Performance of DFT methods in the calculation of isotropic and dipolar contributions to 14N hyperfine coupling constants of nitroxide radicals

A Joint Venture of Ab Initio Molecular Dynamics, Coupled Cluster Electronic Structure Methods, and Liquid-State Theory to Compute Accurate Isotropic Hyperfine Constants of Nitroxide Probes in Water

The isotropic hyperfine coupling constant (HFCC, Aiso) of a pH-sensitive spin probe in a solution, HMI (2,2,3,4,5,5-hexamethylimidazolidin-1-oxyl, C9H19N2O) in water, is computed using an ensemble of state-of-the-art computational techniques and is gauged against X-band continuous wave electron paramagnetic resonance (EPR) measurement spectra at room temperature. Fundamentally, the investigation aims to delineate the cutting edge of current first-principles-based calculations of EPR parameters in aqueous solutions based on using rigorous statistical mechanics combined with correlated electronic structure techniques. In particular, the impact of solvation is described by exploiting fully atomistic, RISM integral equation, and implicit solvation approaches as offered by ab initio molecular dynamics (AIMD) of the periodic bulk solution (using the spin-polarized revPBE0-D3 hybrid functional), embedded cluster reference interaction site model integral equation theory (EC-RISM), and polarizable continuum embedding (using CPCM) of microsolvated complexes, respectively. HFCCs are obtained from efficient coupled cluster calculations (using open-shell DLPNO-CCSD theory) as well as from hybrid density functional theory (using revPBE0-D3). Re-solvation of "vertically desolvated" spin probe configuration snapshots by EC-RISM embedding is shown to provide significantly improved results compared to CPCM since only the former captures the inherent structural heterogeneity of the solvent close to the spin probe. The average values of the Aiso parameter obtained based on configurational statistics using explicit water within AIMD and from EC-RISM solvation are found to be satisfactorily close. Using either such explicit or RISM solvation in conjunction with DLPNO-CCSD calculations of the HFCCs provides an average Aiso parameter for HMI in aqueous solution at 300 K and 1 bar that is in good agreement with the experimentally determined one. The developed computational strategy is general in the sense that it can be readily applied to other spin probes of similar molecular complexity, to aqueous solutions beyond ambient conditions, as well as to other solvents in the longer run.

Performance of the DLPNO-CCSD and recent DFT methods in the calculation of isotropic and dipolar contributions to 14N hyperfine coupling constants of nitroxide radicals

In the present study, the performance of a set of density functionals: BP86, PBE, OLYP, BEEF, PBEpow, TPSS, SCAN, PBEGXPBE, M06L, MN15L, B3LYP, PBE0, mPW1PW, B97, BHandHLYP, mPW1PW, B98, TPSS0, PBE1KCIS, SCAN0, M06, M06-2X, MN15, CAM-B3LYP, ωB97x, B2PLYP, and the B3LYP/N07D and PBE/N07D schemes in the calculation of the ¹⁴N anisotropic hyperfine coupling (HFC) constants of a set of 23 nitroxide radicals is evaluated. The results are compared with those obtained with the DLPNO-CCSD method and experimental HFC values. Harmonic contribution to the ¹⁴N HFC vibrational correction was calculated at the revPBE0/def2-TZVPP level and included in the evaluation. With the vibrational correction, the DLPNO-CCSD method yielded HFC values in good agreement with the experiment (mean absolute deviation (MAD) = 0.3 G for the dipole-dipole contribution and MAD = 0.8 G for the contact coupling contribution). The best DFT results are obtained using the M06 functional with MAD = 0.2 G for the dipole-dipole contribution and MAD = 0.7 G for the contact coupling contribution. In general, vibrational correction significantly improved most DFT functionals' performance but did not change its overall ranking.

Benchmarking Magnetizabilities with Recent Density Functionals

We have assessed the accuracy of the magnetic properties of a set of 51 density functional approximations, including both recently published and already established functionals. The accuracy assessment considers a series of 27 small molecules and is based on comparing the predicted magnetizabilities to literature reference values calculated using coupled-cluster theory with full singles and doubles and perturbative triples [CCSD(T)] employing large basis sets. The most accurate magnetizabilities, defined as the smallest mean absolute error, are obtained with the BHandHLYP functional. Three of the six studied Berkeley functionals and the three range-separated Florida functionals also yield accurate magnetizabilities. Also, some older functionals like CAM-B3LYP, KT1, BHLYP (BHandH), B3LYP, and PBE0 perform rather well. In contrast, unsatisfactory performance is generally obtained with Minnesota functionals, which are therefore not recommended for calculations of magnetically induced current density susceptibilities and related magnetic properties such as magnetizabilities and nuclear magnetic shieldings. We also demonstrate that magnetizabilities can be calculated by numerical integration of magnetizability density; we have implemented this approach as a new feature in the gauge-including magnetically induced current (GIMIC) method. Magnetizabilities can be calculated from magnetically induced current density susceptibilities within this approach even when analytical approaches for magnetizabilities as the second derivative of the energy have not been implemented. The magnetizability density can also be visualized, providing additional information that is not otherwise easily accessible on the spatial origin of magnetizabilities.

Computation of NMR Shielding Constants for Solids Using an Embedded Cluster Approach with DFT, Double-Hybrid DFT, and MP2

In this work, we explore the accuracy of post-Hartree–Fock (HF) methods and double-hybrid density functional theory (DFT) for the computation of solid-state NMR chemical shifts. We apply an embedded cluster approach and investigate the convergence with cluster size and embedding for a series of inorganic solids with long-range electrostatic interactions. In a systematic study, we discuss the cluster design, the embedding procedure, and basis set convergence using gauge-including atomic orbital (GIAO) NMR calculations at the DFT and MP2 levels of theory. We demonstrate that the accuracy obtained for the prediction of NMR chemical shifts, which can be achieved for molecular systems, can be carried over to solid systems. An appropriate embedded cluster approach allows one to apply methods beyond standard DFT even for systems for which long-range electrostatic effects are important. We find that an embedded cluster should include at least one sphere of explicit neighbors around the nuclei of interest, given that a sufficiently large point charge and boundary effective potential embedding is applied. Using the pcSseg-3 basis set and GIAOs for the computation of nuclear shielding constants, accuracies of 1.6 ppm for ⁷Li, 1.5 ppm for ²³Na, and 5.1 ppm for ³⁹K as well as 9.3 ppm for ¹⁹F, 6.5 ppm for ³⁵Cl, 7.4 ppm for ⁷⁹Br, and 7.5 ppm for ²⁵Mg as well as 3.8 ppm for ⁶⁷Zn can be achieved with MP2. Comparing various DFT functionals with HF and MP2, we report the superior quality of results for methods that include post-HF correlation like MP2 and double-hybrid DFT.

How accurate is density functional theory in predicting spin density? An insight from the prediction of hyperfine coupling constants

Electron paramagnetic resonance (EPR) spectroscopy has been proven to be an important technique for studying paramagnetic systems. Probably, the most accessible EPR parameter and the one that provides a significant amount of information about molecular structure and spin density is the hyperfine coupling constant (HFCC). Hence, accurate quantum-chemical modeling of HFCCs is frequently essential to the adequate interpretation of EPR spectra. It requires the precise spin density, which is the difference between the densities of α- and β-electrons, and thus, its quality is expected to reflect the quality of the total electron density. The question of which approximate exchange-correlation density functional yields sufficiently accurate HFCCs, and thus, the spin density remains open. To assess the performance of well-established density functionals for calculating HFCCs, we used a series of 26 small paramagnetic species and compared the obtained results to the CCSD reference values. The performance of DFT was also tested on EPR-studied o-semiquinone radical interacting with water molecules and Mg²⁺ cation. The HFCCs were additionally calculated by the DLPNO-CCSD method, and this wave function-based technique was found superior to all functionals we tested. Although some functionals were found, on average, to be fairly efficient, we found that the most accurate functional is system-dependent, and therefore, the DLPNO-CCSD method should be preferred for theoretical investigations of the HFCCs and spin density.

Probing basis set requirements for calculating hyperfine coupling constants

A series of basis sets optimized for the calculation of the hyperfine coupling constant is proposed. The pcH-n basis sets are defined in qualities from double-ζ to pentuple-ζ for the elements H to Ar. They are derived from the polarization consistent basis sets by addition of two tight s-functions and one tight p-, d-, and f-function and are shown to provide an exponential convergence toward the complete basis set limit, and they have significantly lower basis set errors than other commonly used basis sets for a given ζ quality. The pcH basis sets display very similar basis set convergence with a range of density functional theory methods and may also be suitable for wave function based methods.