The accuracy of density functionals for electric field gradients. Test calculations for ScX, CuX and GaX (X=F, Cl, Br, I, H and Li)

Calculation of electric field gradients with the exact two-component (X2C) quasi-relativistic method and its local approximations

When calculating electric field gradients (EFGs), relativistic and electron correlation effects are crucial for obtaining accurate results, and the commonly used density functional methods produce unsatisfactory results, especially for heavy elements and/or strongly correlated systems. In this work, a stand-alone program is presented, which enables calculation of EFGs from the molecular orbitals supplied by an external high accuracy quantum chemical calculation and includes relativistic effects through the exact two-component (X2C) formalism and efficient local approximations to it. Application to BiN and BiP molecules shows that a high precision can be achieved in the calculation of nuclear quadrupole coupling constants of 209Bi by combining advanced ab initio methods with the X2C approach. For seventeen iron compounds, the Mössbauer nuclear quadrupole splittings (NQS) of 57Fe calculated using a double-hybrid functional method are in very good agreement with the experimental values. It is shown that, for strongly correlated molecules, the double-hybrid functionals are much more accurate than the commonly used hybrid functionals. The computer program developed in this study furnishes a useful utility for obtaining EFGs and related nuclear properties with high accuracy.

DFT exchange: sharing perspectives on the workhorse of quantum chemistry and materials science

In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners. The format of the paper is that of a roundtable discussion, in which the participants express and exchange views on DFT in the form of 302 individual contributions, formulated as responses to a preset list of 26 questions. Supported by a bibliography of 777 entries, the paper represents a broad snapshot of DFT, anno 2022.

57Fe Mössbauer parameters from domain based local pair-natural orbital coupled-cluster theory

We report on applications of the domain based local pair-natural orbital (PNO) coupled-cluster method within the singles and doubles approximation (DLPNO-CCSD) to the calculation of ⁵⁷Fe isomer shifts and quadrupole splittings in a small training set of iron complexes consisting of large molecular ligands and iron atoms in varying charge, spin, and oxidation states. The electron densities and electric field gradients needed for these calculations were obtained within the recently implemented analytic derivative scheme. A method for the direct treatment of scalar relativistic effects in the calculation of effective electron densities is described by using the first-order Douglas-Kroll-Hess Hamiltonian and a Gaussian charge distribution model for the nucleus. The performance of DLPNO-CCSD is compared with four modern-day density functionals, namely, RPBE, TPSS, B3LYP, and B2PLYP, as well as with the second-order Møller-Plesset perturbation theory. An excellent correlation between the calculated electron densities and the experimental isomer shifts is attained with the DLPNO-CCSD method. The correlation constant a obtained from the slope of the linear correlation plot is found to be ≈-0.31 a.u.³ mm s^-1, which agrees very well with the experimental calibration constant α = -0.31 ± 0.04 a.u.³ mm s^-1. This value of a is obtained consistently using both nonrelativistic and scalar relativistic DLPNO-CCSD electron densities. While the B3LYP and B2PLYP functionals achieve equally good correlation between theory and experiment, the correlation constant a is found to deviate from the experimental value. Similar trends are observed also for quadrupole splittings. The value of the nuclear quadrupole moment for ⁵⁷Fe is estimated to be 0.15 b at the DLPNO-CCSD level. This is consistent with previous results and is here supported by a higher level of theory. The DLPNO-CCSD results are found to be insensitive to the intrinsic approximations in the method, in particular the PNO occupation number truncation error, while the results obtained with density functional theory (DFT) are found to depend on the choice of the functional. In a statistical sense, i.e., on the basis of the linear regression analysis, however, the accuracies of the DFT and DLPNO-CCSD results can be considered comparable.

New density functional parameterizations to accurate calculations of electric field gradient variations among compounds

This research provides a performance investigation of density functional theory and also proposes new functional parameterizations to deal with electric field gradient (EFG) calculations at nuclear positions. The entire procedure is conducted within the four-component formalism. First, we noticed that traditional hybrid and long-range corrected functionals are more efficient in the description of EFG variations for a set of elements (indium, antimony, iodine, lutetium, and hafnium) among linear molecules. Thus, we selected the PBE0, B3LYP, and CAM-B3LYP functionals and promoted a reoptimization of their parameters for a better description of these EFG changes. The PBE0q variant developed here showed an overall promising performance in a validation test conducted with potassium, iodine, copper, and gold. In general, the correlation coefficients found in linear regressions between experimental nuclear quadrupole coupling constants and calculated EFGs are improved while the systematic EFG errors also decrease as a result of this reparameterization.

The nuclear electric quadrupole moment of copper

The nuclear electric quadrupole moment (NQM) of the (63)Cu nucleus was determined from an indirect approach by combining accurate experimental nuclear quadrupole coupling constants (NQCCs) with relativistic Dirac-Coulomb coupled cluster calculations of the electric field gradient (EFG). The data obtained at the highest level of calculation, DC-CCSD-T, from 14 linear molecules containing the copper atom give rise to an indicated NQM of -198(10) mbarn. Such result slightly deviates from the previously accepted standard value given by the muonic method, -220(15) mbarn, although the error bars are superimposed.

Does a Molecule-Specific Density Functional Give an Accurate Electron Density? The Challenging Case of the CuCl Electric Field Gradient

In the framework of determining system-specific long-range corrected density functionals, the question is addressed whether such functionals, tuned to satisfy the condition -ε(HOMO) = IP or other energetic criteria, provide accurate electron densities. A nonempirical physically motivated two-dimensional tuning of range-separated hybrid functionals is proposed and applied to the particularly challenging case of a molecular property that depends directly on the ground-state density: the copper electric field gradient (EFG) in CuCl. From a continuous range of functional parametrizations that closely satisfy -ε(HOMO) = IP and the correct asymptotic behavior of the potential, the one that best fulfills the straight-line behavior of E(N), the energy as a function of a fractional electron number N, was found to provide the most accurate electron density as evidenced by calculated EFGs. The functional also performs well for related Cu systems.

Low temperature 65Cu NMR spectroscopy of the Cu+ site in azurin

(65)Cu central-transition NMR spectroscopy of the blue copper protein azurin in the reduced Cu(I) state, conducted at 18.8 T and 10 K, gave a strongly second order quadrupole perturbed spectrum, which yielded a (65)Cu quadrupole coupling constant of +/-71.2 +/- 1 MHz, corresponding to an electric field gradient of +/-1.49 atomic units at the copper site, and an asymmetry parameter of approximately 0.2. Quantum chemical calculations employing second order Møller-Plesset perturbation theory and large basis sets successfully reproduced these experimental results. Sensitivity and relaxation times were quite favorable, suggesting that NMR may be a useful probe of the electronic state of copper sites in proteins.

A solid-state 55Mn NMR spectroscopy and DFT investigation of manganese pentacarbonyl compounds

Central transition (55)Mn NMR spectra of several solid manganese pentacarbonyls acquired at magnetic field strengths of 11.75, 17.63, and 21.1 T are presented. The variety of distinct powder sample lineshapes obtained demonstrates the sensitivity of solid-state (55)Mn NMR to the local bonding environment, including the presence of crystallographically unique Mn sites, and facilitates the extraction of the Mn chemical shift anisotropies, CSAs, and the nuclear quadrupolar parameters. The compounds investigated include molecules with approximate C(4v) symmetry, LMn(CO)(5)(L = Cl, Br, I, HgMn(CO)(5), CH(3)) and several molecules of lower symmetry (L = PhCH(2), Ph(3-n)Cl(n)Sn (n= 1, 2, 3)). For these compounds, the Mn CSA values range from <100 ppm for Cl(3)SnMn(CO)(5) to 1260 ppm for ClMn(CO)(5). At 21.1 T the (55)Mn NMR lineshapes are appreciably influenced by the Mn CSA despite the presence of significant (55)Mn quadrupolar coupling constants that range from 8.0 MHz for Cl(3)SnMn(CO)(5) to 35.0 MHz for CH(3)Mn(CO)(5). The breadth of the solid-state (55)Mn NMR spectra of the pentacarbonyl halides is dominated by the CSA at all three applied magnetic fields. DFT calculations of the Mn magnetic shielding tensors reproduce the experimental trends and the magnitude of the CSA is qualitatively rationalized using a molecular orbital, MO, interpretation based on Ramsey's theory of magnetic shielding. In addition to the energy differences between symmetry-appropriate occupied and virtual MOs, the d-character of the Mn MOs is important for determining the paramagnetic shielding contribution to the principal components of the magnetic shielding tensor.

The Nuclear Quadrupole Moment of 14N from Accurate Electric Field Gradient Calculations and Microwave Spectra of NP Molecule

Extensive series of relativistic coupled cluster calculations of the electric field gradient at N in NP has been carried out. The accurate value of the calculated electric field gradient, combined with the highly accurate experimental value of the nuclear quadrupole coupling constant for the 14N nucleus, gives the 'molecular' value of the nuclear quadrupole moment Q(14N) = 20.46 mb. This result perfectly agrees with the value (20.44 ± 0.03 mb) determined from atomic calculations and atomic spectra. The present study involves also extensive investigations of basis sets which must be used in highly accurate calculations of electric field gradients.

Solid-State 25Mg NMR Spectroscopic and Computational Studies of Organic Compounds. Square-Pyramidal Magnesium(II) Ions in Aqua(magnesium) Phthalocyanine and Chlorophyll a

We report a solid-state (25)Mg NMR spectroscopic study of two magnesium-containing organic compounds: monopyridinated aqua(magnesium) phthalocyanine (MgPc.H(2)O.Py) and chlorophyll a (Chla). Each of these compounds contains a Mg(II) ion coordinating to four nitrogen atoms and a water molecule in a square-pyramidal geometry. Solid-state (25)Mg NMR spectra for MgPc.H(2)O.Py were obtained at 11.7 T (500 MHz for (1)H) for a (25)Mg-enriched sample (99.1% (25)Mg atom) using both Hahn-echo and quadrupole Carr-Purcell Meiboom-Gill (QCPMG) pulse sequences. Solid-state (25)Mg NMR spectra for Chla were recorded at (25)Mg natural abundance (10.1%) at 19.6 T (830 MHz for (1)H). The (25)Mg quadrupole parameters were determined from spectral analyses: MgPc.H(2)O.Py, C(Q) = 13.0 +/- 0.1 MHz and eta(Q) = 0.00 +/- 0.05; Chla, C(Q) = 12.9 +/- 0.1 MHz and eta(Q) = 1.00 +/- 0.05. This work represents the first time that Mg(II) ions in a square-pyramidal geometry have been characterized by solid-state (25)Mg NMR spectroscopy. Extensive quantum mechanical calculations for electric-field-gradient (EFG) and chemical shielding tensors were performed at restricted Hartee-Fock (RHF), density functional theory (DFT), and second-order Møller-Plesset perturbation theory (MP2) levels for both compounds. Computed (25)Mg nuclear quadrupole coupling constants at the RHF and MP2 levels show a reasonable basis-set convergence at the cc-pV5Z basis set (within 7% of the experimental value); however, B3LYP results display a drastic divergence beyond the cc-pVTZ basis set. A new crystal structure for MgPc.H(2)O.Py is also reported.

The quadrupole moment of the Sb nucleus from molecular microwave data and calculated relativistic electric-field gradients

The recently determined accurate values of the nuclear quadrupole coupling constant of the Sb nucleus in SbN, SbP, SbF, and SbCl and the calculated electric-field gradients at Sb in these molecules are used to obtain the nuclear quadrupole moment of 121Sb and 123Sb. The calculation of the electric-field gradient has been carried out by using the infinite-order two-component relativistic method in the scalar approximation. The accompanying change of picture of the electric-field gradient operator has been accounted for by employing the shifted nucleus model of nuclear quadrupoles. The electron correlation effects are calculated at the level of the coupled cluster approximation. The present calculations give the "molecular" value of the nuclear quadrupole moment of 121Sb equal to -556+/-24 mb which is considerably different from the old "recommended" value of -360+/-40 mb and also differs from the recent "solid-state" result (-669+/-15 mb). The validation of the present data is comprehensively discussed.

An Investigation of Lanthanum Coordination Compounds by Using Solid-State139La NMR Spectroscopy and Relativistic Density Functional Theory

Lanthanum-139 NMR spectra of stationary samples of several solid La(III) coordination compounds have been obtained at applied magnetic fields of 11.75 and 17.60 T. The breadth and shape of the 139La NMR spectra of the central transition are dominated by the interaction between the 139La nuclear quadrupole moment and the electric field gradient (EFG) at that nucleus; however, the influence of chemical-shift anisotropy on the NMR spectra is non-negligible for the majority of the compounds investigated. Analysis of the experimental NMR spectra reveals that the 139La quadrupolar coupling constants (C(Q)) range from 10.0 to 35.6 MHz, the spans of the chemical-shift tensor (Omega) range from 50 to 260 ppm, and the isotropic chemical shifts (delta(iso)) range from -80 to 178 ppm. In general, there is a correlation between the magnitudes of C(Q) and Omega, and delta(iso) is shown to depend on the La coordination number. Magnetic-shielding tensors, calculated by using relativistic zeroth-order regular approximation density functional theory (ZORA-DFT) and incorporating scalar only or scalar plus spin-orbit relativistic effects, qualitatively reproduce the experimental chemical-shift tensors. In general, the inclusion of spin-orbit coupling yields results that are in better agreement with those from the experiment. The magnetic-shielding calculations and experimentally determined Euler angles can be used to predict the orientation of the chemical-shift and EFG tensors in the molecular frame. This study demonstrates that solid-state 139La NMR spectroscopy is a useful characterization method and can provide insight into the molecular structure of lanthanum coordination compounds.

The quadrupole moment of the 3∕2+ nuclear ground state of Au197 from electric field gradient relativistic coupled cluster and density-functional theory of small molecules and the solid state

An attempt is made to improve the currently accepted muonic value for the 197Au nuclear quadrupole moment [+0.547(16)x10(-28) m2] for the 3/2+ nuclear ground state obtained by Powers et al. [Nucl. Phys. A230, 413 (1974)]. From both measured Mossbauer electric quadrupole splittings and solid-state density-functional calculations for a large number of gold compounds a nuclear quadrupole moment of +0.60x10(-28) m2 is obtained. Recent Fourier transform microwave measurements for gas-phase AuF, AuCl, AuBr, and AuI give accurate bond distances and nuclear quadrupole coupling constants for the 197Au isotope. However, four-component relativistic density-functional calculations for these molecules yield unreliable results for the 197Au nuclear quadrupole moment. Relativistic singles-doubles coupled cluster calculations including perturbative triples [CCSD(T) level of theory] for these diatomic systems are also inaccurate because of large cancellation effects between different field gradient contributions subsequently leading to very small field gradients. Here one needs very large basis sets and has to go beyond the standard CCSD(T) procedure to obtain any reliable field gradients for gold. From recent microwave experiments by Gerry and co-workers [Inorg. Chem. 40, 6123 (2001)] a significantly enhanced (197)Au nuclear quadrupole coupling constant in (CO)AuF compared to free AuF is observed. Here, these cancellation effects are less important, and relativistic CCSD(T) calculations finally give a nuclear quadrupole moment of +0.64x10(-28) m2 for 197Au. It is argued that it is currently very difficult to improve on the already published muonic value for the 197Au nuclear quadrupole moment.

Contracted basis sets for density functional calculations: Segmented versus general contraction

The differences between segmented and general contracted basis sets of double and triple zeta quality are analyzed for first and second row elements. Based on coverage of the exponent space and the performance for molecular properties, it is shown that a segmented contraction requires duplication of one primitive function compared to a general contraction for double zeta type basis sets. For triple zeta basis sets, segmentation necessitates either addition of one primitive function and expanding to a quadruple valence space, or addition of two primitive functions. For molecular properties depending on the valence orbitals, such as atomization energies, equilibrium distances, and vibrational frequencies, some of the inner functions describing the core orbitals can be removed without significantly affecting the accuracy. Several of the popular basis sets in common use correspond to such core-pruned basis sets.

Solid-State Ru-99 NMR Spectroscopy: A Useful Tool for Characterizing Prototypal Diamagnetic Ruthenium Compounds

The feasibility of (99)Ru NMR spectroscopy as a tool to characterize solid compounds is demonstrated. Results of the first solid-state (99)Ru NMR investigation of diamagnetic compounds are presented for Ru(NH(3))(6)Cl(2), K(4)Ru(CN)(6). xH(2)O (x = 0, 3), LaKRu(CN)(6), and Ru(3)(CO)(12). The sensitivity of the ruthenium magnetic shielding tensor to subtle changes in the local structure about the ruthenium nucleus is highlighted by comparing the (99)Ru isotropic chemical shift of Ru(NH(3))(6)Cl(2) in aqueous solutions and in the solid state. The narrow isotropic (99)Ru NMR peak observed for solid Ru(NH(3))(6)Cl(2) indicates that this compound is an ideal secondary reference sample for solid-state (99)Ru NMR studies. The isotropic (99)Ru chemical shift, (99)Ru nuclear quadrupolar coupling constant, C(Q), and quadrupolar asymmetry parameter of K(4)Ru(CN)(6). xH(2)O (x = 0, 3) are shown to be sensitive to x. For Ru(3)(CO)(12), the magnetic shielding tensors of each of the three nonequivalent Ru nuclei have spans of 1300-1400 ppm, and the (99)Ru C(Q) values are also similar, 1.36-1.85 MHz, and are surprisingly small given that (99)Ru has a moderate nuclear quadrupole moment. Information about the relative orientation of the Ru magnetic shielding and electric field gradient tensors has been determined for Ru(3)(CO)(12) from experimental (99)Ru NMR spectra as well as quantum chemical calculations.