Nuclei-selected NMR shielding calculations: a sublinear-scaling quantum-chemical method

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Nuclear Magnetic Resonance Spectroscopy

Background:

• Traditional ab initio calculations of nuclear magnetic resonance (NMR) shieldings are computationally intensive, scaling poorly with molecular size.
• Calculating all NMR shieldings is often unnecessary, especially for large molecules or specific applications like solvent effects and molecular dynamics.
• Existing methods may suffer from unphysical long-range contributions and inefficient scaling.

Purpose of the Study:

• To develop a novel ab initio method for the direct and efficient calculation of NMR shieldings for selected nuclei.
• To achieve a sublinear computational scaling with molecular size, focusing on the local environment's dominance in chemical shielding.
• To enable faster and more practical NMR shielding calculations for large and complex molecular systems.

Main Methods:

• Developed an ab initio approach calculating NMR shieldings directly for specific nuclei at Hartree-Fock and density-functional theory levels.
• Derived an alternative expression for the shielding tensor using the response density matrix with respect to the nuclear magnetic moment.
• Implemented a screening procedure to truncate the B-field dependent basis set, ensuring sublinear scaling by mitigating unphysical long-range contributions, inspired by Biot-Savart's law.

Main Results:

• The new method exhibits sublinear computational scaling, significantly outperforming conventional methods for large systems.
• Achieved typical speed-ups of approximately one order of magnitude compared to traditional O(N) scaling methods.
• Demonstrated the method's validity on various test systems, including large biomolecules exceeding 1000 atoms and ring-current dominated systems.

Conclusions:

• The presented direct calculation method offers a computationally efficient alternative for determining NMR shieldings of selected nuclei.
• The sublinear scaling and focus on local environments make it highly suitable for large molecules and specialized applications.
• This advancement has significant implications for computational chemistry, enabling more feasible studies of complex molecular systems.