Two-electron Reduced Density Matrices in Quantum Chemistry and Physics

芝加哥大学的大卫Mazziotti是由化学理论，模型和计算方法计划的研究支持，以开发和实施量子力学方法来计算原子和分子的电子结构。 本工作的目标是在不需要波函数的情况下直接确定2电子约化密度矩阵（2-RDM）。该方法的应用包括燃烧和大气化学中的光激发化学反应中的激发态和锥形交叉，非平衡分子电导率中的稳态，材料和生物过程中的能量传递，如生物发光和光捕获，以及各种强相关现象。 本研究的目的是通过两种通用的方法建立和改进低成本和强相关计算的2-RDM方法：1）求解收缩的Schrodinger方程; 2）用N-可表示性条件约束或参数化2-RDM的能量变分最小化。 Mazziotti博士和他的团队的最新进展表明，他们的方法可以恢复萤火虫荧光素以及并苯链和片等分子系统中的强电子相关性，如果可计算的话，其波函数将跨越八次方或更多的分子构型或行列式。 这项工作对我们使用量子力学研究有趣的真实世界系统的能力产生了很大的影响，这是波函数方法所不可能的。Mazziotti博士正在继续和扩展一个新的年度出版物，鼓励高中生追求职业和研究数学科学。他正在开发一个研究生班，使用约化密度矩阵的一般概念来统一化学，物理和数学领域，从电子结构到量子信息。

David Mazziotti of The University of Chicago is supported by the Chemical Theory, Models and Computational Methods program for research to develop and implement quantum mechanical methods to compute the electronic structure of atoms and molecules. The goal of this work is the direct determination of the 2-electron reduced density matrix (2-RDM) without the wave function. Applications of this method include excited states and conical intersections in photo-excited chemical reactions in combustion and atmospheric chemistry, steady states in non-equilibrium molecular conductivity, energy transfer in materials and biological processes such as bioluminescence and light harvesting, and various strong correlation phenomena. The research aims to establish and improve 2-RDM methods for low-cost and strong- correlation computations via two general approaches: 1) Solution of the contracted Schrodinger equation; 2) Variational minimization of the energy with a 2-RDM constrained or parameterized by N-representability conditions. Recent advances by Dr. Mazziotti and his group show that their method can recover strong electron correlation in molecular systems like firefly luciferin as well as acene chains and sheets whose wave functions, if computable, would span an octillion or more molecular configurations or determinants. This work has a large impact on our ability to use quantum mechanics to study interesting, real-world systems that would be impossible with wave function methods. Dr. Mazziotti is continuing and extending a new annual publication that encourages high school students to pursue careers and research in the mathematical sciences. He is developing a graduate class that uses the general concept of reduced density matrices to unite areas of chemistry, physics and mathematics from electronic structure to quantum information.