Multiconfiguration time-dependent Hartree MCTDH method, quantum

Meyer HD, Worth GA (2003) Quantum molecular dynamics propagating wavepackets and density operators using the multiconfiguration time-dependent Hartree (MCTDH) method. Theor Chem Acc 109 251-267... 

The three-pulse EOM-PMA can be formulated not only in terms of density matrices and master equations but also in terms of wavefunctions and Schrodinger equations [29]. The EOM-PMA can therefore be straightforwardly incorporated into computer programs which provide the time evolution of the density matrix or the wavefunction of material systems. Besides the multilevel Redlield theory, the EOM-PMA can be combined with the Lindblad master equation [49], the surrogate Hamiltonian approach [49], the stochastic Liouville equation [18], the quantum Fokker-Planck equation [18], and the density matrix [50] or the wavefunction [14] multiconfigurational time-dependent Hartree (MCTDH) methods. When using the... 

In our computational work, on which the following numerical analysis is based, the multiconfiguration time-dependent Hartree (MCTDH) method is used [18-20]. This method is, the only one at present, which can propagate the multidimensional wave packet and treat the multi-mode quantum dynamics of polyatomic systems with controllable accuracy up to 20-30 modes. 

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]. 

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