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要旨:
Nuclear magnetic resonance (NMR) spectroscopy is an essential analytic technique in chemical, pharmaceutical, and biomedical research and materials sciences. The information that NMR provides about the molecular structure of novel compounds is detailed but indirect, hidden behind the two main quantities that determine the shape of the spectrum: the shielding tensor (observed as a chemical shift) and the indirect spin–spin coupling tensor. Thus, computational methods are often used to predict these properties from first principles and correctly interpret complex spectra. The challenge is to develop methods which are both accurate and robust enough to resolve truly complicated structures, and efficient enough to be routinely applicable to large molecular systems. This work aims to facilitate the fast and accurate calculation of NMR shielding tensors in three complementary ways.
First, two popular approaches for speeding up Hartree–Fock (HF) and density functional theory (DFT) calculations, the resolution of the identity (RI) and chain-of-spheres exchange (COSX) approximations, are applied to NMR shielding calculations using gauge-including atomic orbitals (GIAOs). A benchmark study is performed to assess the errors thus introduced in the calculated shieldings, in comparison to the inherent errors due to the level of theory. After selection of appropriate basis sets and integration grids, it is shown that the RI approximation for Coulomb interactions, combined with either the same for exchange interactions (RIJK), or with COSX (RIJCOSX), are both sufficiently accurate. However, for systems with more than 100 electrons and 1000 basis functions, RIJCOSX is more efficient.
Next, NMR shielding calculations with GIAOs are implemented for RI-based second order Møller–Plesset perturbation theory (RI-MP2) and also, for the first time, for double-hybrid DFT (DHDFT). The latter is shown to be substantially more accurate than either MP2 or regular DFT, reproducing NMR chemical shifts within 2 % of the CCSD(T) (coupled clusters with single, double, and perturbative triple excitations) reference values.
The accuracy and efficiency of the RI-MP2 approximation is also assessed and it is shown that the implementation is suitable for systems with up to 400 electrons and 2500 basis functions.
Finally, the applicability of MP2 and DHDFT is extended to even larger systems by employing the concepts of local electron correlation within the framework of the domain-based local pair natural orbital (DLPNO) approximation. The formally complete analytic second derivatives of DLPNO-MP2 are derived and implemented for both NMR shieldings and electric dipole polarizabilites. Some numerical stability issues, potentially relevant to other local correlation methods, and their avoidance are discussed. The effect of the DLPNO approximation is assessed for medium-sized systems and it is shown that relative deviations from the RI-MP2 reference result are below 0.5 % for both properties when using the default truncation thresholds. For large systems, the implementation achieves quadratic effective scaling of the computational effort with system size. It is more efficient than RI-MP2 starting at 280 correlated electrons and is never more than 5–20 times slower than the equivalent HF or hybrid DFT calculation. The largest system treated here at the DLPNO-DHDFT level is the vancomycin molecule with 176 atoms, 542 correlated electrons, and 4700 basis functions.
