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.     

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.     

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.     

DFT calculations of 31P spin-spin coupling constants and chemical shift in dioxaphosphorinanes

One-bond heteronuclear spin-spin coupling constants (1)J(PX) (X=H, O, S, Se, C and N) between the phosphorus atom and axial and equatorial substituents in dioxaphosphorinanes are computed using density functional theory (DFT). The experimental values of these coupling constants for a variety of substituents can be applied to identify different diastereoisomers. The DFT calculations confirm the systematic trend observed in experiment, and indicate that the computed (1)J(PX) coupling constants are related to the length of the axial and equatorial bonds. A similar relation between the phosphorus chemical shift and the R(PX) bond length appears to be valid, with the exception of selenium substituents.     

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.     

Trivinylphosphine and trivinylphosphine chalcogenides: stereochemical trends of ³¹P-¹H spin-spin coupling constants

A combined theoretical and experimental study of the stereochemical behavior of (31)P-(1)H spin-spin coupling constants has been performed in the series of trivinylphosphine and related trivinylphosphine oxide, sulfide and selenide. Theoretical energy-based conformational analysis of the title compounds performed at the MP2/6-311G** level reveals that each of the four compounds of this series exists in the equilibrium mixture of five true-minimum conformers, namely s-cis-s-cis-s-cis, s-cis-s-cis-gauche, syn-s-cis-gauche-gauche, anti-s-cis-gauche-gauche and gauche-gauche-gauche, which were taken into account in the conformational averaging of (31)P-(1)H spin-spin couplings calculated at the second-order polarization propagator approach/aug-cc-pVTZ-J level of theory. All (31)P-(1)H spin-spin coupling constants involving phosphorus and either of the vinyl protons are found to demonstrate a marked stereochemical dependences with respect to the geometry of the coupling pathway and internal rotation of the vinyl group around the P-C bond which is of major importance in the stereochemical studies of the unsaturated phosphines and phosphine chalcogenides.     

Correlation between C-H and C-C spin-spin coupling constants and s character of hybrids calculated by the maximum overlap method

For some thirty hydrocarbons the s character of hybrids obtained by the application of the maximum overlap method have been correlated with C-H and C-C spin-spin coupling constants. The following relationships were obtained: $$J_{{\text{C}}^{{\text{13}}} - {\text{H}}} = 1079a_{{\text{CH}}}^{\text{2}} /(1 + S_{{\text{CH}}}^{\text{2}} ) - 54.9$$ , $$J_{{\text{C}}_{\text{1}}^{{\text{13}}} - {\text{C}}_{\text{2}}^{{\text{13}}} } = 1020.5a_{{\text{C}}_{\text{1}} }^2 a_{{\text{C}}_{\text{2}} }^{\text{2}} /(1 + S_{{\text{CC}}}^{\text{2}} ) - 8.2$$ . Here the coupling constants are expressed in cps units. In the calculation of the maximum overlap hybrids either the experimental bond lengths or a standard bond lengths were used. For the \(J_{{\text{C}}^{{\text{13}}} - {\text{H}}}\) and \(J_{{\text{C}}^{{\text{13}}} - {\text{H}}} \) coupling constants the standard deviations are 0.9 cps and 1.9 cps respectively. It has been suggested that the large additive constant in the \(J_{{\text{C}}^{{\text{13}}} - {\text{H}}}\) correlation may be attributed to the ionic character of C-H bonds. A good agreement with the experimental data strongly supports the idea that the Fermi contact term and the hybridization are dominant factors in determining carbon-hydrogen and carbon-carbon spin-spin coupling constants across one bond, at least in hydrocarbons.     

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.     

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.     

Three-bond sugar-base couplings in purine versus pyrimidine nucleosides: a DFT study of Karplus relationships for (3)J(C2/4-H1') and (3)J(C6/8-H1') in DNA

(3)J(C2/4-H1') and (3)J(C6/8-H1') scalar spin-spin coupling constants have been calculated for deoxyadenosine, deoxyguanosine, deoxycytidine, and deoxythymidine as functions of the glycosidic torsion angle chi by means of density functional theory. Except for deoxythymidine, (3)J(C2/4-H1') depends little on the base type. On the contrary, (3)J(C6/8-H1') follows the usual trans to cis ratio ((3)J(C-H(cis)) < (3)J(C-H(trans))) for purine nucleosides, but reveals the opposite relation ((3)J(C-H(cis)) > (3)J(C-H(trans))) for pyrimidine nucleosides. Our results compare well with the experiment for deoxyguanosine and predict a novel trend in the case of pyrimidine bases for which no NMR results are available in the syn region. A breakdown of the key Fermi contact part of (3)J(C6/8-H1') into MO contributions rationalizes this trend in terms of an unusual coupling mechanism in the syn orientation that is very effective for pyrimidine nucleosides and considerably weaker for purine nucleosides.     

1hJFH coupling in 2‐fluorophenol revisited: Is intramolecular hydrogen bond responsible for this long‐range coupling?

The present study shows that a hydrogen bond between the OH group and the fluorine atom is not involved in the (1h)J(FH) spin-spin coupling transmission either for 4-bromo-2-fluorophenol or 2-fluorophenol. In fact, according to a quantum theory of atoms in molecules analysis, no bond critical point is found between O-H and F moieties. The nature of the transmission mechanism of the Fermi contact term of the (1h)J(FH) spin-spin coupling is studied by analyzing canonical molecular orbitals (see J. Phys. Chem. A 2010, 114, 1044), and it is observed that virtual orbitals play only a quite minor role in its transmission. This is typical of a Fermi contact term transmitted mainly through exchange interactions owing to the overlap of proximate electronic clouds; therefore, it is suggested to identify them as (nTS)J(FH) coupling where n stands for the number of formal bonds separating the coupling nuclei. In the cases studied in this work is n = 4. Results presented in this work could provide an interesting rationalization for different experimental signs known in the current literature for proximate J(FH) couplings.     

Dynamics of dilute water in carbon tetrachloride

A dilute solution of water in a hydrophobic solvent, such as carbon tetrachloride (CCl4), presents an opportunity to study the rotational properties of water without the complicating effects of hydrogen bonds. We report here the results of theoretical, experimental, and semiempirical studies of a 0.03 mole percent solution of water in CCl4. It is shown that for this solution there are negligible water-water interactions or water-CCl4 interactions; theoretical and experimental values for proton NMR chemical shifts (deltaH) are used to confirm the minimal interactions between water and the CCl4. Calculated ab initio values and semiempirical values for oxygen-17 and deuterium quadrupole coupling constants (chi) of water/CCl4 clusters are reported. Experimental values for the 17O, 2H, and 1H NMR spin-lattice relaxation times, T1, of 0.03 mole percent water in dilute CCl4 solution at 291 K are 94+/-3 ms, 7.0+/-0.2 s, and 12.6+/-0.4 s, respectively. These T1 values for bulk water are also referenced. "Experimental" values for the quadrupole coupling constants and relaxation times are used to obtain accurate, experimental values for the rotational correlation times for two orthogonal vectors in the water molecule. The average correlation time, tauc, for the position vector of 17O (orthogonal to the plane of the molecule) in monomer water, H2(17)O, is 91 fs. The average value for the deuterium correlation time for the deuterium vector in 2H2O is 104 fs; this vector is along the OD bond. These values indicate that the motion of monomer water in CCl4 is anisotropic. At 291 K, the oxygen rotational correlation time in bulk 2H2(17)O is 2.4 ps, the deuterium rotational correlation time in the same molecule is 3.25 ps. (Ropp, J.; Lawrence, C.; Farrar, T. C.; Skinner, J. L. J. Am. Chem. Soc. 2001, 123, 8047.) These values are a factor of about 20 longer than the tauc value for dilute monomer water in CCl4.     

Characterization of fluxional hydrogen-bonded complexes of acetic acid and acetate by NMR: geometries and isotope and solvent effects

1H, (2)H, and (13)C NMR spectra of enriched CH(3)(13)COOH acid without and in the presence of tetra-n-butylammonium acetate have been measured around 110 K using a liquefied Freon mixture CDF(3)/CDF(2)Cl as a solvent, as a function of the deuterium fraction in the mobile proton sites. For comparison, spectra were also taken of the adduct CH(3)(13)COOH.SbCl(5) 1 and of CH(2)Cl(13)COOH under similar conditions, as well as of CH(3)(13)COOH and CH(3)(13)COO(-) dissolved in H(2)O and D(2)O at low and high pH at 298 K. The low temperatures employed allowed us to detect several well-known and novel hydrogen-bonded complexes in the slow hydrogen bond exchange regime and to determine chemical shifts and coupling constants as well as H/D isotope effects on chemical shifts from the fine structure of the corresponding signals. The measurements show that self-association of both carboxylic acids in Freon solution gives rise exclusively to the formation of cyclic dimers 2 and 3 exhibiting a rapid degenerate double proton transfer. For the first time, a two-bond coupling of the type (2)J(CH(3)COOH) between a hydrogen-bonded proton and the carboxylic carbon has been observed, which is slightly smaller than half of the value observed for 1. In addition, the (1)H and (2)H chemical shifts of the HH, HD, and the DD isotopologues of 2 and 3 have been determined as well as the corresponding HH/HD/DD isotope effects on the (13)C chemical shifts. Similar "primary", "vicinal", and "secondary" isotope effects were observed for the novel 2:1 complex "dihydrogen triacetate" 5 between acetic acid and acetate. Another novel species is the 3:1 complex "trihydrogen tetraacetate" 6, which was also characterized by a complex degenerate combined hydrogen bond- and proton-transfer process. For comparison, the results obtained previously for hydrogen diacetate 4 and hydrogen maleate 7 are discussed. Using an improved (1)H chemical shift-hydrogen bond geometry correlation, the chemical shift data are converted into hydrogen bond geometries. They indicate cooperative hydrogen bonds in the cyclic dimers; i.e., widening of a given hydrogen bond by H/D substitution also widens the other coupled hydrogen bond. By contrast, the hydrogen bonds in 5 are anticooperative. The measurements show that ionization shifts the (13)C signal of the carboxyl group to low field when the group is immersed in water, but to high field when it is embedded in a polar aprotic environment. This finding allows us to understand the unusual ionization shift of aspartate groups in the HIV-pepstatin complex observed by Smith, R.; Brereton, I. M.; Chai, R. Y.; Kent, S. B. H. Nature Struct. Biol. 1996, 3, 946. It is demonstrated that the Freon solvents used in this study are better environments for model studies of amino acid interactions than aqueous or protic environments. Finally, a novel correlation of the hydrogen bond geometries with the H/D isotope effects on the (13)C chemical shifts of carboxylic acid groups is proposed, which allows one to estimate the hydrogen bond geometries and protonation states of these groups. It is shown that absence of such an isotope effect is not only compatible with an isolated carboxylate group but also with the presence of a short and strong hydrogen bond.     

1H and 13C NMR chemical shifts and spin-spin coupling constants in trans- and cis-decalins

The NMR parameters characterizing the spectra of trans- and cis-decalins were determined from theoretical calculations and experimental spectra. The calculated values of the shielding constants are in good agreement with the measured chemical shifts, with a small but noticeable difference in accuracy for the bridgehead atoms. Of all the spin-spin coupling constants, only most of (1)J(C,C) and (1)J(C,H) values could be extracted from the spectra, and the corresponding computed values are in good agreement with experiment. It appears that the applied density functional theory (DFT) approach overestimates slightly the J(C,C) coupling and underestimates the differences between one-bond (1)J(C,H) coupling constants. For all these constants [J(C,C), J(C,H) and J(H,H)] through one to three bonds, which could not be obtained experimentally, the predicted values are in good agreement with the general rules relating spin-spin coupling to the number and spatial arrangement of the intervening bonds.     

Comparative analysis of hydrogen bonding with participation of the nitrogen, oxygen and sulfur atoms in the 2(2'-heteroaryl)pyrroles and their trifluoroacetyl derivatives based on the 1H, 13C, 15N spectroscopy and DFT calculations

The N-H...X (X = N,O,S) intramolecular hydrogen bond in the series of 2(2'-heteroaryl)pyrroles and their trifluoroacetyl derivatives is examined by the (1)H, (13)C, (15)N spectroscopy and density functional theory (DFT) calculations. The influence of the hydrogen bond on coupling and shielding constants is considered. It is shown that the N-H...N intramolecular hydrogen bond causes a larger increase in the absolute size of the (1)J(N,H) coupling constant and a larger deshielding of the bridge proton than the N-H...O hydrogen bond. The effect of the N-H...S interaction on the (1)J(N,H) coupling constant and the shielding of the bridge proton is small. The NMR parameter changes in the series of the 2(2'-heteroaryl)pyrroles due to N-H...X hydrogen bond and the series of the 1-vinyl-2-(2'-heteroaryl)-pyrroles due to C-H...X hydrogen bond have the same order. The proximity of the nitrogen, oxygen or sulfur lone pair to the F...H hydrogen bridge quenches the trans-hydrogen bond spin-spin couplings (1h)J(F,H-1) and (2h)J(F,N).     

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.     

A detailed evaluation of the dependence of 3J(H?H) on bond angle in alkenes and cycloalkenes

Newly determined and accurate data for the magnitudes of cis vinyl proton-proton spin-spin coupling constants in cis-dialkylethylenes and cycloalkenes have been obtained. With these new data and also values taken from the recent literature, it has proved possible to make a critical determination of the correlation between ³J(H? H) and C?C? H bond angles in ethylenic systems. It is suggested that it is possible to obtain accurate estimates of bond angles using NMR coupling constants, even though much more data will be required to fully substantiate this proposal. Whereas cis-³J(H? H) decreases rapidly with increasing C?C? H bond angles, evidence is presented that the opposite is the case for trans-³J(H? H). A brief theoretical discussion of these trends in coupling constants is given.     

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.     

Theoretical determination of the zero-field splitting in copper acetate monohydrate

The zero-field splitting of the copper acetate monohydrate complex is studied using wave function based calculations. The anisotropy parameters extracted from highly correlated methods are in excellent agreement with the most accurate experimental results; in particular, the negative sign of the axial anisotropy parameter D is reproduced. During several decades, the interpretation of experimental data based on an analytical expression derived from perturbation theory led to a positive D-value. Although the validity of this expression is confirmed, it is explained that the incorrect attribution of a positive D is related to the assumption of an antiferromagnetic coupling between excited states. We have found in the present work that this coupling is actually ferromagnetic. The analysis of the various contributions to the anisotropy parameters shows that both spin-spin and spin-orbit couplings participate in the magnetic anisotropy of this complex. Although the anisotropy arising from the spin-spin coupling is essentially independent of the level of calculation, the zero-field-splitting parameters resulting from the spin-orbit coupling are strongly sensitive to the effects of dynamic correlation. This works provides important new insights into the physical origin of the zero-field-splitting parameters in copper dimers.     

Vibrational contributions to indirect spin-spin coupling constants calculated via variational anharmonic approaches

Zero-point vibrational contributions to indirect spin-spin coupling constants for N2, CO, HF, H2O, C2H2, and CH4 are calculated via explicitly anharmonic approaches. Thermal averages of indirect spin-spin coupling constants are calculated for the same set of molecules and for C2X4, X = H, F, Cl. Potential energy surfaces have been calculated on a grid of points and analytic representations have been obtained by a linear least-squares fit in a direct product polynomial basis. Property surfaces have been represented by a fourth-order Taylor expansion around the equilibrium geometry. The electronic structure calculations employ density functional theory, and vibrational contributions to indirect spin-spin coupling constants are calculated employing vibrational self-consistent-field and vibrational configuration-interaction methods. The performance of vibrational perturbation theory and various approximate variational calculations are discussed. Thermal averages are computed by state-specific and virtual vibrational self-consistent-field methods.