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.     

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.     

Effect of molecular size on the parity-non-conserving contributions to the nuclear magnetic resonance shielding constant

We present density-functional theory studies on the effects of molecular size on the parity-violating contribution to the nuclear magnetic shielding constant. We focus on models with different backbone and side chain lengths, as well as the details of geometry optimization for certain helical polysilylenes and investigate the parity-violating contribution to the shielding constant of the ²⁹Si nucleus of the backbone. Our calculations show that the molecular geometry has a large influence on the magnitude of the parity-violating shielding contribution, a result that is in line with the previous studies on much smaller molecules. In addition, we find convergence in the magnitude of the PV effect with respect to system size, when using geometries that preserve the helical Si backbone structure optimized for the largest of the present systems. This can be interpreted in terms of the non-size-extensive nature of the parity-violating operator influencing the leading-order effect on nuclear magnetic shielding, as opposed to the size-extensive interaction affecting the energy difference between enantiomers. Our molecules are truncated models of large polysilylene systems, for which a difference in the ²⁹Si chemical shift between enantiomers has been observed to be 0.06 ppm (Fujiki in Macromol Rapid Commun 22, 669–674, 2001). As expected based on earlier first principles studies of small molecules, we do not find support for the difference to be of the parity-violating origin. Instead, the predicted parity-violation-induced splitting of the ²⁹Si resonance is found to converge at values around 10^?8 ppm with increasingly large Si backbone.     

Density functional theory study of indirect nuclear spin-spin coupling constants with spin-orbit corrections

This work outlines the calculation of indirect nuclear spin-spin coupling constants with spin-orbit corrections using density functional response theory. The nonrelativistic indirect nuclear spin-spin couplings are evaluated using the linear response method, whereas the relativistic spin-orbit corrections are computed using quadratic response theory. The formalism is applied to the homologous systems H2X (X=O,S,Se,Te) and XH4 (X=C,Si,Ge,Sn,Pb) to calculate the indirect nuclear spin-spin coupling constants between the protons. The results confirm that spin-orbit corrections are important for compounds of the H2X series, for which the electronic structure allows for an efficient coupling between the nuclei mediated by the spin-orbit interaction, whereas in the case of the XH4 series the opposite situation is encountered and the spin-orbit corrections are negligible for all compounds of this series. In addition we analyze the performance of the density functional theory in the calculations of nonrelativistic indirect nuclear spin-spin coupling constants.     

Gauge invariance of the nuclear spin/electron orbit interaction and NMR spectral parameters

A gauge transformation of the vector potential A(m(I) ), associated to the magnetic dipole m(I) of nucleus I in a molecule, has been studied. The conditions for gauge invariance of nuclear magnetic shielding, nuclear spin/electron orbit contribution to spin-spin coupling between two nuclei, I and J, and electronic current density induced by m(I), have been expressed via quantum mechanical sum rules that are identically satisfied for exact and optimal variational wavefunctions. It is shown that separate diamagnetic and paramagnetic contributions to the properties transform into one another in the gauge transformation, whereas their sum is invariant. Therefore, only total response properties have a physical meaning. In particular, the disjoint diamagnetic and paramagnetic components of nuclear spin/electron orbit contributions to coupling constants are not uniquely defined. The diamagnetic contribution to the nuclear spin-spin coupling tensor, evaluated as an expectation value in the Ramsey theory, can alternatively be expressed as a sum-over-states formula, by rewriting the second-order Hamiltonian in commutator form a? la Geertsen, as previously reported by Sauer. Other sum-over-states formulae are obtained via a gauge transformation, by a procedure formally allowing for a continuous translation of the origin of the m(I)-induced current density, analogous to those previously proposed for magnetizabilities and nuclear magnetic shielding.     

Ab-initio SOS-CI calculations of magnetic properties of the first- and second-row hydrides

Non-empirical SOS-CI calculations based on Nakatsuji's theory are reported for the nuclear spin-spin coupling constants, (considering all the four spininteractions), magnetic shielding constants and magnetic susceptibilities of all the first- and second-row hydrides. The calculated values, except for ²J(HH), correlate satisfactorily with the available experimental data and with the corresponding CHF results, and prove that the SOS-CI model according to Nakatsuji may be a convenient alternative to the time-consuming CHF procedures in order to get accurate estimates of second-order magnetic properties.     

One-electron versus electron-electron interaction contributions to the spin-spin coupling mechanism in nuclear magnetic resonance spectroscopy: analysis of basic electronic effects

For the first time, the nuclear magnetic resonance (NMR) spin-spin coupling mechanism is decomposed into one-electron and electron-electron interaction contributions to demonstrate that spin-information transport between different orbitals is not exclusively an electron-exchange phenomenon. This is done using coupled perturbed density-functional theory in conjunction with the recently developed J-OC-PSP [=J-OC-OC-PSP: Decomposition of J into orbital contributions using orbital currents and partial spin polarization)] method. One-orbital contributions comprise Ramsey response and self-exchange effects and the two-orbital contributions describe first-order delocalization and steric exchange. The two-orbital effects can be characterized as external orbital, echo, and spin transport contributions. A relationship of these electronic effects to zeroth-order orbital theory is demonstrated and their sign and magnitude predicted using simple models and graphical representations of first order orbitals. In the case of methane the two NMR spin-spin coupling constants result from totally different Fermi contact coupling mechanisms. (1)J(C,H) is the result of the Ramsey response and the self-exchange of the bond orbital diminished by external first-order delocalization external one-orbital effects whereas (2)J(H,H) spin-spin coupling is almost exclusively mitigated by a two-orbital steric exchange effect. From this analysis, a series of prediction can be made how geometrical deformations, electron lone pairs, and substituent effects lead to a change in the values of (1)J(C,H) and (2)J(H,H), respectively, for hydrocarbons.     

High resolution NMR study of T1 magnetic relaxation dispersion. II. Influence of spin-spin couplings on the longitudinal spin relaxation dispersion in multispin systems

Effects of scalar spin-spin interactions on the nuclear magnetic relaxation dispersion (NMRD) of coupled multispin systems were analyzed. Taking spin systems of increasing complexity we demonstrated pronounced influence of the intramolecular spin-spin couplings on the NMRD of protons. First, at low magnetic fields where there is strong coupling of spins the apparent relaxation times of the coupled spins become equal. Second, there are new features, which appear at the positions of the nuclear spin level anticrossings. Finally, in coupled spin systems there can be a coherent contribution to the relaxation kinetics present at low magnetic fields. All these peculiarities caused by spin-spin interactions are superimposed on the features in NMRD, which are conditioned by changes of the motional regime. Neglecting the effects of couplings may lead to misinterpretation of the NMRD curves and significant errors in determining the correlation times of molecular motion. Experimental results presented are in good agreement with theoretical calculations.     

An NMR and relativistic DFT investigation of one-bond nuclear spin-spin coupling in solid triphenyl group-14 chlorides

A solid-state nuclear magnetic resonance and zeroth-order regular approximation density functional theory, ZORA-DFT, study of one-bond nuclear spin-spin coupling between group-14 nuclei and quadrupolar 35/37Cl nuclei in triphenyl group-14 chlorides, Ph3XCl (X = C, Si, Ge, Sn and Pb), is presented. This represents the first combined experimental and theoretical systematic study of spin-spin coupling involving spin-pairs containing quadrupolar nuclei. Solid-state NMR spectra have been acquired for all compounds in which X has a spin-1/2 isotope--13C, 29Si, [117/119]Sn and 207Pb-at applied magnetic fields of 4.70, 7.05 and 11.75 T. From simulations of these spectra, values describing the indirect spin-spin coupling tensor-the isotropic indirect spin-spin coupling constant, 1J(X, 35/37Cl)iso and the anisotropy of the J tensor, Delta1J(X, 35/37Cl)--have been determined for all but the lead-chlorine spin-pair. To better compare the indirect spin-spin coupling parameters between spin-pairs, 1J(iso) and Delta1J values were converted to their reduced coupling constants, 1K(iso) and Delta1K. From experiment, the sign of 1K(iso) was found to be negative while the sign of Delta1K is positive for all spin-pairs investigated. The magnitude of both 1K(iso) and Delta1K was found to increase as one moves down group-14. Theoretical values of the magnitude and sign of 1K(iso) and Delta1K were obtained from ZORA-DFT calculations and are in agreement with the available experimental data. From the calculations, the Fermi-contact mechanism was determined to provide the largest contribution to 1K(iso) for all spin-pairs while spin-dipolar and paramagnetic spin-orbit mechanisms make significant contributions to the anisotropy of K. The inclusion of relativistic effects was found to influence K(Sn,Cl) and K(Pb,Cl).     

19F single-quantum and 19F-33S heteronuclear multiple-quantum coherence NMR of SF6 in thermotropic nematogens and in the gas phase

(19)F single-quantum (SQC) and (19)F-(33)S heteronuclear multiple-quantum coherence (HMQC) NMR spectroscopy of sulfur hexafluoride (SF(6)) dissolved in thermotropic liquid crystals (TLCs) were used to investigate the properties of TLCs. On one hand, environmental effects on the NMR parameters of SF(6), (19)F nuclear shielding, (19)F-(33)S spin-spin coupling, secondary isotope effects of sulfur on (19)F shielding, and the self-diffusion coefficient in the direction of the external magnetic field were studied as well. The temperature dependence of the (19)F shielding of SF(6) in TLCs was modeled with a function that takes into account the properties of both TLC and SF(6). It appears that the TLC environment deforms the electronic system of SF(6) so that the (19)F shielding tensor becomes slightly anisotropic, with the anisotropy being from -0.5 to -1.4 ppm, depending upon the TLC solvent. On the contrary, no sign of residual dipolar coupling between (19)F and (33)S was found, meaning that the so-called deformational effects, which arise from the interaction between vibrational and reorientational motions of the molecule, on the geometry of the molecule are insignificant. Diffusion activation energies, E(a), were determined from the temperature dependence of the self-diffusion coefficients. In each TLC, E(a) increases when moving from an isotropic phase to a nematic phase. The spin-spin coupling constant, J((19)F,(33)S), increases by ca. 10 Hz when moving from the gas phase to TLC solutions. The secondary isotope shifts of (19)F shielding are practically independent of TLC solvent and temperature. For the first time, (19)F-(33)S heteronuclear multiple-quantum NMR spectra were recorded for SF(6) in the gas phase and in a liquid-crystalline solution.     

High resolution NMR study of T(1) magnetic relaxation dispersion. III. Influence of spin 1∕2 hetero-nuclei on spin relaxation and polarization transfer among strongly coupled protons

Effects of spin-spin interactions on the nuclear magnetic relaxation dispersion (NMRD) of protons were studied in a situation where spin [fraction one-half] hetero-nuclei are present in the molecule. As in earlier works [K. L. Ivanov, A. V. Yurkovskaya, and H.-M. Vieth, J. Chem. Phys. 129, 234513 (2008); S. E. Korchak, K. L. Ivanov, A. V. Yurkovskaya, and H.-M. Vieth, ibid. 133, 194502 (2010)], spin-spin interactions have a pronounced effect on the relaxivity tending to equalize the longitudinal relaxation times once the spins become strongly coupled at a sufficiently low magnetic field. In addition, we have found influence of (19)F nuclei on the proton NMRD, although in the whole field range, studied protons and fluorine spins were only weakly coupled. In particular, pronounced features in the proton NMRD were found; but each feature was predominantly observed only for particular spin states of the hetero-nuclei. The features are explained theoretically; it is shown that hetero-nuclei can affect the proton NMRD even in the limit of weak coupling when (i) protons are coupled strongly and (ii) have spin-spin interactions of different strengths with the hetero-nuclei. We also show that by choosing the proper magnetic field strength, one can selectively transfer proton spin magnetization between spectral components of choice.     

The absolute sign of J coupling constants determined using the order matrix calculation

A novel methodology using the order matrix calculation to determine the absolute sign of spin-spin couplings based on the structure of organic compounds is presented. The sign of the residual dipolar coupling (RDC) depends on the sign of corresponding scalar spin-spin coupling constant and the sign of the RDC has a dramatic influence on the order matrix calculation. Therefore, the sign of the spin-spin coupling constant can be obtained by an order matrix calculation through the corresponding RDC. Six types of spin-spin coupling constants, including 2J(H,H), 1J(C,F), 2J(C,F), 3J(C,F), 2J(F,H) and 3J(F,H), were obtained simultaneously. Except for 3J(C,F) where the measured RDCs have very small magnitudes, the signs were determined unambiguously.     

Calculation of nuclear spin-spin coupling constants by SCF perturbation theory with MINDO/3 approximation

LCAO-MO-SCF-MINDO/3 approximation is used to calculate nuclear spin-spin couplings, ⁿ J ^AB, between magnetic nuclei A and B (A, B ¹H,¹³C,¹⁹F) separated byn bonds in a number of molecules. The theory predicts reasonably good values for directly bonded couplings (except those involving fluorine), but the results for multi-bond couplings are not so encouraging. Reasons for this deficiency of the theory are examined in the text.Based on Ph.D. Thesis of P. K. K. Pandey, Banaras Hindu University, 1977.     

Theoretical investigation of the apparently irregular behavior of pt-pt nuclear spin-spin coupling constants

One-bond Pt-Pt nuclear spin-spin coupling constants J(Pt-Pt) for closely related dinuclear Pt complexes can differ by an order of magnitude without any obvious correlation with Pt-Pt distances. As representative examples, the spin-spin couplings of the dinuclear Pt(I) complexes [Pt(2)(CO)(6)](2+) (1) and [Pt(2)(CO)(2)Cl(4)](2-) (2) have been computationally studied with a recently developed relativistic density functional method. The experimental values are (1)J((195)Pt-(195)Pt) = 5250 Hz for 2 but 551 Hz for 1. Many other examples are known in the literature. The experimental trends are well reproduced by the computations and can be explained based on the nature of the ligands that are coordinated to the Pt-Pt fragment. The difference for J(Pt-Pt) of an order of magnitude is caused by a sensitive interplay between the influence of different ligands on the Pt-Pt bond, and relativistic effects on metal-metal and metal-ligand bonds as well as on "atomic orbital contributions" to the nuclear spin-spin coupling constants. The results can be intuitively rationalized with the help of a simple qualitative molecular orbital diagram.     

Insight into the structure of silver cyanide from (13)C and (15)N solid-state NMR spectroscopy

The structure of silver cyanide has been investigated by solid-state multinuclear magnetic resonance spectroscopy. Carbon-13 and nitrogen-15 NMR spectra of magic-angle-spinning (MAS) and stationary powder samples of isotopically enriched Ag(13)CN, Ag(13)C(15)N, and AgC(15)N have been acquired at the external applied magnetic field strengths 4.7, 7.05, and 9.4 T. Axially symmetric carbon and nitrogen chemical shift (CS) tensors provide evidence for linearity of the polymeric (-Ag-CN-)(n)() chains. A two-site model is required to successfully simulate the (13)C MAS NMR line shape, which is dominated by indirect nuclear spin-spin coupling between (109/107)Ag and (13)C nuclei. In combination with relativistic zeroth-order regular approximation density functional theory (ZORA-DFT) calculations on model AgCN fragments, the (13)C MAS NMR results show that 30 +/- 10% of the silver sites are disordered, that is, either -NC-Ag-CN- or -CN-Ag-NC-, and 70 +/- 10% of the silver sites are ordered, that is, -NC-Ag-NC-. Effective dipolar coupling data extracted from (13)C NMR spectra of stationary samples allow an upper limit of 1.194 A to be placed on the carbon-nitrogen internuclear distance. After incorporation of the effects of anisotropic indirect nuclear spin-spin coupling and motional averaging on the NMR-derived distance, a corrected value of r(CN) = 1.16 +/- 0.03 A is obtained. This work provides an example of the type of information which may be obtained from solid-state NMR studies of disordered materials and how such information may complement that available from diffraction studies.     

Theoretical studies of nuclear magnetic resonance parameters for the proton-exchange pathways in porphyrin and porphycene

The nuclear magnetic resonance (NMR) parameters in porphyrin and porphycene have been calculated to investigate their changes during the process of proton exchange, using density-functional theory (DFT) for both the spin-spin coupling constants and the shielding constants. In addition, in calculations on the smaller 1,3-bis(arylimino)isoindoline molecule, we have tested the performance of our computational approach against experimental data. The calculated nuclear spin-spin coupling constants and shielding constants have been analyzed as functions of the progress of the proton transfer between two nitrogen atoms. The one-bond couplings between proton and nitrogen, dominated by the Fermi-contact term, decay steeply as the internuclear distance increases. The small changes in the intramolecular J(HH) coupling between two inner protons are mainly determined by the sum of relatively large spin-orbit terms. The isotropic shielding constant shows a strong deshielding of the nitrogen nuclei as the proton migrates away. Both the isotropic shielding of the exchanged protons and the shielding anisotropy exhibit a minimum close to the transition states.     

Experimental and theoretical NMR and IR studies of the side-chain orientation effects on the backbone conformation of dehydrophenylalanine residue

Conformation of N-acetyl-(E)-dehydrophenylalanine N', N'-dimethylamide (Ac-(E)-ΔPhe-NMe(2)) in solution, a member of (E)-α, β-dehydroamino acids, was studied by NMR and infrared spectroscopy and the results were compared with those obtained for (Z) isomer. To support the spectroscopic interpretation, the Φ, Ψ potential energy surfaces were calculated at the MP2/6-31 + G(d,p) level of theory in chloroform solution modeled by the self-consistent reaction field-polarizable continuum model method. All minima were fully optimized by the MP2 method and their relative stabilities were analyzed in terms of π-conjugation, internal H-bonds and dipole interactions between carbonyl groups. The obtained NMR spectral features were compared with theoretical nuclear magnetic shieldings, calculated using Gauge Independent Atomic Orbitals (GIAO) approach and rescaled to theoretical chemical shifts using benzene as reference. The calculated indirect nuclear spin-spin coupling constants were compared with available experimental parameters.     

Chloroplast biogenesis 45: molecular structures of protochlorophyllide (e443 f625) and of chlorophyllide A (e458 f674)

The divinyl structure of protochlorophyllide (E443 F625) and of its chlorophyllide $\text{a}$ (E458 F674) photoreduction product was ascertained by nuclear magnetic resonance spectroscopy and by fast atom bombardment mass spectroscopy. These two phorbins are two newly discovered intermediates of the chlorophyll $\text{a}$ biosynthetic pathway in higher plants. Both tetrapyrroles exhibited recognizable ABX spin-spin splitting patterns which ar characteristic of divinyl tetrapyrroles. Fast atom bombardment mass spectroscopic data further confirmed the presence of two vinyl groups per molecule of protochlorophyllide (E443 F625) and of chlorophyllide $\text{a}$ (E458 F674).     

Decomposition of nuclear magnetic resonance spin-spin coupling constants into active and passive orbital contributions

The theory of the J-OC-PSP (decomposition of J into orbital contributions using orbital currents and partial spin polarization) method is derived to distinguish between the role of active, passive, and frozen orbitals on the nuclear magnetic resonance (NMR) spin-spin coupling mechanism. Application of J-OC-PSP to the NMR spin-spin coupling constants of ethylene, which are calculated using coupled perturbed density functional theory in connection with the B3LYP hybrid functional and a [7s,6p,2d/4s,2p] basis set, reveal that the well-known pi mechanism for Fermi contact (FC) spin coupling is based on passive pi orbital contributions. The pi orbitals contribute to the spin polarization of the sigma orbitals at the coupling nuclei by mediating spin information between sigma orbitals (spin-transport mechanism) or by increasing the spin information of a sigma orbital by an echo effect. The calculated FC(pi) value of the SSCC (1)J(CC) of ethylene is 4.5 Hz and by this clearly smaller than previously assumed.