Multi-configuration time-dependent Hartree

Meyer, H.-D., Manthe, U., and Cederbaum, L.S. (1990). The multi-configurational time-dependent Hartree approach, Chem. Phys. Lett. 165, 73-78. 

A. Capellini, A.P. Jansen, Convergence study of multi-configuration time-dependent Hartree simulations H2 scattering from LiF(OOl), J. Chem. Phys., 104 (1996) 3366. 

The Hamiltonian in Eq. (4.1) has an almost product-like form since the majority of coordinates are treated as harmonic oscillators. This makes it rather suitable for quantum dynamics simulations, either in the time-dependent Hartree approximation [31] or using the more general multi-configuration time-dependent Hartree approach [36, 37]. 

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... 

When considering the femtosecond photoionization dynamics of complex systems, a completely exact evaluation of the time and energy resolved photoelectron spectrum is often not really necessary. Approximative schemes which require significantly lower computational effort are valuable in such cases. Within the nonperturbative formalism, Meier et al. have proposed an efficient computational scheme which incorporates the multi-configuration time-dependent Hartree method.An approximate method which is based on a classical-trajectory description of the nuclear dynamics has been elaborated by Hartmann, Heidenreich, Bonacic-Koutecky and coworkers and applied, among other systems,to the time-resolved photoionization spectroscopy of conical intersections in sodium fluoride clusters. 

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. 

M. Sala, F. Gatti and S. Guerin, Coherent destruction of tunneling in a six-dimensional model of NHD2 a computational study using the multi-configuration time-dependent Hartree method , J. Chem. Phys. 141, 164326 (2014)... 

Hammer T, Manthe U (2011) Intramolecular proton transferin malonaldehyde Accurate multilayer multi-configurational time-dependent Hartree calculations. J Chem Phys 134 224305... 

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. 

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. 

The multi-configurational time-dependent Hartree approach... 

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

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