The calculation of 2J(HH) couplings in benzyl groups

The results of FPT/INDO theory together with the observed ²J(HH) coupling in benzyl groups (Ph · CH₂X) leads to a simple equation ²J(HH) = A+B cos θ+C cos 2θ where θ is the C.C.C.X dihedral angle, and X = C,H. The extension to other X substituents can be obtained from additivity rules.     

Density-functional calculations of relativistic spin-orbit effects on nuclear magnetic shielding in paramagnetic molecules

Terms arising from the relativistic spin-orbit effect on both hyperfine and Zeeman interactions are introduced to density-functional theory calculation of nuclear magnetic shielding in paramagnetic molecules. The theory is a generalization of the former nonrelativistic formulation for doublet systems and is consistent to O(alpha4), the fourth power of the fine structure constant, for the spin-orbit terms. The new temperature-dependent terms arise from the deviation of the electronic g tensor from the free-electron g value as well as spin-orbit corrections to hyperfine coupling tensor A, the latter introduced in the present work. In particular, the new contributions include a redefined isotropic pseudocontact contribution that consists of effects due to both the g tensor and spin-orbit corrections to hyperfine coupling. The implementation of the spin-orbit terms makes use of all-electron atomic mean-field operators and/or spin-orbit pseudopotentials. Sample results are given for group-9 metallocenes and a nitroxide radical. The new O(alpha4) corrections are found significant for the metallocene systems while they obtain small values for the nitroxide radical. For the isotropic shifts, none of the three beyond-leading-order hyperfine contributions are negligible.     

Experimental and theoretical study of hyperconjugative interaction effects on NMR 1J(CH) scalar couplings

Hyperconjugative and electrostatic interactions effects on 1J(CH) spin-spin coupling constants (SSCCs) are critically studied from both theoretical and experimental points of view. A qualitative model is used to predict how the former affect such SSCCs, while electrostatic interactions are modeled with a point charge placed in the vicinity of the corresponding sigma(CH) bond. Hyperconjugative interactions are calculated using the "natural bond orbital" approach, and using the point-charge model, it is shown how intertwined are both types of interactions. Several members of the series 1-X-bicyclo[1.1.1]pentane and 1-X-3-methylbicyclo[1.1.1]pentane are chosen as model compounds for measuring 1J(CH) SSCCs; in some of them were performed also DFT-SSCC calculations. The strained cage substrate in these series defines strong sigma-hyperconjugative interactions, making these compounds excellent examples to verify the qualitative model presented in this work. It is verified that (a) hyperconjugative interactions from the sigma(CH) bond or into the sigma(CH) antibond containing the coupling nuclei yield a decrease of the corresponding 1J(CH) SSCC and (b) hyperconjugative interactions from other bonds involving the coupling C nucleus yield an increase of that 1J(CH) SSCC.     

The additivity of substituent effects upon J(FF) in polysubstituted fluorobenzenes: An update

Substituent effects upon ³J(FF) are demonstrated to be additive, and a previous analysis of ⁴J(FF) and ⁵J(FF) in polysubstituted fluorobenzenes is updated.     

Effect of electronic interactions on NMR 1J(CF) and 2J(CF) couplings in cis- and trans-4-t-butyl-2-fluorocyclohexanones and their alcohol derivatives

In order to study the influence of hyperconjugative, inductive, steric, and hydrogen-bond interactions on (1)J(CF) and (2)J(CF) NMR spin-spin coupling constants (SSCCs), they were measured in cis- and trans-4-t-butyl-2-fluorocyclohexanones and their alcohol derivatives. The four isotropic terms of those SSCCs, Fermi contact (FC), spin dipolar (SD), paramagnetic spin-orbit (PSO), and diamagnetic spin-orbit (DSO), were calculated at the SOPPA(CCSD)/EPR-III level. Significant changes in FC and PSO terms along that series of compounds were rationalized in terms of their transmission mechanisms by employing a qualitative analysis of their expressions in terms of the polarization propagator formalism. The PSO term is found to be sensitive to proximate interactions like steric compression and hydrogen bonding; we describe how it could be used to gauge such interactions. The FC term of (2)J(CF) SSCC in cis-4-t-butyl-2-fluorocyclohexanone is rationalized as transmitted in part by the superposition of the F and O electronic clouds.     

Geminal 2J(29Si‐O‐29Si) couplings in oligosiloxanes and their relation to direct 1J(29Si‐13C) couplings

Absolute values of (79) geminal ²J(²⁹Si‐O‐²⁹Si) couplings were measured in an extensive series of (55) unstrained siloxanes dissolved in chloroform‐d. Signs of ²J(²⁹Si‐O‐²⁹Si) in some (9) silicon hydrides were determined relative to ¹J(²⁹Si‐¹H) which are known to be negative. It is supposed that positive sign of the ²J(²⁹Si‐O‐²⁹Si) coupling found in all studied hydrides is common to all siloxanes. Theoretical calculations for simple model compounds failed to reproduce this sign and so their predictions of bond length and angle dependences cannot be taken as reliable. Useful empirical correlations were found between the ²J(²⁹Si‐O‐²⁹Si) couplings on one side and the total number m of oxygen atoms bonded to the silicon atoms, sum of ²⁹Si chemical shifts or product of ¹J(²⁹Si‐¹³C) couplings on the other side. The significance of these correlations is briefly discussed. Copyright © 2011 John Wiley & Sons, Ltd.     

Trans-hydrogen-bond (h2)J(NN) and (h1)J(NH) couplings in the DNA A-T base pair: natural bond orbital analysis

Natural bond orbital (NBO) analysis described here demonstrates that trans-hydrogen-bond (trans-H-bond) NMR J couplings in the DNA A-T base pair, h2JNN and h1JNH, are determined largely by three terms: two Lewis-type contributions (the single-orbital contribution from the adenine lone pair and the contribution from the sigmaN3H3 natural bond orbital of the thymine ring) and one contribution from pairwise delocalization of spin density (between the lone pair in adenine and the sigma* antibonding orbital linking N3 and H3 of thymine). For h2JNN coupling, all three contributions are positive, whereas for h1JNH coupling, the delocalization term is negative, and the other two terms are positive, resulting in a small net positive coupling constant. This result rationalizes the experimental findings that the two-bond coupling (h2JNN approximately 9 Hz) is larger than the one-bond coupling (h1JNH approximately 3 Hz) and demonstrates that the same hyperconjugative and steric mechanisms that stabilize the H-bond are involved in the transmission of J coupling information. The N1...H3-N3 H-bond of the DNA A-T base pair is found to exhibit significant covalent character, but steric effects contribute almost equally to the trans-H-bond coupling.     

Variation in protein C(alpha)-related one-bond J couplings

Four types of polypeptide (1)J(C alpha X) couplings are examined, involving the main-chain carbon C(alpha) and either of four possible substituents. A total 3105 values of (1)J(C alpha H alpha), (1)J(C alpha C beta), (1)J(C alpha C'), and (1)J(C alpha N') were collected from six proteins, averaging 143.4 +/- 3.3, 34.9 +/- 2.5, 52.6 +/- 0.9, and 10.7 +/- 1.2 Hz, respectively. Analysis of variances (ANOVA) reveals a variety of factors impacting on (1)J and ranks their relative statistical significance and importance to biomolecular NMR structure refinement. Accordingly, the spread in the (1)J values is attributed, in equal proportions, to amino-acid specific substituent patterns and to polypeptide-chain geometry, specifically torsions phi, psi, and chi(1) circumjacent to C(alpha). The (1)J coupling constants correlate with protein secondary structure. For alpha-helical phi, psi combinations, (1)J(C alpha H alpha) is elevated by more than one standard deviation (147.8 Hz), while both (1)J(C alpha N') and (1)J(C alpha C beta) fall short of their grand means (9.5 and 33.7 Hz). Rare positive phi torsion angles in proteins exhibit concomitant small (1)J(C alpha H alpha) and (1)J(C alpha N') (138.4 and 9.6 Hz) and large (1)J(C alpha C beta) (39.9 Hz) values. The (1)J(C alpha N') coupling varies monotonously over the phi torsion range typical of beta-sheet secondary structure and is largest (13.3 Hz) for phi around -160 degrees. All four coupling types depend on psi and thus help determine a torsion that is notoriously difficult to assess by traditional approaches using (3)J. Influences on (1)J stemming from protein secondary structure and other factors, such as amino-acid composition, are largely independent.     

Substituent effects on scalar J(13C, 13C) couplings in pyrimidines. An experimental and DFT study

One- two- and three 13C, 13C (n = 1, 2, 3) scalar couplings, (n)J(C,C) in a set of pyrimidine derivatives were studied both experimentally at natural abundance and theoretically by their DFT calculation of all four contributions. Trends of non-contact terms are discussed and substituent effects are rationalized, comparing some of them with the corresponding values in benzene and pyridine. Although substituent effects on non-contact terms are relatively important, the whole trend is dominated by the Fermi contact term. According to the current literature, substituent effects on 1J(C,C) couplings in benzene derivatives are dominated by the inductive effect, which, apparently, is also the case in nitrogen heteroaromatic compounds. However, some differences observed in this work for substituent effects on 1J(C,C) couplings in pyrimidine derivatives suggest that in the latter type of compounds substituent effects can be affected by the orientation of the ring nitrogen lone pairs.     

Lanthanide-binding peptides for NMR measurements of residual dipolar couplings and paramagnetic effects from multiple angles

Lanthanide-binding peptide tags (LBTs) containing a single cysteine residue can be attached to proteins via a disulfide bond, presenting a flexible means of tagging proteins site-specifically with a lanthanide ion. Here we show that cysteine residues placed in different positions of the LBT can be used to expose the protein to different orientations of the magnetic susceptibility anisotropy (delta chi) tensor and to generate different molecular alignments in a magnetic field. Delta chi tensors determined by nuclear magnetic resonance (NMR) spectroscopy for LBT complexes with Yb3+, Tm3+, and Er3+ suggest a rational way of producing alignment tensors with different orientations. In addition, knowledge of the delta chi tensor of LBT allows modeling of the protein-LBT structures. Despite evidence for residual mobility of the LBTs with respect to the protein, the pseudocontact shifts and residual dipolar couplings displayed by proteins disulfide-bonded to LBTs are greater than those achievable with most other lanthanide binding tags.     

Insights into the mobility of methyl-bearing side chains in proteins from (3)J(CC) and (3)J(CN) couplings

Side-chain dynamics in proteins can be characterized by the NMR measurement of (13)C and (2)H relaxation rates. Evaluation of the corresponding spectral densities limits the slowest motions that can be studied quantitatively to the time scale on which the overall molecular tumbling takes place. A different measure for the degree of side-chain order about the C(alpha)-C(beta) bond (chi(1) angle) can be derived from (3)J(C)(')(-)(C)(gamma) and (3)J(N)(-)(C)(gamma) couplings. These couplings can be measured at high accuracy, in particular for Thr, Ile, and Val residues. In conjunction with the known backbone structures of ubiquitin and the third IgG-binding domain of protein G, and an extensive set of (13)C-(1)H side-chain dipolar coupling measurements in oriented media, these (3)J couplings were used to parametrize empirical Karplus relationships for (3)J(C)(')(-)(C)(gamma) and (3)J(N)(-)(C)(gamma). These Karplus curves agree well with results from DFT calculations, including an unusual phase shift, which causes the maximum (3)J(CC) and (3)J(CN) couplings to occur for dihedral angles slightly smaller than 180 degrees, particularly noticeable in Thr residues. The new Karplus curves permit determination of rotamer populations for the chi(1) torsion angles. Similar rotamer populations can be derived from side-chain dipolar couplings. Conversion of these rotamer populations into generalized order parameters, S(J)(2) and S(D)(2), provides a view of side-chain dynamics that is complementary to that obtained from (13)C and (2)H relaxation. On average, results agree well with literature values for (2)H-relaxation-derived S(rel)(2) values in ubiquitin and HIV protease, but also identify a fraction of residues for which S(J,D)(2) < S(rel)(2). This indicates that some of the rotameric averaging occurs on a time scale too slow to be observable in traditional relaxation measurements.     

Integrated paramagnetic resonance of high-spin Co(II) in axial symmetry: chemical separation of dipolar and contact electron-nuclear couplings

Integrated paramagnetic resonance, utilizing electron paramagnetic resonance (EPR), NMR, and electron-nuclear double resonance (ENDOR), of a series of cobalt bis-trispyrazolylborates, Co(Tp ( x )) 2, are reported. Systematic substitutions at the ring carbons and on the apical boron provide a unique opportunity to separate through-bond and through-space contributions to the NMR hyperfine shifts for the parent, unsubstituted Tp complex. A simple relationship between the chemical shift difference (delta H - delta Me) and the contact shift of the proton in that position is developed. This approach allows independent extraction of the isotropic hyperfine coupling, A iso, for each proton in the molecule. The Co..H contact coupling energies derived from the NMR, together with the known metrics of the compounds, were used to predict the ENDOR couplings at g perpendicular. Proton ENDOR data is presented that shows good agreement with the NMR-derived model. ENDOR signals from all other magnetic nuclei in the complex ( (14)N, coordinating and noncoordinating, (11)B and (13)C) are also reported.     

A quantum wave packet dynamical study of the electronic and spin-orbit coupling effects on the resonances in Cl(2P) + H2 scattering

Dynamical resonances in Cl(2P) + H2 scattering are investigated with the aid of a time-dependent wave packet approach using the Capecchi-Werner coupled ab initio potential energy surfaces [Phys. Chem. Chem. Phys. 2004, 6, 4975]. The resonances arising from the prereactive van der Waals well (approximately 0.5 kcal/mol) and the transition-state (TS) region of the 2Sigma(1/2) ground spin-orbit (SO) state of the Cl(2P) + H2 system are calculated and assigned by computing their eigenfunctions and lifetimes. The excitation of even quanta along the bending coordinate of the resonances is observed. The resonances exhibit an extended van der Waals progression, which can be attributed to the dissociative states of ClH2. Excitation of H2 vibration is also identified in the high-energy resonances. The effect of the excited 2P(1/2) SO state of Cl on these resonances is examined by considering the electronic and SO coupling in the dynamical simulations. While the electronic coupling has only a minor impact on the resonance structures, the SO coupling has significant effect on them. The nonadiabatic effect due to the SO coupling is stronger, and as a result, the spectrum becomes broad and diffuse particularly at high energies. We also report the photodetachment spectrum of ClD2- and compare the theoretical findings with the available experimental results.     

The ligand-ligand and spin-orbit interactions in Fe(phen) 3 +2 and Ru(phen) 3 +2 ions

To explain the differences in the spectral properties of the complex ions (–)-Fe(phen) ₃ ⁺² and (–)-Ru(phen) ₃ ⁺² the interaction between the ligands and spin-orbit coupling energies have been calculated. It is shown that the spinorbit coupling energy in case of Ru(II) complex is more important than the ligand-ligand interaction. This leads to a sequence of the lowest excited states ³A₂<¹A₂<¹E.     

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.