Relativistic corrections to the diamagnetic term of the nuclear magnetic shielding: analysis of contributions from localized orbitals

We have calculated the relativistic corrections to the diamagnetic term of the nuclear magnetic shielding constants for a series of molecules containing heavy atoms. An analysis of the contributions from localized orbitals is performed. We establish quantitatively the relative importance of inner core and valence shell molecular orbitals in each correcting term. Contributions from the latter are much less important than those from the former. The calculated values of the correction sigma(L-PSO), first derived within the linear response elimination of small component formalism, show a power-law dependence on the nuclear charge approximately Z(3.5), in contrast with the approximately Z(3.1) behavior of the mass-velocity external-field correction to the paramagnetic term previously reported.     

The appearance of an interval of energies that contain the whole diamagnetic contribution to NMR magnetic shieldings

Working within relativistic polarization propagator approach, it was shown in a previous article that the electronic origin of diamagnetic contributions to NMR nuclear magnetic shielding, sigmad, are mostly excitations that fit in a well defined interval of energies such that 2mc2相似文献   

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.     

Integration of electron density and molecular orbital techniques to reveal questionable bonds: the test case of the direct Fe-Fe bond in Fe2(CO)9

The article illustrates the advantages of partitioning the total electron density rho(rb), its Laplacian (inverted Delta)2 rho(rb), and the energy density H(rb) in terms of orbital components. By calculating the contributions of the mathematically constructed molecular orbitals to the measurable electron density, it is possible to quantify the bonding or antibonding character of each MO. This strategy is exploited to review the controversial existence of direct Fe-Fe bonding in the triply bridged Fe2(CO)9 system. Although the bond is predicted by electron counting rules, the interaction between the two pseudo-octahedral metal centers can be repulsive because of their fully occupied t(2g) sets. Moreover, previous atoms in molecules (AIM) studies failed to show a Fe-Fe bond critical point (bcp). The present electron density orbital partitioning (EDOP) analysis shows that one sigma bonding combination of the t(2g) levels is not totally overcome by the corresponding sigma* MO, which is partially delocalized over the bridging carbonyls. This suggests the existence of some, albeit weak, direct Fe-Fe bonding.     

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.     

Relativistic effects in low-energy spin-dependent electron collisions with rare-gas atoms

The relativistic effects in low-energy spin-dependent electron scattering from rare-gas atoms Ar, Kr and Xe are analyzed by comparing the results obtained respectively with Dirac-Fock, Cowan's quasirelativistic Hartree-Fock and non-relativistic Hartree-Fock wave functions for target atoms. It is shown that the intra-target relativistic effects, in particular the explicit spin dependences of the one-electron orbitals of Dirac-Fock atomic wave function, create apparet quantitative changes in the spin polarization parameters at some collision energies and scattering angles.     

Orbital magnetism in finite size systems

The orbital magnetism in atoms is described in terms of Larmor diamagnetic and van Vleck paramagnetic contributions. The orbital magnetism in metals is described by Landau diamagnetism. Here, a discussion of the intermediate, mesoscopic regime is presented using a simple free-particle-in-a-box approximation. It is argued that, in general, one cannot separate Larmor and van Vleck contributions, and that the total susceptibility is expected to be small. The conclusions are illustrated on some experimental results.     

Gauge invariance of the spin-other-orbit contribution to the g-tensors of electron paramagnetic resonance

The spin-other-orbit (SOO) contribution to the g-tensor (DeltagSOO) of electron paramagnetic resonance arises due to the interaction of electron-spin magnetic moment with the magnetic field produced by the orbital motion of other electrons. A similar mechanism is responsible for the leading term in nuclear magnetic-shielding tensors sigma. We demonstrate that analogous to sigma, paramagnetic DeltagSOO contribution exhibits a pronounced dependence on the choice of the magnetic-field gauge. The gauge corrections to DeltagSOO are similar in magnitude, and opposite in sign, to the paramagnetic SOO term. We calculate gauge-invariant DeltagSOO values using gauge-including atomic orbitals and density-functional theory. For organic radicals, complete gauge-invariant DeltagSOO values typically amount to less than 500 parts per million (ppm), and are small compared to other g-tensor contributions. For the first-row transition-metal compounds, DeltagSOO may contribute several thousand ppm to the g-tensor, but are negligible compared to the remaining deviations from experiment. With popular choices for the magnetic-field gauge, the individual gauge-variant contributions may be an order of magnitude higher, and do not provide a reliable estimation of DeltagSOO.     

Fast calculation of excited-state potentials for rare-gas diatomic molecules: Ne2 and Ar2

A fast method for obtaining excited-state potentials of rare-gas diatomic molecules is described. Two types of excited orbitals are used: molecular orbitals calculated in the field of a singly charged molecular ion, and atomic orbitals (properly symmetrized) obtained in a similar atomic system. The RPA equations are solved within the manifold of excitations from the highest occupied orbital in each symmetry to the lowest excited orbital of either type in each symmetry. A simple model for estimating the dynamic correlation correction to excitation (and ionization) energies is given. Applications to excited states of Ne₂(^1,3Σ⁺_{g, u}, ^1,3Π_{g, u}) and Ar₂(^1,3Σ⁺_{g, u}) are described. Two-electron integral transformations involve only three orbitals of each symmetry, and the RPA matrices are four-dimensional. The computational effort required for all excited-state potentials adds less than one-tenths (in terms of computer time) to the effort involved in the preliminary ground state Hartree—Fock calculations. The resulting potentials compare favorably with more elaborate CI calculations and give good agreement with spectroscopic and scattering data. Potential curves for the molecular ions are also given.     

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.     

Resonant two-photon ionization spectroscopy of jet-cooled OsC

The optical spectrum of diatomic OsC has been investigated for the first time, with transitions recorded in the range from 17 390 to 22 990 cm(-1). Six bands were rotationally resolved and analyzed to obtain ground and excited state rotational constants and bond lengths. Spectra for six OsC isotopomers, 192 Os 12C (40.3% natural abundance), 190 Os 12C(26.0%), 189 Os 12C(16.0%), 188 Os 12C(13.1%), 187 Os 12C(1.9%), and 186 Os 12C(1.6%), were recorded and rotationally analyzed. The ground state was found to be X 3 Delta 3, deriving from the 4 delta 3 16 sigma 1 electronic configuration. Four bands were found to originate from the X 3 Delta 3 ground state, giving B 0"=0.533 492(33) cm(-1) and r 0 "=1.672 67(5) A for the 192 Os 12C isotopomer (1 sigma error limits); two of these, the 0-0[19.1]2<--X 3 Delta 3 and 1-0[19.1]2<--X 3 Delta 3 bands, form a vibrational progression with Delta G' 1/2=953.019 cm(-1). The remaining two bands were identified as originating from an Omega"=0 level that remains populated in the supersonic expansion. This level is assigned as the low-lying A 3 Sigma 0+ (-) state, which derives from the 4 delta 2 16 sigma 2 electronic configuration. The OsC molecule differs from the isovalent RuC molecule in having an X 3 Delta 3 ground state, rather than the X 2 delta 4, 1 Sigma+ ground state found in RuC. This difference in electronic structure is due to the relativistic stabilization of the 6s orbital in Os, an effect which favors occupation of the 6s-like 16 sigma orbital. The relativistic stabilization of the 16 sigma orbital also lowers the energy of the 4 delta 2 16 sigma 2, 3 Sigma(-) term, allowing this term to remain populated in the supersonically cooled molecular beam.     

Relativistic theory for indirect nuclear spin–spin couplings within the polarization propagator approach

We present a relativistic theory for the nuclear spin–spin coupling tensor within the polarization propagator approach using the particle-hole Dirac–Coulomb–Breit Hamiltonian and the full four-component wave function. We give explicit expressions for the coupling tensor in the random-phase approximation, neglecting the Breit interaction. A purely relativistic perturbative electron–nuclear Hamiltonian is used and it is shown how the single relativistic contribution to the coupling tensor reduces to Ramsey's three second-order terms (Fermi contact, spin–dipole, and paramagnetic spin–orbit) in the nonrelativistic limit. The principal propagator becomes complex and the leading property integrals mix atomic orbitals of different parity. The well-known propagator expressions for the coupling tensor in the nonrelativistic limit is obtained neglecting terms of the order c^?n (n ? 1). © 1993 John Wiley & Sons, Inc.     

Lone-pair orbital interactions in polythiaadamantanes

The electronic structures of a series of polythiaadamantanes from thiaadamantane through 2,4,6,8,9,10-hexathiaadamantane (HTA) have been analyzed using density functional theory calculations in conjunction with Hückel and natural bond orbital analysis. The effects of multiple sulfur p-type lone-pair orbital interactions on ionization potentials, hole mobilities, and electronic coupling have been determined. An overall increase in the average energy of the lone-pair orbitals as the number of sulfur atoms increases is predicted, with the exact positioning of the HOMO depending on specific lone-pair interactions. Separation of through-bond (TB) and through-space (TS) interactions between intramolecular sulfur atoms has been performed using localized molecular orbitals and model systems based on interacting hydrogen sulfide molecules. TB interations were found to reduce orbital splitting, while TS interactions were found to increase orbital splitting. TS interactions were more or less constant from one polythiaadamantane to the next, and the contributions of TB effects to individual orbital energies vary depending on the relative orientation of sulfur atoms as determined by the sigma molecular framework. Electronic coupling between intermolecular sulfur lone-pair orbitals was determined by investigating unique dimer pairs observed in the crystal structure of HTA. Electronic coupling is not as strong as expected given the short intermolecular S-S distances observed in the crystal structure. In general, B3LYP/6-31G(d) and B3LYP/6-311+G(d,p) give very similar orbital energies and splittings.     

Orbital symmetry as a tool for understanding the bonding in Krossing's cation

The geometric and electronic structure of Krossing's cation, Ag(eta(2)-P(4))(2)(+), which shows an unexpected planar coordination environment at the metal center and D(2)(h) symmetry both in solution and in the solid state, have been investigated using density functional theory and orbital-symmetry-based energy decomposition. The analysis reveals that the contribution from electrostatic interactions to the bond energy is greater than that of orbital interactions. Partitioning of the latter term into the irreducible representations shows that, in addition to the 5s orbital, 5p orbitals of silver act as acceptor orbitals for electron donation from sigma(P-P) orbitals (a(1)(g), b(1)(u)) and n(P) orbitals (b(3)(u)). Back-donation from the 4d(10) closed shell of Ag into sigma orbitals of the pnictogen cages (b(2)(g)) is also important. However, this contribution is shown not to determine the D(2)(h) structure, contradicting conclusions from the pioneering study of the title cation (J. Am. Chem.Soc. 2001, 123, 4603). The contributions from the irreducible representations to the stabilizing orbital interactions in the D(2)(h) structure and in its D(2)(d)-symmetric conformer are analogous, indicating that the planar coordination environment at the metal center in Ag(eta(2)-P(4))(2)(+) is induced by intermolecular rather than by intramolecular interactions. Because ethylene coordination to a metal ion is an elementary reaction step in industrial processes, the bonding in Ag(C(2)H(4))(2)(+) has been analyzed as well and compared to that in Krossing's cation. Surprisingly, similar contributions to the bond energies and an involvement of metal 4d and 5p orbitals have been found, whereas a recent atoms in molecules analysis suggested that the metal-ligand interactions in silver(I) olefin complexes fundamentally differ from those in tetrahedro P(4) complexes. The only qualitative difference between the bonding patterns in Ag(eta(2)-P(4))(2)(+) and Ag(C(2)H(4))(2)(+) is the negligible energy contribution from the b(3)(u) irreducible representation in the ethylene complex because a respective symmetry-adapted linear combination of ligand orbitals is not available.     

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.     

Relativistic effects on nuclear magnetic shielding constants in HX and CH3X (X=Br,I) based on the linear response within the elimination of small component approach

Numerical calculations of relativistic effects on nuclear magnetic shielding constants sigma corresponding to all one-body operators obtained within a formalism developed in previous work were carried out. In this formalism, the elimination of small component scheme is applied to evaluate all quantities entering a four-component RSPT(2) expression of magnetic molecular properties. HX and CH3X (X=Br,I) were taken as model compounds. Calculations were carried out at the Hartree-Fock level for first-order quantities, and at the random-phase approximation (RPA) level for second- and third-order ones. It was found that values of sigma(X) are largely affected by several relativistic corrections not previously considered in the bibliography. sigma Values of the H nucleus are in close agreement with four-component RPA ones. Overall relativistic effects on the shift of sigma(X) from HX to CH3X are smaller than the nonrelativistic shifts.     

Unexpected geometrical effects on paramagnetic spin-orbit and spin-dipolar 2J(FF) couplings

The second-rank tensor character of the paramagnetic spin-orbit and spin-dipolar contributions to nuclear spin-spin coupling constants is usually ignored when NMR measurements are carried out in the isotropic phase. However, in this study it is shown that isotropic (2)J(FF) couplings strongly depend on the relative orientation of the C-F bonds containing the coupling nuclei and the eigenvectors of such tensors. Predictions about such effect are obtained using a qualitative approach based on the polarization propagator formalism at the RPA, and results are corroborated performing high-level ab initio spin-spin coupling calculations at the SOPPA(CCSD)/EPR-III//MP2/EPR-III level in a model system. It is highlighted that no calculations at the RPA level were carried out in this work. The quite promising results reported in this paper suggest that similar properties are expected to hold for the second-rank nuclear magnetic shielding tensor.     

Relativistic density functional calculations of EPR g tensor for eta1{CuNO}(11) species in discrete and zeolite-embedded states

Spin-unrestricted zeroth order regular approximation (ZORA) and the scalar relativistic method based on Pauli Hamiltonian implemented in the Amsterdam Density Functional suite were used to calculate the electronic g tensor for isolated covalent {CuNO}(11) and electrostatic {q-NO}(1) species and for various model molecular and nonmolecular {CuNO}(11)-containing systems, epitomizing copper nitrosyl cage adducts in the ZSM-5 zeolite. The predicted g tensor values using the ZORA/VWN scheme were in satisfactory agreement with experimental EPR results. Relativistic, diamagnetic, and paramagnetic contributions to the calculated g tensor were quantified. The nature of the observed Deltag shifts was discussed in terms of the molecular orbital contributions due to the magnetic field-induced couplings and their structure sensitivity. The influence of basis set and exchange-correlation functional on the results was also briefly evaluated.     

Superexchange in magnetic insulators: an interpretation of the metal-metal charge transfer energy in the Anderson theory

The superexchange interactions in four three-center model systems A-L-B, for A and B being paramagnetic centers and L a diamagnetic bridging ligand, are analyzed by valence bond configuration interaction models in combination with fourth-order perturbation theory. We analyze the four distinct cases where a bridging ligand orbital simultaneously interacts with half-filled orbitals localized on A and B (case i), a half-filled orbital localized on A and an empty orbital localized on B (case ii), a full orbital localized on A and a half-filled orbital localized on B (case iii), and finally a full orbital localized on A and an empty orbital localized on B (case iv). In all four cases we compare our new results using localized orbitals with the equivalent results obtained using the Anderson ansatz of delocalized (magnetic) orbitals. The effective metal-to-metal electron transfer energy Ueff in the old formalism with delocalized orbitals is expressed in terms of the metal-to-metal electron transfer energy U and the ligand-to-metal electron transfer energy delta using localized orbitals. We find that the old formalism containing only Ueff is in general not sufficient. For cases i and ii we show that Ueff can be regarded as an effective U strongly reduced with respect to the free ion as a result of hybridization effects, whereas the same reduction of U for the cases iii and iv is not possible. The relevance and applicability of our theoretical results is demonstrated on magnetochemical data from the literature.