DFT study of the NMR properties of xenon in covalent compounds and van der waals complexes-implications for the use of 129Xe as a molecular probe

The NMR properties (chemical shift and spin-spin coupling constants) of (129)Xe in covalent compounds and weakly bound complexes have been investigated by DFT methods including relativistic effects. For covalent species, a good agreement between experimental and calculated results is achieved without scalar relativistic effects, but their inclusion (with a triple-zeta, double-polarization basis set) leads to some improvement in the quality of the correlation. The spin-orbit coupling term has a significant effect on the shielding constant, but makes a small contribution to the chemical shift. Coupling constants contain substantial contributions from the Fermi contact and paramagnetic spin-orbit terms; unlike light nuclei the spin-dipole term is also large, whereas the diamagnetic spin-orbit term is negligible. For van der Waals dimers, the dependence of the xenon chemical shift and anisotropy is calculated as a function of the distance. Small (<1 Hz) but non-negligible through-space coupling constants between (129)Xe and (13)C or (1)H are predicted. Much larger couplings, of the order of few Hz, are calculated between xenon and (17)O in a model silicate residue.     

Second-order polarization propagator calculations of indirect nuclear spin-spin coupling tensors in the water molecule

The contribution to indirect nuclear spin-spin coupling tensors provided by the Fermi contact, the spin-dipolar, the Fermi contact/spin-dipolar crossterm, and the paramagnetic spin-orbit interactions are investigated in a zeroth-, first- (the same as the coupled Hartree-Fock method), and second-order polarization propagator approach. Numerical applications to the water molecule show that the second-order results for both the HO and the HH coupling constants are in good agreement with experimental data - especially if vibrational corrections and the diamagnetic spin-orbit contributions are taken into account. We find that the correlation corrections beyond coupled Hartree-Fock are important. We also report how the second-order results are influenced by neglect of some of the most time-consuming steps in the calculation.     

Calculations of the indirect nuclear spin–spin coupling constants of PbH4

We report ab initio calculations of the indirect nuclear spin–spin coupling constants of PbH₄ using a basis set which was specially optimized for correlated calculations of spin–spin coupling constants. All nonrelativistic contributions and the most important part of the spin–orbit correction were evaluated at the level of the random phase approximation. Electron correlation corrections to the coupling constants were calculated with the multiconfigurational linear-response method using extended complete and restricted active space wavefunctions as well as with the second-order polarization propagator approximation and the second-order polarization propagator approximation with coupled-cluster singles and doubles amplitudes. The effects of nuclear motion were investigated by calculating the coupling constants as a function of the totally symmetric stretching coordinate. We find that the Fermi contact term dominates the Pb‐H coupling, whereas for the H‐H coupling it is not more important than the orbital paramagnetic and diamagnetic contributions. Correlation affects mainly the Fermi contact term. Its contribution to the one-bond coupling constant is reduced by correlation, independent of the method used; however, the different correlated methods give ambiguous results for the Fermi contact contribution to the H‐H couplings. The dependence of both coupling constants on the Pb‐H bond length is dominated by the change in the Fermi contact term. The geometry dependence is, however, overestimated in the random phase approximation. Received: 16 November 1998 / Accepted: 30 March 1999 / Published online: 14 July 1999     

Complete prediction of the 1H NMR spectrum of organic molecules by DFT calculations of chemical shifts and spin-spin coupling constants

1H NMR chemical shifts and coupling constants for several aromatic and aliphatic organic molecules have been calculated with DFT methods. In some test cases (furan, o-dichlorobenzene and n-butyl chloride) the performance of several functionals and basis sets has been analyzed, and the various contributions to spin-spin coupling (Fermi-contact, diamagnetic and paramagnetic spin-orbit) have been evaluated. The latter two components cancel each other, so that the calculation of the contact term only is sufficient for an accurate evaluation of proton-proton couplings. Such calculated values are used to simulate the 1H NMR spectra of organic molecules with complicated spin systems (e.g. naphthalene, o-bromochlorobenzene), obtaining a generally very good agreement with experimental spectra with no prior knowledge of the involved parameters.     

Elucidation of the electronic structure of molecules with the help of NMR spin-spin coupling constants: the FH molecule

It is demonstrated how the one-bond NMR spin-spin coupling constant (SSCC) (1)J(FH) can be used as a source of information on the electronic structure of the FH molecule. For this purpose, the best possible agreement between measured and calculated SSCC is achieved by large basis set coupled perturbed density functional theory calculations. Then, the calculated value is dissected into its four Ramsey terms: Fermi contact, the paramagnetic spin-orbit term, the diamagnetic spin-orbit term, and the spin dipole term, which in turn are decomposed into orbital contributions and then described by their spin densities and orbital current densities. In this way, the SSCC gives detailed information about the electronegativity of F, the bond polarity, the bond polarizability, the volume and the polarizability of sigma and pi lone pair orbitals, the s- or p-character of the bond orbital, the nature of the LUMO, and the density distribution around F.     

Electron bridging dihydrogen bond in the imidazole-contained anion derivatives

The large contact distance of electron bridging dihydrogen bond (EBDB), which is over 2.4 A, is the most prominent characteristic for the imidazole-contained anion derivatives. The elongation of N-H bond and the shortening of H...H distance can be observed upon hydration and hydrogenation. Transformation from EBDB to dissociative H2 is convenient upon sequential hydrogenation. The H...H distance decreases with the enhancement of the electronegativity of the heavy atom which contacts directly with one of these two hydrogen atoms. NMR shielding of the bonding N varies significantly upon hydration and hydrogenation. The spin-spin coupling constants, 1J(H-H), is dominated predominantly by the paramagnetic spin-orbit and diamagnetic spin-orbit contributions instead of the Fermi-contact term. Enhancement of electronegativity of the heavy atom leads to the increase of 1J(H-H) coupling constants. The stabilization is enhanced upon hydration predominantly for the formation of O-H...N H bond, while it is reversed upon hydrogenation for the cleavage of big pi bond, Pi5(6). Enhancement of the stability is demonstrated by the increase of stabilization energy and vertical electron detachment energy with the electronegativity of the heavy atom. The dominant contributions for the formation of such electron bridging dihydrogen bond are the high polarity of each fragment, large electron density between two fragments, and strong bonding interaction of the bridging electron with H(N) atoms. The H...H interaction can be formed by X-Hdelta+ and Hdelta- -Y polar molecules in Hdelta+...Hdelta- and Hdelta+...e...Hdelta+ of two forms.     

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.     

Calculations of the orbital diamagnetic contribution to nuclear spin-spin coupling constants for molecules with multiple bonds

Ab initio SCF and Cl calculations of the orbital diamagnetic contribution to nuclear spin-spin coupon constants have been performed for a series of molecules containing multiple bonds. A striking feature of the results is the prediction of consistently large contributions to vicinal (trans) and geminal proton-proton couplings which oppose and dominate the corresponding orbital paramagnetic contributions.     

Interaction energies and NMR indirect nuclear spin-spin coupling constants in linear HCN and HNC complexes

The cooperativity effects on both the electronic energy and NMR indirect nuclear spin-spin coupling constants J of the linear complexes (HCN)n and (HNC)n (n = 1-6) are discussed. The geometries of the complexes were optimized at the MP2 level by using the cc-pVTZ basis sets. The spin-spin coupling constants were calculated at the level of the second-order polarization propagator approximation with use of the local dense basis set scheme based on the cc-pVTZ-J basis sets. We find strong correlations in the patterns of different properties such as interaction energy, hydrogen bond distances, and spin-spin coupling constants for both series of compounds. The intramolecular spin-spin couplings are with two exceptions dominated by the Fermi contact (FC) mechanism, while the FC term is the only nonvanishing contribution for the intermolecular couplings. The latter do not follow the Dirac vector model and are important only between nearest neighbors.     

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.     

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.     

Unusual long-range spin-spin coupling in fluorinated polyenes: a mechanistic analysis

Nuclear magnetic resonance (NMR) is a prospective means to realize quantum computers. The performance of a NMR quantum computer depends sensitively on the properties of the NMR-active molecule used, where one requirement is a large indirect spin-spin coupling over large distances. F-F spin-spin coupling constants (SSCCs) for fluorinated polyenes F-(CH==CH)n-F (n=1cdots, three dots, centered5) are >9 Hz across distances of more than 10 A. Analysis of the F,F spin-spin coupling mechanism with our recently developed decomposition of J into Orbital Contributions with the help of Orbital Currents and Partial Spin Polarization (J-OCOC-PSP=J-OC-PSP) method reveals that coupling is dominated by the spin-dipole (SD) term due to an interplay between the pi lone-pair orbitals at the F atoms and the pi(C2n) electron system. From our investigations we conclude that SD-dominated SSCCs should occur commonly in molecules with a contiguous pi-electron system between the two coupling nuclei and that a large SD coupling generally is the most prospective way to provide large long-range spin-spin coupling. Our results give guidelines for the design of suitable active molecules for NMR quantum computers.     

The use of localized molecular orbitals and the polarization propagator to identify transmission mechanisms in nuclear spin-spin couplings

An extension of the IPPP (inner projections of the polarization propagator) method to theoretically analyze transmission mechanisms of indirect nuclear spin-spin couplings is presented. The localization technique used is modified so that all the canonical molecular orbitals of a compound may be localized to represent chemical bonds, lone pairs, and the corresponding antibonding molecular orbitals. These localized molecular orbitals, together with the polarization propagator, are used to obtain an intuitive picture of how a coupling is generated as a sum of terms, each one consisting of two particle-hole single excitations. This picture can be used to identify underlying transmission mechanisms and quantitatively evaluate their importance toward the total coupling. The paramagnetic spin-orbit and the spin-dipole interactions are studied in detail.     

Electric field effects on one-bond indirect spin-spin coupling constants and possible biomolecular perspectives

Electric field (EF) induced changes of one-bond indirect spin-spin coupling constants are investigated on a wide range of molecules including peptide models. EFs were both externally applied and internally calculated without external EF application by the hybrid density functional theory method. Reliable agreement with experimental data has been obtained for calculated one-bond J-couplings. The role of the EF sign and direction, internal and induced components, hydrogen bonding, internuclear distance and hyperconjugative interactions on the one-bond J-coupling vs EF interconnection is analyzed. A linear dependence of 1J on EF projection along the bond is obtained, if the bound atoms possess different enough electron densities and an EF determined by the electronic polarization exists along the bond. Accentuating the 1JNH couplings as possible EF sensitive parameters, a systematic study is done in two sets of molecules with a large variation of the native internal EF value. The most EF affected component of the 1JNH coupling constant is the spin-dipole term of Ramsey's formulation; however, in the total J-coupling formation, the EF influence on the Fermi contact term is the most significant. The induced EF projection along the bond is 6.7 times weaker in magnitude than the simulated external uniform field. The absolute EF dependence of the one-bond J-coupling involves only the internal field, which is the sum of the induced field (if the external field exists) and the internuclear field determined by the native polarization. That linear and universal dependence joins the corresponding couplings in a diverse set of molecules under various electrostatic conditions. Many types of the one-bond J-couplings can be potentially measured in biomolecules, and the study of their relation with the electrostatic properties at the corresponding sites opens a new avenue to the full exploitation of the NMR measurable parameters with novel and exciting applications.     

Theoretical calculation of the NMR spin-spin coupling constants and the NMR shifts allow distinguishability between the specific direct and the water-mediated binding of a divalent metal cation to guanine

The calculated intermolecular and intramolecular indirect NMR spin-spin coupling constants and NMR shifts were used for the discrimination between the inner-shell and the outer-shell binding motif of hydrated divalent cations Mg(2+) or Zn(2+) with a guanine base. The intermolecular coupling constants (1)J(X,O6) and (1)J(X,N7) (X = Mg(2+), Zn(2+)) can be unambiguously assigned to the specific inner-shell binding motif of the hydrated cation either with oxygen O6 or with nitrogen N7 of guanine. The calculated coupling constants (1)J(Mg,O6) and (1)J(Zn,O6) were 6.2 and -17.5 Hz, respectively, for the inner-shell complex of cation directly interacting with oxygen O6 of guanine. For the inner-shell coordination of the cation at nitrogen N7, the calculated coupling constants (1)J(Mg,N7) and (1)J(Zn,N7) were 5.6 and -36.5 Hz, respectively. When the binding of the cation is water-mediated, the coupling constant is zero. To obtain reliable shifts in NMR parameters, hydrated guanine was utilized as the reference state. The calculated change of NMR spin-spin coupling constants due to the hydration and coordination of the cation with guanine is caused mainly by the variation of Fermi-contact coupling contribution while the variation of diamagnetic spin-orbit, paramagnetic spin-orbit, and spin-dipolar coupling contributions is small. The change of s-character of guanine sigma bonding, sigma antibonding, and lone pair orbitals upon the hydration and cation coordination (calculated using the Natural Bond Orbital analysis) correlates with the variation of the Fermi-contact term. The calculated NMR shifts delta(N7) of -15.3 and -12.2 ppm upon the coordination of Mg(2+) and Zn(2+) ion are similar to the NMR shift of 19.6 ppm toward the high field measured by Tanaka for N7 of guanine upon the coordination of the Cd(2+) cation (Tanaka, Y.; Kojima, C.; Morita, E. H.; Kasai. Y.; Yamasaki, K.; Ono, A.; Kainosho, M.; Taira, K. J. Am. Chem. Soc. 2002, 124, 4595-4601). The present data indicate that measurements of NMR intermolecular coupling constants may be used to discriminate between the specific inner- and outer-shell binding of divalent cations to nucleobases in DNA and RNA.     

Ab initio MO studies of nuclear spin-spin coupling constants in CH4, SiH4, AlH 4 − and GeH4 systems

Summary Ab initio molecular orbital calculations of electron coupled nuclear spin-spin coupling constants are performed for CH₄, SiH₄, AlH ₄ ^– and GeH₄ systems using the SCF perturbation theory. Basis set dependence of the major contributing terms such as orbital diamagnetic, orbital paramagnetic, spin dipolar and Fermi contact terms are studied. The study also illustrates the relative importance of bond centred functions and nuclear centred polarization functions in predicting the directly bonded and geminal couplings in the systems selected. Basis sets having uncontracted cores functions and augmented with bond functions seem to predict most of these couplings fairly satisfactorily when compared to the experimental values.