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.     

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.     

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.     

DFT studies on the magnetic exchange across the cyanide bridge

Exchange coupling across the cyanide bridge in a series of novel cyanometalate complexes with CuII-NC-MIII (M = Cr and low-spin Mn, Fe) fragments has been studied using the broken-symmetry DFT approach and an empirical model, which allows us to relate the exchange coupling constant with sigma-, pi-, and pi*-type spin densities of the CN- bridging ligand. Ferromagnetic exchange is found to be dominated by pi-delocalization via the CN- pi pathway, whereas spin polarization with participation of sigma orbitals (in examples, where the dz2 orbital of MIII is empty) and pi* orbitals of CN- yields negative spin occupations in these orbitals, and reduces the CuII-MIII exchange coupling constant. When the dz2 orbital of MIII is singly occupied, an additional positive spin density appears in the sigma(CN) orbital and leads to an increase of the ferromagnetic Cu-NC-M exchange constant. For low-spin [MIII(CN)6]3- complexes, the dz2 orbital occupancy results in high-spin metastable excited states, and this offers interesting aspects for applications in the area of molecular photomagnetism. The DFT values of the exchange coupling parameters resulting from different occupations of the t2g orbitals of low-spin (t2g5) FeIII are used to discuss the effect of spin-orbit coupling on the isotropic and anisotropic exchange coupling in linear Cu-NC-Fe pairs.     

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.     

Symmetry and bonding in metalloporphyrins. A modern implementation for the bonding analyses of five- and six-coordinate high-spin iron(III)-porphyrin complexes through density functional calculation and NMR spectroscopy

Bonding interactions between the iron and the porphyrin macrocycle of five- and six-coordinate high-spin iron(III)-porphyrin complexes are analyzed within the framework of approximate density functional theory with the use of the quantitative energy decomposition scheme in combination with removal of the vacant pi orbitals of the porphyrin from the valence space. Although the relative extent of the iron-porphyrin interactions can be evaluated qualitatively through the spin population and orbital contribution analyses, the bond strengths corresponding to different symmetry representations can be only approximated quantitatively by the orbital interaction energies. In contrast to previous suggestions, there are only limited Fe --> P pi back-bonding interactions in high-spin iron(III)-porphyrin complexes. It is the symmetry-allowed bonding interaction between d(z)2 and a(2u) orbitals that is responsible for the positive pi spin densities at the meso-carbons of five-coordinate iron(III)-porphyrin complexes. Both five- and six-coordinate complexes show significant P --> Fe pi donation, which is further enhanced by the movement of the metal toward the in-plane position for six-coordinate complexes. These bonding characteristics correlate very well with the NMR data reported experimentally. The extraordinary bonding interaction between d(z)2 and a(2u) orbitals in five-coordinate iron(III)-porphyrin complexes offers a novel symmetry-controlled mechanism for spin transfer between the axial ligand sigma system and the porphyrin pi system and may be critical to the electron transfer pathways mediated by hemoproteins.     

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.     

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.     

Stereoelectronic interaction and their effects on conformational preference for 2-substituted methylenecyclohexane: an experimental and theoretical investigation

Conformational preferences for 2-substituted methylenecyclohexanes were determined using (3) J H 2 H 3 spin-spin coupling constants, while stereoelectronic interactions were obtained by means of theoretical calculations and NBO analysis. The conformational equilibrium of compounds studied can be represented by their axial and equatorial conformers, the axial conformers being the most stable form in polar and nonpolar solvents. These conformational preferences were attributed to the hyperconjugative interactions between the pi C-C-->sigma* C-Xax. and sigma C-H-->sigma* C-Xax. orbitals, and the repulsive steric interaction observed between sigma C-H-->n Xeq..     

Geometric and electronic structure of the heme-peroxo-copper complex [(F8TPP)FeIII-(O22-)-CuII(TMPA)](ClO4)

The geometric and electronic structure of the untethered heme-peroxo-copper model complex [(F(8)TPP)Fe(III)-(O(2)(2)(-))-Cu(II)(TMPA)](ClO(4)) (1) has been investigated using Cu and Fe K-edge EXAFS spectroscopy and density functional theory calculations in order to describe its geometric and electronic structure. The Fe and Cu K-edge EXAFS data were fit with a Cu...Fe distance of approximately 3.72 A. Spin-unrestricted DFT calculations for the S(T) = 2 spin state were performed on [(P)Fe(III)-(O(2)(2)(-))-Cu(II)(TMPA)](+) as a model of 1. The peroxo unit is bound end-on to the copper, and side-on to the high-spin iron, for an overall mu-eta(1):eta(2) coordination mode. The calculated Cu...Fe distance is approximately 0.3 A longer than that observed experimentally. Reoptimization of [(P)Fe(III)-(O(2)(2)(-))-Cu(II)(TMPA)](+) with a 3.7 A Cu...Fe constrained distance results in a similar energy and structure that retains the overall mu-eta(1):eta(2)-peroxo coordination mode. The primary bonding interaction between the copper and the peroxide involves electron donation into the half-occupied Cu d(z)2 orbital from the peroxide pi(sigma) orbital. In the case of the Fe(III)-peroxide eta(2) bond, the two major components arise from the donor interactions of the peroxide pi*(sigma) and pi*(v) orbitals with the Fe d(xz) and d(xy) orbitals, which give rise to sigma and delta bonds, respectively. The pi*(sigma) interaction with both the half-occupied d(z)2 orbital on the copper (eta(1)) and the d(xz) orbital on the iron (eta(2)), provides an effective superexchange pathway for strong antiferromagnetic coupling between the metal centers.     

Illumination of the effect of the overlap of lone-pairs on indirect nuclear spin-spin coupling constants

The effect of electron lone-pairs on the Fermi-contact (FC) contribution to indirect nuclear spin-spin coupling constants is analyzed using new tools for their interpretation. In particular, visualization of spin-spin coupling pathways using the coupling deformation density (CDD) has been employed. Furthermore, the recently developed perturbation-stable localization procedure has been applied for decomposition of CDD and the calculated value of couplings into contributions from localized molecular orbitals (LMOs). Correlation between the overlap of densities of LMOs representing lone-pairs and the Fermi-contact contribution to spin-spin coupling constants has been demonstrated. A new way for analyzing spin-spin couplings using the expansion of CDD as a linear combination of the products of molecular orbitals has been suggested. The considered examples include two- and three-bond phosphor-phosphor couplings. Significance of the obtained insight is not restricted to spin-spin couplings of nuclei possessing lone-pairs, as demonstrated in the example of vicinal hydrogen-hydrogen coupling in ethane.     

Towards understanding of magnetic interactions within a series of tetrathiafulvalene-pi conjugated-verdazyl diradical cation system: a density functional theory study

The intramolecular magnetic exchange coupling constants (J) for a series of tetrathiafulvalene (TTF) and verdazyl diradical cations connected by a range of pi conjugated linkers have been investigated by means of methodology based on unrestricted density functional theory. The magnetic interaction between radicals is transmitted via pi-electron conjugation for all considered compounds. The calculation of J yields strong or medium ferromagnetic coupling interactions (in the range of 56 and 300 K) for diradical cations connected by linkers with an even number of carbon atoms that are able to provide a spin polarization pathway, while antiferromagnetic coupling is predicted when linkers with an odd number of carbon atoms are employed. The topological analysis of spin density distributions have been used to reveal the effects of the spin polarization on both linkers and spin carriers. The absence of heteroatoms that impede the spin polarization pathway, and the existence of a unique spin polarization path instead of several possible competitive routes are factors which contribute to large positive J values favoring ferromagnetic interactions between the two terminal pi-radicals. The magnitude of J depends strongly on the planarity of the molecular structure of the diradical cation since a more effective orbital overlap between the two pi-systems can be achieved. Hence, the dependence of J on the torsion angle (theta) of each spin carrier has been analyzed. In this respect, our findings show that this geometrical distortion reduces largely the calculated J values for ferromagnetic couplings, leading to weak antiferromagnetic interactions for a torsion angle of 90 degrees .     

Natural J-coupling analysis: interpretation of scalar J-couplings in terms of natural bond orbitals.

The natural J-coupling (NJC) method presented here analyzes the Fermi contact portion of J-coupling in the framework of finite perturbation theory applied to ab initio/density function theory (DFT) wave functions, to compute individual and pairwise orbital contributions to the net J-coupling. The approach is based on the concepts and formalisms of natural bond orbital (NBO) methods. Computed coupling contributions can be classified as Lewis (individual orbital contributions corresponding to the natural Lewis structure of the molecule), delocalization (resulting from pairwise donor-acceptor interactions), and residual repolarization (corresponding to correlation-like interactions). This approach is illustrated by an analysis of the angular and distance dependences of the contributions to vicinal (3)J(HH) couplings in ethane and to the long-range (6)J(HH) couplings in pentane. The results indicate that approximately 70% or more of the net J-coupling is propagated by steric exchange antisymmetry interactions between Lewis orbitals (predominantly sigma bonding orbitals). Hyperconjugative sigma to sigma delocalization interactions account for the remainder of the coupling. Calculated pairwise-steric and hyperconjugative-delocalization energies provide a means for relating coupling mechanisms to molecular energetics. In this way, J-coupling contributions can be related directly to the localized features of the molecular electronic structure in order to explain measured J-coupling patterns and to predict J-coupling trends that have yet to be measured.     

Vibrational mode selectivity in hyperfine interactions: polarization quantum beat spectroscopy of HCF(A1A")

We report on the vibrational mode dependence of the 19F and 1H hyperfine interaction constants in the A1A" state of HCF, determined using polarization quantum beat spectroscopy. The nuclear spin/overall rotation coupling constants display a pronounced energy dependence and mode selectivity which can be traced to variations in both the A rotational constant and nuclear spin/electron orbital coupling constant a. In particular, modes containing C-F stretching excitation display significantly larger 19F spin-rotation constants, which is explained in terms of a decrease in back donation of electron density into the C 2p(pi) orbitals.     

Computational study of analogues of the uranyl ion containing the -N=U=N- unit: density functional theory calculations on UO2(2+), UON+, UN2, UO(NPH3)3+, U(NPH3)2(4+), [UCl4[NPR3]2] (R = H, Me), and [UOCl4[NP(C6H5)3]

The electronic and geometric structures of the title species have been studied computationally using quasi-relativistic gradient-corrected density functional theory. The valence molecular orbital ordering of UO2(2+) is found to be pi g < pi u < sigma g < sigma u (highest occupied orbital), in agreement with previous experimental conclusions. The significant energy gap between the sigma g and sigma u orbitals is traced to the "pushing from below" mechanism: a filled-filled interaction between the semi-core uranium 6p atomic orbitals and the sigma u valence level. The U-N bonding in UON+ and UN2 is significantly more covalent than the U-O bonding in UON+ and UO2(2+). UO(NPH3)3+ and U(NPH3)2(4+) are similar to UO2(2+), UON+, and UN2 in having two valence molecular orbitals of metal-ligand sigma character and two of pi character, although they have additional orbitals not present in the triatomic systems, and the U-N sigma levels are more stable than the U-N pi orbitals. The inversion of U-N sigma/pi orbital ordering is traced to significant N-P (and P-H) sigma character in the U-N sigma levels. The pushing from below mechanism is found to destabilize the U-N f sigma molecular orbital with respect to the U-N d sigma level in U(NPH3)2(4+). The uranium f atomic orbitals play a greater role in metal-ligand bonding in UO2(2+), UN2, and U(NPH3)2(4+) than do the d atomic orbitals, although, while the relative roles of the uranium d and f atomic orbitals are similar in UO2(2+) and U(NPH3)2(4+), the metal d atomic orbitals have a more important role in the bonding in UN2. The preferred UNP angle in [UCl4(NPR3)2] (R = H, Me) and [UOCl4(NP(C6H5)3)]- is found to be close to 180 degrees in all cases. This preference for linearity decreases in the order R = Ph > R = Me > R = H and is traced to steric effects which in all cases overcome an electronic preference for bending at the nitrogen atom. Comparison of the present iminato (UNPR3) calculations with previous extended Hückel work on d block imido (MNR) systems reveals that in all cases there is little or no preference for linearity over bending at the nitrogen when R is (a) only sigma-bound to the nitrogen and (b) sterically unhindered. The U/N bond order in iminato complexes is best described as 3.     

1JCH correlates with alcohol hydrogen bond strength

The strength of the H-bond donation by alcohols is reflected in the carbon-hydrogen bond of the H-C-O-H functional group. The one-bond 13C-1H spin-spin coupling constant of hexafluoroisopropanol (HFIP) correlates with the strength of the H-bond in various HFIP-amine complexes with a slope of approximately -0.2 Hz in 1JCH per approximately 1 kJ mol(-1) increase in the H-bond enthalpy. The decrease in 1JCH is attributed to an increased overlap of the H-bonding sigma orbital with the antibonding sigma orbitals of the vicinal C-H bonds.     

Mechanism of a strongly anisotropic MoIII-CN-MnII spin-spin coupling in molecular magnets based on the [Mo(CN)(7)](4-) heptacyanometalate: a new strategy for single-molecule magnets with high blocking temperatures

Unusual spin coupling between Mo(III) and Mn(II) cyano-bridged ions in bimetallic molecular magnets based on the [Mo(III)(CN)(7)](4-) heptacyanometalate is analyzed in terms of the superexchange theory. Due to the orbital degeneracy and strong spin-orbit coupling on Mo(III), the ground state of the pentagonal-bipyramidal [Mo(III)(CN)(7)](4-) complex corresponds to an anisotropic Kramers doublet. Using a specially adapted kinetic exchange model we have shown that the Mo(III)-CN-Mn(II) superexchange interaction is extremely anisotropic: it is described by an Ising-like spin Hamiltonian JS(z)(Mo) S(z)(Mn) for the apical pairs and by the J(z)S(z)(Mo) S(z)(Mn) + J(xy)(Sx(Mo) Sx(Mn) + Sy(Mo) Sy(Mn)) spin Hamiltonian for the equatorial pairs (in the latter case J(z) and J(xy) can have opposite signs). This anisotropy resulted from an interplay of several Ising-like (Sz(Mo) Sz(Mn)) and isotropic (S(Mo)S(Mn)) ferro- and antiferromagnetic contributions originating from metal-to-metal electron transfers through the pi and sigma orbitals of the cyano bridges. The Mo(III)-CN-Mn(II) exchange anisotropy is distinct from the anisotropy of the g-tensor of [Mo(III)(CN)(7)](4-); moreover, there is no correlation between the exchange anisotropy and g-tensor anisotropy. We indicate that highly anisotropic spin-spin couplings (such as the Ising-like JS(z)(Mo) S(z)(Mn)) combined with large exchange parameters represent a very important source of the global magnetic anisotropy of polyatomic molecular magnetic clusters. Since the total spin of such clusters is no longer a good quantum number, the spin spectrum pattern can differ considerably from the conventional scheme described by the zero-field splitting of the isotropic spin of the ground state. As a result, the spin reorientation barrier of the magnetic cluster may be considerably larger. This finding opens a new way in the strategy of designing single-molecule magnets (SMM) with unusually high blocking temperatures. The use of orbitally degenerate complexes with a strong spin-orbit coupling (such as [Mo(III)(CN)(7)](4-) or its 5d analogues) as building blocks is therefore very promising for these purposes.     

Spin-spin coupling tensors in fluoromethanes

All spin-spin coupling tensors J of the fluoromethanes CH3F, CH2F2, and CHF3 are obtained theoretically by multiconfiguration self-consistent field linear response (MCSCF LR) ab initio calculations. Furthermore the principal values and the orientation of the principal axis systems of each theoretical J tensor are specified. Experimental liquid crystal NMR (LC NMR) data on the tensorial properties of the CF spin spin coupling in CH3F and CH2F2, and the FF spin-spin coupling in CHF3 are also reported. In the analysis of the experiments, the contributions from molecular vibrations, as well as that of the correlation of vibrational and rotational motion to the experimental anisotropic couplings, D(exp), are taken into account. The information of the anisotropic indirect coupling, 1/2J(aniso), is detected as the difference between D(exp) and the calculated dipolar coupling, D(calc). The extracted indirect contributions, 1/2J(aniso), are in fair agreement with the ab initio results. All relative (experimental and theoretical) CF and FF indirect contributions, 1/2J(aniso)/D(exp), are negative and under 1.7% in magnitude, when the observed molecular orientations are used. Therefore, in the one bond CF couplings and in the two bond FF couplings, the indirect contribution can normally be ignored without introducing serious error to the determination of molecular orientation and/or structure. However, a more accurate method is to partially correct for the indirect contribution by utilising the transferability of the spin-spin coupling tensors in related molecules. This is due to the fact that even small contributions may be significant, if the order parameter of the internuclear direction is negligibly small, leading to dominating indirect contributions. The very good agreement of the experimental values with the calculated coupling constants and the reasonable agreement in the anisotropic properties, which are experimentally much more difficult to define, indicates that the MCSCF LR method is capable of producing reliable J tensors for these systems, contrary to the case of density-functional theory.