Development of Linear-Scaling Methods for Calculating Energy Gradients and NMR Chemical Shifts at the Second-Order Møller-Plesset Perturbation Level

核磁共振化学屏蔽的可靠量子化学计算是联系理论和实验的重要纽带，其中二阶微扰理论(MP2)可以为许多分子体系提供可靠的数据。然而，对于大分子系统，计算工作量与分子大小的陡峭的五阶比例限制了这样的计算。因此，该项目旨在减少这种标度，并开发一种快速、线性标度的基于原子轨道(AO)的MP2核磁共振方法，为计算具有1000个或更多原子的系统开辟了道路。同时，对结构确定或直接Born-Oppenheimer分子动力学非常重要的密切相关的线性标度AO-MP2能量梯度将被开发出来。此外，为了计算选定核的MP2核磁共振屏蔽张量，将设计一种合适的方法，将五阶标度降低到随分子尺寸变化的次线性标度(即，渐近独立)。通过这种方式，该项目有望大大增加对核磁共振谱进行可靠的量子化学指定的可能性。

The reliable quantum-chemical calculation of NMR chemical shieldings represents an important link between theory and experiment, where second-order Møller-Plesset perturbation theory (MP2) can provide reliable data for many molecular systems. However, for large molecular systems the steep fifth-order scaling of the computational effort with molecular size prohibits such calculations. Therefore, the project aims to reduce this scaling and to develop a fast, linear-scaling atomic-orbital (AO) based MP2 NMR method that opens the way to compute systems with 1000 and more atoms. At the same time, the closely related linear-scaling AO-MP2 energy gradients important for structure determination or direct Born-Oppenheimer molecular dynamics will be developed. Moreover, for computing the MP2 NMR shielding tensor for selected nuclei, a suitable method will be devised that reduces the fifth-order scaling to sublinear scaling (i.e., asymptotically independently) with molecular size. In this way, the project is expected to substantially increase the possibilities for reliable quantum-chemical assignments of NMR spectra.