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

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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.