Nonadiabatic quantum dynamics with MCTDH and CPMD
In this tutorial, the full nuclear quantum dynamics package MCTDH and the on-the-fly TDDFT-based trajectory surface hopping approach within the CPMD code will be used to fill a void in the training on nonadiabatic quantum dynamic, giving the opportunity to learn aboutthe fundamental theory of these processes and (especially) the available methodological andapplicative tools.
May 10, 2012 08:00 AM
May 12, 2012 06:00 PM
|Where||CECAM HQ, Lausanne|
|Contact Name||Ivano Tavernelli|
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In systems which contain multiple pathways and nuclear quantum effects, an explicit quantum treatment of the nuclear degrees of freedom is required. Multi Configuration Time Dependent Hartree, MCTDH is currently the method of choice, and can treat systems up to about 1000 degrees of freedom. However, the computational cost of such simulations and the requirement of an a priori knowledge of the potential energy surfaces (PESs) is often a limiting factor. On-the-fly calculation of the PESs with MCTDH formulation is now possible but is still in the early stages of development.
On-the-fly nonadiabatic dynamics with TDDFT potential energy surfaces
In many systems of interest quantum nuclear effects are small and therefore one can use the mixed quantum/classical approximation where electrons are treated at quantum mechanical level (using DFT and TDDFT), while the nuclei follow mainly classical trajectories on a surface (or average surface) determined by the nonadiabatic couplings. The most widely used approach for excited state dynamics using trajectories is Tully’s surface hopping (TSH). This scheme relies on the idea that a complete swarm of independent trajectories can reproduce the dynamics of the density probability of a nuclear wavepacket. Following Tully’s algorithm, trajectories are allowed to ”hop” between electronic surfaces reproducing therefore the splitting of the nuclear wavefunction. Many different implementations of trajectory surface hopping have been proposed, which differ mainly in the way PESs, forces, nonadiabatic couplings, etc. are computed. Within post Hartree Fock methods, multireference configuration interaction singles doubles (MR-CISD) has been successfully coupled to TSH. From the density functional theory side, linear response time-dependent density functional theory (LR-TDDFT) has become the method of choice to perform nonadiabatic dynamics. This method can be applied to the study of rather large system (up to several hundreds of atoms) at the cost of a (sometimes) less accurate description of the potential energy surfaces (see for example). An alternative approach to nonadiabatic dynamics is Ehrenfest dynamics. In this formulation, all quantities required for the dynamics are calculated as mean expectation values giving rise to a so called mean field type of dynamics. When coupled to TDDFT, Ehren- fest dynamics can be performed on-the-fly, the electrons being propagated according to the time-dependent Kohn-Sham equations and the nuclei moving on the corresponding time-dependent mean field electronic potential.