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CECAM- E-CAM Extended Software Development Workshop Quantum Molecular Dynamics I, Dublin, 17-28 July 2017

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Quantum dynamics simulations solve the time-dependent Schroedinger equation (TDSE) or equivalently the quantum Liouville equation, for the nuclei of a molecular system and can follow the fundamental behaviour including, in principle, all quantum effects. These are often crucial for simulating fundamental reactivity, e.g. after a molecular collision, or the absorption of a photon, and are required for the understanding of many state-of-the-art experiments. Examples are found in the description of energy flow in photoexcited benzene, a basic building block of organic chemistry [1], and the FMO complex, a paradigm in quantum biology [2]. This understanding is also becoming important for emerging technologies that need optimal properties of materials, for example in photo-activated technology molecules need to be engineered such that the energy flow into destructive pathways is suppressed. Other obvious uses are in technologies that rely directly on quantum properties, such as quantum computing.

Details including the workshop programme are available at the CECAM workshop webpage The second concluding part of this workshop is due to take place in November 2017.

Despite a huge advance in algorithms over the last couple of decades, quantum dynamics simulations require large computational resources and suffer from poor scaling with respect to system size. Accurate calculations are restricted to treating only a few atoms. The field is also fragmented, with few standard benchmarks and most work done as single codes within a research group. This makes it difficult to assess the usefulness of approximate methods and compare systematically their performance. The situation can be contrasted to the more mature field of quantum chemistry, in which the electronic problem is solved for static nuclei, where people work within the framework of a few large packages (Gaussian, Molpro, Qchem etc) with recognised benchmarks.

The field is starting to change, with greater collaboration, spurred also by a recent series of thematic workshops and schools held at CECAM-HQ, and the emergence of community codes such as the Quantics package [3]. The first E-CAM ESDW held in Paris June 2016 began work to provide benchmark routines to allow the comparison of methods. This workshop also looked at coding new algorithms and optimising and documenting codes, both for non adiabatic dynamics using the so called exact factorisation method [4] and for approximate quantum time dependent correlation functions [5]. The second workshop aims to carry this work forward, looking at state-of-the-art methods for exact calculations [6], sampling algorithms to improve trajectory calculations [7] and a new approach based on the exact factorisation of the wavefunction into electronic and nuclear parts [4].

We plan to advertise the possibility to develop software both for academic and industrial purposes with an open call to close about a month before the start date of the workshop. These software development projects will be assessed by the organisers in collaboration with E-CAM’s software manager and the software developer associated to WP3, ranked and accepted according to the availability of human and logistic resources. To ensure the successful delivery of modules to the E-CAM library, we have already defined 4 projects to be worked on, each of which will provide a module for the E-cam library.

1. Eigensolvers (leader G. Worth)
While it is impossible in general to calculate all the eigenstates of a polyatomic Hamiltonian, it is often important to obtain a number of them. These are required to interpret a spectrum, or provide the initial wavepacket for a quantum dynamics simulation. Iterative schemes, such as Lanczos or Davidson are general and powerful algorithms that can be provided as library modules, coded to take advantage of modern HPC.

2. Sparse grids for exact dynamics (leader D. Lavergnat)
Exact quantum dynamics requires a multi-dimensional grid representation. In their usual form, however, these suffer from exponential growth with system size as they are based on a full direct product of one-dimensional grids. Recent developments in using sparse grids (Smolyak grids) are providing impressive results, truncating the basis in an optimal way and allowing larger systems (8-9 degrees of freedom rather than 3) to be treated. A module which makes the transformation between a Smolyak grid and a basis representation will be provided.

3. Path Sampling (Donal MacKernan)
Surface hopping is a well-used algorithm in non-adiabatic quantum dynamics in which classical trajectories simulate the quantum wavepacket by switching between electronic states. The more rigorous formulations of the method, however, based on the Wigner-Liouville formalism suffer from poor convergence. Sampling schemes will be developed and coded that aim to optimise the convergence. Modern HPC can be utilised here to maximise efficiency.

4. Quantum-Classical Propagation (F. Agostini)
A scheme for propagating the nucleii based on the exact factorisation of the nuclear and electronic parts of the TDSE is a promising new direction in quantum dynamics in which nuclei move over time-dependent potential surfaces. Initial work has already been done as part of the 1st WP3 ESDW on modules required (adiabatic electronic surfaces and non-adiabatic couplings). The module to be provided by this workshop will integrate the equations of motion for the nuclei.

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