A new method for calculating nuclear magnetic shielding in solutions is developed based on the reference interaction site model self-consistent field (RISM-SCF) with spatial electron density distribution (SEDD). In RISM-SCF-SEDD, the electrostatic interaction between the solute and the solvent is described by considering the spread of electron to obtain more realistic electronic structure in solutions. It is thus expected to allow us to predict more quantitative chemical shifts of a wide variety of chemical species in solutions. In this study, the method is applied to a water molecule in water and is validated by examining the dependence of the solvent temperature and density on chemical shifts. The dependence of solvent species is also investigated, and more accurate results are obtained for polar solvents compared to the previous RISM-SCF study. Another application example of this method is the 15 N chemical shifts of two azines in water, which is difficult to predict with the polarizable continuum model (PCM). Our results are in good agreement with the previous quantum mechanical/molecular mechanics study and experimental results. It is also shown that our method gives more realistic results for methanol and acetone than the PCM.
We propose a new hybrid approach combining quantum chemistry and statistical mechanics of liquids for calculating the nuclear magnetic resonance (NMR) chemical shifts of solvated molecules. Based on the reference interaction site model self-consistent field with constrained spatial electron density distribution (RISM–SCF–cSED) method, the electronic structure of molecules in solution is obtained, and the expression for the nuclear magnetic shielding tensor is derived as the second-order derivative of the Helmholtz energy of the solution system. We implemented a method for calculating chemical shifts and applied it to an adenine molecule in water, where hydrogen bonding plays a crucial role in electronic and solvation structures. We also performed the calculations of 17O chemical shifts, which showed remarkable solvent dependence. While converged results could not be sometimes obtained using the conventional method, in the present framework with RISM–SCF–cSED, an adequate representation of electron density is guaranteed, making it possible to obtain an NMR shielding constant stably. This introduction of cSED is key to extending the method’s applicability to obtain the chemical shift of various chemical species. The present demonstration illustrates our approach’s superiority in terms of numerical robustness and accuracy.
The NMR chemical shifts of hydride and fluoride ions in the solution phase are evaluated from the first principle. The cluster structure in the first solvation shell is calculated by density functional theory and MP2 theory, and the solvent effect around the cluster is considered by PCM and RISM-SCF-SEDD methods. The obtained shifts are analyzed in terms of electronic structure and solvent effects and are compared with available experimental data. The fluoride ion is deshielded in the presence of solvent molecules compared to the isolated state due to a larger paramagnetic contribution from the 2p orbital. On the other hand, there is no such change for the hydride ion. The paramagnetic and diamagnetic contributions are slightly changed due to the solvation, but they are canceled out. As a result, the chemical shift of the hydride ion is less affected by the solvent than that of the fluoride ion. The increased diamagnetic contribution of hydride ion dissolved in the solvent is attributed to the change in electron density coupled with microscopic solvation.
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