Multi-configuration time-dependent Hartree MCTDH

For the H+CH4 -F H2+CH3[20] and O+CH4 —i OH+CH3[21] reactions, accurate Multi Configurational Time Dependent Hartree (MCTDH) calculations have been performed. These calculations include all vibrational modes and are for a total angular momentum J = 0. The ffux correlation function fornialism[68, 69, 70] was employed to calculate cumulative reaction probabilities for J — 0,... 

The multi-configuration time-dependent Hartree (MCTDH) method combines the benefits of these two extremes. As the name... 

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. 

Usually, the propagator (7(r, to) is approximated by various schemes [55,60,137], and there are plenty of wonderful articles that have explained each in detail, such as the split operator method and higher order split operator methods [11, 36, 130], Chebyshev polynomial expansion [131], Faber polynomial expansion [51, 146], short iterative Lanczos propagation method [95], Crank-Nicholson second-order differencing [10,56,57], symplectic method [14,45], recently proposed real Chebyshev method [24,44,125], and Multi-configuration Time-Dependent Hartree (MCTDH) Method [ 12,73,81-83]. For details, one may refer to the corresponding references. 

In the multi-configurational time-dependent Hartree (MCTDH) approach [24, 25], the wavefunction V (xi,. .,Xf,t) is represented as... 

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. 

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