基于非正交定域分子轨道的含时密度泛函方法的开发

To satisfy both the high accuracy and high efficiency requirements when computing the excited states properties of large bio- or materials molecules using quantum chemistry programs, in this project, we propose to develop a new time-dependent density functional theory (TDDFT) approach that is based on the non-orthogonal localized molecular orbital (NOLMO). NOLMO is the most localized representation of electronic degrees of freedom. Thus it is a very hot area lately. In this project, we will firstly develop a set of equations for NOLMO-TDDFT based on both the work our group has done on NOLMO-DFT development and our experience of developing a NOLMO-TDHF method. Then we will implement the equations into working code and optimize the code via sparse matrix technique. And finally, we will use CPU+GPU technology to parallelize the code. Some systems will be used to test both the accuracy and efficiency of the method. By finishing this project, 1. A powerful linear scale tool will be provided for studying the excited states properties of large bio-molecules and/or for designing new types of materials; and 2. The TDDFT method will become the first NOLMO based linear scaling ab initio method in our country.

本申请基于高精度高效率的量子化学激发态计算在研究生物和材料大分子性质的需求，拟发展一套基于非正交定域分子轨道的含时密度泛函(NOLMO-TDDFT)方法和程序。由于轨道定域性好的优势，NOLMO是近年研究的一个热点，也是计算化学领域今后的发展方向之一。本申请首先将在合作课题组正在开发的NOLMO-DFT方法的基础上，结合我们开发的NOLMO- TDHF方法的经验推导出NOLMO-TDDFT的相关公式。之后将编制高效率的NOLMO-TDDFT的程序并使用稀疏矩阵技术优化代码。最后我们将使用CPU+GPU技术来实现程序的并行化。本项目的完成将：1. 为研究大体系的激发态性质提供一个有力的线性标度工具；2. 成为第一个自主研发的基于NOLMO的量子化学从头计算TDDFT程序，从而填补一项空白。

本项目“基于非正交定域分子轨道的含时密度泛函方法的开发”（项目批准号：21403075，执行日期2015.1.1-2017.12.31）是基于高精度高效率的量子化学激发态计算在研究生物和材料大分子性质的需求，发展一套基于非正交定域分子轨道的含时密度泛函(NOLMO-TDDFT)方法和程序。利用空轨道与占据轨道必须正交的特性，并加上定域性的限制条件，构建新的目标函数进行优化，从而得到非正交定域分子空轨道，得到的空轨道可以具有良好的定域性，为大体系非线性光学性质和激发态的计算实现线性标度成为可能。本项目完成了基于非正交定域分子轨道的TDHF/TDDFT方法的公式推导和程序编制，实现了非正交定域分子轨道的方法从简单的基态能量计算拓展到能量梯度及激发态的计算，使得其应用范围更加广阔，从而可以用来计算大体系的非线性光学性质以及激发态性质。