Multiconfiguration time-dependent Hartree MCTDH method

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. 

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... 

Wavepacket calculations at r = 0 K were carried out for the combined 4-mode subsystem plus 20-mode bath, using the multiconfiguration time-dependent Hartree (MCTDH) method [51-53]. The explicit representation of all bath modes is not a necessity (and, in fact, the general method is designed so as to treat only the effective modes explicitly) however, an explicit wavepacket dynamics for all modes is convenient to demonstrate the convergence of the procedure for a zero-temperature system. In Refs. [32,33], we have shown that explicit calculations for high-dimensional system-plus-bath wavefunctions are in excellent agreement with reduced density matrix calculations. 

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. 

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