## POpSiCLE: A photoelectron spectrum library for laser-matter interactions

**eCSE04-03**

#### Key Personnel

**PI/Co-I:** Daniel Dundas - Queen's University Belfast

**Technical:** Alejandro de la Calle - Queen's University Belfast

#### Relevant documents

**eCSE Technical Report:** POpSiCLE:
A photoelectron spectrum library for laser-matter interactions

### Project summary

Molecules driven out of equilibrium by intense, ultrashort laser pulses are of central importance in many areas of science and technology. In such a non-equilibrium situation, charge and energy transfer can be induced across the molecule on a femtosecond timescale. Understanding and controlling these transfer processes is fundamental to many chemical processes and key to future ultrafast technologies: examples include the design of electronic devices, probes and sensors, biological repair and signalling processes, and development of optically driven ultrafast electronics.

During the interaction of these pulses with molecules, various processes occur such as ionization, dissociation and harmonic generation. In order to understand and control the interactions, we must be able to analyse the photo-fragments produced, i.e. the electrons, ions and photons. Being able to calculate the photoelectron energy spectra of ionizing electrons provides an extremely sensitive tool with which we can study the electronic structure of the molecule at the point of ionization or dissociation. However, calculating photoelectron spectra is notoriously difficult. This is because the spectrum should be calculated as the projection of the electronic wavepacket onto continuum states at the end of the pulse. This presents a real challenge as electrons ionized during the pulse attain high velocities and can readily travel extremely large distances in a short time. This makes the calculation prohibitively expensive since the wavepacket must be calculated on a large numerical grid. In general, approximate methods are used whereby the electron energies are calculated during the pulse as they pass detector points or measuring surfaces before being removed from the simulation volume.

In describing laser-molecule interactions, many different community codes are used. Each code generally provides its own implementation of an approach for calculating photoelectron spectra (or in some cases no implementation is available). This means that much effort goes into implementing the same approach many times.

In this project we developed POpSiCLE (PhOtoelectron SpeCtra for Laser-matter intEractions), a parallel library that implements three methods for calculating photoelectron spectra. These are the surface flux method, the sampling point method and the Fourier transform of the spatial wavefunction into momentum space. In particular the surface flux method provides an inexpensive approach for calculating angularly resolved spectra. This opens the door to the study of ultrafast processes in molecules of key importance in chemistry, biology and electronics. This will allow us to study these processes in greater detail for the same amount of computational resource.

The library has been written to be as portable as possible and can be interfaced straightforwardly with other codes that are used for modelling laser-molecule interactions. These include several codes written by the applicants that solve the time-dependent Schrödinger equation for simple molecules (THEReMIN and RHYthMIC) and solve the Kohn-Sham equations of time-dependent density functional theory (TDDFT) for complex molecules (EDAMAME). In addition, other TDDFT community codes (GPAW, PW-TELEMAN and OCTOPUS) can also easily use the library. We have shared our library with one of the developers of OCTOPUS.

One immediate application of the POpSiCLE library for us will be to study photoangular distributions of chiral molecules interacting with attosecond laser pulses. Chiral molecules lack an internal plane of symmetry and thus have non-superimposable mirror images. Enantiomers (pairs of chiral molecules) often interact with biological systems differently. This is a consequence of the inherent homochirality found in nature, where nearly all amino acids are L-isomers (left-handed) while sugars are D-isomers (right-handed). It is therefore important to know which isomer is present in a particular sample of chiral molecules. The classic example of this is thalidomide: one enantiomer cures morning sickness while the other causes birth defects. The goal of this work is to understand if the interaction of ultrashort laser pulses with chiral molecules can be used for the identification of enantiomers. We aim to do this using photoelectron circular dichroism.

#### Achievement of objectives

The original objectives of the project were as follows.

**Objective 1:** Production of a library of routines with associated
documentation to calculate photoelectron spectra for molecules
interacting with intense laser pulses using the surface flux method.
The aim was for the library to be as general as possible so that it can be used with
a wide variety of codes, in particular two codes (THeREMIN and EDAMAME)
that run on ARCHER.

The library - POpSiCLE - was delivered along with associated documentation. The structure of the code allowed us to easily make use of additional methods for calculating photoelectron spectra. In particular we have also implemented the “sampling point method”, as introduced by the group of Prof. Suraud in Toulouse.

**Objective 2:** To calculate angularly resolved photoelectron spectra to
allow comparison with experimental results for a wide variety of codes
including THeREMIN and EDAMAME.

Functionality within POpSiCLE allows for angularly-resoved photoelectron spectra to be calculated using a wide variety of codes provided wavefunction information can be input into the appropriate library routines. As well as interfacing with THeREMIN and EDAMAME, we have also interfaced PoPSiCLE with another of our codes called RHYthMIC (vibRating HYdrogen Molecular Ion in Cartesians).

**Objective 3:** To calculate photoelectron spectra for dissociative
ionization of the hydrogen molecular ion using wavefunctions calculated
from full-dimensional calculations of the time-dependent Schrödinger
equation.

The coding was carried out, but insufficient time remained for full testing. While present in the library it should be currently considered alpha level software. The code is now being fully tested and optimised by another PhD student during calculations as part of an ARCHER RAP project.

**Objective 4:** Calculate photoelectron spectra by brute force for the
hydrogen atom in order to measure the accuracy and efficiency of the
surface flux method.

Techniques to calculate the photoelectron spectra by Fourier transforming the wavefunction at the end of a calculation have been added. These implement both parallel FFT methods and spherical Bessel transforms and are thus applicable to calculations in different coordinate systems.

#### Summary of the Software

POpSiCLE is freely available to download from the CCPForge website: https://ccpforge.cse.rl.ac.uk/gf/project/popsicle/. At the minute potential users are asked to join the project in order to be able to obtain the source code. This restriction is due to the fact that some of the functionality of the library has not been fully tested. Once this testing is complete, the code will be made completely open access.

Much of the remaining testing will be carried out on ARCHER. This will include planned work as part of an ARCHER RAP project that aims to study dissociation of the hydrogen molecular ion by circularly polarised laser pulses. This work will use the alpha version routines developed as part of Objective 3. Thus, while the code is not officially available yet on ARCHER it easily runs on the system. Hence, anyone wanting to use the code can do so at the minute by installing the code from CCPForge.