Using the method of modified Shepard's interpolation to construct potential energy surfaces of the H2O, O3, and HCOOH molecules, we compute vibrationally averaged isotropic nuclear shielding constants ⟨σ⟩ of the three molecules via quantum diffusion Monte Carlo (QDMC). The QDMC results are compared to that of second-order perturbation theory (PT), to see if second-order PT is adequate for obtaining accurate values of nuclear shielding constants of molecules with large amplitude motions. ⟨σ⟩ computed by the two approaches differ for the hydrogens and carbonyl oxygen of HCOOH, suggesting that for certain molecules such as HCOOH where big displacements away from equilibrium happen (internal OH rotation), ⟨σ⟩ of experimental quality may only be obtainable with the use of more sophisticated and accurate methods, such as quantum diffusion Monte Carlo. The approach of modified Shepard's interpolation is also extended to construct shielding constants σ surfaces of the three molecules. By using a σ surface with the equilibrium geometry as a single data point to compute isotropic nuclear shielding constants for each descendant in the QDMC ensemble representing the ground state wave function, we reproduce the results obtained through ab initio computed σ to within statistical noise. Development of such an approach could thereby alleviate the need for any future costly ab initio σ calculations.
Isotropic nuclear shielding constants at the equilibrium molecular structure σeq and zero‐point vibrational corrections (ZPVCs) to σeq are evaluated using the B3LYP/aug‐cc‐pVTZ level of theory, as well as the KT2/aug‐cc‐pVTZ level of theory. Various scaling factors and systematic corrections are obtained by linear regression to experimental shielding constants. Comparisons of the scaled and systematically corrected equilibrium and vibrationally averaged shielding constants reveal that, at the 99% confidence level, the ZPVCs via second‐order perturbation theory do not improve the agreement of B3LYP/aug‐cc‐pVTZ and KT2/aug‐cc‐pVTZ calculated shielding constants with experiment. This holds true when the same analysis is applied to CCSD(T)/aug‐cc‐pCV[TQ]Z calculated σeq of Teale et al. [Journal of Chemical Physics 2013, 138, 024111]. In addition, at the 99% confidence level, B3LYP/aug‐cc‐pVTZ and KT2/aug‐cc‐pVTZ scaled and systematically corrected shielding constants are found to be statistically no different from CCSD(T)/aug‐cc‐pCV[TQ]Z calculated σeq. The use of scaling factors and systematic corrections could thus provide a cheaper but yet reasonably accurate alternative for the study of nuclear shielding constants of larger systems.
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