... 

Time-dependent quantum mechanical calcnlations have also been perfomied to study the HCO resonance states [90,91]. The resonance energies, linewidths and quantum number assigmnents detemiined from these calcnlations are in excellent agreement with the experimental results. 

In time-dependent quantum mechanics, vibrational motion may be described as the motion of the wave packet... 

Section II discusses the real wave packet propagation method we have found useful for the description of several three- and four-atom problems. As with many other wave packet or time-dependent quantum mechanical methods, as well as iterative diagonalization procedures for time-independent problems, repeated actions of a Hamiltonian matrix on a vector represent the major computational bottleneck of the method. Section III discusses relevant issues concerning the efficient numerical representation of the wave packet and the action of the Hamiltonian matrix on a vector in four-atom dynamics problems. Similar considerations apply to problems with fewer or more atoms. Problems involving four or more atoms can be computationally very taxing. Modern (parallel) computer architectures can be exploited to reduce the physical time to solution and Section IV discusses some parallel algorithms we have developed. Section V presents our concluding remarks. 

The RWP method also has features in common with several other accurate, iterative approaches to quantum dynamics, most notably Mandelshtam and Taylor s damped Chebyshev expansion of the time-independent Green s operator [4], Kouri and co-workers time-independent wave packet method [5], and Chen and Guo s Chebyshev propagator [6]. Kroes and Neuhauser also implemented damped Chebyshev iterations in the time-independent wave packet context for a challenging surface scattering calculation [7]. The main strength of the RWP method is that it is derived explicitly within the framework of time-dependent quantum mechanics and allows one to make connections or interpretations that might not be as evident with the other approaches. For example, as will be shown in Section IIB, it is possible to relate the basic iteration step to an actual physical time step. 

G. C. Schatz and M. A. Ratner (1993) Quantum Mechanics in Chemistry (Prentice-Hall, Englewood Cliffs, NJ). An advanced text emphasizing molecular symmetry and rotations, time-dependent quantum mechanics, collisions and rate processes, correlation functions, and density matrices. 

Prepared State by a Time-Dependent Quantum Mechanical Method. 

R. Kosloff,/. Pbys. Cbem., 92, 2087 (1988). Time-Dependent Quantum-Mechanical Meth-... 

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... 

Application of time-dependent quantum mechanical theory then gives the rate of the change. 

A second concern for quantum mechanical models of electron-transfer is the level at which the model is constructed. There is a wide-range of possibilities, ranging from Hiickel and tight binding models which can be used for qualitative reasoning, to sophisticated ab initio methods. Likewise, time-dependent studies can be made with classical molecular dynamics (MD) simulations, or time-dependent quantum mechanical calculations. 

B. Maiti, S. Mahapatra, N. Sathyamurthy, A time-dependent quantum mechanical investigation of dynamical resonances in three-dimensional HeH) and HeHD+ systems, J. Chem. Phys. 113 (2000) 59. 

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,... 

Das, S., and Tannor, D.J. (1990). Time dependent quantum mechanics using picosecond time steps Application to predissociation of Hel2, J. Chem. Phys. 92, 3403-3409. 

Dixon, R.N., Marston, C.C., and Balint-Kurti, G.G. (1990). Photodissociation dynamics and emission spectroscopy of H2S in its first absorption band A time dependent quantum mechanical study, J. Chem. Phys. 93, 6520-6534. 

Sawada, S.-I., Heather, R., Jackson, B., and Metiu, H. (1985). A strategy for time dependent quantum mechanical calculations using a Gaussian wave packet representation of the wave function, J. Chem. Phys. 83, 3009-3027. 

The general theory for the absorption of light and its extension to photodissociation is outlined in Chapter 2. Chapters 3-5 summarize the basic theoretical tools, namely the time-independent and the time-dependent quantum mechanical theories as well as the classical trajectory picture of photodissociation. The two fundamental types of photofragmentation — direct and indirect photodissociation — will be elucidated in Chapters 6 and 7, and in Chapter 8 I will focus attention on some intermediate cases, which are neither truly direct nor indirect. Chapters 9-11 consider in detail the internal quantum state distributions of the fragment molecules which contain a wealth of information on the dissociation dynamics. Some related and more advanced topics such as the dissociation of van der Waals molecules, dissociation of vibrationally excited molecules, emission during dissociation, and nonadiabatic effects are discussed in Chapters 12-15. Finally, we consider briefly in Chapter 16 the most recent class of experiments, i.e., the photodissociation with laser pulses in the femtosecond range, which allows the study of the evolution of the molecular system in real time. 

Molecular time-dependent quantum mechanics, typically called Quantum Dynamics (QD),... 

Time-Dependent Quantum-Mechanical Spectral Analysis 149... 

TIME-DEPENDENT QUANTUM-MECHANICAL SPECTRAL ANALYSIS... 

These results were obtained by using the time-dependent quantum mechanical evolution of a state vector. We have generalized these to non-equilibrium situations [16] with the given initial state in a thermodynamic equilibrium state. This theory employs the density matrix which obeys the von Neumann equation. To incorporate the thermodynamic initial condition along with the von Neumann equation, it is advantageous to go to Liouville (L) space instead of the Hilbert (H) space in which DFT is formulated. This L-space quantum theory was developed by Umezawa over the last 25 years. We have adopted this theory to set up a new action principle which leads to the von Neumann equation. Appropriate variants of the theorems above are deduced in this framework. 

The time evolution of molecular systems - i.e. systems containing particles of atomic dimensions ( electrons, nuclei etc) - can be adequately described within the framework of time-dependent quantum mechanics. All information about the system is contained in the time dependent wave function 0(r,r2,...,rN t) wherein the Ti are the position vectors (possibly containing also a spin component) for the i-th particle and t is the time. The wave function is a solution of the time-dependent Schrodinger equation... 

Blinder, S. M. (1974). Foundations of Quantum Dynamics, Academic Press, London. The author s earlier monograph on the fundamental principles of time-dependent quantum mechanics, including transitions and time-dependent perturbation theory. 

Balakrishnan, N., Kalyanaranian, C. and Sathr-amurthy, N. (1997) Time-dependent quantum mechanical approach to reactive scattering and related processes Phys. Repts.-Review section of Phy.sics Letters 280. 80-144. 

In order to understand how proton NMR of polymers may be used as presented in the current chapter, it is useful to remind ourselves of some of the results of the formalism used in describing the time-dependent quantum mechanics of spin which are not so well understood by those familiar with only the rudimentary pulse NMR experiment. We do so in Section 6.1.2. In Section 6.1.3, examples are given of the uses of the mechanics outlined in Section 6.1.2 to provide information about chemical functionality, motion... 

The explicit development of the time-dependent quantum mechanics necessary for the present chapter has been presented previously. The reader is referred to those sourees [1, 8] as well as in Chapters 2 and 3 of the current volume for the full development. However, for the purpose of self-consistency, and for the intended audience of this chapter, a terse summary of the results necessary for clarification of later sections is presented in the hope that the basic ideas and results obtained using them, if not understandable in detail, may be seen at least as believable possibilities. 

Review of the time-dependent quantum mechanics of spins... 

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... 

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