CAREER: Novel Green's function methods for predicting experimentally relevant quantities for solids and molecules

密歇根大学的Dominika Zgid获得了化学学部化学理论、模型和计算方法项目的奖励，她开发了新的计算工具来研究大分子和固体，其中电子的相关运动非常重要。在现代科学技术中，材料化学在先进光电材料、半导体和超导体、太阳能电池和电池材料的生产中发挥着重要作用。为了发现新材料和回答实验问题，理论必须预测与实验相关的、可测量的量。在过去的五十年里，大多数量子化学研究都集中在分子系统方法的发展上。目前分子问题可以非常精确地描述。然而，对于大型强相关分子和固体，量子化学仍然缺乏以系统改进的方式准确描述电子相关并提供实验有用预测的计算工具。本研究的主要目的是发展量子化学和凝聚态物理相结合的新型从头算理论方法，并能够为固体提供有用的实验预测。这个跨学科项目包括培训和指导研究生和博士后，使他们能够从最广泛的意义上理解他们的研究。这项研究为他们从事更广泛的职业做好了准备。Zgid博士还积极参与科学、技术、教育和数学（STEM）领域少数民族的公共宣传活动，为中学女生组织讲习班。格林的函数语言提供了与实验的自然联系，因为谱可以很容易地计算，而不需要波函数或密度理论中出现的繁琐的激发态形式。格林函数方法是可控的、可靠的、可系统地改进的，并且可以很容易地通过采用嵌入方法推广到固体或大分子中。为了计算激发谱，本课题采用二阶格林函数法和自能量嵌入法实现了Bethe-Salpeter方程。形式体系在小分子上进行校准，随后通过嵌入方法扩展到固体。由于量子力学模拟的现实性和预测能力取决于对所有电子建模的准确性，因此对有效哈密顿方法的研究得到了极大的关注，这些方法旨在使格林函数嵌入方法定量地应用于现实的分子和晶体系统。最后，由于格林函数是一个可以并行计算的大对象，因此研究的重点是在计算机实现中表达格林函数的有效方法。该项目的一个主要成果是向公众发布的包含有效、可靠和系统改进的固体格林函数嵌入方法的软件。此外，Zgid博士的研究小组正在为研究生准备一系列解释格林函数的课堂笔记，以减少量子化学家在使用格林函数形式主义时经常遇到的语言障碍。拟议的跨学科研究包括对研究生和博士后的培训和指导，使他们能够从最广泛的意义上理解他们的研究，并为他们广泛的职业生涯做好准备。此外，Zgid博士还参加了密歇根州服务不足社区中学生的“科学为明天”计划。

Dominika Zgid, of the University of Michigan, is supported by an award from the Chemical Theory, Models and Computational Methods program in the Chemistry Division to develop new computational tools to study large molecules and solids in which the correlated motion of electrons is very important. In modern science and technology, materials chemistry plays an big role in the production of advanced optoelectronic materials, semiconductors and superconductors, solar cell and battery materials. To enable the discovery of new materials and to answer experimental questions, theory has to predict experimentally relevant, measurable quantities. In the last fifty years, the majority of quantum chemistry research was focused on the development of methodological advances for molecular systems. Currently molecular problems can be described very accurately. However, for large strongly correlated molecules and solids, quantum chemistry still lacks computational tools that describe electronic correlation accurately in a systematically improvable manner and deliver experimentally useful predictions. The development of novel ab-initio theoretical methods that are at the interface of quantum chemistry and condensed matter physics and are capable of delivering useful experimental predictions for solids is the major aim of this research. This interdisciplinary project involves training and mentoring of graduate students and postdocs by allowing them to understand their research in the broadest possible sense. The research prepares them for a wide range of careers. Dr. Zgid is also actively engaged in public outreach for minorities in Science, Technology, Education and Mathematics (STEM) by organizing workshops for middle school girls. The Green's function language provides a natural link to experiment, since spectra can be readily calculated without the cumbersome excited state formalism present in wave function or density theories. Green's function methods are controlled, reliable, and systematically improvable and may easily be generalized by employing embedding methods to work for solids or large molecules. In order to calculate excitation spectra, this project implements the Bethe-Salpeter equation with a second order Green's function method and self-energy embedding approaches. The formalism is calibrated on small molecules and subsequently extended to solids by using embedding methods. Since the realism and predictive power of quantum mechanical simulations depend on the accuracy of modelling all electrons, significant attention is given to the investigation of effective Hamiltonian approaches that aim to make Green's function embedding methods quantitative for realistic molecular and crystalline systems. Finally, since the Green's function is a large object that can be calculated in parallel, the investigation focuses on efficient ways of expressing Green's functions in computer implementations. A major outcome of the project is software containing efficient, reliable and systematically improvable Green's function embedding methods for solids that is released to the public. Additionally, Dr. Zgid's research group is preparing a series of lecture notes for graduate students explaining Green's functions in order to reduce the language barrier frequently experienced by quantum chemists when working with the Green's function formalism. The proposed interdisciplinary research involves training and mentoring of graduate students and postdocs allowing them to understand their research in the broadest possible sense and prepares them for wide range of careers. Additionally, Dr. Zgid also takes part in the "Science for tomorrow" program for middle school students from underserved communities in Michigan.