Self-Consistent Field Calculation of Nuclear Magnetic Resonance Chemical Shielding Constants Using Gauge-Including Atomic Orbitals and Approximate Two-Electron Integrals

Abstract

The chain-of-spheres method (COS) for approximating two-electron integrals is applied to Hartree-Fock and density functional theory calculations of nuclear magnetic resonance chemical shielding tensors, based on gauge-including atomic orbitals. The accuracy of the approximation is compared to that of the resolution of the identity (RI) approach, using a benchmark test set of 15 small molecules. Reasonable auxiliary basis sets and grid sizes are selected on the basis of a careful investigation of how approximating each of the two-electron terms in the self-consistent field (SCF) and coupled perturbed SCF equations affects the calculated shielding constants. It is found that the errors are linearly additive but can have either sign. The mean absolute relative error due to applying the RI/COS approximations with the chosen settings to all two-electron terms is on the order of 0.01% and therefore negligible compared to the errors due to basis set incompleteness (∼1%) and the method used (10-50%). Several larger organic systems are used to assess the efficiency of the RI approximation for both Coulomb- and exchange-type integrals (RIJK) as well as a combination of RI for Coulomb and COS for exchange contributions (RIJCOSX). The RIJK approximation is more efficient for small molecules, while for systems of over 100 electrons and 1000 basis functions, the RIJCOSX approximation is superior.

Phosphorus mononitride: A difficult case for theory

“…The reported 31 P CCSD result (33.4 ppm) is closely reproduced by our CCSD/aug‐pcJ‐n CBS value (34.19 ppm). However, reported 15 N shieldings calculated at the CCSD(T) levels differ by about 7 ppm. This is in contrast to our CCSD(T) CBS nitrogen shielding values obtained with different families of basis sets (aug‐cc‐pCV X Z, aug‐pcJ‐n, and aug‐pcSseg‐n) that differ by only ∼0.21 to ∼0.81 ppm.…”

“…Note that PN and N 2 constitute an isoelectronic pair; thus, several theoretical studies have been devoted to the structure and spectroscopic properties of PN and their comparison with N 2 . The monoconfigurational nature of the ground state of PN was verified theoretically .…”

“…Interestingly, no experimental nuclear magnetic resonance (NMR) data for PN molecule have been published so far even though NMR is the most common method for structural characterization in organic synthesis. The only two theoretical studies on the quantitative prediction of PN nuclear magnetic shielding constants were reported by Auer and coworkers . They reported on a huge correlation effect on the 31 P nuclear shieldings, showing the difference between the HF‐SCF and CCSD(T) values (with the qz3d1f basis set) to be ∼170 ppm.…”

“…They corrected their theoretical shielding using the zero‐point vibrational correction (ZPVC, −4.4 ppm for phosphorus at combined CCSD(T)/cc‐pVTZ//CCSD(T)/qz3d1f level and −5.3 ppm for nitrogen at the B3LYP/aug‐cc‐pCVTZ level). Recently, Neese and Auer published another theoretical study on NMR shieldings of PN at the CCSD(T) level . They utilized a polarization‐consistent pcSseg‐4 basis set, designed by Jensen for accurate predictions of NMR properties.…”

“…[15,16] Note that PN and N 2 constitute an isoelectronic pair; thus, several theoretical studies have been devoted to the structure and spectroscopic properties of PN and their comparison with N 2 . [17][18][19][20][21][22] The monoconfigurational nature of the ground state of PN was verified theoretically. [23] Woon studied several diatomic molecules consisting of the first-or the second-row atoms [17] using correlated molecular wave functions and correlationconsistent basis sets.…”