# Numerical Quantum Dynamics (NQD)

Simulations of quantum molecular dynamics is challenging due to solving the, possibly explicit, time-dependent Schrödinger equation with many degrees of freedom. It is an active research field where experimental and theoretical methods are constantly being developed to study even more complex chemical reactions. The research field has been awarded several Nobel prices in Chemistry e.g. in1998, 1999 and 2013.

The research in the NQD group concerns developing and analyzing new accurate numerical techniques and tools for simulating molecular dynamics, using different levels of approximations of the Schrödinger equation for describing the electronic and nuclear dynamics in molecular reactions. Focus is on interaction with ultra-fast laser pulses, photo-electron spectroscopy and reactive scattering.

To handle the large number of degrees of freedom we are currently analyzing different types of tensor decomposition methods as e.g. the MCTDH and DMRG approaches, but also semi-classical methods with a special interest in the quantum-classical limit.

To be able to compute the nuclear dynamics, accurate descriptions of the electron structures for the system is needed. This can be achieved by parametric potential surface models or by using an ab-initio model, where the time-independent Schrödinger equation is solved to determine the electron structure.

## Subprojects

### Active

- Electronic structure calculations Computation of the electronic structure allows for studies of molecular properties and computing potential energy surfaces.
- Spatial discretization schemes Since solutions to the TDSE are usually very smooth, high-order methods are convenient for this type of problems. We analyze and devise methods based on summation-by-parts difference methods, radial basis functions, and spectral element methods.

### Finished or dormant

- Semiclassical methods If the atoms are heavy, solutions to the Schrödinger equation become highly oscillatory. Solution with standard methods is then expensive or intractable. Asymptotic methods which are valid in the high frequency regime can reduce the computational complexity. Such methods are called semiclassical.
- Time propagators Exponential integrators are a suitable tool for numerical simulations of the Schrödinger equation. Error estimation, adaptive step size control, and parallel scalability are analyzed and improved.
- Dissociative systems For chemical reactions that can lead to dissociation scattering boundary conditions must be enforced, which pose difficulties at the numerical boundaries. We have formulated perfectly matched layers for the Schrödinger equations which work well as boundary closures.
- Quantum optimal control Laser pulses can be used to control chemical reactions. The outcome is affected by the shape of the pulse. The search for the ideal pulse can be formulated as an optimization problem.

## Parallel implementation and software

- The Chunks and Tasks programming model Computer programs are written in terms of subtasks that operate on chunks of data. This allows for efficient use of computers with many processors. Source code for Chunks and Tasks library implementations available at chunks-and-tasks.org.
- Ergo, an open source (GPL) program for large-scale electronic structure calculations. The source code is available for download at www.ergoscf.org. Work is ongoing to parallelize Ergo using the Chunks & Tasks programming model.
- HAParaNDA, an implementation framework for high-dimensional time-dependent partial differential equations, targeting large-scale parallel computers. A solver for the TDSE is implemented as a pilot application problem.

## Group information

Full list of publications and conference contributions

### Participants

- Gunilla Kreiss (Professor)
- Hans Karlsson (Professor)
- Emanuel Rubensson (Associate Professor, Docent)

### Alumni

- Anastasia Kruchinina (PhD thesis 2019, Principal advisor: E. Rubensson)
- Emil Kieri (PhD thesis 2016, Prinicipal advisor: S. Holmgren)
- Magnus Grandin (PhD thesis 2014, Principal advisor: S. Holmgren)
- Katharina Kormann (PhD thesis 2012, Principal advisor: S. Holmgren)
- Anna Nissen (PhD thesis 2011, Principal advisor: G. Kreiss).

### Collaboration

- Katharina Kormann, Ruhr-Universität Bochum, Germany.
- Anders Niklasson, Los Alamos National Laboratory, NM, USA.
- Quantum Dynamics Network (QDN)