MCTDH time-dependent Hartree method

To calculate numerically the quantum dynamics of the various cations in time-dependent domain, we shall use the multiconfiguration time-dependent Hartree method (MCTDH) [79-82, 113, 114]. This method for propagating multidimensional wave packets is one of the most powerful techniques currently available. For an overview of the capabilities and applications of the MCTDH method we refer to a recent book [114]. Additional insight into the vibronic dynamics can be achieved by performing time-independent calculations. To this end Lanczos algorithm [115,116] is a very suitable algorithm for our purposes because of the structural sparsity of the Hamiltonian secular matrix and the matrix-vector multiplication routine is very efficient to implement [6]. 

Full dimensional quantum dynamics calculations on polyatomic molecules will hopefully lead to a deeper understanding on molecule/surface interactions mechanisms, as the six-dimensional quantum dynamics calculations have already done for H2/metal surfaces. These kind of simulations are required to describe accurately processes involving the breaking of a X-R bond, beyond dissociation of CH4 on H and CH3. A description along the lines of the MCTDH (multi-configurational time-dependent Hartree) method would be worth exploring. For these polyatomic molecules, a better description of the molecule-lattice coupling is also desirable. 

If the PES are known, the time-dependent Schrbdinger equation, Eq. (1), can in principle be solved directly using what are termed wavepacket dynamics [15-18]. Here, a time-independent basis set expansion is used to represent the wavepacket and the Hamiltonian. The evolution is then carried by the expansion coefficients. While providing a complete description of the system dynamics, these methods are restricted to the study of typically 3-6 degrees of freedom. Even the highly efficient multiconfiguration time-dependent Hartree (MCTDH) method [19,20], which uses a time-dependent basis set expansion, can handle no more than 30 degrees of freedom. 

Multiconfiguration time-dependent Hartree (MCTDH) method, direct molecular dynamics ... 

M.H. Beck, et al.. The multiconfiguration time-dependent Hartree (MCTDH) method A highly efficient algorithm for propagating wavepackets, Phys. Rep.-Rev. Seet. Phys. Lett. 324 (1) (2000)... 

The Multiconfiguration Time-Dependent Hartree (MCTDH) Method... 

Beck, M.H., Jackie, A., Worth, G.A. and Meyer, H.D. (2000) The multiconfigurational time-dependent Hartree (MCTDH) method a highly efficient algorithm for propagating wavepackets, P/ryi. Rep. 324,1-105 and references therein. 

The methodology of molecular quantum dynamics applied to non-adiabatic systems is presented from a time-dependent perspective in Chap. 4. The representation of the molecular Hamiltonian is first discussed, with a focus on the choice of the coordinates to parametrize the nuclear motion and on the discrete variable representation. The multi-configuration time-dependent Hartree (MCTDH) method for the solution of the time-dependent Schrddinger equation is then presented. The chapter ends with a presentation of the vibronic coupling model of Kdppel, Domcke and Cederbaum and the methodology used in the calculation of absorption spectra. 

Ndengue SA, Gatti F, Schinke R, Meyer H-D, lost R (2010) Absorption cross section of ozone Isotopologues calculated with the multiconflguration time-dependent Hartree (MCTDH) method I. The Hartley and Huggins bands. J Phys Chem A 114 9855-9863... 

Low-dimensional quantum dynamics studies of the dissociative adsorption of CH4 on Ni(l 11), as a function of the vibrational initial state, have also been carried out [52]. In this case, quantum dynamics simulations were performed using the multiconflguration time-dependent Hartree (MCTDH) method [1], Results obtained from this study are similar to those obtained for Ni(lOO) the efficacies of the stretching modes are larger than those of the bending modes, also in good agreement with experiments. 

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