ERA Chemistry - Generalized tensor methods in quantum chemistry

在现代化学和材料科学中，电子结构的计算对于分子工程具有极其重要的意义。在这种情况下，电子相关的精确计算是一个基本而又极其困难的问题。与密度泛函理论（DFT）用于扩展系统或耦合簇方法用于高精度计算在计算弱相关系统方面取得的巨大进展相比，目前的量子化学方法有两类主要的系统存在不足：(1)具有大量未配对电子的开壳系统，因为它们出现在多个过渡金属配合物或分子磁体中；(2)无带隙的扩展或周期系统，其中可用的尺寸一致方法的适用性已达到极限。本文的目的是开发一种基于通用张量网络状态（TNS）的算法，该算法可以有效地应用于量子化学中的这些开放性问题。这种算法的实现依赖于执行各种复杂的任务。必须设计一些新的张量分解的形式化方法和方法论概念，以符合哈密顿量的特定非局部性质，为此，申请人将加入他们在强大的DMRG方法和类似的物理，数学和信息技术的最新发展方面相当互补的专业知识。为了达到量子化学TNS算法的有效实现，我们的贡献将基于QC-DMRG- Budapest [Legeza-2011]和TTNS-Vienna [Murg-2010c]代码的现有程序结构进行实现和测试。

The computation of the electronic structure is of utmost importance for the task of molecular engineering in modern chemistry and material science. In this context, the accurate computation of the electron correlation is a fundamental and extremely difficult problem. In contrast to the tremendous progress made in calculating weakly correlated systems by Density Functional Theory (DFT) for extended systems or Coupled Cluster Methods for highly accurate calculations, there are two major types of systems for which current quantum chemical methods have deficiencies: (1) Open-shell systems with a large number of unpaired electrons, as they occur in multiple transition metal complexes or in molecular magnets; (2) Extended or periodic systems without a band gap, where the limit of the applicability of the available size consistent methods is reached.The aim of this proposal is to develop a general tensor network state (TNS) based algorithm that can be applied efficiently to these open problems of quantum chemistry. Realization of such an algorithm relies on carrying out a variety of complex tasks. Several new formal methods and methodological concepts of tensor decompositions will have to be designed to comply with the specific, nonlocal nature of the Hamiltonian, and to this end, the applicants will join their rather complementary expertise regarding the powerful DMRG method and similar recent developments from physics, mathematics and information technology. To arrive at an efficient implementation of the quantum chemistry TNS algorithm, our contributions will be implemented and tested based on existing program structures of the QC-DMRG- Budapest [Legeza-2011] and the TTNS-Vienna [Murg-2010c] codes.