Local correlation approaches for ground and excited states of periodic systems

微观性质的计算机模拟是设计和理解新材料的关键，而拟议研究的目的是开发一套新的工具来执行固体的精确模拟，这可以在未来被我们或其他团体大大扩展，在加拿大或其他地方。在过去的十年中，基于波函数的分子系统量子化学方法的发展取得了重大进展。一个主要的创新是局部相关耦合簇方法的发展，使用所谓的对自然轨道（PNOs）的非常紧凑的表示。虽然分子系统的计算是准确的、通用的和高效的，但对于周期性固体来说，目前还不是这样。密度泛函理论，通常与平面波和伪势相结合，是最广泛使用的，但这种计算固体的方法远不如用于分子的波函数方法精确或可靠。在这个建议的目的是推广已证明的方法分子的周期性固体领域，直到完整的三维晶体。我们策略的新颖之处在于利用平移对称与局部PNO相关方法相结合，完全类比于分子系统。关键思想是定义一组反映系统对称性/周期性的局域已占轨道，但它们通常是线性相关的。这种新方法需要对传统方法进行重大修改（这些方法已经在分子的试点实施中进行了部分测试）。将开发一种新的自动代码生成器，这将极大地促进有效的计算机实现。库仑势的长程部分对固体，特别是金属起着至关重要的作用，平面波技术的使用已被证明特别有效。因此，在第二项研究中，我们计划将固态和分子计算的最佳部分整合在一起，方法是将全库仑势划分为短程和纯远程部分。短程部分通过直接空间（类分子）技术处理，而远程部分在紧互易空间中处理，使用傅里叶变换，即平面波。通过公正地结合这两个世界的优点，我们预计我们可以开发一个基于波函数的计算机程序来计算固体系统的结构，能量学，材料和光谱特性，其精度和效率与最先进的分子密码相同。该研究是开放式的，因为使用代码生成器将使目前仍有待于未来的方法能够顺利实施，并将为学生提供非常高水平的培训。

Computer simulations of microscopic properties are key to the design and understanding of new materials, and the aim of the proposed research is to develop a new set of tools to perform accurate simulations for solids, which can be greatly expanded on in the future by us or other groups, in Canada or elsewhere.The past decade has seen major progress in the development of highly accurate, systematic, and efficient wave function based quantum chemistry methods for molecular systems. A major innovation has been the development of local correlation coupled cluster methods using a very compact representation using so-called pair natural orbitals (PNOs). While calculations for molecular systems are accurate, versatile and efficient, this is currently not true for periodic solids. Density functional theory, often in conjunction with plane waves and pseudo potentials are most widely used, but such calculations for solids are not nearly as accurate or reliable as wave function methods used for molecules. In this proposal the aim is to generalize the proven methodology for molecules to the domain of periodic solids, up to full 3-dimensional crystals. The novelty of our strategy is the use of translational symmetry in conjunction with local PNO correlation approaches, in complete analogy to molecular systems. The key idea is to define a set of localized occupied orbitals that reflect the symmetry/periodicity of the system, but which will in general be linear dependent. This new approach requires non-trivial modifications to conventional methodologies (that have been partially tested in a pilot implementation for molecules). A new automatic code generator will be developed and this will greatly facilitate effcicient computer implementations. The long-range part of the Coulomb potential plays an essential role for solids, in particularly for metals, and the use of plane wave techniques have been proven particularly effective. In a second line of research we therefore plan to consolidate the best parts of solid state and molecular calculations by partitioning the full Coulomb potential in a short-range and an essentially pure longrange part. The short-range part is treated by direct space (molecular-like) techniques, while the long-range part is treated in a compact reciprocal space, using Fourier transforms, i.e. plane waves. By judicially combining the best of both worlds we anticipate we can develop a wave function based computer program to calculate structure, energetics, material and spectroscopic properties of solid state systems at the same level of accuracy and efficiency as state-of-the-art molecular codes. The research is open-ended as the use of a code generator will enable smooth implementation of methodology that currently still lies in the future, and will provide very high level training for students.