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Computing molecular properties with controlled precision using multi-resolution analysis

使用多分辨率分析以受控精度计算分子特性

基本信息

批准号：
247396018
负责人：
Dr. Florian Bischoff
金额：
--
依托单位：
Institut für Chemie
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2013
资助国家：
德国
起止时间：
2012-12-31 至 2019-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/247396018?language=en
关键词：
Computing molecular properties controlled precision

项目摘要

The project aims at the accurate description of molecular properties using novel wavelet bases for the wave function. Multi-resolution analysis (MRA) algorithms will be developed that provide a high-quality numerical representation of the correlated molecular wave function.In MRA the basis for each function, i. e. orbital, pair function, or molecular potential, is constructed fully adaptively up to a requested accuracy threshold.This accuracy is maintained throughout the computation and leads to controlled precision in the final results. Orthonormality and compact support of the wavelets avoid several of the drawbacks of conventional wave function representations, such as artificially high scaling with respect to the system size, linear dependencies of the basis functions, basis set incompleteness or basis set superposition error. MRA can be combined with common quantum chemical methods, such as second order perturbation theory (MP2) or the Coupled-Cluster Singles and Doubles (CCSD). By including terms that depend explicitly on the interelectronic distance in the wave function expansion the working equations can be regularized and the numerical stability and performance of the algorithms are improved. The high dimensionality of the wave functions can be overcome by the use of low-rank tensor approximations. Moreover, the removal of the cusps from the wave function also lowers the separation ranks in the tensor approximations. MRA methods are naturally local and low-scaling, which leads to fast algorithms, they fit into modern massively parallel computer architectures, and are thus potentially applicable to large molecules.The objective of the project is to develop correlated quantum chemical methods using MRA, specifically, to develop and implement MRA-CCSD energies, and first order properties for MRA-MP2. Further development of the algorithmic framework will be the second focus of the proposed research. Finally the new methods will be validated and used to investigate physisorption and chemisorption processes of molecules on extended surfaces using a multi-level QM/QM framework.

该项目的目标是使用新型波函数小波基准确描述分子特性。多分辨率分析（MRA）算法将被开发，提供一个高质量的数值表示的相关分子波函数。e.轨道，对函数，或分子势，是完全自适应地构造的，直到达到要求的精度阈值。2这种精度在整个计算过程中保持不变，并导致最终结果的控制精度。小波的正交性和紧支持避免了传统波函数表示的几个缺点，例如相对于系统大小的人为高缩放、基函数的线性依赖性、基集不完整性或基集叠加误差。MRA可以与常见的量子化学方法相结合，例如二阶微扰理论（MP2）或耦合簇单重和双重（CCSD）。通过在波函数展开式中加入明确依赖于电子间距的项，可以使工作方程正则化，提高算法的数值稳定性和性能。波函数的高维性可以通过使用低秩张量近似来克服。此外，从波函数中去除尖点也降低了张量近似中的分离秩。MRA方法具有局部性和低尺度性，因此算法速度快，适合现代大规模并行计算机体系结构，因此对大分子具有潜在的应用价值。本项目的目标是利用MRA开发相关量子化学方法，具体来说，开发和实现MRA-CCSD能量，以及MRA-MP2的一阶性质。算法框架的进一步发展将是拟议研究的第二个重点。最后，新的方法将被验证，并用于研究物理吸附和化学吸附过程的分子在扩展的表面上使用多层次的QM/QM框架。