Tutorial on SHARC

For the last workshop of the year, the university of Vienna was chosen as the host for the workshop on excited state dynamics with emphasis on the use and basic principles underlying the molecular dynamics package SHARC.

SHARC stands for Surface Hopping including Arbitrary Couplings is developed in the González group, which also organized the workshop. Undergraduate courses on quantum chemistry typically focus on different approaches to solve the time-independent electronic Schrödinger equation (TISE), where only a parametric dependence of the wavefunction on the nuclear coordinates is assumed. Additionally the kinetic energy operator for the nuclei is not considered. Nevertheless chemical reactions involve the motion of atoms and molecules. In the case of photochemical reactions, this process is triggered by photoexcitation of the system into an excited state. These time-dependent phenomena cannot be described by the TISE and so the time-dependent Schrödinger equations (TDSE) needs to be solved.

From a mathematical perspective, the time-dependent Schrödinger equation is an initial value problem, which is much easier to solve than the eigenvalue problem of the TISE. The TDSE can be solved numerically to perform full quantum dynamics. The state of the art method to do this is the so-called multi-configurational time-dependent Hartree Method (MCTDH) developed by Meyer and Manthe. But full quantum dynamics is computationally very demanding, even by using MCTDH, which takes advantage of a lot of tricks to reduce the computational costs. Therefore only the MCTDH Method can only be applied to systems, that have only a few nuclear degrees of freedom and with only a very limited number of important excited states. As a consequence more approximate methods are needed to treat larger systems. The main topic of the workshop was hereby the surface hopping approach, a hybrid approach, where the nuclei are treated as particles that follow the classical equation of motions, while the electrons are treated full quantum mechanically. In the first sessions basic concepts of photochemistry were presented and ways to solve the timedependent Schrödinger equation were revisited. The main focus was on the accurate description of excited states. Afterwards a closer look was taken on the visualisation and interpretation of the output of excited state calculations, with a main focus on the interpretation of properties of the electronic wavefunction. In this context the program suit TheoDORE (Theoretical Density, Orbital Relaxation and Exciton analysis) was introduced and its many options for the analysis of excited states. The second day was entirely devoted to explore different types of dynamics, starting by classical and semi-classical methods and arriving at full quantum dynamics. After this general overview the third and forth days were purely dedicated to surface hopping, as the main topic of the course. In this context Tully’s fewest switches method was discussed, as well as the difference with respect to the method used in the SHARC program. At this point the focus was on different representations of the potential hypersurfaces, on which the nuclei move. Hands on session were a good occasion for the attendants to gain experience with SHARC program suite and to see how SHARC works in practice, from the setting of the different trajectories to the analysis of the output.

To complete the picture on excited state dynamics, different invited speakers presented their approaches on the fifth and final day. During the morning session the MCTDH method and its variants, the Gaussian-MCTDH and the variational Multi-Configurational Gaussians (vMCG) were explained, by on of the main developers Graham Worth. Afterwards Basile Curchod gave a lecture on the more approximate multiple spawning method, followed by the last speaker Gerrit Groenhof, who gave an introduction to experimental methods to study excited states. Afterwards an interesting group discussion about big challenges in chemical dynamics and future applications followed. During the discussion a particular emphasis was given to options to realise a better interplay between experiment and theory. With this pleasant final experience, the workshop on SHARC and Excited State Dynamics ended.

Maximilian Menger

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