Positive Semidefinite Programming for Many-body Quantum Mechanics with Applications to Physical and Chemical Systems

芝加哥大学的David Mazziotti得到了理论和计算化学计划的支持，该计划利用多体理论和一阶正定规划的最新进展来计算两粒子约化密度矩阵。有了这种处理中大型分子的新能力，这种方法将准确和有效地提供几何构型、键极性、激发态转变、过渡态结构和势能表面拓扑。应用领域包括卡宾化学中的分子解离、单重态-三重态分裂以及高温金属氧化物超导体中的量子相变。这项研究将带来新的、准确的预测化学性质的方法，该程序的某些方面可能适用于全球经济模型。此外，高中生将通过他们自己出版物的新的年度期刊来鼓励他们学习数学科学。

David Mazziotti of the University of Chicago is supported by the Theoretical and Computational Chemistry Program to compute two-particle reduced density matrices using recent advances in many-body theory and first-order positive definite programming. With this new ability to treat medium- to large-sized molecules, this methodology will provide geometries, bond polarities, excited-state transitions, transition state structures, and potential energy surface topologies both accurately and efficiently. Applications include molecular dissociation, singlet-triplet splitting in carbene chemistry, and quantum phase transitions in high-temperature metal-oxide superconductors.This research will lead to new, accurate methods for predicting chemical properties, and some aspects of the programming may be applicable to global economic models. In addition, high school students will be encouraged in the mathematical sciences through a new annual journal of their own publications.