Quantum wave packets methods

In an alternative approach, exact (numerical) time-dependent quantum wave-packet methods have been employed since the early eighties of the last century to explore the d3mamics of ob-initio-haseA models of conical intersections, see Refs. 6-8 for reviews. It has been found by these calculations that the fundamental dissipative processes of population and phase relaxation at femtosecond time scales are clearly expressed already in fewmode systems, if a directly accessible conical intersection of the PE surfaces is involved. The results strongly support the idea that conical intersections provide the microscopic mechanism for ultrafast relaxation processes in polyatomic molecules. " More recently, these calculations have been extended to describe photodissociation and photoisomerization processes associated with conical intersections. The latter are particularly relevant for our understanding of the elementary mechanisms of photochemistry. 

Section 8.3 reports the applications of our developed nonadiabatic quantum wave packet methods and the adiabatic quantum wave packet method to the computation of rate constants of tri-atomic, tetra-atomic and polyatomic reactions. These include the rate constant computations for the nonadaibatic tri-atomic F(P3/2, Pi/2) + D2 (v = 0, y = 0) reactions and for the nonadiabatic tetra-atomic nonadiabatic 02(a A) - - 02(a A) quenching process and the rate constant computations for the adiabatic tri-atomic N( D) + H2(v = 0,7 = 0 5) reaction and for the adiabatic polyatomic F-f CH4 reaction. 

The following part of this section describes our recent advances in applying accurate quantum wave packet methods to compute rate constants and to understand nonadiabatic effects in tri-atomic and tetra-atomic molecular reactions. The quantum nonadiabatic approaches that we present here are based on solving the time-dependent Schrodinger equation formulated within an electronically diabatic representation. 

In this chapter we present the time-dependent quantum wave packet approaches that can be used to compute rate constants for both nonadiabatic and adiabatic chemical reactions. The emphasis is placed on our recently developed time-dependent quantum wave packet methods for dealing with nonadiabatic processes in tri-atomic and tetra-atomic reaction systems. Quantum wave packet studies and rate constants computations of nonadiabatic reaction processes have been dynamically achieved by implementing nuclear wave packet propagation on multiple electronic states, in combination with the coupled diabatic PESs constructed from ab initio calculations. To this end, newly developed propagators are incorporated into the solution of the time-dependent Schrodinger equation in matrix formulism. Applications of the nonadiabatic time-dependent wave packet approaches and the adiabatic ones to the rate constant computations of the nonadiabatic tri-atomic F (P3/2, P1/2) + D2 (v = 0,... 

Theory by Quantum Wave Packet Method 4.3.1 Overall Theory... 

Using DMBE IV potential, Meijer and coworkers carried out wavepacket calculations of the initial state selected total cross sections for the H + O2, including partial waves up to / = 35. All of the projections of J onto the intermolecular axis have been incorporated in the calculations. They found that the calculated cross sections are lower than the experiment, which indicated the deficiencies in the DMBE IV potentials. In 2005, Xu et al. constructed a new potential (XXZLG PES) for this reaction at the internally contracted multireference configuration interaction plus the Davidson correction level with the augmented correlation consistent polarized valence quadruple zeta (aug-cc-pVQZ) basis set. It has been shown that there is remarkable improvement over the previous DMBE IV potential. Based upon this new potential and using the recent developed RGB quantum wave packet method. Sun et al. calculated state-to-state DCS and ICS of the H + O2 reaction up to 1.5 eV. 

The atmospherically important reaction O -f O2 with three heavy atoms and deep potential well has also been studied at the state-to-state DCS level by quantum wave packet method. It reveals the failure of the statisical model from the calculated strong non-statistical effects and some quantum effects in the reaction [128]. 

After persistent endeavors of decades, the quantum wave packet method has been well developed and currently it is quite mature for calculating product state-resolved different cross sections of triatomic and tetra-atomic reactive scatterings. However, due to numerical scaling of a quantum calculation, in order to study more complicated systems, developments of more efficient numerical methods are still very important in the future, such as the search and develop more efficient grid representation for angular degree of freedom and more compact Hamiltonian forms etc. 

Cvitas M, Althorpe S (2(X)9) Quantum wave packet method for state-to-state reactive scattering calculations on AB -F CD ABC -F D reactions. J Chem Phys 113 4557... 

Garcia-Vela, A., Gerber, R. B. Hybrid quantum-semiclassical wave packet method for molecular dynamics Application to photolysis of Ar...HCl. J. Chem. Phys. 98 (1993) 427-43... 

The real wave packet (RWP) method, developed by Gray and Bahnt-Kuiti [ 1], is an approach for obtaining accurate quantum dynamics information. Unlike most wave packet methods [2] it utilizes only the real part of the generally complex-valued, time-evolving wave packet, and the effective Hamiltonian operator generating the dynamics is a certain function of the actual Hamiltonian operator of interest. Time steps in the RWP method are accomphshed by a simple three-term Chebyshev... 

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. 

To uniquely associate the unusual behavior of the collision observables with the existence of a reactive resonance, it is necessary to theoretically characterize the quantum state that gives rise to the Lorentzian profile in the partial cross sections. Using the method of SQ, it is possible to extract a Siegert state wavefunction from time-dependent quantum wave packets using the Fourier relation Eq. (28). The state obtained in this way for / = 0 is shown in Figure 3.7 this state is localized in the collinear F-H-D arrangement with three quanta of excitations in the asymmetric stretch... 

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 ... 

Goldfield, E.M. and Gray. S.K. (2002) A quantum dvnamics study of H2-rOH H2O-PH employing the Wu-Schatz-Lendvay-Fang-Hardiug potential function and a four-atom implementation of the real wave packet method. J. Cham. Phys. 117. 1604-1613. 

Abstract. Over the last deeade, advances in quantum dynamics, notably the development of the initial state selected time-dependent wave packet method, coupled with advances in constructing ab initio potential energy surfaces, have made it possible for some four-atom reactions to be addressed from first principles, in their full six internal degrees of freedom. Attempts have been made to extend the time-dependent wave packet method to reactions with more internal degrees of freedom. Here, we review the full-dimensional theory for the A + BCD four-atom reaction and use it to guide the reduced-dimensionality treatment of the X + YCZ3 reaction. Comparison of rigorous calculations with recent experiments are presented for (a) the benchmark H + H2O abstraction reaction, and (b) the H + CH4 H2 + CH3 reaction. 

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