A comparison of two-component and four-component approaches for calculations of spin-spin coupling constants and NMR shielding constants of transition metal cyanides

Relativistic density functional theory (DFT) calculations of nuclear spin-spin coupling constants and shielding constants have been performed for selected transition metal (11th and 12th group of periodic table) and thallium cyanides. The calculations have been carried out using zeroth-order regular approximation (ZORA) Hamiltonian and four-component Dirac-Kohn-Sham (DKS) theory with different nonrelativistic exchange-correlation functionals. Two recent approaches for representing the magnetic balance (MB) between the large and small components of four-component spinors, namely, mDKS-RMB and sMB, have been employed for shielding tensor calculations and their results have been compared. Relativistic effects have also been analysed in terms of scalar and spin-orbit contributions at the two-component level of theory, including discussion of heavy-atom-on-light-atom effects for (1)J(CN), σ(C), and σ(N). The results for molecules containing metals from 4th row of periodic table show that relativistic effects for them are small (especially for spin-spin coupling constants). The biggest effects are observed for the 6th row where nonrelativistic theory reproduces only about 50%-70% of the two-component ZORA results for (1)J(MeC) and about 75% for heavy metal shielding constants. It is important to employ a full Dirac picture for calculations of heavy metal shielding constants, since ZORA reproduces only 75%-90% of the DKS results. Smaller discrepancies between ZORA-DFT and DKS are observed for nuclear spin-spin coupling constants. No significant differences are observed between the results obtained using mDKS-RMB and sMB approaches for magnetic balance in four-component calculations of the shielding constants.     

Four-component relativistic calculations of NMR shielding constants of the transition metal complexes. Part 1: Pentaammines of cobalt,rhodium, and iridium

The nonrelativistic and four-component fully relativistic calculations of ¹H, ¹⁵N, ⁵⁹Co, ¹⁰³Rh, and ¹⁹³Ir shielding constants of pentaammineaquacomplexes of cobalt(III), rhodium(III), and iridium(III) were carried out at the density functional theory (DFT) level of theory. The noticeable deshielding relativistic corrections were observed for nitrogen shielding constants (chemical shifts), whereas those corrections were found to be negligible for protons. For the transition metals cobalt, rhodium, and iridium, relativistic corrections to their nuclear magnetic resonance (NMR) shielding constants were found to be rather small for cobalt and rhodium (some 5–10%), whereas they are essentially larger for iridium (up to 70%).     

Nuclear magnetic resonance shielding constants and chemical shifts in linear 199Hg compounds: a comparison of three relativistic computational methods

We investigate the importance of relativistic effects on NMR shielding constants and chemical shifts of linear HgL(2) (L = Cl, Br, I, CH(3)) compounds using three different relativistic methods: the fully relativistic four-component approach and the two-component approximations, linear response elimination of small component (LR-ESC) and zeroth-order regular approximation (ZORA). LR-ESC reproduces successfully the four-component results for the C shielding constant in Hg(CH(3))(2) within 6 ppm, but fails to reproduce the Hg shielding constants and chemical shifts. The latter is mainly due to an underestimation of the change in spin-orbit contribution. Even though ZORA underestimates the absolute Hg NMR shielding constants by ～2100 ppm, the differences between Hg chemical shift values obtained using ZORA and the four-component approach without spin-density contribution to the exchange-correlation (XC) kernel are less than 60 ppm for all compounds using three different functionals, BP86, B3LYP, and PBE0. However, larger deviations (up to 366 ppm) occur for Hg chemical shifts in HgBr(2) and HgI(2) when ZORA results are compared with four-component calculations with non-collinear spin-density contribution to the XC kernel. For the ZORA calculations it is necessary to use large basis sets (QZ4P) and the TZ2P basis set may give errors of ～500 ppm for the Hg chemical shifts, despite deceivingly good agreement with experimental data. A Gaussian nucleus model for the Coulomb potential reduces the Hg shielding constants by ～100-500 ppm and the Hg chemical shifts by 1-143 ppm compared to the point nucleus model depending on the atomic number Z of the coordinating atom and the level of theory. The effect on the shielding constants of the lighter nuclei (C, Cl, Br, I) is, however, negligible.     

Nuclear magnetic shielding constants of liquid water: insights from hybrid quantum mechanics/molecular mechanics models

We present a gauge-origin independent method for the calculation of nuclear magnetic shielding tensors of molecules in a structured and polarizable environment. The method is based on a combination of density functional theory (DFT) or Hartree-Fock wave functions with molecular mechanics. The method is unique in the sense that it includes three important properties that need to be fulfilled in accurate calculations of nuclear magnetic shielding constants: (i) the model includes electron correlation effects, (ii) the model uses gauge-including atomic orbitals to give gauge-origin independent results, and (iii) the effect of the environment is treated self-consistently using a discrete reaction-field methodology. The authors present sample calculations of the isotropic nuclear magnetic shielding constants of liquid water based on a large number of solute-solvent configurations derived from molecular dynamics simulations employing potentials which treat solvent polarization either explicitly or implicitly. For both the (17)O and (1)H isotropic shielding constants the best predicted results compare fairly well with the experimental data, i.e., they reproduce the experimental solvent shifts to within 4 ppm for the (17)O shielding and 1 ppm for the (1)H shielding.     

Nuclear-magnetic-resonance shielding constants calculated by pseudospectral methods

We have developed an algorithm based upon pseudospectral (PS) ab initio electronic structure methods for evaluating nuclear magnetic shielding constants using gauge-including atomic orbitals (GIAOs) in the spin-restricted and spin-unrestricted formalisms of Hartree-Fock (HF) theory and density-functional theory (DFT). The nuclear magnetic shielding constants for both 1H and 13C calculated using PS methodology for 21 small molecules have absolute mean errors of less than 0.3 ppm in comparison with analytic integral results. CPU timing comparisons between PS methods and conventional methods carried out for seven large molecules ranging from 510 to 1285 basis functions demonstrate that the PS methods are an order of magnitude more efficient than the conventional methods. PS-HF was between 9 and 26 times faster than conventional integral technology, and PS-DFT (Becke three-parameter Lee-Yang-Parr) was between 6 and 21 times faster.     

Methodological aspects in the calculation of parity-violating effects in nuclear magnetic resonance parameters

We examine the quantum chemical calculation of parity-violating (PV) electroweak contributions to the spectral parameters of nuclear magnetic resonance (NMR) from a methodological point of view. Nuclear magnetic shielding and indirect spin-spin coupling constants are considered and evaluated for three chiral molecules, H2O2, H2S2, and H2Se2. The effects of the choice of a one-particle basis set and the treatment of electron correlation, as well as the effects of special relativity, are studied. All of them are found to be relevant. The basis-set dependence is very pronounced, especially at the electron correlated ab initio levels of theory. Coupled-cluster and density-functional theory (DFT) results for PV contributions differ significantly from the Hartree-Fock data. DFT overestimates the PV effects, particularly with nonhybrid exchange-correlation functionals. Beginning from third-row elements, special relativity is of importance for the PV NMR properties, shown here by comparing perturbational one-component and various four-component calculations. In contrast to what is found for nuclear magnetic shielding, the choice of the model for nuclear charge distribution--point charge or extended (Gaussian)--has a significant impact on the PV contribution to the spin-spin coupling constants.     

Magnetic shielding tensor components in a highly strained phosphorus molecule: 1,2,3-triphenylphosphirene

Using the magic-angle spinning (MAS) technique the principal values of the ³¹P NMR magnetic shielding tensor were measured in 1,2,3-triphenylphosphirene: σ₁₁ = −58; σ₂₂ = 23 and σ₃₃ = 636 ppm. The anisotropy is quite large for a three-coordinate phosphorus compound. The high-field component σ₃₃ corresponds to the direction perpendicular to the ring, and is responsible for the high-field resonance in the isotropie phase.     

Proton magnetic shielding in malonic acid by multiple pulse techniques

The proton NMR in single crystals of malonic acid has been studied by multiple pulse line narrowing techniques. The nuclear magnetic shielding tensors σ⁽ⁱ⁾ of all protons in malonic acid could be determined from the spectra. There are two magnetically distinct carboxyl protons. The principal components of their shielding tensors are found to be σ⁽¹⁾_ZZ= ?0.8 ppm, σ⁽¹⁾_YY = ?19.2 ppm, σ⁽¹⁾_XX = ?21.8 ppm, and σ⁽²⁾_ZZ = ?1.0 ppm, σ⁽²⁾_ZZ = ?21.3 ppm relative to adamantane. The error limits are estimated to be ± 1 ppm. The most shielded directions lie along the hydrogen bond directions to within 8 degrees. The least shielded directions are essentially perpendicular to the plane of the carboxyl groups. Within experimental accuracy the shielding of the aliphatic protons is axially symmetric about the CH bond axes. The anisotropy Δσ = σ_? ? σ_⊥ is (4 ± 1) ppm. The gross features of the anisotropy of the carboxyl protons are shown to be governed by the diamagnetic effect.     

Nuclear magnetic shielding of the 113Cd(II) ion in aqua solution: a combined molecular dynamics/density functional theory study

We present a combined molecular dynamics simulation and density functional theory investigation of the nuclear magnetic shielding constant of the (113)Cd(II) ion solvated in aqueous solution. Molecular dynamics simulations are carried out for the cadmium-water system in order to produce instantaneous geometries for subsequent determination of the nuclear magnetic shielding constant at the density functional theory level. The nuclear magnetic shielding constant is computed using a perturbation theory formalism, which includes nonrelativistic and leading order relativistic contributions to the nuclear magnetic shielding tensor. Although the NMR shielding constant varies significantly with respect to simulation time, the value averaged over increasing number of snapshots remains almost constant. The paramagnetic nonrelativistic contribution is found to be most sensitive to dynamical changes in the system and is mainly responsible for the thermal and solvent effects in solution. The relativistic correction features very little sensitivity to the chemical environment, and can be disregarded in theoretical calculations when a Cd complex is used as reference compound in (113)Cd NMR experiments, due to the mutual cancelation between individual relativistic corrections.     

Relativistic effects on the nuclear magnetic resonance shielding of FX (X = F, Cl, Br, I, and At) molecular systems

We present ab inito full four-component and spin-free calculations of the NMR shielding parameter, σ, in the FX (X = F, Cl, Br, I and At) molecular systems. A different expression that overcomes the traditional non-relativistic (NR) approximation used to calculate the relationship between spin-rotation constants and the paramagnetic terms of σ(p) are given. Large deviations from NR results are obtained for σ(X; X = I and At) and for σ(F; FAt). σ(∥)(p)(I; FI) is zero within the NR approach but -447.4 parts per million from our calculations. The electronic origin of relativistic corrections are analyzed. All passive SO contributions are obtained as a difference between full four-component calculations and spin-free ones. Considering relativistic effects on the anisotropy, we obtain a deviation of 10% for I and 25% for At. σ(∥)(SO)(X) is always negative and σ(∥)(SF)(X) is always positive; the passive SO becomes larger than the SF one for X = Br, I, and At. Both σ(∥)(SO)(X) and σ(⊥)(SO)(X) have a functional dependence such as a Z(X)(b) being the exponent 3.5 and 3.65, respectively. The passive SO contribution to the anisotropy has a similar functional dependence with an exponent of 3.60, meaning that its perpendicular component is larger than its corresponding parallel component.     

NMR shielding constants of CuX,AgX, and AuX (X = F,Cl, Br,and I) investigated by density functional theory based on the Douglas–Kroll–Hess Hamiltonian

Two‐component relativistic density functional theory (DFT) with the second‐order Douglas–Kroll–Hess (DKH2) one‐electron Hamiltonian was applied to the calculation of nuclear magnetic resonance (NMR) shielding constant. Large basis set dependence was observed in the shielding constant of Xe atom. The DKH2‐DFT‐calculated shielding constants of I and Xe in HI, I₂, CuI, AgI, and XeF₂ agree well with those obtained by the four‐component relativistic theory and experiments. The Au NMR shielding constant in AuF is extremely more positive than in AuCl, AuBr, and AuI, as reported recently. This extremely positive shielding constant arises from the much larger Fermi contact (FC) term of AuF than in others. Interestingly, the absolute values of the paramagnetic and the FC terms are considerably larger in CuF and AuF than in others. The large paramagnetic term of AuF arises from the large d‐components in the Au d_π –F p_π and Au sd_σ–F p_σ molecular orbitals (MOs). The large FC term in AuF arises from the small energy difference between the Au sd_σ + F p_σ and Au sd_σ–F p_σ MOs. The second‐order magnetically relativistic effect, which is the effect of DKH2 magnetic operator, is important even in CuF. This effect considerably improves the overestimation of the spin‐orbit effect calculated by the Breit–Pauli magnetic operator. © 2013 Wiley Periodicals, Inc.     

Analyzing NMR shielding tensors calculated with two-component relativistic methods using spin-free localized molecular orbitals

A recently developed analysis method [J. Chem. Phys. 127, 124106 (2007)] for NMR spin-spin coupling constants employing two-component (spin-orbit) relativistic density functional theory along with scalar relativistic natural localized molecular orbitals (NLMOs) and natural bond orbitals (NBOs) has been extended for analyzing NMR shielding tensors. Contributions from a field-dependent basis set (gauge-including atomic orbitals) have been included in the formalism. The spin-orbit NLMO/NBO nuclear magnetic shielding analysis has been applied to methane, plumbane, hydrogen iodide, tetracholoplatinate(II), and hexachloroplatinate(IV).     

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.     

Gauge invariant calculations of nuclear magnetic shielding constants using the continuous transformation of the origin of the current density approach. II. Density functional and coupled cluster theory

The quantum mechanical current density induced in a molecule by an external magnetic field is invariant to translations of the coordinate system. This fundamental symmetry is exploited to formally annihilate the diamagnetic contribution to the current density via the approach of "continuous transformation of the origin of the current density-diamagnetic zero" (CTOCD-DZ). The relationships obtained by this method for the magnetic shielding at the nuclei are intrinsically independent of the origin of the coordinate system for any approximate computational scheme relying on the algebraic approximation. The authors report for the first time an extended series of origin-independent estimates of nuclear magnetic shielding constants using the CTOCD-DZ approach at the level of density functional theory (DFT) with four different types of functionals and unrelaxed coupled cluster singles and doubles linear response (CCSD-LR) theory. The results obtained indicate that in the case of DFT the procedure employed is competitive with currently adopted computational methods allowing for basis sets of gauge-including atomic orbitals, whereas larger differences between CTOCD-DZ and common origin CCSD-LR results are observed due to the incomplete fulfillment of hypervirial relations in standard CCSD-LR theory. It was found furthermore that the unrelaxed CCSD-LR calculations predict larger correlation corrections for the shielding constants of almost all nonhydrogen atoms in their set of molecules than the usual relaxed energy derivative CCSD calculations. Finally the results confirm the excellent performance of Keal and Tozer's third functional, in particular, for the multiply bonded systems with a lot of electron correlation, but find also that the simple local density functional gives even better results for the few singly bonded molecules in their study where correlation effects are small.     

The calculation of NMR shielding tensors based on density functional theory and the frozen-core approximation

The application of the frozen-core approximation to the calculation of the shielding tensor of nuclear magnetic resonance (NMR) spectroscopy is discussed and an implementation is presented. A complete formulation of the shielding calculation within the frozen-core approximation is given, both in general terms and for the special case of density functional theory (DFT) and “gauge including atomic orbitals” (GIAOs). The practical implementation is validated by a detailed discussion of the consequences of the approximation. The general conclusion is drawn that the frozen-core approximation is a useful tool for shielding calculations—if the valence space is increased to contain at least the ns, np, (n − 1)p, (n − 1)d (fourth period and higher) shells, where n is the number of the given period in the periodic table of elements. The new method is applied to ⁷⁷Se shieldings and chemical shifts for a small number of compounds. The agreement between theory and experiment is good for relative shifts, whereas calculated absolute shieldings are generally too small by about 300–400 ppm. This difference is attributed to the relativistic contraction of the core density at the selenium atom that had been explicitly incorporated into the experimental absolute shielding scale. © 1996 John Wiley & Sons, Inc.     

Relativistic effects on nuclear magnetic shielding constants in HX and CH3X (X=Br,I) based on the linear response within the elimination of small component approach

Numerical calculations of relativistic effects on nuclear magnetic shielding constants sigma corresponding to all one-body operators obtained within a formalism developed in previous work were carried out. In this formalism, the elimination of small component scheme is applied to evaluate all quantities entering a four-component RSPT(2) expression of magnetic molecular properties. HX and CH3X (X=Br,I) were taken as model compounds. Calculations were carried out at the Hartree-Fock level for first-order quantities, and at the random-phase approximation (RPA) level for second- and third-order ones. It was found that values of sigma(X) are largely affected by several relativistic corrections not previously considered in the bibliography. sigma Values of the H nucleus are in close agreement with four-component RPA ones. Overall relativistic effects on the shift of sigma(X) from HX to CH3X are smaller than the nonrelativistic shifts.     

95Mo nuclear magnetic resonance parameters of molybdenum hexacarbonyl from density functional theory: appraisal of computational and geometrical parameters

Solid-state (95)Mo nuclear magnetic resonance (NMR) properties of molybdenum hexacarbonyl have been computed using density functional theory (DFT) based methods. Both quadrupolar coupling and chemical shift parameters were evaluated and compared with parameters of high precision determined using single-crystal (95)Mo NMR experiments. Within a molecular approach, the effects of major computational parameters, i.e. basis set, exchange-correlation functional, treatment of relativity, have been evaluated. Except for the isotropic parameter of both chemical shift and chemical shielding, computed NMR parameters are more sensitive to geometrical variations than computational details. Relativistic effects do not play a crucial part in the calculations of such parameters for the 4d transition metal, in particular isotropic chemical shift. Periodic DFT calculations were tackled to measure the influence of neighbouring molecules on the crystal structure. These effects have to be taken into account to compute accurate solid-state (95)Mo NMR parameters even for such an inorganic molecular compound.     

Four-component relativistic theory for nuclear magnetic shielding constants: the orbital decomposition approach

The authors present a scheme to simplify four-component relativistic calculations of nuclear magnetic shielding constants. The central idea is to decompose each first order orbital into two terms, one is magnetically balanced and directly leads to the diamagnetic term, and the other is, to leading order of relativity, kinetically balanced and can therefore simply be represented in the basis of unperturbed positive energy states. As a matrix formulation, the present approach is far simpler than other operator theories. Combined with the Dirac-Kohn-Sham ansatz, the nuclear magnetic shielding constants for the Kr, Xe, and Rn atoms as well as the HBr and HI molecules are calculated, and the results compare favorably with those of other schemes.     

Analysis of the bond‐valence method for calculating 29Si and 31P magnetic shielding in covalent network solids

²⁹Si and ³¹P magnetic‐shielding tensors in covalent network solids have been evaluated using periodic and cluster‐based calculations. The cluster‐based computational methodology employs pseudoatoms to reduce the net charge (resulting from missing co‐ordination on the terminal atoms) through valence modification of terminal atoms using bond‐valence theory (VMTA/BV). The magnetic‐shielding tensors computed with the VMTA/BV method are compared to magnetic‐shielding tensors determined with the periodic GIPAW approach. The cluster‐based all‐electron calculations agree with experiment better than the GIPAW calculations, particularly for predicting absolute magnetic shielding and for predicting chemical shifts. The performance of the DFT functionals CA‐PZ, PW91, PBE, rPBE, PBEsol, WC, and PBE0 are assessed for the prediction of ²⁹Si and ³¹P magnetic‐shielding constants. Calculations using the hybrid functional PBE0, in combination with the VMTA/BV approach, result in excellent agreement with experiment. © 2016 Wiley Periodicals, Inc.