Spin-orbit correction to NMR shielding constants from density functional theory

Relativistic calculation of nuclear magnetic shielding tensor including two-electron spin-orbit interactions

A relativistic calculation of nuclear magnetic shielding tensor including two-electron spin-orbit interactions is performed. In order to reduce the computational load in evaluating the two-electron relativistic integrals, the charge density is approximated by a linear combination of the squares of s-type spatial basis functions. Including the two-electron spin-orbit interaction effect is found to improve the calculation results.

Molecular structures of arachno-decaborane derivatives 6,9-X2B8H10 (X = CH2, NH, Se) including a gas-phase electron-diffraction study of 6,9-C2B8H14

The molecular structures of the three heterodecaboranes arachno-6,9-C2B8H14, arachno-6,9-N2B8H12, and arachno-6,9-Se2B8H10 have been determined by ab initio MO theory. In addition, the structure of arachno-6,9-C2B8H14 was experimentally determined using gas-phase electron diffraction (GED). The accuracy of all four of these structures has been confirmed by the good agreement of the (11)B chemical shifts calculated at the GIAO-MP2 level with the experimental values. A comparison of the GIAO-HF and GIAO-MP2 methods shows that for these heteroborane clusters, electron correlation effects on the computed delta((11)B) values are quite substantial and that it is necessary to go beyond the HF level in the NMR computation.

Density-functional computation of 53Cr NMR chemical shifts

53Cr chemical shifts of CrO4(2-), Cr2O7(2-), CrO3X-, CrO2X2(X = F, Cl), and Cr(CO)5L (L = CO, PF3, CHNH2, CMeNMe2) are computed, using geometries optimized with the gradient-corrected BP86 density functional, at the gauge-including atomic orbitals (GIAO)-, BPW91-, and B3LYP levels. For this set of compounds, substituent effects on delta(53Cr) are better described with the pure BPW91 functional than with B3LYP, in contrast to most other transition-metal chemical shifts studied so far. For selected cases, 53Cr NMR line widths can be rationalized in terms of electric field gradients (EFGs) computed with the BPW91 functional, but in general other factors such as molecular correlation times appear to be dominating. 53Cr chemical shifts and EFGs are predicted for CrO3, Cr(C6H6)2, Cr(C6H6)CO3, and, with reduced reliability, for Cr2(mu2-O2CH)4.

Relativistic calculation of nuclear magnetic shielding using normalized elimination of the small component

The normalized elimination of the small component (NESC) theory, recently proposed by Filatov and Cremer, is extended to include magnetic interactions and applied to the calculation of the nuclear magnetic shielding in HX (X=F, Cl, Br, I) systems. The NESC calculations are performed at the levels of the zeroth-order regular approximation (ZORA) and the second-order regular approximation (SORA). The calculations show that the NESC-ZORA results are very close to the NESC-SORA results, except for the shielding of the I nucleus. Both the NESC-ZORA and NESC-SORA calculations yield very similar results to the previously reported values obtained using the relativistic infinite-order two-component coupled Hartree-Fock method. The difference between NESC-ZORA and NESC-SORA results is significant for the shieldings of iodine.

Relativistic effects on the nuclear magnetic shieldings of rare-gas atoms and halogen in hydrogen halides within relativistic polarization propagator theory

In this work an analysis of the electronic origin of relativistic effects on the isotropic dia- and paramagnetic contributions to the nuclear magnetic shielding sigma(X) for noble gases and heavy atoms of hydrogen halides is presented. All results were obtained within the 4-component polarization propagator formalism at different level of approach [random-phase approximation (RPA) and pure zeroth-order approximation (PZOA)], by using a local version of the DIRAC code. From the fact that calculations of diamagnetic contributions to sigma within RPA and PZOA approaches for HX(X=Br,I,At) and rare-gas atoms are quite close each to other and the finding that the diamagnetic part of the principal propagator at the PZOA level can be developed as a series [S(Delta)], it was found that there is a branch of negative-energy "virtual" excitations that contribute with more than 98% of the total diamagnetic value even for the heavier elements, namely, Xe, Rn, I, and At. It contains virtual negative-energy molecular-orbital states with energies between -2 mc2 and -4 mc2. This fact can explain the excellent performance of the linear response elimination of small component (LR-ESC) scheme for elements up to the fifth row in the Periodic Table. An analysis of the convergency of S(Delta) and its physical implications is given. It is also shown that the total contribution to relativistic effects of the innermost orbital (1s1/2) is by far the largest. For the paramagnetic contributions results at the RPA and PZOA approximations are similar only for rare-gas atoms. On the other hand, if the mass-correction contributions to sigma(p) are expressed in terms of atomic orbitals, a different pattern is found for 1s1/2 orbital contributions compared with all other s-type orbitals when the whole set of rare-gas atoms is considered.

Calculation of nuclear magnetic shieldings using an analytically differentiated relativistic shielding formula

Two expressions for nuclear-magnetic-shielding tensor components based on analytically differentiating the electronic energy of a system are presented. The first is based on a second-order Douglas-Kroll-Hess approach, in which the off-diagonal block terms of the transformed Dirac Hamiltonian are diminished to second order with respect to both the electrostatic nuclear attraction potential V and the magnetic vector potential A. The second expression is based on the method of Barysz-Sadlej-Snijders, in which the off-diagonal block terms in the transformed Dirac Hamiltonian are completely eliminated with respect to purely V terms, while they are diminished to second order with respect to terms including A. The two approaches are applied to the calculation of nuclear magnetic shieldings of HX (X=F, Cl, Br, I), H2X (X=O, S, Se, Te), and noble gas X (X =He,Ne,Ar,Kr,Xe) systems with common gauge origins. The results show that relativistic corrections of higher than second order are negligibly small, except for the paramagnetic parts of I, Te, and Xe shieldings. The present calculations yield very large positive values for the anisotropy of proton shielding, deltasigma(H) = sigmaparallel(H)-sigmaperpendicular(H), of HI compared to previous reports. Unfortunately, no experimental values for the anisotropy of proton shielding in HI are available for verification.

Relativistic corrections to the diamagnetic term of the nuclear magnetic shielding: Analysis of contributions from localized orbitals

We have calculated the relativistic corrections to the diamagnetic term of the nuclear magnetic shielding constants for a series of molecules containing heavy atoms. An analysis of the contributions from localized orbitals is performed. We establish quantitatively the relative importance of inner core and valence shell molecular orbitals in each correcting term. Contributions from the latter are much less important than those from the former. The calculated values of the correction sigma(L-PSO), first derived within the linear response elimination of small component formalism, show a power-law dependence on the nuclear charge approximately Z(3.5), in contrast with the approximately Z(3.1) behavior of the mass-velocity external-field correction to the paramagnetic term previously reported.

Estimates of methyl 13C and 1H CSA values (Deltasigma) in proteins from cross-correlated spin relaxation

Simple pulse schemes are presented for the measurement of methyl (13)C and (1)H CSA values from (1)H-(13)C dipole/(13)C CSA and (1)H-(13)C dipole/(1)H CSA cross-correlated relaxation. The methodology is applied to protein L and malate synthase G. Average (13)C CSA values are considerably smaller for Ile than Leu/Val (17 vs 25 ppm) and are in good agreement with previous solid state NMR studies of powders of amino acids and dipeptides and in reasonable agreement with quantum-chemical DFT calculations of methyl carbon CSA values in peptide fragments. Small averaged (1)H CSA values on the order of 1 ppm are measured, consistent with a solid state NMR determination of the methyl group (1)H CSA in dimethylmalonic acid.

Recent developments in solid-state magic-angle spinning, nuclear magnetic resonance of fully and significantly isotopically labelled peptides and proteins

In recent years, a large number of solid-state nuclear magnetic resonance (NMR) techniques have been developed and applied to the study of fully or significantly isotopically labelled ((13)C, (15)N or (13)C/(15)N) biomolecules. In the past few years, the first structures of (13)C/(15)N-labelled peptides, Gly-Ile and Met-Leu-Phe, and a protein, Src-homology 3 domain, were solved using magic-angle spinning NMR, without recourse to any structural information obtained from other methods. This progress has been made possible by the development of NMR experiments to assign solid-state spectra and experiments to extract distance and orientational information. Another key aspect to the success of solid-state NMR is the advances made in sample preparation. These improvements will be reviewed in this contribution. Future prospects for the application of solid-state NMR to interesting biological questions will also briefly be discussed.

13C NMR study of halogen bonding of haloarenes: measurements of solvent effects and theoretical analysis

Solvent effects on the NMR spectra of symmetrical (X = F (1), X = Cl (2), X = Br (3), X = I (4), X = NO2 (5), X = CN (6)) and unsymmetrical (X = I, Y = MeO (7), Y = PhO (8)) para-disubstituted acetophenone azines X-C6H4-CMe=N-N=CMe-C6H4-Y and of models X-C6H4-CMe=N-Z (X = I, Z = H (9), Z = NH2 (10)), 4-iodoacetophenone (11), and iodobenzene (12) were measured in CDCl(3), DMSO, THF, pyridine, and benzene to address one intramolecular and one intermolecular issue. Solvent effects on the (13)C NMR spectra are generally small, and this finding firmly establishes that the azine bridge indeed functions as a "conjugation stopper," an important design concept in our polar materials research. Since intermolecular halogen bonding of haloarenes do occur in polar organic crystalline materials, the NMR solution data pose the question as to whether the absence of solvent shifts indicates the absence of strong halogen bonding in solution. This question was studied by the theoretical analysis of the DMSO complexes of iodoarenes 4, 9-12, and of iodoacetylene. DFT and MP2 computations show iodine bonding, and characteristic structural and electronic features are described. The nonrelativistic complexation shifts and the change in the spin-orbit induced heavy atom effect of iodine compensate each other, and iodine bonding thus has no apparent effect on Ci in the iodoarenes. For iodides, complexation by DMSO occurs and may or may not manifest itself in the NMR spectra. The absence of complexation shifts in the NMR spectra of halides does not exclude the occurrence of halogen bonding in solution.

The Syntheses of Carbocations by Use of the Noble-Gas Oxidant, [XeOTeF5][Sb(OTeF5)6]: The Syntheses and Characterization of the CX3+ (X = Cl, Br, OTeF5) and CBr(OTeF5)2+ Cations and Theoretical Studies of CX3+ and BX3 (X = F, Cl, Br, I, OTeF5)

The CCl(3)(+) and CBr(3)(+) cations have been synthesized by oxidation of a halide ligand of CCl(4) and CBr(4) at -78 degrees C in SO(2)ClF solvent by use of [XeOTeF(5)][Sb(OTeF(5))(6)]. The CBr(3)(+) cation reacts further with BrOTeF(5) to give CBr(OTeF(5))(2)(+), C(OTeF(5))(3)(+), and Br(2). The [XeOTeF(5)][Sb(OTeF(5))(6)] salt was also found to react with BrOTeF(5) in SO(2)ClF solvent at -78 degrees C to give the Br(OTeF(5))(2)(+) cation. The CCl(3)(+), CBr(3)(+), CBr(OTeF(5))(2)(+), C(OTeF(5))(3)(+), and Br(OTeF(5))(2)(+) cations and C(OTeF(5))(4) have been characterized in SO(2)ClF solution by (13)C and/or (19)F NMR spectroscopy at -78 degrees C. The X-ray crystal structures of the CCl(3)(+), CBr(3)(+), and C(OTeF(5))(3)(+) cations have been determined in [CCl(3)][Sb(OTeF(5))(6)], [CBr(3)][Sb(OTeF(5))(6)].SO(2)ClF, and [C(OTeF(5))(3)][Sb(OTeF(5))(6)].3SO(2)ClF at -173 degrees C. The CCl(3)(+) and CBr(3)(+) salts were stable at room temperature, whereas the CBr(n)(OTeF(5))(3-n)(+) salts were stable at 0 degrees C for several hours. The cations were found to be trigonal planar about carbon, with the CCl(3)(+) and CBr(3)(+) cations showing no significant interactions between their carbon atoms and the fluorine atoms of the Sb(OTeF(5))(6)(-) anions. In contrast, the C(OTeF(5))(3)(+) cation interacts with an oxygen of each of two SO(2)ClF molecules by coordination along the three-fold axis of the cation. The solid-state Raman spectra of the Sb(OTeF(5))(6)(-) salts of CCl(3)(+) and CBr(3)(+) have been obtained and assigned with the aid of electronic structure calculations. The CCl(3)(+) cation displays a well-resolved (35)Cl/(37)Cl isotopic pattern for the symmetric CCl(3) stretch. The energy-minimized geometries, natural charges, and natural bond orders of the CCl(3)(+), CBr(3)(+), CI(3)(+), and C(OTeF(5))(3)(+) cations and of the presently unknown CF(3)(+) cation have been calculated using HF and MP2 methods have been compared with those of the isoelectronic BX(3) molecules (X = F, Cl, Br, I, and OTeF(5)). The (13)C and (11)B chemical shifts for CX(3)(+) (X = Cl, Br, I) and BX(3) (X = F, Cl, Br, I) were calculated by the GIAO method, and their trends were assessed in terms of paramagnetic contributions and spin-orbit coupling.

Relativistic spin-orbit effects on hyperfine coupling tensors by density-functional theory

A second-order perturbation theory treatment of spin-orbit corrections to hyperfine coupling tensors has been implemented within a density-functional framework. The method uses the all-electron atomic mean-field approximation and/or spin-orbit pseudopotentials in incorporating one- and two-electron spin-orbit interaction within a first-principles framework. Validation of the approach on a set of main-group radicals and transition metal complexes indicates good agreement between all-electron and pseudopotential results for hyperfine coupling constants of the lighter nuclei in the system, except for cases in which scalar relativistic effects become important. The nonrelativistic Fermi contact part of the isotropic hyperfine coupling constants is not always accurately reproduced by the exchange-correlation functionals employed, particularly for the triplet and pi-type doublet radicals in the present work. For this reason, ab initio coupled-cluster singles and doubles with perturbative triples results for the first-order contributions have been combined in the validation calculations with the density-functional results for the second-order spin-orbit contributions. In the cases where spin-orbit corrections are of significant magnitude relative to the nonrelativistic first-order terms, they improve the agreement with experiment. Antisymmetric contributions to the hyperfine tensor arise from the spin-orbit contributions and are discussed for the IO2 radical, whereas rovibrational effects have been evaluated for RhC, NBr, and NI.

Relativistic spin-orbit coupling effects on secondary isotope shifts of (13)C nuclear shielding in CX(2) (X = O, S, Se, Te)

Rovibrational corrections, temperature dependence, and secondary isotope shifts of the (13)C nuclear shielding in CX(2) (X = O, S, Se, Te) are calculated taking into account the relativistic spin-orbit (SO) interaction. The SO effect is considered for the first time for the secondary isotope shifts. The nuclear shielding hypersurface in terms of nuclear displacements is calculated by using a density-functional theory method. Ab initio multiconfiguration self-consistent field calculations are done at the equilibrium geometry for comparison. (13)C NMR measurements are carried out for CS(2). The calculated results are compared with both present and earlier experimental data on CO(2), CS(2), and CSe(2). The heavy-atom SO effects on the rovibrational corrections of (13)C shielding are shown to be significant. For CSe(2) and CTe(2), reliable prediction of secondary isotope effects and their temperature dependence requires the inclusion of the SO corrections. In particular, earlier discrepancies of theory and experiment for CSe(2) are fully resolved by taking the SO interactions into account.