kMap.py: A Python program for simulation and data analysis in photoemission tomography

Ultra-violet photoemission spectroscopy is a widely-used experimental technique to investigate the valence electronic structure of surfaces and interfaces. When detecting the intensity of the emitted electrons not only as a function of their kinetic energy, but also depending on their emission angle, as is done in angle-resolved photoemission spectroscopy (ARPES), extremely rich information about the electronic structure of the investigated sample can be extracted. For organic molecules adsorbed as well-oriented ultra-thin films on metallic surfaces, ARPES has evolved into a technique called photoemission tomography (PT). By approximating the final state of the photoemitted electron as a free electron, PT uses the angular dependence of the photocurrent, a so-called momentum map or k-map, and interprets it as the Fourier transform of the initial state’s molecular orbital, thereby gaining insights into the geometric and electronic structure of organic/metal interfaces. In this contribution, we present kMap.py which is a Python program that enables the user, via a PyQt-based graphical user interface, to simulate photoemission momentum maps of molecular orbitals and to perform a one-to-one comparison between simulation and experiment. Based on the plane wave approximation for the final state, simulated momentum maps are computed numerically from a fast Fourier transform (FFT) of real space molecular orbital distributions, which are used as program input and taken from density functional calculations. The program allows the user to vary a number of simulation parameters, such as the final state kinetic energy, the molecular orientation or the polarization state of the incident light field. Moreover, also experimental photoemission data can be loaded into the program, enabling a direct visual comparison as well as an automatic optimization procedure to determine structural parameters of the molecules or weights of molecular orbitals contributions. With an increasing number of experimental groups employing photoemission tomography to study molecular adsorbate layers, we expect kMap.py to serve as a helpful analysis software to further extend the applicability of PT.

紫外光电子能谱（Ultra-violet Photoemission Spectroscopy）是一种应用广泛的实验技术，用于探究表面与界面的价电子结构。若不仅将发射电子的强度作为其动能的函数进行检测，同时还依据其发射角度开展测量——即角分辨光电子能谱（Angle-resolved Photoemission Spectroscopy, ARPES）所采用的检测方式，则可从被研究样品中提取极为丰富的电子结构相关信息。对于以高度取向超薄薄膜形式吸附于金属表面的有机分子而言，角分辨光电子能谱已发展为一种被称为光电子断层扫描（Photoemission Tomography, PT）的技术。

通过将光电子的末态近似为自由电子，光电子断层扫描技术利用光电流的角度依赖性——即所谓的动量图谱（或称k图谱）——并将其解读为初始态分子轨道的傅里叶变换，从而得以深入剖析有机/金属界面的几何与电子结构。在本研究工作中，我们介绍了一款名为kMap.py的Python程序，该程序借助基于PyQt的图形用户界面，可实现分子轨道光电子动量图谱的模拟，并完成模拟结果与实验数据的一一比对。

基于末态平面波近似，程序通过对实空间分子轨道分布进行快速傅里叶变换（Fast Fourier Transform, FFT），数值计算得到模拟动量图谱；这些实空间分子轨道分布可作为程序输入，取自密度泛函计算结果。该程序允许用户调整多项模拟参数，例如末态动能、分子取向，或入射光场的偏振态。此外，实验光电子数据也可导入程序，既支持直接可视化比对，也可通过自动优化流程确定分子的结构参数，或是各分子轨道贡献的权重。

随着采用光电子断层扫描技术研究分子吸附层的实验团队数量不断增加，我们预计kMap.py将作为一款实用的分析软件，进一步拓展光电子断层扫描技术的应用范围。