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Quantum control of large molecular systems using the Multi-Layer MCTDH method

Final Report Summary - QMOLML (Quantum control of large molecular systems using the Multi-Layer MCTDH method)

The objective of the project was to develop and apply for the first time the Multi-Layer (ML) variant of the MCTDH (Multi-Configuration Time-Dependent Hartree) method to coherent control in large polyatomic molecules (i.e. more than 10 atoms). As we have already highlighted in the mid-term report, the initial benchmark system of benzopyran was substituted by the study of photo-induced electron transfer in cryptochrome-type proteins. Describing photo-induced electron transfer in cryptochrome-type proteins can be considered considerably more challenging than the ring-opening benzopyran due to the much larger dimensionality to take into account (up to 1000 compared to 48 degrees of freedom). The model applied has a simpler form using a system coupled to a bath made of harmonic oscillators, yet the vast number constituted an important challenge as expected in terms of the construction an efficient ML tree and the numerical convergence of its respective quantum dynamical equations of motion. Furthermore such a problem is, indeed, a "hot topic" in biology in the context of the experimental measurement and theoretical description of long-lived coherences in proteins and how these relate to the underlaying biochemical mechanisms. In the particular case of cryptochromes the regulation of daily rhythms in plants, animals and as more recently postulated the magneto-reception system of migratory birds.

* Project tasks

During the project, we first updated some of the analysis tools within the MCTDH package. As described in the proposal (Part B of the application), this code development rather than incidental was of major importance since all the forthcoming applications in terms of analysis of the dynamics required new extraction and new analysis tools for the nuclear wavefunction. Secondly, we implemented a new algorithm for adaptively expanding the size of every node on-the-fly (i.e. ML-spawning) and a derived guiding criterion for the selection of an efficient tree’s branching. In order to do so, significant coding had to be performed, which we have only recently successfully finished. Therefore, the computation ML-MCTDH quantum dynamics of cryptochromes became possible at reasonable computational costs only by the end of the funded period but this is a great success by itself. We note, that a proposal has been written and submitted to the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) with the aim to continue and extend this promising line of work.

The so-called ML-spawning algorithm allows any user of the MCTDH package to systematically converge an ML-wavefunction on-the-fly, thus removing the individual benchmarking of every node. Furthermore, from an efficiency’s point of view it also reduces the computational cost as the size of the wavefunction, which adaptably grows during the propagation, is considerably smaller at the beginning of the simulation. The implementation, numerical performance and general features of the algorithm were tested in two representative examples, the S2 excited state decay in pyrazine and the quantum dissipative dynamics in a spin-boson bath for the aforementioned cryptochrome protein.

* Project results and outcomes

In terms of scientific progress the project has been a success, leading to a significant improvement of the ML-MCTDH code and methodology of quantum nuclear dynamics that will have a considerable effect on the field of theoretical reaction dynamics. Overall, the development of the ML-spawning algorithm and application can be seen as a first step to define automatic procedures to choose the numbers of basis set functions and the way how to combine DOFs in the MCTDH and ML-MCTDH approaches. The newly developed ML-spawning algorithm provides a systematic route towards convergence of a ML propagation and access to larger dimensionalities and longer time-scales thanks due to the gained efficiency.

In terms of the publication and dissemination of these code development and the derived results the initial bibliographic and computational work on the photochromic properties of benzopyran still could be profit through a published article concerning a joint theoretical–experimental investigation of the electron transfer in the spiropyran radical cation. On the other hand the implementation and testing of the ML-spawning algorithm has been already published as well in an article focusing on the technical and computational aspects. Last, a final article on the photo-induced electron transfer in cryptochromes aimed to the chemistry and biology community is in preparation for its publication soon after this report.