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This study evaluates the performance of doubles-corrected random phase approximation (RPA) and higher random phase approximation (HRPA) approaches in predicting nuclear magnetic resonance (NMR) coupling constants involving fluorine. Their performance is benchmarked against experimental data and compared with that of higher-level theoretical methods, specifically second-order polarization propagator (SOPPA) and SOPPA(CCSD). Additionally, we discuss their performance relative to density functional theory (DFT). We find that RPA(D) is severely constrained by (near) triplet instabilities, while HRPA(D) demonstrates markedly improved stability. Statistical analysis reveals stronger patterns for carbon-fluorine couplings across the methods and systems investigated compared with fluorine-hydrogen couplings. While SOPPA-based methodologies prove to be superior in accuracy, HRPA(D) shows promising performance in reducing the computational burden of these calculations, albeit with a tendency to underestimate the coupling strength. These findings highlight the potential of HRPA(D) as a practical alternative to SOPPA methods, even for such difficult properties as NMR spin-spin coupling constants involving fluorine, emphasizing its role in improving predictive accuracy and efficiency across diverse chemical environments.

Spectroscopic characterization of Hg(II)-thiolate complexes is central to the bioinorganic chemistry of Hg(II). Interpretation of 199 Hg NMR usually relies on data recorded for reference compounds; however, here, it is demonstrated that 199 Hg NMR chemical shifts may be calculated within 40 ppm of experimental values for 2-, 3-, and 4-coordinate Hg(II)-thiolate complexes, using the PBE0 functional, the QZ4P basis set on Hg and S and TZP on all other atoms, and SO-ZORA to account for relativistic effects. The chemical shift is particularly sensitive to the Hg-S bond length (ca. 300 ppm/0.1 Å per Hg-S bond), while it is less sensitive to changes of S-Hg-S angles (up to 40 ppm/10 degrees 1 ). Rigid rotation of the methyl groups around the Hg-S axis in model complexes, [Hg(SCH 3 ) n ] 2- n ( n = 2, 3, 4), may give rise to changes of up to 100 ppm. Finally, calculations of the 199 Hg NMR chemical shift for a model system of the Hg(II) binding site in the MerR protein demonstrate that experimental 199 Hg NMR chemical shift data in combination with DFT calculations may be used as a constraint in the optimization of Hg(II) sites in proteins.

In this study, the mechanism of selfpromoted N-glycosylations is extensively investigated through kinetic experiments, computational studies, and nucleophilic competition experiments. Based on the findings, the mechanism is proposed to be initiated by proton transfer from the acidic sulfonyl carbamate to the trichloroacetimidate, upon formation of an associated contact ion pair. This ion pair then collapses in an SN1-like fashion, with formation of an oxocarbeniumion-like intermediate. According to the proposed mechanism, stereospecificity arises from the associated nature of all intermediates formed throughout the reaction. During the mechanistic study, it was also found that the sulfonyl carbamates have catalytic properties if a competing nucleophile is present., (© 2024 Wiley‐VCH GmbH.)

Calculating molecular properties using quantum devices can be performed through the quantum linear response (qLR) or, equivalently, the quantum equation of motion (qEOM) formulations. Different parameterizations of qLR and qEOM are available, namely naïve, projected, self-consistent, and state-transfer. In the naïve and projected parameterizations, the metric is not the identity, and we show that it depends on redundant orbital rotations. This dependency may lead to divergences in the excitation energies for certain choices of the redundant orbital rotation parameters in an idealized noiseless setting. Furthermore, this leads to a significant variance when calculations include statistical noise from finite quantum sampling., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

Thiolate containing mercury(II) complexes of the general formula [Hg(SR) n ] 2 - n have been of great interest since the toxicity of mercury was recognized. 199 Hg nuclear magnetic resonance spectroscopy (NMR) is a powerful tool for characterization of mercury complexes. In this work, the Hg shielding constants in a series of [Hg(SR) n ] 2 - n complexes are therefore investigated computationally with particular emphasis on their geometry dependence. Geometry optimizations and NMR chemical shift calculations are performed at the density functional theory (DFT) level with both the zeroth-order regular approximation (ZORA) and four-component relativistic methods. The four exchange-correlation (XC) functionals PBE0, PBE, B3LYP, and BLYP are used in combination with either Dyall's Gaussian-type (GTO) or Slater-type orbitals (STOs) basis sets. Comparing ZORA and four-component calculations, one observes that the calculated shielding constants for a given molecular geometry have a constant difference of ∼ 1070 ppm. This confirms that ZORA is an acceptable relativistic method to compute NMR chemical shifts. The combinations of four-component/PBE0/v3z and ZORA/PBE0/QZ4P are applied to explore the geometry dependence of the isotropic shielding. For a given coordination number, the distance between mercury and sulfur is the key factor affecting the shielding constant, while changes in bond and dihedral angles and even different side groups have relatively little impact., (© 2024 The Authors. Magnetic Resonance in Chemistry published by John Wiley & Sons Ltd.)

The prediction of spectral properties via linear response (LR) theory is an important tool in quantum chemistry for understanding photoinduced processes in molecular systems. With the advances of quantum computing, we recently adapted this method for near-term quantum hardware using a truncated active space approximation with orbital rotation, named quantum linear response (qLR). In an effort to reduce the classic cost of this hybrid approach, we here derive and implement a reduced density matrix (RDM) driven approach of qLR. This allows for the calculation of spectral properties of moderately sized molecules with much larger basis sets than so far possible. We report qLR results for benzene and R -methyloxirane with a cc-pVTZ basis set and study the effect of shot noise on the valence and oxygen K-edge absorption spectra of H 2 O in the cc-pVTZ basis.

We test the performance of the polarizable embedding variational quantum eigensolver self-consistent field (PE-VQE-SCF) model for computing electric field gradients with comparisons to conventional complete active space self-consistent-field (CASSCF) calculations and experimental results. We compute quadrupole coupling constants for ice VIII and ice IX. We find close agreement of the quantum-computing PE-VQE-SCF results with the results from the classical PE-CASSCF calculations and with experiment. Furthermore, we observe that the inclusion of the environment is crucial for obtaining results that match the experimental data. The calculations for ice VIII are within the experimental uncertainty for both CASSCF and VQE-SCF for oxygen and lie close to the experimental value for ice IX as well. With the VQE-SCF, which is based on an adaptive derivative-assembled problem-tailored (ADAPT) ansatz, we find that the inclusion of the environment and the size of the different basis sets do not directly affect the gate counts. However, by including an explicit environment, the wavefunction and therefore the optimization problem become more complicated, which usually results in the need to include more operators from the operator pool, thereby increasing the depth of the circuit.

The interest in mercury radioisotopes, 197m Hg ( t 1/2 = 23.8 h) and 197g Hg ( t 1/2 = 64.14 h), has recently been reignited by the dual diagnostic and therapeutic nature of their nuclear decays. These isotopes emit γ-rays suitable for single photon emission computed tomography imaging and Auger electrons which can be exploited for treating small and metastatic tumors. However, the clinical utilization of 197m/g Hg radionuclides is obstructed by the lack of chelators capable of securely binding them to tumor-seeking vectors. This work aims to address this challenge by investigating a series of chemically tailored macrocyclic platforms with sulfur-containing side arms, namely, 1,4,7,10-tetrakis[2-(methylsulfanyl)ethyl]-1,4,7,10-tetraazacyclododecane (DO4S), 1,4,7-tris[2-(methylsulfanyl)ethyl]-1,4,7,10-tetraazacyclododecane (DO3S), and 1,7-bis[2-(methylsulfanyl)ethyl]-1,4,7,10-tetraazacyclododecane-4,10-diacetic acid (DO2A2S). 1,4,7,10-Tetrazacyclododecane-1,4,7,10-tetracetic acid (DOTA), the widest explored chelator in nuclear medicine, and the nonfunctionalized backbone 1,4,7,10-tetrazacyclododecane (cyclen) were considered as well to shed light on the role of the sulfanyl arms in the metal coordination. To this purpose, a comprehensive experimental and theoretical study encompassing aqueous coordination chemistry investigations through potentiometry, nuclear magnetic resonance (NMR) spectroscopy, X-ray crystallography, and density functional theory (DFT) calculations, as well as concentration- and temperature-dependent [ 197m/g Hg]Hg 2+ radiolabeling and in vitro stability assays in human serum was conducted. The obtained results reveal that the investigated chelators rapidly complex Hg 2+ in aqueous media, forming extremely thermodynamically stable 1:1 metal-to-ligand complexes with superior stabilities compared to those of DOTA or cyclen. These complexes exhibited 6- to 8-fold coordination environments, with donors statically bound to the metal center, as evidenced by the presence of 1 H- 199 Hg spin-spin coupling via NMR. A similar octacoordinated environment was also found for DOTA in both solution and solid state, but in this case, multiple slowly exchanging conformers were detected at ambient temperature. The sulfur-rich ligands quantitatively incorporate cyclotron-produced [ 197m/g Hg]Hg 2+ under relatively mild reaction conditions (pH = 7 and T = 50 °C), with the resulting radioactive complexes exhibiting decent stability in human serum (up to 75% after 24 h). By developing viable chelators and understanding the impact of structural modifications, our research addresses the scarcity of suitable chelating agents for 197m/g Hg, offering promise for its future in vivo application as a theranostic Auger-emitter radiometal.

In this paper, benchmark results are presented on the calculation of vertical electronic excitation energies using a long-range second-order polarization propagator approximation (SOPPA) description with a short-range density functional theory description based on the Perdew-Burke-Ernzerhof (PBE) functional. The excitation energies are investigated for 132 singlet states and 71 triplet states across 28 medium-sized organic molecules. The results show that overall SOPPA-srPBE always performs better than PBE and that SOPPA-srPBE performs better than SOPPA for singlet states, but slightly worse than SOPPA for triplet states when CC3 results are the reference values., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

Determining the properties of molecules and materials is one of the premier applications of quantum computing. A major question in the field is how to use imperfect near-term quantum computers to solve problems of practical value. Inspired by the recently developed variants of the quantum counterpart of the equation-of-motion (qEOM) approach and the orbital-optimized variational quantum eigensolver (oo-VQE), we present a quantum algorithm (oo-VQE-qEOM) for the calculation of molecular properties by computing expectation values on a quantum computer. We perform noise-free quantum simulations of BeH 2 in the series of STO-3G/6-31G/6-31G* basis sets and of H 4 and H 2 O in 6-31G using an active space of four electrons and four spatial orbitals (8 qubits) to evaluate excitation energies, electronic absorption, and, for twisted H 4 , circular dichroism spectra. We demonstrate that the proposed algorithm can reproduce the results of conventional classical CASSCF calculations for these molecular systems.

Linear response (LR) theory is a powerful tool in classic quantum chemistry crucial to understanding photoinduced processes in chemistry and biology. However, performing simulations for large systems and in the case of strong electron correlation remains challenging. Quantum computers are poised to facilitate the simulation of such systems, and recently, a quantum linear response formulation (qLR) was introduced [Kumar et al., J. Chem. Theory Comput. 2023 , 19 , 9136-9150]. To apply qLR to near-term quantum computers beyond a minimal basis set, we here introduce a resource-efficient qLR theory, using a truncated active-space version of the multiconfigurational self-consistent field LR ansatz. Therein, we investigate eight different near-term qLR formalisms that utilize novel operator transformations that allow the qLR equations to be performed on near-term hardware. Simulating excited state potential energy curves and absorption spectra for various test cases, we identify two promising candidates, dubbed "proj LRSD" and "all-proj LRSD".

We explore Davidson methods for obtaining excitation energies and other linear response properties within the recently developed quantum self-consistent linear response (q-sc-LR) method. Davidson-type methods allow for obtaining only a few selected excitation energies without explicitly constructing the electronic Hessian since they only require the ability to perform Hessian-vector multiplications. We apply the Davidson method to calculate the excitation energies of hydrogen chains (up to H 10 ) and analyze aspects of statistical noise for computing excitation energies on quantum simulators. Additionally, we apply Davidson methods for computing linear response properties such as static polarizabilities for H 2 , LiH, H 2 O, OH - , and NH 3 , and show that unitary coupled cluster outperforms classical projected coupled cluster for molecular systems with strong correlation. Finally, we formulate the Davidson method for damped (complex) linear response, with application to the nitrogen K-edge X-ray absorption of ammonia, and the C 6 coefficients of H 2 , LiH, H 2 O, OH - , and NH 3 .

We formulate and implement the Variational Quantum Eigensolver Self Consistent Field (VQE-SCF) algorithm in combination with polarizable embedding (PE), thereby extending PE to the regime of quantum computing. We test the resulting algorithm, PE-VQE-SCF, on quantum simulators and demonstrate that the computational stress on the quantum device is only slightly increased in terms of gate counts compared to regular VQE-SCF. On the other hand, no increase in shot noise was observed. We illustrate how PE-VQE-SCF may lead to the modeling of real chemical systems using a simulation of the reaction barrier of the Diels-Alder reaction between furan and ethene as an example., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

Previous theoretical investigations of the reactions between an OH radical and a nucleobase have stated the most important pathways to be the C5-C6 addition for pyrimidines and the C8 addition for purines. Furthermore, the abstraction of a methyl hydrogen from thymine has also been proven an important pathway. The conclusions were based solely on gas-phase calculations and harmonic vibrational frequencies. In this paper, we supplement the calculations by applying solvent corrections through the polarizable continuum model (PCM) solvent model and applying anharmonicity in order to determine the importance of anharmonicity and solvent effects. Density functional theory (DFT) at the ωB97-D/6-311++G(2df,2pd) level with the Eckart tunneling correction is used. The total reaction rate constants are found to be 1.48 ×10-13 cm 3 molecules -1 s -1 for adenine, 1.02 ×10-11 cm 3 molecules -1 s -1 for guanine, 5.52 ×10-13 cm 3 molecules -1 s -1 for thymine, 1.47 ×10-13 cm 3 molecules -1 s -1 for cytosine and 7.59 ×10-14 cm 3 molecules -1 s -1 for uracil. These rates are found to be approximately two orders of magnitude larger than experimental values. We find that the tendencies observed for preferred pathways for reactions calculated in a solvent are comparable to the preferred pathways for reactions calculated in gas phase. We conclude that applying a solvent has a larger impact on more parameters compared to the inclusion of anharmonicity. For some reactions the inclusion of anharmonicity has no effect, whereas for others it does impact the energetics.

In this study, the performance of the doubles-corrected higher random-phase approximation [HRPA(D)] has been investigated in calculations of nuclear magnetic resonance spin-spin coupling constants (SSCCs) for 58 molecules with the experimental values used as the reference values. HRPA(D) is an approximation to the second-order polarization propagator approximation (SOPPA) and is, therefore, computationally less expensive than SOPPA. HRPA(D) performs comparable and sometimes even better than SOPPA, and therefore, when calculating SSCCs, it should be considered as an alternative to SOPPA. Furthermore, it was investigated whether a coupled-cluster singles, doubles and perturbative triples [CCSD(T)] or Møller-Plesset second order (MP2) geometry optimization was optimal for a SOPPA and a HRPA(D) SSCC calculation for eight smaller molecules. CCSD(T) is the optimal geometry optimization for the SOPPA calculation, and MP2 was optimal for HRPA(D) SSCC calculations., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

Traditional nuclear magnetic resonance (NMR) calculations typically treat systems with a Born-Oppenheimer-derived electronic wave function that is solved for a fixed nuclear geometry. One can numerically account for this neglected nuclear motion by averaging over property values for all nuclear geometries with a vibrational wave function and adding this expectation value as a correction to an equilibrium geometry property value. Presented are benchmark coupled-cluster singles and doubles (CCSD) vibrational corrections to spin-spin coupling constants (SSCCs) computed at the level of vibrational second-order perturbation theory (VPT2) using the vibrational averaging driver of the CFOUR program. As CCSD calculations of vibrational corrections are very costly, cheaper electronic structure methods are explored via a newly developed Python vibrational averaging program within the Dalton Project. Namely, results obtained with the second-order polarization propagator approximation (SOPPA) and density functional theory (DFT) with the B3LYP and PBE0 exchange-correlation functionals are compared to the benchmark CCSD//CCSD(T) and experimental values. CCSD//CCSD(T) corrections are also combined with literature CC3 equilibrium geometry values to form the highest-order vibrationally corrected values available (i.e., CC3//CCSD(T) + CCSD//CCSD(T)). CCSD//CCSD(T) statistics showed favorable statistics in comparison to experimental values, albeit at an unfavorably high computational cost. A cheaper CCSD//CCSD(T) + B3LYP method showed quite similar mean absolute deviation (MAD) values as CCSD//CCSD(T), concluding that CCSD//CCSD(T) + B3LYP is optimal in terms of cost and accuracy. With reference to experimental values, a vibrational correction was not worth the cost for all of the other methods tested. Finally, deviation statistics showed that CC3//CCSD(T) + CCSD//CCSD(T) vibrational-corrected equilibrium values deteriorated in comparison to CCSD//CCSD(T) attributed to the use of a smaller basis set or lack of solvation effects for the CC3 equilibrium calculations.

All practically possible hydrogen abstraction reactions for guanosine and uridine have been investigated through quantum chemical calculations of energy barriers and rate constants. This was done at the level of density functional theory (DFT) with the ωB97X-D functional and the 6-311++G(2df,2pd) Pople basis set. Transition state theory with the Eckart tunneling correction was used to calculate the rate constants. The results show that the reaction involving the hydrogen labelled C4' in the ribofuranose part has the largest rate constant for guanosine with the value 5.097×1010 L mol-1s-1 and the largest for uridine with the value 1.62×1010 L mol-1s-1. Based on the results for these two nucleosides, there is a noticeable similarity between the rate constants in the ribofuranose part of the molecule, even though they are bound to two entirely different nucleobases.

With this work we first test various DFT functionals against CCSD(T) for calculation of EFGs at the position of Cd(II) in a very small model system, Cd(SCH 3 ) 2 . Moreover, the available basis sets in ADF are tested in terms of basis set convergence, and the effect of including relativistic effects using the scalar relativistic and spin orbit ZORA Hamiltonians is explored. The results indicate that an error of up to around 10% on the calculated EFG may be expected using spin-orbit ZORA and the BHandHLYP functional with a locally dense basis set. Next, this method was applied to model systems of the CueR protein, aiming to interpret 111 Ag-PAC spectroscopic data. Note that 111 Ag decays to 111 Cd on which the PAC data are recorded. Surprisingly, model systems truncated - as is often done - at the first C-C bond from the central Cd(II) are inadequate in size, and larger model systems must be employed to achieve reliable EFG calculations. The calculated EFGs agree well with experimental PAC data, and indicate that shortly after the nuclear decay the structure relaxes from linear two-coordinate AgS 2 in the native protein, to a structure (or structures) where Cd(II) recruits additional ligands such as backbone carbonyl oxygens to achieve higher coordination number(s).

In this article, a modification of the second-order polarization propagator approximation (SOPPA) method is introduced and illustrated for the calculation of the indirect nuclear spin-spin couplings. The standard SOPPA method, although cheaper in terms of computational cost, offers less accurate results than the ones obtained with coupled cluster methods. A new method, named SOPPA+A3-3, was therefore developed by adding the terms of the third-order A matrix that rely on the second-order double amplitudes. The performance of this third-order contribution was studied using the coupled cluster singles and doubles method as a reference, calculating the spin-spin couplings of molecules of diverse sizes and compositions, and comparing them to the SOPPA method. The results show that inclusion of this third-order contribution gives more accurate results than the standard SOPPA method with a level of accuracy close to that of the coupled cluster method with only a small increase in the computational cost of the response calculation that dominates the computational cost for small- to medium-sized molecules. The implementation of the first contributions to the third-order polarization propagator approximation in the Dalton program, thus, already shows a significant change in these molecular properties over those obtained with the standard SOPPA method.

A test set of N,N,N',N' -tetrasubstituted p -phenylenediamines are experimentally explored using ESR (electron spin resonance) spectroscopy and analysed from a computational standpoint thereafter. This computational study aims to further aid structural characterisation by comparing experimental ESR hyperfine coupling constants (hfccs) with computed values calculated using ESR-optimised "J-style" basis sets (6-31G(d,p)-J, 6-31G(d,p)-J, 6-311++G(d,p)-J, pcJ-1, pcJ-2 and cc-pVTZ-J) and hybrid-DFT functionals (B3LYP, PBE0, TPSSh, ωB97XD) as well as MP2. PBE0/6-31g(d,p)-J with a polarised continuum solvation model (PCM) correlated best with the experiment, giving an R 2 value of 0.8926. A total of 98% of couplings were deemed satisfactory, with five couplings observed as outlier results, thus degrading correlation values significantly. A higher-level electronic structure method, namely MP2, was sought to improve outlier couplings, but only a minority of couples showed improvement, whilst the remaining majority of couplings were negatively degraded.

The complexation of Mg II with adenosine 5'-triphosphate (ATP) is omnipresent in biochemical energy conversion, but is difficult to interrogate directly. Here we use the spin- 1 / 2 β-emitter 31 Mg to study Mg II -ATP complexation in 1-ethyl-3-methylimidazolium acetate (EMIM-Ac) solutions using β-radiation-detected nuclear magnetic resonance (β-NMR). We demonstrate that (nuclear) spin-polarized 31 Mg, following ion-implantation from an accelerator beamline into EMIM-Ac, binds to ATP within its radioactive lifetime before depolarizing. The evolution of the spectra with solute concentration indicates that the implanted 31 Mg initially bind to the solvent acetate anions, whereafter they undergo dynamic exchange and form either a mono- ( 31 Mg-ATP) or di-nuclear ( 31 MgMg-ATP) complex. The chemical shift of 31 Mg-ATP is observed up-field of 31 MgMg-ATP, in accord with quantum chemical calculations. These observations constitute a crucial advance towards using β-NMR to probe chemistry and biochemistry in solution., (© 2022 The Authors. Angewandte Chemie International Edition published by Wiley-VCH GmbH.)

The experimental and theoretical determination of the mean excitation energy, I(0), and the stopping power, S(v), of a material is of great interest in particle and material physics and radiation therapy. For calculations of I(0), the complete set of electronic transitions in a given basis set is required, effectively limiting such calculations to systems with a small number of electrons, even at the random-phase approximation (RPA)/time-dependent Hartree-Fock (TDHF) or time-dependent density-functional theory level. To overcome such limitations, we present here the implementation of a Lanczos algorithm adapted for the paired RPA/TDHF eigenvalue problem in the Dalton program and show that it provides good approximation of the entire RPA eigenspectra in a reduced space. We observe rapid convergence of I(0) with the number of Lanczos vectors as the algorithm favors the transitions with large contributions. In most cases, the algorithm recovers RPA I(0) values of up to 0.5% accuracy at less than a quarter of the full space size. The algorithm not only exploits the RPA paired structure to save computational resources but also preserves certain sum-over-states properties, as first demonstrated by Johnson et al. [Comput. Phys. Commun. 120, 155 (1999)]. The block Lanczos RPA solver, as presented here, thus shows promise for computing mean excitation energies for systems larger than what was computationally feasible before.

One-bond spin-spin coupling constants (SSCCs) between F and C are computed with density functional theory (DFT). Surprisingly, M06L stands out for its striking accuracy, outperforming any other investigated functional, including PBE0, otherwise considered one of the most reliable for couplings involving F. Although the computation of nuclear magnetic resonance (NMR) parameters involving F is known to be a challenging task, even with a rather small basis set as pcJ-1, M06L provides results with a MAD = 11.7 Hz, whereas the average deviation gets as much as 5 times larger for PBE0 (MAD = 60.0 Hz). In the context of SSCCs on the order of 300 Hz, this is particularly remarkable. We find that the accuracy of M06L/pcJ-1 in predicting 1 J FC constants does not stem from a well-suited exchange or correlation part of the functional. Instead, it is believed to arise from a fortuitous cancellation of errors, as revealed by investigating the convergence of the basis set. Our findings also indicate that 1 J FC constants are highly dependent on the amount of exact exchange included in the expression of the functional, with large fractions being critically important to achieving satisfactory results. Studying the effects of the geometry on 1 J FC , we find that optimizing the geometry at the level of theory used to calculate SSCCs generally improves the quality of the results, although the combination of a M06-2X/aug-cc-pVTZ geometry with M06L/pcJ-1 1 J FC constants best reproduces the experimental data for organofluorine compounds (with the exception of fluoroalkenes).

A series of five intramolecularly hydrogen-bonded arylhydrazone (aryl = phenol, p-nitrophenol, anisole, quinoline) derived molecular switches have been synthesized and characterized by NMR and HRMS techniques. It was found that the compounds exist as different isomers in solution. An investigation of both conformational and/or configurational changes of the azo-hydrazone compounds was carried out by 1D 1 H- and 13 C- spectra, 2D NOESY, COSY, HSQC, and HMBC techniques. It was found that these stimuli-responsive molecular switches exist mainly in the E form by intramolecularly hydrogen bonded between NH and the pyridine nitrogen at equilibrium. Deprotonation of the neutral E form yields the E' deprotonated isomer. Prediction of 13 C-NMR chemical shifts was achieved by DFT quantum mechanical calculations. Anions have traditionally been difficult to calculate correctly, so calculations of the anion using different functionals, basis sets, and solvent effects are also included. Deuterium isotope effects on the 13 C-NMR chemical shifts were employed in the assignments and furthermore utilized as indicators of intramolecular hydrogen bonding. Studies in various organic solvents including CDCl 3 , CD 3 CN, and DMSO-d 6 were also performed aiming to monitor dynamic changes over several days. The effect of the hydrogen bonded solvents leads to Z forms., (© 2021 John Wiley & Sons, Ltd.)

The aug-cc-pVTZ-J basis set family is extended to include the fourth-row p-block elements Ga, Ge, As, Se, and Br. We use the established approach outlined by Sauer and coworkers (J. Chem. Phys. 115, 1324 [2001], J. Chem. Phys. 133, 054308 [2010], J. Chem. Theory Comput. 7, 4070 [2011], and J. Chem. Theory Comput. 7, 4077 [2011]) where the completely uncontracted aug-cc-pVTZ basis set is saturated with tight s-, p-, d-, and f-functions to form the aug-cc-pVTZ-Juc basis set for the tested elements. The saturation is carried out on the simplest hydrides possible for the tested elements GaH, GeH 4 , AsH 3 , H 2 Se, and HBr until an improvement is less than 0.01% for all s-, p-, and d-functions added. f-Functions are added to an improvement less than or equal to 1.0% due to the computational expense these functions add. The saturated aug-cc-pVTZ-Juc (26s16p12d5f) is then recontracted using the molecular orbital coefficients from self-consistent field calculations on the simple hydrides to improve computational efficiency. During contraction of the basis set, we observe that the linear hydrogen bromide molecule has a slower convergence than the other tested molecules which sets a limit on the accuracy obtained. All calculations with the contracted aug-cc-pVTZ-J [17s10p7d5f] gives results that are within 1.0% of the uncontracted results at considerable computational savings., (© 2021 John Wiley & Sons, Ltd.)

The formal potentials for the reversible one-electron oxidation of N , N , N ', N ' tetrasubstituted p -phenylenediamines in acetonitrile have been applied as a test set for benchmarking computational methods for a series of compounds with only small structural differences. The aim of the study is to propose a simple method for calculating the standard oxidation potentials, and therefore, the protocol is progressively developed by adding more terms in the energy expression. In addition, the effect of including implicit solvation models (IEFPCM, CPCM, and SMD), larger basis sets, and correlation methods are investigated. The oxidation potentials calculated using the G3MP2B3 approach with IEFPCM resulted in the best fit ( R 2 = 0.9624), but the slope of the correlation line, 0.74, is far from the optimal value, 1.00. B3LYP/6-311++G(d,p) and TPSSh/6-311++G(2d,p) yielded only slightly less consistent data ( R 2 = 0.9388 and R 2 = 0.9425), but with much better slopes, 1.00 and 0.94, respectively. We conclude that it is important to investigate the basis set size and treatment of electron correlation when calculating oxidation potentials for N , N , N ', N ' tetrasubstituted p -phenylenediamines.

The prediction of 13 C chemical shifts can be challenging with density functional theory (DFT). In this study 39 different functionals and three different basis sets were tested on three neutral alkylpyrroles and their corresponding protonated species. The calculated shielding constants were compared to experimental data and results from previous calculations at the MP2. We find that the meta-hybrid functional TPSSh with either the Pople style basis set 6-311++G(2d,p) or the polarization consistent basis set pcSseg-1 gives the best results for the 13 C chemical shifts, whereas for the 1 H chemical shifts it is the TPSSh functional with either the 6-311++G(2d,p) or pcSseg-2 basis set. Including an explicit solvent molecule hydrogen bonded to NH in the alkylpyrroles improves the results slightly for the 13 C chemical shifts. On the other hand, for 1 H chemical shifts the opposite is true. Compared to calculations at the MP2 level none of the DFT functionals can compete with MP2 for the 13 C chemical shifts but for the 1 H chemical shifts the investigated DFT functionals are shown to give better agreement with experiment than MP2 calculations., (© 2021 Wiley Periodicals LLC.)

Due to the importance of predicting static and dynamic polarizabilities, the performance of various correlated linear response methods including random phase approximation (RPA), RPA(D), higher-order random phase approximation (HRPA), HRPA(D), second-order polarization propagator approximation (SOPPA), SOPPA(CC2), SOPPA(CCSD), CC2, and CCSD has been evaluated against CCSD(T) (static case) and CCSD (dynamic cases) for the T145 set of 145 organic molecules. The benchmark reveals that the HRPA(D) method has the best performance for both static and dynamic polarizabilities apart from CCSD. RPA(D) ranks second for the dynamic cases and third for the static case. Using coupled-cluster amplitudes in SOPPA(CCSD) and SOPPA(CC2), the SOPPA results are significantly improved. The HRPA method has the largest deviations from the reference values for both cases. In general, according to the performance and computational cost of the methods, the HRPA(D) and RPA(D) methods are proposed for calculations of static and dynamic polarizabilities of this and similar sets of molecules.

We present time-dependent density functional theory (TDDFT) calculations of the electronic optical rotation (ORP) for seven oxirane and two aziridine derivatives in the gas phase and in solution and compare the results with the available experimental values. For seven of the studied molecules it is the first time that their optical rotation was studied theoretically and we have therefore investigated the influence of several settings in the TDDFT calculations on the results. This includes the choice of the one-electron basis set, the exchange-correlation functional or the particular polarizable continuum model (PCM). We can confirm that polarized quadruple zeta basis sets augmented with diffuse functions are necessary for converged results and find that the aug-pc-3 basis set is a viable alternative to the frequently employed aug-cc-pVQZ basis set. Based on our study, we cannot recommend the generalized gradient functional KT3 for calculations of the ORP in these compounds, whereas the hybrid functional PBE0 gives results quite similar to the long-range correct CAM-B3LYP functional. Finally, we observe large differences in the solvent effects predicted by the integral equation formalism of PCM and the SMD variant of PCM. For the majority of solute/solvent combinations in this study, we find that the SMD model in combination with the PBE0 functional and the aug-pc-3 basis set gives the best agreement with the experimental values., (© 2021 Wiley-VCH GmbH.)

We present a detailed theoretical study of the electronic absorption spectra and thermochemistry of molecular photoswitches composed of one and two photochromic units of dihydroazulene (DHA)/vinylheptafulvene (VHF) molecules. Six different isomers are considered depending on the ring opening/closure forms of the DHA units. The solvent effect of acetonitrile is investigated using a sequential Molecular Mechanics/Quantum Mechanics approach. The thermochemical investigations of these photochromic molecules were performed using the Free Energy Perturbation method, and the simulations were performed using Configurational Bias Monte Carlo. We show that to open the 5-member ring of the DHA, there is no significant gain in thermal release of energy for the back reaction when a unit or two DHA units are considered. Overall, we found agreement between the solvation free energy based on Monte Carlo simulations and the continuum solvent model. However, the cavitation term in the continuum model is shown to be a source of disagreement when the non-electrostatic terms are compared. The electronic absorption spectra are calculated using TDDFT CAM-B3LYP/cc-pVDZ. Agreement with experiment is obtained within 0.1 eV, considering statistically uncorrelated configurations from the simulations. Inhomogeneous broadening is also considered and found to be well described in all cases., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2021 Elsevier B.V. All rights reserved.)

Accurate nuclear quadrupole moment values are essential as benchmarks for nuclear structure models and for the interpretation of experimentally determined nuclear quadrupole interactions in terms of electronic and molecular structure. Here, we present a novel route to such data by combining perturbed γ-γ angular correlation measurements on free small linear molecules, realized for the first time within this work, with state-of-the-art ab initio electronic structure calculations of the electric field gradient at the probe site. This approach, also feasible for a series of other cases, is applied to Hg and Cd halides, resulting in Q(^{199}Hg,5/2^{-})=+0.674(17)  b and Q(^{111}Cd,5/2^{+})=+0.664(7)  b.

Lytic polysaccharide monooxygenases (LPMOs) are enzymes that bind polysaccharides followed by an (oxidative) disruption of the polysaccharide surface, thereby boosting depolymerization. The binding process between the LPMO catalytic domain and polysaccharide is key to the mechanism and establishing structure-function relationships for this binding is therefore crucial. The hyperfine coupling constants (HFCs) from EPR spectroscopy have proven useful for this purpose. Unfortunately, EPR does not provide direct structural data and therefore the experimental EPR parameters have to be supported with parameters calculated with density functional theory. Yet, calculated HFCs are extremely sensitive to the employed computational setup. Using the LPMO Ls (AA9)A catalytic domain, we here quantify the importance of several choices in the computational setup, ranging from the use of specialized basis, the underlying structures, and the employed exchange-correlation functional. We show that specialized basis sets are an absolute necessity, and also that care has to be taken in the optimization of the underlying structure: only by allowing large parts of the protein around the active site to structurally relax could we obtain results that uniformly reproduced experimental trends. We compare our results to previously published X-ray structures and experimental HFCs for Ls (AA9)A as well as to recent experimental/theoretical results for another (AA10) family of LPMOs., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2020 The Authors.)

NMR shielding and spin-spin coupling constants of cis and trans isomers of FNNF have been determined to near-quantitative accuracy from ab initio calculations. The FNNF system, containing multiple N-F bonds and fluorine atoms, provides a severe test of computational methods. Coupled-cluster methods were used with large basis sets and complete basis set (CBS) extrapolations of the equilibrium geometry results, with vibrational and relativistic corrections. Shielding constants were calculated with basis sets as large as aug-cc-pCV7Z, together with coupled-cluster expansions up to CCSDT, at the all-electron CCSD(T)/aug-cc-pCVQZ optimized geometries. Spin-spin coupling constants have been determined with specialized versions of the correlation consistent basis sets ccJ-pVXZ, further augmented with diffuse functions. All-electron coupled-cluster methods up to CC3 were applied in these calculations. The results of this work highlight the application of state-of-the-art theoretical techniques, and provide the most accurate NMR properties of FNNF to date, which can serve to guide and supplement NMR experimentation.

The performance of different polarization propagator methods, such as RPA, RPA(D), HRPA, HRPA(D), and SOPPA, have been tested against CC3 values for both static and dynamic polarizabilities. The test set consists of 14 (hetero-)aromatic medium-sized organic molecules, mostly with a high degree of symmetry. The benchmark of the methods remarkably reveals that RPA and HRPA(D) yield results comparable with the CC3 values and that they outperform SOPPA for these molecules. For a subset of the molecules, a comparison could be made to experimental values. The comparison for static polarizabilities proves that RPA and HRPA(D) as well as RPA(D) reproduce experimental values to a satisfying precision, whereas the SOPPA method compared to these three methods appears to perform only adequately. An investigation of the performance of Sadlej's polarized triple zeta basis set against Dunning's aug-cc-pVTZ basis set was also carried out. It is found that in contrast to other methods, Sadlej's basis set did not perform sufficiently compared to the larger aug-cc-pVTZ basis set for the RPA based methods.

Assembled together with the most common qubits used in nuclear resonance magnetic (NMR) quantum computation experiments, spin-1/2 nuclei, such as 113 Cd, 199 Hg, 125 Te, and 77 Se, could leverage the prospective scalable quantum computer architectures, enabling many and heteronuclear qubits for NMR quantum information processing (QIP) implementations. A computational design strategy for prescreening recently synthesized complexes of cadmium, mercury, tellurium, selenium, and phosphorus (called MRE complexes) as suitable qubit molecules for NMR QIP is reported. Chemical shifts and spin-spin coupling constants (SSCCs) in five MRE complexes were examined using the spin-orbit zeroth order regular approximation (ZORA) at the density functional theory level and the four-component relativistic Dirac-Kohn-Sham approach. In particular, the influence of different conformers, basis sets, exchange-correlation functionals, and methods to treat the relativistic as well as solvent effects were studied. The differences in the chemical shifts and SSCCs between different low energy conformers of the studied complexes were found to be very small. The TZ2P basis set was found to be the optimum choice for the studied chemical shifts, while the TZ2P-J basis set was the best for the couplings studied in this work. The PBE0 exchange-correlation functional exhibited the best performance for the studied MRE complexes. The addition of solvent effects has not improved on the gas phase results in comparison to the experiment, with the exception of the phosphorus chemical shift. The use of MRE complexes as qubit molecules for NMR QIP could face the challenges in single qubit control and multiqubit operations. They exhibit chemical shifts appropriately dispersed, allowing qubit addressability and exceptionally large spin-spin couplings, which could reduce the time of quantum gate operations and likely preserve the coherence.

The Dalton Project provides a uniform platform access to the underlying full-fledged quantum chemistry codes Dalton and LSDalton as well as the PyFraME package for automatized fragmentation and parameterization of complex molecular environments. The platform is written in Python and defines a means for library communication and interaction. Intermediate data such as integrals are exposed to the platform and made accessible to the user in the form of NumPy arrays, and the resulting data are extracted, analyzed, and visualized. Complex computational protocols that may, for instance, arise due to a need for environment fragmentation and configuration-space sampling of biochemical systems are readily assisted by the platform. The platform is designed to host additional software libraries and will serve as a hub for future modular software development efforts in the distributed Dalton community.

A benchmark study of several correlated second-order methods for frequency-dependent polarizabilities has been carried out. For the benchmark, a set of 14 (hetero)aromatic medium-sized molecules has been chosen. For the first time, CC3 polarizabilities are reported for these molecules using Sadlej's polarized triple-ζ basis set, and for a subset of these molecules the polarizabilities were obtained at the CC3 level also with the larger aug-cc-pVTZ basis set. These CC3 values are used as the reference values for benchmarking the second-order methods: SOPPA, SOPPA(CC2), SOPPA(CCSD), CC2, as well as CCSD. The influence of different basis sets, aug-cc-pVDZ, aug-cc-pVTZ, aug-cc-pVQZ, d-aug-cc-pVTZ, and Sadlej's polarized triple-ζ basis set, on static and frequency-dependent polarizabilities was investigated for the full set of molecules at the SOPPA level. It was found that the choice of basis set had a somewhat greater influence on the frequency-dependent polarizabilities than on the static polarizabilities, but all effects were small. The aug-cc-pVTZ basis set performed adequately for both static and frequency-dependent polarizabilities, having an insignificant offset from the values obtained with the larger d-aug-cc-pVTZ and aug-cc-pVQZ basis sets. Comparing the second-order methods, SOPPA, SOPPA(CC2), SOPPA(CCSD), CC2, as well as CCSD, to the CC3 reference values, it was found that the best performing method was CCSD, as expected. The SOPPA method, on the contrary, outperformed the CC2 method, suggesting the use of SOPPA rather than CC2 for polarizabilities, at least for these kinds of molecules. The SOPPA results were found to improve further when the Møller-Plesset correlation coefficients in the wave function were replaced by coupled-cluster amplitudes in the SOPPA(CC2) and SOPPA(CCSD) methods. Finally, a comparison was made for a small subset of the molecules between experimental data and calculated polarizabilities. It shows that, for this set of molecules, the trend in the performance of the different second-order methods does not depend on whether the reference values are calculated CC3 values or experimental values.

A theoretical framework for understanding molecular structures is crucial for the development of new technologies such as catalysts or solar cells. Apart from electronic excitation energies, however, only spectroscopic properties of molecules consisting of lighter elements can be computationally described at a high level of theory today since heavy elements require a relativistic framework, and thus far, most methods have only been derived in a non-relativistic framework. Important new technologies such as those mentioned above require molecules that contain heavier elements, and hence, there is a great need for the development of relativistic computational methods at a higher level of accuracy. Here, the Second-Order-Polarization-Propagator-Approximation (SOPPA), which has proven to be very successful in the non-relativistic case, is adapted to a relativistic framework. The equations for SOPPA are presented in their most general form, i.e., in a non-canonical spin-orbital basis, which can be reduced to the canonical case, and the expressions needed for a relativistic four-component SOPPA are obtained. The equations are one-index transformed, giving more compact expressions that correspond to those already available for the four-component RPA. The equations are ready for implementation in a four-component quantum chemistry program, which will allow both linear response properties and excitation energies to be calculated relativistically at the SOPPA level.

The second-order noniterative doubles-corrected random phase approximation (RPA) method has been extended to triplet excitation energies and the doubles-corrected higher RPA method as well as a shifted version for calculating singlet and triplet excitation energies are presented here for the first time. A benchmark set consisting of 20 molecules with a total of 117 singlet and 71 triplet excited states has been used to test the performance of the new methods by comparison with previous results obtained with the second-order polarization propagator approximation (SOPPA) and the third order approximate coupled cluster singles, doubles and triples model CC3. In general, the second-order doubles corrections to RPA and HRPA significantly reduce both the mean deviation as well as the standard deviation of the errors compared to the CC3 results. The accuracy of the new methods approaches the accuracy of the SOPPA method while using only 10-60% of the calculation time. © 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc., (© 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc.)

In multicellular organisms, duplicated genes can diverge through tissue-specific gene expression patterns, as exemplified by highly regulated expression of RUNX transcription factor paralogs with apparent functional redundancy. Here we asked what cell-type-specific biologies might be supported by the selective expression of RUNX paralogs during Langerhans cell and inducible regulatory T cell differentiation. We uncovered functional nonequivalence between RUNX paralogs. Selective expression of native paralogs allowed integration of transcription factor activity with extrinsic signals, while non-native paralogs enforced differentiation even in the absence of exogenous inducers. DNA binding affinity was controlled by divergent amino acids within the otherwise highly conserved RUNT domain and evolutionary reconstruction suggested convergence of RUNT domain residues toward submaximal strength. Hence, the selective expression of gene duplicates in specialized cell types can synergize with the acquisition of functional differences to enable appropriate gene expression, lineage choice and differentiation in the mammalian immune system.

Binding of anions using macrocyclic structures with a nonpolar interior using the CH···anion interaction as the recognition motif has gained popularity in the past few years, and such receptors often rely on a subtle interplay between enthalpic and entropic factors. For these types of receptors solvation of both the anion and the binding pocket of the macrocyclic host play important roles in the overall energetic picture of the binding event. Systematic chemical modifications of synthetic receptors that are able to bind anions in a variety of solvents is an important tool to gain understanding of the factors that determine the supramolecular chemistry of anions. Here we present the chiral macrocyclic structure biotin-l-sulfoxide[6]uril as a host molecule that binds anions in both water and in organic solvents. Biotin-l-sulfoxide[6]uril is prepared in a highly diastereoselective one-pot synthesis from the macrocycle biotin[6]uril. We compare the binding properties with that of biotin[6]uril, also studied in acetonitrile and in aqueous buffer at neutral pH. The biotin-l-sulfoxide[6]uril generally exhibits stronger recognition of anions in acetonitrile, but weaker binding in water as compared to the biotin[6]uril macrocycle. We have studied the binding events using a combination of NMR spectroscopy, isothermal titration calorimetry (ITC), and computational methods.

Prediction of chemical shifts in organic cations is known to be a challenge. In this article we meet this challenge for α-protonated alkylpyrroles, a class of compounds not yet studied in this context, and present a combined experimental and theoretical study of the 13 C and 1 H chemical shifts in three selected pyrroles. We have investigated the importance of the solvation model, basis set, and quantum chemical method with the goal of developing a simple computational protocol, which allows prediction of 13 C and 1 H chemical shifts with sufficient accuracy for identifying such compounds in mixtures. We find that density functional theory with the B3LYP functional is not sufficient for reproducing all 13 C chemical shifts, whereas already the simplest correlated wave function model, Møller-Plesset perturbation theory (MP2), leads to almost perfect agreement with the experimental data. Treatment of solvent effects generally improves the agreement with experiment to some extent and can in most cases be accomplished by a simple polarizable continuum model. The only exception is the NH proton, which requires inclusion of explicit solvent molecules in the calculation., (© 2019 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.)

In this article, the RPA(D) and HRPA(D) models for the calculation of linear response functions are presented. The performance of the new RPA(D) and HRPA(D) models is compared to the performance of the established RPA, HRPA, and SOPPA models in calculations of indirect nuclear spin-spin coupling constants using the CCSD model as a reference. The doubles correction offers a significant improvement on both the RPA and HRPA models; however, the improvement is more dramatic in the case of the RPA model. For all coupling types investigated in this study, the results obtained using the HRPA(D) model are comparable in accuracy to those given by the SOPPA model, while requiring between 30% and 90% of the calculation time needed for SOPPA. The RPA(D) model, while of slightly lower accuracy compared to the CCSD model than HRPA(D), offered calculation times of only approximately 25% of those required for SOPPA for all the investigated molecules. © 2018 Wiley Periodicals, Inc., (© 2018 Wiley Periodicals, Inc.)

Relativistic and nonrelativistic calculations have been performed on hydrogen peroxide, dihydrogen disulfide, dihydrogen diselenide, and dihydrogen ditelluride, H 2 X 2 (X = O, S, Se, Te), to investigate the consequences of relativistic effects on their structures as well as their nuclear magnetic resonance (NMR) spin-spin coupling constants and spin-spin coupling constant polarizabilites. The study has been performed using both one-component nonrelativistic and four-component relativistic calculations at the density functional theory (DFT) level with the B3LYP exchange-correlation functional. The calculation of nuclear spin-spin coupling constant polarizabilities has been performed by evaluating the components of the third order tensor, nuclear spin-spin coupling polarizability, using quadratic response theory. From this, the pseudoscalar associated with this tensor has also been calculated. The results show that relativistic corrections become very important for H 2 Se 2 and H 2 Te 2 and hint that a new chiral discrimination technique via NMR spectroscopy might be possible for molecules containing elements like Se or Te. © 2018 Wiley Periodicals, Inc., (© 2018 Wiley Periodicals, Inc.)

NMR spectra of Mg2+ ions in ionic liquids were recorded using a highly sensitive variant of NMR spectroscopy known as β-NMR. The β-NMR spectra of MgCl2 in EMIM-Ac and EMIM-DCA compare favourably with conventional NMR, and exhibit linewidths of ∼3 ppm, allowing for discrimination of species with oxygen and nitrogen coordination.

The pcJ-n basis set, optimized for spin-spin coupling constant calculations using density functional theory methods, are expanded to also include the s-block elements Li, Be, Na, and Mg, by studying several small molecules containing these elements. This is done by decontracting the underlying pc-n basis sets, followed by augmentation with additional tight functions. As was the case for the p-block elements, the convergence of the results can be significantly improved by augmentation with tight s-functions. For the p-block elements, additional tight functions of higher angular momentum were also needed, but this is not the case for the s-block elements. A search for the optimum contraction scheme is carried out using the criterion that the contraction error should be lower than the inherent error of the uncontracted pcJ-n relative to the uncontracted pcJ-4 basis set. A large search over possible contraction schemes is done for the Li 2 and Na 2 molecules, and based on this search contracted pcJ-n basis sets for the four atoms are recommended. This work shows that it is more difficult to contract the pcJ-n basis sets, than the underlying pc-n basis sets. However, it also shows that the pcJ-n basis sets for Li and Be can be more strongly contracted than the pcJ-n basis sets for the p-block elements. For Na and Mg, the contractions are to the same degree as for the p-block elements.

All mean excitation energies for second and third row atoms and their ions are calculated in the random-phase approximation using large basis sets. To a very good approximation, it turns out that mean excitation energies within an isoelectronic series are a quadratic function of the nuclear charge. It is demonstrated that this behavior is linked to the fact that the contributions from continuum electronic states give the dominate contributions to the mean excitation energies and that these contributions for atomic ions appear hydrogen-like. We argue that this finding may present a method to get a first estimate of mean excitation energies also for other non-relativistic atomic ions.

The performance of relativistic density functional theory (DFT) methods has been investigated for the calculation of the recently measured hyperfine coupling constants of hexafluorido complexes [ReF 6 ] 2- and [IrF 6 ] 2- . Three relativistic methods were employed at the DFT level of theory: the 2-component zeroth-order regular approximation (ZORA) method, in which the spin-orbit coupling was treated either variationally (EV ZORA) or as a perturbation (LR ZORA), and the 4-component Dirac-Kohn-Sham (DKS) method. The dependence of the results on the basis set and the choice of exchange-correlation functional was studied. Furthermore, the effect of varying the amount of Hartree-Fock exchange in the hybrid functionals was investigated. The LR ZORA and DKS methods combined with DFT led to very similar deviations (about 20 %) from the experimental values for the coupling constant of complex [ReF 6 ] 2- by using hybrid functionals. However, none of the methods were able to reproduce the large anisotropy of the hyperfine coupling tensor of complex [ReF 6 ] 2- . For [IrF 6 ] 2- , the EV ZORA and DKS methods reproduced the experimental tensor components with deviations of ≈10 and ≈5 % for the hybrid functionals, whereas the LR ZORA method predicted the coupling constant to be around one order of magnitude too large owing to the combination of large spin-orbit coupling and very low excitation energies., (© 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.)