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

密歇根大学的Dominika Zgid得到了化学系化学理论，模型和计算方法项目的支持，以开发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。为了能够发现新材料并回答实验问题，理论必须预测实验相关的可测量的量。在过去的50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，分子问题可以非常准确地描述。然而，对于大的强相关分子和固体，量子化学仍然缺乏计算工具，以系统可改进的方式准确描述电子相关性，并提供实验上有用的预测。本研究的主要目的是开发新的从头算理论方法，这些方法处于量子化学和凝聚态物理学的界面，能够为固体提供有用的实验预测。这个跨学科项目涉及研究生和博士后的培训和指导，让他们尽可能广泛地了解他们的研究。 这项研究为他们从事广泛的职业做好了准备。Zgid博士还通过为中学女生组织讲习班，积极参与科学、技术、教育和数学（STEM）方面的少数群体公共外联活动。 绿色的函数语言提供了一个自然的联系，实验，因为光谱可以很容易地计算，没有繁琐的激发态形式主义波函数或密度理论。绿色函数法是可控的、可靠的、可系统地改进的，并且可以容易地通过采用嵌入方法来推广以用于固体或大分子。为了计算激发光谱，本计画以二阶绿色函数法与自能嵌入法来实现Bethe-Salpeter方程。的形式主义校准小分子，随后扩展到固体通过使用嵌入方法。 由于现实主义和预测能力的量子力学模拟依赖于所有电子建模的准确性，显着的注意力给予有效的哈密顿方法，旨在使绿色的功能嵌入方法定量现实的分子和晶体系统的调查。最后，由于绿色的功能是一个大的对象，可以并行计算，调查的重点是有效的方式来表达绿色的功能在计算机实现。 该项目的一个主要成果是向公众发布的软件，其中包含高效、可靠和系统可改进的固体绿色函数嵌入方法。此外，Zgid博士的研究小组正在为研究生准备一系列讲座笔记，解释绿色的功能，以减少量子化学家在使用绿色函数形式主义时经常遇到的语言障碍。拟议的跨学科研究涉及研究生和博士后的培训和指导，使他们能够在最广泛的意义上理解他们的研究，并为他们的广泛职业做好准备。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.