Benchmark Study of Isotropic Hyperfine Coupling Constants for Hydrogen:  Influence of Geometry, Correlation Method, and Basis Set

Abstract

Isotropic hyperfine coupling constants (iHFCCs) can be easily measured by electron spin resonance spectroscopy in solution, but they have proven difficult to calculate from first principles. We test the performance of the newly developed (aug-)cc-pVXZ-t5s basis sets for hydrogen with Dunning's (aug-)cc-pVXZ and -pCVXZ basis sets for non-hydrogen atoms. Correlation is included by CCSD and CCSD(T) using UHF and ROHF references. A two-point extrapolation of cc-pVDZ:cc-pVDZ-t5s-a5 and cc-pVTZ:cc-pVTZ-t5s-a6 hydrogen iHFCCs is found to be very useful. Diffuse functions have nearly no influence on extrapolated iHFCCs. We also explore the dependence of the calculated iHFCCs on the level of theory used in optimizing the geometries. For this purpose, we optimized geometries up to the UHF-CCSD/cc-pCVQZ and UHF-CCSDT/cc-pCVTZ levels and extrapolated to the "complete basis set" limit. The calculated iHFCCs are compared to reference values, which are experimental numbers corrected for solvent and the most important vibrational effects. Our test molecules are the CH 3 • , C 2 H 3 • , and H 2 CN • radicals. At the highest level of theory, the largest deviations from the reference values are smaller than 3.5 G and 6%. The rms errors are below 2.1 G and 4%. The cc-pVXZ:cc-pVXZ-t5s basis set combinations perform better than the EPR-n and the Chipman [631|41] basis set. All of them are better than similarly sized basis sets that were not developed for iHFCCs. The calculated iHFCCs are influenced most strongly by the choice of basis set, the perturbative inclusion of connected triple excitations, and the choice of reference wave function and the level of theory in geometry optimization. Core correlation is necessary for the computation of iHFCCs for non-hydrogen atoms but has very little influence on the iHFCCs of hydrogen atoms. A good compromise between the cost and accuracy of hydrogen iHFCCs seems to be reached by two-point extrapolated ROHF-CCSD(T)-fc iHFCCs at UHF-MBPT(2)-fc/cc-pVTZ geometries. ROHF-MBPT(2)-fc or UHF-CCSD-fc/cc-pVTZ geometries are necessary when single excitations are not negligible.

Gaussian Basis Sets for Highly Accurate Calculations of Isotropic Hyperfine Coupling Constants at Hydrogen

“…This will be investigated in the following article on small organic radicals, together with the influences of the optimization method and correlation methods used in calculating HFCCs. 34 cc-pVDZ-t5s- following nomenclature: harm denotes a harmonic basis set; f2 indicates that exponents are separated by a factor of 2; and s100-20-5 tells us that one of the s exponents is 1.00, with 20 tighter and 5 more diffuse functions.…”

A theoretical study of the CH2N isomers: Molecular structure and energetics

“…[10], extrapolation to the CBS limit, core-valence correlation corrections and effects due to higher excitations have been considered, but instead of performing all the geometry optimizations required, the authors resorted to the use of approximations (see Ref. [10] and the corresponding Supporting Information for all details). Furthermore, the cc-pVQZ basis was the largest set considered.…”

“…Extrapolation to the basis set limit (CBS) as well as core-valence (CV) correlation corrections have been accounted in order to get an accurate estimate of the equilibrium structure. In a previous paper, Bartlett and coworkers also performed a systematic investigation of the molecular structure of H 2 CN at the coupled-cluster level with the aim of studying the influence of geometry on the isotropic hyperfine coupling constants of hydrogen [10].…”

Role of zero-point vibrational corrections to carbon hyperfine coupling constants in organic π radicals

“…[7][8][9][10][11][12][13][14][15][16][17][18] The lack of such analysis tools forced early investigations of EPR data to rely on rules-of-thumb or simple principles that relate the spin density to the measured hyperfine coupling constants (HFCCs). One such relation is the McConnell relation that states that the spin density ρ C on the carbon of a C-H fragment in an organic π radical is linearly dependent on the isotropic hyperfine constant of hydrogen.…”

“…One such relation is the McConnell relation that states that the spin density ρ C on the carbon of a C-H fragment in an organic π radical is linearly dependent on the isotropic hyperfine constant of hydrogen. [1][2][3] Although such relations or structure-property tools have frequently been used in the field of EPR, [4][5][6] recent advances in the quantum chemical modeling of HFCCs in organic radicals [7][8][9][10][11][12][13][14][15][16][17][18] offer an alternative way for exploring the physical origin of these constants.…”