SBIR PHASE II: Gridless Density Functional Calculations

这个小型企业创新研究（SBIR）二期项目旨在构建用于量子化学的新密度泛函。目前使用的所有流行的泛函都导致难以精确计算的三维积分，这些积分是使用大型三维网格近似估计的。这个项目通过设计功能来解决这个问题，通过结构，可以精确地集成，因此不需要网格。这项工作将分几个阶段进行，并将产生交换能和相关能的“无网格”函数。它也应该产生动能的“无网格”函数。研究结果将发表在权威期刊上，并在国际科学会议上发表。与目前的方法相比，使用无网格密度泛函有两个优点：(1)结果不会受到“网格噪声”的污染，即有限数值网格所提供的不完全正交所带来的误差。(2)精确积分比三维网格（每个原子有数千个网格点）上的正交更有效，因此，无网格计算比基于网格的计算所需的计算时间要少得多。新功能将在软件包中实现，并在未来的版本中向计算科学家提供商业服务。因为与基于网格的计算相比，无网格密度泛函计算在数值上更健壮，计算效率更高，它们的可用性将使计算科学家能够对比以前更大、更复杂的系统进行第一原理量子力学研究。这将有利于生物化学、制药、新材料和其他领域的研究。

This Small Business Innovation Research (SBIR) Phase II project seeks to construct new density functionals for use in quantum chemistry. All of the popular functionals in use today lead to difficult three-dimensional integrals that cannot be computed exactly and which are estimated approximately using large three-dimensional grids. This project approaches the problem by devising functionals which, by construction, can be integrated exactly and which, therefore, require no grids. The work will proceed in a number of stages and should yield "gridless" functionals for the exchange and correlation energies. It should also yield "gridless" functionals for the kinetic energy. The results will be published in respected journals and presented at international scientific conferences.The use of gridless density functionals offers two advantages over present methods: (1) The results will not be contaminated by "grid noise", the error introduced by the imperfect quadrature afforded by a finite numerical grid. (2) Exact integration is much more efficient than quadrature on a three-dimensional grid (with thousands of grid points per atom) and, as a result, gridless calculations should require much less computing time than grid-based ones. The new functionals, will be implemented within the software package and made available commercially to computational scientists in a future release. Because gridless density functional calculations will be both more numerically robust and more computationally efficient than grid-based calculations, their availability will allow computational scientists to undertake first principles quantum mechanical studies of larger and more complicated systems than were previously accessible. This will benefit research in biochemistry, pharmaceuticals, new materials and elsewhere.