Calculation of nuclear magnetic resonance shieldings using frozen-density embedding

Abstract

We have extended the frozen-density embedding ͑FDE͒ scheme within density-functional theory ͓T. A. Wesolowski and A. Warshel, J. Phys. Chem. 97, 8050 ͑1993͔͒ to include external magnetic fields and applied this extension to the nonrelativistic calculation of nuclear magnetic resonance ͑NMR͒ shieldings. This leads to a formulation in which the electron density and the induced current are calculated separately for the individual subsystems. If the current dependence of the exchange-correlation functional and of the nonadditive kinetic-energy functional are neglected, the induced currents in the subsystems are not coupled and each of them can be determined without knowledge of the induced current in the other subsystem. This allows the calculation of the NMR shielding as a sum of contributions of the individual subsystems. As a test application, we have calculated the solvent shifts of the nitrogen shielding of acetonitrile for different solvents using small geometry-optimized clusters consisting of acetonitrile and one solvent molecule. By comparing to the solvent shifts obtained from supermolecular calculations we assess the accuracy of the solvent shifts obtained from FDE calculations. We find a good agreement between supermolecular and FDE calculations for different solvents. In most cases it is possible to neglect the contribution of the induced current in the solvent subsystem to the NMR shielding, but it has to be considered for aromatic solvents. We demonstrate that FDE can describe the effect of induced currents in the environment accurately.

Chromophore-specific theoretical spectroscopy: From subsystem density functional theory to mode-specific vibrational spectroscopy

“…[345] under the assumption that the current density of the total system can also be partitioned into subsystem contributions. Solventinduced shifts on NMR shielding constants were modeled for acetonitrile in complexes with different solvent molecules.…”

Toward Closing the Gap: Quantum Mechanical Calculations and Experimentally Measured Chemical Shifts of a Microcrystalline Lectin

“…The prediction of NMR chemical shifts from quantum mechanical (QM) methods is an alternative approach 20–22 and has undergone major advancements within the last decade, including improvements in the basis sets and the extension of higher levels of theory, as well as Density Functional Theory (DFT) techniques. 9, 23–26 DFT calculations are accurate enough to yield good agreements between chemical shift and molecular structure for medium-sized molecules, 27–28 and have also been explored for protein structure validation and refinement.…”

Self-consistency in frozen-density embedding theory based calculations

“…Six hydrogen-bonded dimers are considered for this purpose. The choice of hydrogenbonded complexes is, on the other hand, motivated by the fact that the case of non-covalently bounded environments appears to be the main domain of applicability of FDET based multi-level computational methods (see the validations concerning the potential energy surface energy [28][29][30] and increasing number of applications for various electronic properties 11,19,20,31 ).…”