Relativistic effects on group-12 metal nuclear shieldings

The leading-order perturbation theory approach to relativistic effects on the nuclear magnetic shielding provides an economic method for obtaining the chemical shifts in heavy-element containing systems. The method features detailed analysis potential in terms of the different physical mechanisms affecting the shielding tensors of heavy nuclei. The perturbative nature, however, results in an increasing error with increasingly heavy elements in the system. In this work, we investigate the performance of the Breit-Pauli perturbation theory (BPPT) against fully relativistic four-component theory in computing the nuclear shielding constants as well as the chemical shifts with respect to corresponding atomic ions of group-12 metals, M = Zn, Cd, and Hg, in dimethyl M(CH(3))(2) and aqueous M(H(2)O)(6)(2+) complexes. It is shown that five out of the total of sixteen BPPT correction terms are responsible for most of the relativistic corrections for the chemical shift of studied metals. The relativity is important already for Cd and BPPT is proven to work well up to Hg for the chemical shift, as calibrated with the fully relativistic method.     

Formal relations connecting different approaches to calculate relativistic effects on molecular magnetic properties

In the present work a set of formal relations connecting different approaches to calculate relativistic effects on magnetic molecular properties are proven. The linear response (LR) within the elimination of the small component (ESC), Breit Pauli, and minimal-coupling approaches are compared. To this end, the leading order ESC reduction of operators within the minimal-coupling four-component approach is carried out. The equivalence of all three approaches within the ESC approximation is proven. It is numerically verified for the NMR nuclear-magnetic shielding tensor taking HX and CH3X (X=Br,I) as model compounds. Formal relations proving the gauge origin invariance of the full relativistic effect on the NMR nuclear-magnetic shielding tensor within the LR-ESC approach are presented.     

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.     

Relativistic effect of iodine in <Superscript>13</Superscript>C NMR chemical shifts of iodomethanes from quantum chemical calculations within the framework of the full four-component relativistic Dirac—Coulomb scheme

¹³C NMR shielding constants (chemical shifts) of iodomethanes were calculated within the framework of the full four-component relativistic Dirac—Coulomb scheme. As the number of iodine atoms in the molecule increases, the relativistic counterpart of the ¹³C NMR chemical shift increases from a few tens to several hundreds of ppm. Calculations of ¹³C NMR chemical shifts of organoiodine compounds should be performed at the relativistic level using relativistic Dyall’s basis sets dyall.vXz and dyall.xvXz (x = a, c, ac, ae; X = 2, 3, 4) of at least triple-zeta quality or at the correlated non-relativistic level taking into account relativistic corrections. Solvent effects are not of prime importance; however, taking into account the solvent corrections causes the mean absolute error of determination of the ¹³C NMR chemical shifts to decrease by 1—2 ppm.     

MP2 calculation of 77Se NMR chemical shifts taking into account relativistic corrections

The main factors affecting the accuracy and computational cost of the Second‐order Möller‐Plesset perturbation theory (MP2) calculation of ⁷⁷Se NMR chemical shifts (methods and basis sets, relativistic corrections, and solvent effects) are addressed with a special emphasis on relativistic effects. For the latter, paramagnetic contribution (390–466 ppm) dominates over diamagnetic term (192–198 ppm) resulting in a total shielding relativistic correction of about 230–260 ppm (some 15% of the total values of selenium absolute shielding constants). Diamagnetic term is practically constant, while paramagnetic contribution spans over 70–80 ppm. In the ⁷⁷Se NMR chemical shifts scale, relativistic corrections are about 20–30 ppm (some 5% of the total values of selenium chemical shifts). Solvent effects evaluated within the polarizable continuum solvation model are of the same order of magnitude as relativistic corrections (about 5%). For the practical calculations of ⁷⁷Se NMR chemical shifts of the medium‐sized organoselenium compounds, the most efficient computational protocols employing relativistic Dyall's basis sets and taking into account relativistic and solvent corrections are suggested. The best result is characterized by a mean absolute error of 17 ppm for the span of ⁷⁷Se NMR chemical shifts reaching 2500 ppm resulting in a mean absolute percentage error of 0.7%. Copyright © 2015 John Wiley & Sons, Ltd.     

Halogen effect on structure and 13C NMR chemical shift of 3,6‐disubstituted‐N‐alkyl carbazoles

Structures of selected 3,6‐dihalogeno‐N‐alkyl carbazole derivatives were calculated at the B3LYP/6‐311++G(3df,2pd) level of theory, and their ¹³C nuclear magnetic resonance (NMR) isotropic shieldings were predicted using density functional theory (DFT). The model compounds contained 9H, N‐methyl and N‐ethyl derivatives. The relativistic effect of Br and I atoms on nuclear shieldings was modeled using the spin–orbit zeroth‐order regular approximation (ZORA) method. Significant heavy atom shielding effects for the carbon atom directly bonded with Br and I were observed (~?10 and ~?30 ppm while the other carbon shifts were practically unaffected). The decreasing electronegativity of the halogen substituent (F, Cl, Br, and I) was reflected in both nonrelativistic and relativistic NMR results as decreased values of chemical shifts of carbon atoms attached to halogen (C3 and C6) leading to a strong sensitivity to halogen atom type at 3 and 6 positions of the carbazole ring. The predicted NMR data correctly reproduce the available experimental data for unsubstituted N‐alkylcarbazoles. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

A gauge-independent zeroth-order regular approximation to the exact relativistic Hamiltonian--formulation and applications

A simple modification of the zeroth-order regular approximation (ZORA) in relativistic theory is suggested to suppress its erroneous gauge dependence to a high level of approximation. The method, coined gauge-independent ZORA (ZORA-GI), can be easily installed in any existing nonrelativistic quantum chemical package by programming simple one-electron matrix elements for the quasirelativistic Hamiltonian. Results of benchmark calculations obtained with ZORA-GI at the Hartree-Fock (HF) and second-order Moller-Plesset perturbation theory (MP2) level for dihalogens X(2) (X=F,Cl,Br,I,At) are in good agreement with the results of four-component relativistic calculations (HF level) and experimental data (MP2 level). ZORA-GI calculations based on MP2 or coupled-cluster theory with single and double perturbations and a perturbative inclusion of triple excitations [CCSD(T)] lead to accurate atomization energies and molecular geometries for the tetroxides of group VIII elements. With ZORA-GI/CCSD(T), an improved estimate for the atomization energy of hassium (Z=108) tetroxide is obtained.     

Theoretical calculations of the chemical shifts of cyclo[n]phosphazenes for n = 2, 3, 4 and 5 (X2PN)n with X = CH3, F,Cl and Br: the effect of relativistic corrections

Abstract

Di, tri, tetra and pentacyclophosphazenes substituted on the phosphorus atoms by CH₃, F, Cl and Br atoms corresponding to (X₂PN)_n structures have been studied theoretically at the B3LYP/6-311++G(d,p) level. After a brief discussion of their geometries comparing them to those of the conjugated carbocycles, (CH)_n, of the same size, the absolute shieldings calculated with the GIAO and ZORA approximations will be reported. For the Cl and mainly for the Br substituted cyclo[n]-phosphazenes, relativistic corrections are absolutely necessary for ³¹P and useful for ¹⁵N chemical shifts.     

103Rh NMR chemical shifts in organometallic complexes: a combined experimental and density functional study

Experimental 103Rh NMR chemical shifts of mono- and binuclear rhodium(I) complexes containing s- or as-hydroindacenide and indacenediide bridging ligands with different ancillary ligands (1,5-cyclooctadiene, ethylene, carbonyl) are presented. A protocol, based on density functional theory calculations, was established to determine 103Rh NMR shielding constants in order to rationalise the effects of electronic and structural variations on the spectroscopic signal, and to gain insight into the efficiency of this computational method when applied to organometallic systems. Scalar and spin-orbit relativistic effects based on the ZORA (zeroth order regular approximation) level have been taken into account and discussed. A good agreement was found for model compounds over a wide range of chemical shifts of rhodium (approximately 10,000 ppm). This allowed us to discuss the experimental and calculated delta(103Rh) in larger complexes and to relate it to their electronic structure.     

Relativistic effects on the shielding of SnH2XY and PbH2XY (X, Y?=?F, Cl, Br and I) heavy atom�Ccontaining molecules

The relativistic polarization propagator approach is one of the most reliable methods available today for the calculation of NMR spectroscopic parameters on heavy atom?Ccontaining molecules, though its implementation is still at RPA or FOPPA (first-order) level of approach. Two-component methods like the LR-ESC method make possible the analysis of the electronic origin of relativistic effects due to its splitting in several mechanisms which are (or not) sensitive to the molecular structure or the nature of the chemical environment of the atom under study. In this article we present the study of some nuclear magnetic shieldings on the heavy atom for the following systems: SnXH₃ (X?=?H, F, Cl, Br, I), SnXYH₂ (X,?Y = F, Cl, Br, I) and PbXH₃ (X?=?H, F, Br, I). Total LR-ESC calculations are confronted to benchmark RPA calculations and then analyzed in order to get the main trends and discuss the electronic origin of the shielding of two kinds of atoms involved in such systems: central and substituent atoms. The electronic origin of the heavy atom effects on vicinal heavy atoms (HAVHA), recently proposed, is analyzed. It is shown that the passive third-order Spin orbit mechanism does not explain the total pattern though is still the most important. There are two other mechanisms involved: the so called here PSO-OZ and the L-PSO-K. Both mechanisms do contain the PSO perturbative Hamiltonian (which also include kinetic energy correcting terms). In the case of $\hbox{SnH}_2\hbox{I}_2$ , the HAVHA effect on ??(Sn) is of the order of 16%. When the central atom is as heavy as Sn, the active SO contribution on the shielding of such atom becomes larger than the passive SO, which is small in this case. This would mean that the HALA-type effect is strongly diminished when applied on a vicinal heavy atom. Quite a similar pattern though with larger relativistic effects is observed for the central lead atom.     

Fully relativistic coupled cluster and DFT study of electric field gradients at Hg in 199Hg compounds

We investigate the magnitude and interplay of relativistic and electron correlation effects on the electric field gradient (EFG) at the position of Hg in linear and bent HgL(2) (L = CH(3), Cl, Br, I) and trigonal planar [HgCl(3)](-) compounds using four-component relativistic Dirac-Coulomb (DC) and non-relativistic (NR) calculations at the Hartree-Fock (HF), DFT, MP2 and coupled cluster (CC) levels. The relativistic and electron correlation contributions to EFG have opposite signs and are not additive, demonstrating the importance of taking into account relativistic and electron correlation contributions on an equal footing. DC-MP2 overestimates the electron correlation correction by 0.48-0.56 a.u. for Hg-halides and by 0.8 a.u. for Hg(CH(3))(2), respectively, while DC-CCSD underestimates the correlation correction by 0.57-0.66 a.u. compared to the reference DC-CCSD-T data. EFGs obtained at the DC-DFT level vary considerably with the functional; DC-CAMB3LYP and DC-BH&H reproduce DC-CCSD-T results within 0.08-0.24 a.u. (1%-3%) for Hg(CH(3))(2) and Hg-halides, respectively. An updated value of the nuclear quadrupole moment of the I = 5/2 excited state of (199)Hg, Q((199)Hg) = 0.675(12) b is derived from the literature. This value compares well with that derived from our calculated EFG at the DC-CCSD-T level and the experimental data for Hg(CH(3))(2); Q((199)Hg) = 0.650 b.     

A fully relativistic method for calculation of nuclear magnetic shielding tensors with a restricted magnetically balanced basis in the framework of the matrix Dirac-Kohn-Sham equation

A new relativistic four-component density functional approach for calculations of NMR shielding tensors has been developed and implemented. It is founded on the matrix formulation of the Dirac-Kohn-Sham (DKS) method. Initially, unperturbed equations are solved with the use of a restricted kinetically balanced basis set for the small component. The second-order coupled perturbed DKS method is then based on the use of restricted magnetically balanced basis sets for the small component. Benchmark relativistic calculations have been carried out for the (1)H and heavy-atom nuclear shielding tensors of the HX series (X=F,Cl,Br,I), where spin-orbit effects are known to be very pronounced. The restricted magnetically balanced basis set allows us to avoid additional approximations and/or strong basis set dependence which arises in some related approaches. The method provides an attractive alternative to existing approximate two-component methods with transformed Hamiltonians for relativistic calculations of chemical shifts and spin-spin coupling constants of heavy-atom systems. In particular, no picture-change effects arise in property calculations.     

33S NMR spectroscopy 3. Substituent effects on 33S NMR parameters in 2-substituted ethanesulfonates

33S NMR parameters (chemical shifts and linewidths) in 2-substituted sodium ethanesulfonates, XCH2CH2SO3Na (X = H, CH3, OH, SH, NH2, Cl, Br, NH3+) depend upon the electronic properties of substituents. To explain experimental results and obtain additional information on the origin of the observed substituent effect (SE), sulfur isotropic absolute shielding constants have been calculated at DFT level of theory (B3LYP/6-311++G(2d,p)) by gauge-including atomic orbitals (GIAO) method. Data have been interpreted with the aid of natural bond orbital (NBO) method and natural chemical shielding (NCS) analysis. It has been demonstrated that in the class of compounds considered the diamagnetic contribution to sulfur-shielding constant is constant and the observed upfield shift of 33S resonance induced by electron-withdrawing substituents (reverse chemical shift effect) can be related to variations of the paramagnetic contribution. Substituents with different electronic properties cause variations in the polarization of S-C and S-O bonds of the -C-SO3- moiety thus determining changes of the electron density at sulfur nucleus and consequently the expansion or contraction of 3p sulfur orbitals. Also oxygen lone-pairs and sulfur core 2p electrons can play an active role in determining the paramagnetic contribution to sulfur shielding. With regard to linewidth variations, they can be ascribed primarily to changes in the nuclear quadrupole coupling constant values. B3LYP/6-311++G(2d,p) method allows obtaining a good reproducibility of SE on the electric field gradient (EFG) at sulfur, although its values tend to be underestimated significantly. Moreover, 17O shielding constants have been calculated.     

Experimental and quantum-chemical studies of 1H, 13C and 15N NMR coordination shifts in Pd(II) and Pt(II) chloride complexes with quinoline, isoquinoline, and 2,2'-biquinoline

1H, 13C, and 15N NMR studies of platinide(II) (M=Pd, Pt) chloride complexes with quinolines (L=quinoline-quin, or isoquinoline-isoquin; LL=2,2'-biquinoline-bquin), having the general formulae trans-/cis-[ML2Cl2] and [M(LL)Cl2], were performed and the respective chemical shifts (delta1H, delta13C, delta15N) reported. 1H coordination shifts of various signs and magnitudes (Delta1Hcoord=delta1Hcomplex-delta1Hligand) are discussed in relation to the changes of diamagnetic contribution to the relevant 1H shielding constants. The comparison to the literature data for similar complexes containing auxiliary ligands other than chlorides exhibited a large dependence of delta1H parameters on electron density variations and ring-current effects (inductive and anisotropic phenomena). The influence of deviations from planarity, concerning either MN2Cl2 chromophores or azine ring systems, revealed by the known X-ray structures of [Pd(bquin)Cl2] and [Pt(bquin)Cl2], is discussed in respect to 1H NMR spectra. 15N coordination shifts (Delta15Ncoord=delta15Ncomplex-delta15Nligand) of ca. 78-100 ppm (to lower frequency) are attributed mainly to the decrease of the absolute value of paramagnetic contribution in the relevant 15N shielding constants, this phenomenon being noticeably dependent on the type of a platinide metal and coordination sphere geometry. The absolute magnitude of Delta15Ncoord parameter increased by ca 15 ppm upon Pd(II)-->Pt(II) replacement but decreased by ca. 15 ppm following trans-->cis transition. Experimental 1H, 13C, 15N NMR chemical shifts are compared to those quantum-chemically calculated by B3LYP/LanL2DZ+6-31G**//B3LYP/LanL2DZ+6-31G*, both in vacuo and in CHCl3 or DMF solution.     

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%).     

A combined experimental and quantum chemistry study of selenium chemical shift tensors

A comprehensive investigation of selenium chemical shift tensors is presented. Experimentally determined chemical shift tensors were obtained from solid-state 77Se NMR spectra for several organic, organometallic, or inorganic selenium-containing compounds. The first reported indirect spin-spin coupling between selenium and chlorine is observed for Ph(2)SeCl(2) where 1J(77Se,35Cl)iso is 110 Hz. Selenium magnetic shielding tensors were calculated for all of the molecules investigated using zeroth-order regular approximation density functional theory, ZORA DFT. The computations provide the orientations of the chemical shift tensors, as well as a test of the theory for calculating the magnetic shielding interaction for heavier elements. The ZORA DFT calculations were performed with nonrelativistic, scalar relativistic, and scalar with spin-orbit relativistic levels of theory. Relativistic contributions to the magnetic shielding tensor were found to be significant for (NH4)2WSe4 and of less importance for organoselenium, organophosphine selenide, and inorganic selenium compounds containing lighter elements.     

Studies on main group metal-transition-metal bonded compounds 7. A 199Hg NMR study of home group of some group VI trasition-metal mercury compounds

A ¹⁹⁹Hg Fourier Tranformation NMR study has been carried out on Hg[M(CO)₃C₅H₅]₂ (M = Cr, Mo, W), [C₅H₅(CO)₃M]HgCl, and [C₅H₅(CO)₃W]HgX (X = Cl, Br, I, SCN). The ¹⁹⁹Hg chemical shifts are ?80, +115 and ?348 ppm respectively for the symmetrical compounds, ?542, ?617, and ?997 ppm for the chloride and ?1200, ?1529 and ?924 ppm for the Br, I, SCN-tungsten derivatives respectively. The ₁₉₉Hg chemical shifts for several other mercury derivatives are reported for comparison. All chemical shifts are relative to 90% HgMe₂/10% internal lock C₆F₆ with positive values indicating decreasing shielding. The J_199Hg-183W values are 151, 706, 690, 630 and 684 Hz for the symmetrical compound and the Cl, Br, I and SCN derivatives respectively. The factors which may influence these parameters are discussed briefley.     

Time-dependent quasirelativistic density-functional theory based on the zeroth-order regular approximation

A time-dependent quasirelativistic density-functional theory for excitation energies of systems containing heavy elements is developed, which is based on the zeroth-order regular approximation (ZORA) for the relativistic Hamiltonian and a noncollinear form for the adiabatic exchange-correlation kernel. To avoid the gauge dependence of the ZORA Hamiltonian a model atomic potential, instead of the full molecular potential, is used to construct the ZORA kinetic operator in ground-state calculations. As such, the ZORA kinetic operator no longer responds to changes in the density in response calculations. In addition, it is shown that, for closed-shell ground states, time-reversal symmetry can be employed to simplify the eigenvalue equation into an approximate form that is similar to that of time-dependent nonrelativistic density-functional theory. This is achieved by invoking an independent-particle approximation for the induced density matrix. The resulting theory is applied to investigate the global potential-energy curves of low-lying LambdaS- and omega omega-coupled electronic states of the AuH molecule. The derived spectroscopic parameters, including the adiabatic and vertical excitation energies, equilibrium bond lengths, harmonic and anharmonic vibrational constants, fundamental frequencies, and dissociation energies, are in good agreement with those of time-dependent four-component relativistic density-functional theory and ab initio multireference second-order perturbation theory. Nonetheless, this two-component relativistic version of time-dependent density-functional theory is only moderately advantageous over the four-component one as far as computational efforts are concerned.     

NMR shielding constants in PH3, absolute shielding scale, and the nuclear magnetic moment of 31P

Ab initio values of the absolute shielding constants of phosphorus and hydrogen in PH(3) were determined, and their accuracy is discussed. In particular, we analyzed the relativistic corrections to nuclear magnetic resonance (NMR) shielding constants, comparing the constants computed using the four-component Dirac-Hartree-Fock approach, the four-component density functional theory (DFT), and the Breit-Pauli perturbation theory (BPPT) with nonrelativistic Hartree-Fock or DFT reference functions. For the equilibrium geometry, we obtained σ(P) = 624.309 ppm and σ(H) = 29.761 ppm. Resonance frequencies of both nuclei were measured in gas-phase NMR experiments, and the results were extrapolated to zero density to provide the frequency ratio for an isolated PH(3) molecule. This ratio, together with the computed shielding constants, was used to determine a new value of the nuclear magnetic dipole moment of (31)P: μ(P) = 1.1309246(50) μ(N).