Multiconfiguration 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]. 

Meyer, H.D. and Worth, G.A., Quantum molecular dynamics propagating wave-packets and density operators using the multiconfiguration time-dependent Hartree method, Theor. Chem. Acc., 109, 251-267, 2003. 

Joubert Doriol L, Gatti F, lung C, Meyer H-D (2008) Computation of vibrational energy levels and eigenstates of fluoroform using the multiconfiguration time-dependent Hartree method. J Chem Phys 129 224109... 

Beck MH, Jackie A, Worth GA, Meyer HD (2000) The multiconfiguration time-dependent Hartree method a highly efScient algorithm for propagating wavepackets. Phys Rep 324 1... 

Meyer H-D (2012) Studying molecular quantum dyntimics with the multiconfiguration time-dependent Hartree method. Whey Intentiscip Rev Comput Mol Sci 2 351... 

Vendrell O, Meyer H-D (2011) Multilayer multiconfiguration time-dependent Hartree method implementation and applications to a Henon-Heiles Hamiltonian and to pyrazine. J Chem Phys 134 044135... 

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... 

Multiconfigurational time-dependent Hartree-Fock method Semiclassical 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. 

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