Transition metal NMR chemical shifts from optimized effective potentials

Effects of the locality of a potential derived from hybrid density functionals on Kohn-Sham orbitals and excited states

Density functional theory (DFT) has been an essential tool for electronic structure calculations in various fields. In particular, its hybrid method including the Hartree-Fock (HF) exchange term remarkably improves the reliability of DFT for chemical applications and computational material design. There are two different types of exchange-correlation potential that can be derived from hybrid functionals. The conventional approach adopts a non-multiplicative potential including the non-local HF exchange operator. Herein, we propose to use a local multiplicative potential as an alternative for accurate excited state calculations. We show that such a local potential can be derived from existing global hybrid functionals using the optimized effective potential method. As a proof-of-concept, we chose PBE0 and investigated its performance for the Caricato benchmark set. Unlike the conventional one, the local potential produced orbital energy gaps with no strong dependence on the mixing ratio as a good approximation for optical excitations. Furthermore, its time-dependent DFT resulted in a surprisingly small mean absolute error even with a local density approximation kernel, surpassing all reported values with various popular functionals. In particular, most excitations were dictated by single orbital transitions due to physically meaningful virtual orbitals, which is beneficial to clear interpretations in the molecular orbital picture.

Benchmarking density-functional theory calculations of NMR shielding constants and spin-rotation constants using accurate coupled-cluster calculations

Accurate sets of benchmark nuclear-magnetic-resonance shielding constants and spin-rotation constants are calculated using coupled-cluster singles-doubles (CCSD) theory and coupled-cluster singles-doubles-perturbative-triples [CCSD(T)] theory, in a variety of basis sets consisting of (rotational) London atomic orbitals. The accuracy of the calculated coupled-cluster constants is established by a careful comparison with experimental data, taking into account zero-point vibrational corrections. Coupled-cluster basis-set convergence is analyzed and extrapolation techniques are employed to estimate basis-set-limit quantities, thereby establishing an accurate benchmark data set. Together with the set provided for rotational g-tensors and magnetizabilities in our previous work [O. B. Lutnæs, A. M. Teale, T. Helgaker, D. J. Tozer, K. Ruud, and J. Gauss, J. Chem. Phys. 131, 144104 (2009)], it provides a substantial source of consistently calculated high-accuracy data on second-order magnetic response properties. The utility of this benchmark data set is demonstrated by examining a wide variety of Kohn-Sham exchange-correlation functionals for the calculation of these properties. None of the existing approximate functionals provide an accuracy competitive with that provided by CCSD or CCSD(T) theory. The need for a careful consideration of vibrational effects is clearly illustrated. Finally, the pure coupled-cluster results are compared with the results of Kohn-Sham calculations constrained to give the same electronic density. Routes to future improvements are discussed in light of this comparison.

Density functional theory for transition metals and transition metal chemistry

We introduce density functional theory and review recent progress in its application to transition metal chemistry. Topics covered include local, meta, hybrid, hybrid meta, and range-separated functionals, band theory, software, validation tests, and applications to spin states, magnetic exchange coupling, spectra, structure, reactivity, and catalysis, including molecules, clusters, nanoparticles, surfaces, and solids.

A solid-state 53Cr NMR study of chromate and dichromate salts

Solid-state (53)Cr NMR spectra of a series of chromate (CrO4(2-)) and dichromate (Cr2O7(2-)) salts have been examined by employing the stepped-frequency quadrupolar Carr-Purcell Meiboom-Gill (QCPMG) experiment and high applied magnetic field strengths, 11.75 and 18.8 T. Cr-53 nuclear quadrupolar coupling constants, CQ(53Cr), ranging from 1.23 to 5.01 MHz for the Cr(4(2-) salts and 7.25 to 8.14 MHz for the Cr2O7(2-) salts have been measured. For the dichromate salts, this corresponds to central transition 53Cr NMR lineshapes of 200-250 kHz at 18.8 T. The use of hyperbolic secant (HS) pulses in combination with the Hahn-echo (HE) or QCPMG experiment results in significant sensitivity enhancements when acquiring 53Cr NMR spectra of magic-angle spinning (MAS) samples, provided the MAS rate is fast with respect to the second-order quadrupolar interaction. For the CrO4(2-) and Cr2O7(2-) salts, the anisotropic chromium magnetic shielding interaction is generally negligible compared to the second-order 53Cr nuclear quadrupolar interaction. No simple correlation between the structure of the CrO4(2-) and Cr2O7(2-) anions and the observed CQ(53Cr) values has been found.

Modeling the adiabatic connection in H2

Full configuration interaction (FCI) data are used to quantify the accuracy of approximate adiabatic connection (AC) forms in describing the ground state potential energy curve of H2, within spin-restricted density functional theory (DFT). For each internuclear separation R, accurate properties of the AC are determined from large basis set FCI calculations. The parameters in the approximate AC form are then determined so as to reproduce these FCI values exactly, yielding an exchange-correlation energy expressed entirely in terms of FCI-derived quantities. This is combined with other FCI-derived energy components to give the total electronic energy; comparison with the FCI energy quantifies the accuracy of the AC form. Initial calculations focus on a [1/1]-Padé-based form. The potential energy curve determined using the procedure is a notable improvement over those from existing DFT functionals. The accuracy near equilibrium is quantified by calculating the bond length and vibrational wave numbers; errors in the latter are below 0.5%. The molecule dissociates correctly, which can be traced to the use of virtual orbital eigenvalues in the slope in the noninteracting limit, capturing static correlation. At intermediate R, the potential energy curve exhibits an unphysical barrier, similar to that noted previously using the random phase approximation. Alternative forms of the AC are also considered, paying attention to size extensivity and the behavior in the strong-interaction limit; none provide an accurate potential energy curve for all R, although good accuracy can be achieved near equilibrium. The study demonstrates how data from correlated ab initio calculations can provide valuable information about AC forms and highlight areas where further theoretical progress is required.