Multiconfiguration time-dependent Hartree dynamics

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 ... 

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. 

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]. 

Joubert-Doriol L, Lasome B, Gatti F, Schroder M, Vendrell O, Meyer H-D (2012) Suitable coordinates for quantum dynamics applications using the multiconfiguration time-dependent Hartree (MCTDH) algorithm. Comput Theor Chem 990 75-89 Chemical reactivity, from accurate theories to simple models, in honor of Professor Jean-Claude Rayez... 

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. 

Chapter 3 treats nuclear motions on the adiabatic potential energy surfaces (PES). One of the most powerful and simplest means to study chemical dynamics is the so-called ab initio molecular dynamics (or the first principle dynamics), in which nuclear motion is described in terms of the Newtonian d3mamics on an ab initio PES. Next, we review some of the representative time-dependent quantum theory for nuclear wavepackets such as the multiconfigurational time-dependent Hartree approach. Then, we show how such nuclear wavepacket d3mamics of femtosecond time scale can be directly observed with pump>-probe photoelectron spectroscopy. 

Giri K, Chapman E, Sanz CS, Worth G (2011) A full-dimensional coupled-surface study of the photodissociation dynamics of ammonia using the multiconfiguration time-dependent Hartree method. J Chem Phys 135 044311... 

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. 

Classical Dynamics of Nonequilibrium Processes in Fluids Integrating the Classical Equations of Motion Control of Microworld Chemical and Physical Processes Mixed Quantum-Classical Methods Multiphoton Excitation Non-adiabatic Derivative Couplings Photochemistry Rates of Chemical Reactions Reactive Scattering of Polyatomic Molecules Spectroscopy Computational Methods State to State Reactive Scattering Statistical Adiabatic Channel Models Time-dependent Multiconfigurational Hartree Method Trajectory Simulations of Molecular Collisions Classical Treatment Transition State Theory Unimolecular Reaction Dynamics Valence Bond Curve Crossing Models Vibrational Energy Level Calculations Vibronic Dynamics in Polyatomic Molecules Wave Packets. 

Electron-Molecule Scattering Mixed Quantum-Classical Methods Path Integral Methods Photodissociation Dynamics Rates of Chemical Reactions Reaction Path Hamiltonian and its Use for Investigating Reaction Mechanisms Reactive Scattering of Polyatomic Molecules Time-dependent Multiconfigurational Hartree Method. 

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