Toward the Next Generation of Density Functionals: Escaping the Zero-Sum Game by Using the Exact-Exchange Energy Density.

ConspectusKohn-Sham density functional theory (KS DFT) is arguably the most widely applied electronic-structure method with tens of thousands of publications each year in a wide variety of fields. Its importance and usefulness can thus hardly be overstated. The central quantity that determines the accuracy of KS DFT calculations is the exchange-correlation functional.

Implementation and First Evaluation of Strong-Correlation-Corrected Local Hybrid Functionals for the Calculation of NMR Shieldings and Shifts.

Local hybrid functionals containing strong-correlation factors (scLHs) and range-separated local hybrids (RSLHs) have been integrated into an efficient coupled-perturbed Kohn-Sham implementation for the calculation of nuclear shielding constants. Several scLHs and the ωLH22t RSLH have then been evaluated for the first time for the extended NS372 benchmark set of main-group shieldings and shifts and the TM70 benchmark of 3d transition-metal shifts. The effects of the strong-correlation corrections have been analyzed with respect to the spatial distribution of the sc-factors, which locally diminish exact-exchange admixture at certain regions in a molecule.

Revisiting Gauge-Independent Kinetic Energy Densities in Meta-GGAs and Local Hybrid Calculations of Magnetizabilities.

In a recent study [J. Chem. Theory Comput.

Unusually Large Effects of Charge-assisted C-H⋅⋅⋅F Hydrogen Bonds to Anionic Fluorine in Organic Solvents: Computational Study of F NMR Shifts versus Thermochemistry.

A comparison of computed F NMR chemical shifts and experiment provides evidence for large specific solvent effects for fluoride-type anions interacting with the σ*(C-H) orbitals in organic solvents like MeCN or CH Cl . We show this for systems ranging from the fluoride ion and the bifluoride ion [FHF] to polyhalogen anions [ClF ] . Discrepancies between computed and experimental shifts when using continuum solvent models like COSMO or force-field-based descriptions like the 3D-RISM-SCF model show specific orbital interactions that require a quantum-mechanical treatment of the solvent molecules.

Systematic Evaluation of Modern Density Functional Methods for the Computation of NMR Shifts of 3d Transition-Metal Nuclei.

A wide range of density functionals from all rungs of Jacob's ladder have been evaluated systematically for a set of experimental 3d transition-metal NMR shifts of 70 complexes encompassing 12 × Ti, 10 × V, 10 × Cr, 11 × Mn, 9 × Fe, 9 × Co, and 9 × Ni shift values, as well as a diverse range of electronic structure characteristics. The overall 39 functionals evaluated include one LDA, eight GGAs, seven meta-GGAs (including their current-density-functional─CDFT─versions), nine global hybrids, four range-separated hybrids, eight local hybrids, and two double hybrids, and we also include Hartree-Fock and MP2 calculations. While recent evaluations of the same functionals for a very large coupled-cluster-based benchmark of main-group shieldings and shifts achieved in some cases aggregate percentage mean absolute errors clearly below 2%, the best results for the present 3d-nuclei set are in the range between 4 and 5%.

Extended Benchmark Set of Main-Group Nuclear Shielding Constants and NMR Chemical Shifts and Its Use to Evaluate Modern DFT Methods.

An extended theoretical benchmark set, NS372, for light main-group nuclear shieldings and NMR shifts has been constructed based on high-level GIAO-CCSD(T)/pcSseg-3//CCSD(T)/cc-pVQZ reference data. After removal of the large static-correlation cases O, F, and BH from the statistical evaluations for the O, F, and B subsets, the benchmark comprises overall 372 shielding values in 117 molecules with a wide range of electronic-structure situations, containing 124 H, 14 B, 93 C, 43 N, 31 O, 47 F, 14 P, and 6 S shielding constants. The CCSD(T)/pcSseg-3 data are shown to be close to the basis-set and method limit and thus provide an excellent benchmark to evaluate more approximate methods, such as density functional approaches.

Implementation and Validation of Local Hybrid Functionals with Calibrated Exchange-Energy Densities for Nuclear Shielding Constants.

A recently reported coupled-perturbed Kohn-Sham implementation to compute nuclear shielding constants with gauge-including atomic orbitals and local hybrid functionals has been extended to cover higher derivatives of the density in the local mixing function (LMF) of the local hybrid as well as the calibration function (CF) needed to deal with the ambiguity of exchange-energy densities. This allowed the first evaluation of state-of-the-art local hybrids with "calibrated" exchange-energy densities for nuclear shieldings. Compared to previously evaluated simpler local hybrids without a CF, appreciable improvements are found for proton shieldings.

Effect of the Current Dependence of Tau-Dependent Exchange-Correlation Functionals on Nuclear Shielding Calculations.

Exchange-correlation functionals that depend on the local kinetic energy τ are widely used in many fields. This includes meta-generalized gradient approximation (GGA) functionals and their global hybrid versions as well as local hybrid functionals with τ-dependent local mixing functions to determine position-dependent exact-exchange admixture. Under the influence of an external magnetic field, τ becomes dependent on the gauge of the magnetic vector potential and should thus be extended to a gauge-invariant formulation.

Nuclear Spin-Spin Couplings: Efficient Evaluation of Exact Exchange and Extension to Local Hybrid Functionals.

We present an efficient implementation for the computation of nuclear spin-spin coupling tensors within density functional theory into the TURBOMOLE software suite. Emphasis is put on methods to efficiently evaluate the Hartree-Fock exchange needed for hybrid functionals: resolution of the identity and seminumerical evaluation on a grid. Our algorithm allows for the selection of specific nuclei for the reduction of calculation times.

An Efficient Coupled-Perturbed Kohn-Sham Implementation of NMR Chemical Shift Computations with Local Hybrid Functionals and Gauge-Including Atomic Orbitals.

Nuclear shielding calculations for local hybrid (LH) functionals with position-dependent exact-exchange admixtures within a coupled-perturbed Kohn-Sham (CPKS) framework have been implemented into the Turbomole code using efficient seminumerical integration techniques to deal with two-electron integrals. When using gauge-including atomic orbitals, LHs generate additional terms within the "pre-loop" section of the CPKS scheme compared to global hybrid (GH) functionals, related to perturbed electron-repulsion integrals. These terms have been implemented and tested in detail, together with dependencies on grid sizes and integral screening procedures.

Lessons from the Spin-Polarization/Spin-Contamination Dilemma of Transition-Metal Hyperfine Couplings for the Construction of Exchange-Correlation Functionals.

Hyperfine couplings (HFCs) of open-shell transition-metal centers are known to often depend crucially on core-shell spin polarization (CSSP). The latter is typically underestimated by semilocal density functionals, while admixture of exact exchange (EXX) in (global) hybrid functionals enhances CSSP. Unfortunately, a metal-ligand antibonding character of one or more of the singly occupied molecular orbitals of the complex will cause substantial valence-shell spin polarization (VSSP), which for global hybrids with higher EXX admixtures may lead to substantial spin contamination, thereby deteriorating the overall electronic structure and the dipolar couplings.