Multiconfiguration time-dependent

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 ... 

Figure 9.1 displays the computed J(t), and 2(0 for the first 100 fs, according to Ref. [30]. The J(t) plot is in excellent agreement with the equivalent multiconfiguration time- dependent Hartree results shown in Figure 6 of Ref [58], with any small differences arising from the use of only 176 basis states in the Q-space, for the reasons discussed earlier. 

Kotler, Z., Nitzan, A., and Kosloff, R. (1988). Multiconfiguration time-dependent self-consistent field approximation for curve crossing in presence of a bath. A fast Fourier transform study, Chem. Phys. Lett. 153, 483-489. 

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)... 

U. Manthe, H.-D. Meyer and L.S. Cederbaum, Multiconfiguration time dependent Hartree study of complex dynamics Photodissociation of NO2, J. Chem. Phys., 97 (1992) 9062. 

A. Jackie and H.-D. Meyer, Reactive scattering using the multiconfiguration time-dependent Hartee approximation General aspects and application to the collinear H+H2 -> H2+H reaction, J. Chem. Phys., 102 (1995) 5605. 

A.P. Jansen, A multiconfiguration time-dependent Hartree approximation based on natural single-particle states, J. Chem. Phys., 99 (1993) 4055. 

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

Trin, J., M. Monnerville, B. Pouilly, and H. D. Meyer 2003, Photodissociation of the ArHBr complex investigated with the multiconfiguration time-dependent Hartree approach . J. Chem. Phys. 118, 600 609. 

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]. 

The Multiconfiguration Time-Dependent Hartree (MCTDH) Method... 

Multiconfigurational time-dependent Hartree-Fock method Semiclassical method... 

There are two possible approaches to solution of the Schrbdinger equation with the model Hamiltonian (9.3). The first is based on direct solution using grid [17] and basis [18] methods or the so-called multiconfiguration time-dependent Har-tree method [19]. (The latter method is a combination of grid and basis set methods in the sense that the time-dependent basis functions are represented on a suitable grid). The second approach uses a Bom-Oppenheimer type separation between the motions of the light and heavy nuclei (the method of adiabatic separation between vibrational variables) [20]. In the second approach the wave function F(s,R) is written as ... 

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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