Density functional perturbational orbital theory of spin polarization in electronic systems. II. Transition metal dimer complexes

We present a theoretical scheme for a semiquantitative analysis of electronic structures of magnetic transition metal dimer complexes within spin density functional theory (DFT). Based on the spin polarization perturbational orbital theory [D.-K. Seo, J. Chem. Phys. 125, 154105 (2006)], explicit spin-dependent expressions of the spin orbital energies and coefficients are derived, which allows to understand how spin orbitals form and change their energies and shapes when two magnetic sites are coupled either ferromagnetically or antiferromagnetically. Upon employment of the concept of magnetic orbitals in the active-electron approximation, a general mathematical formula is obtained for the magnetic coupling constant J from the analytical expression for the electronic energy difference between low-spin broken-symmetry and high-spin states. The origin of the potential exchange and kinetic exchange terms based on the one-electron picture is also elucidated. In addition, we provide a general account of the DFT analysis of the magnetic exchange interactions in compounds for which the active-electron approximation is not appropriate.     

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.     

Steric effects in electron transfer from potassium to pi-bonded oriented molecules CH3CN, CH3NC, and CCl3CN

Electron transfer from K atoms to oriented CH3CN, CH3NC, and CCl3CN is studied in crossed beams at energies near the threshold for forming an ion pair. For the methyl compounds, the dominant ions are K+ and CN-; the steric asymmetry is very small and energy-independent, characteristic of sideways attack with the electron apparently entering the pi*CN antibonding orbital. Migration of the electron to the sigma*CC orbital to break the C-C bond is greatly facilitated by interaction with the atomic donor. CH2CN- is formed in collisions preferring CH3-end attack, and the steric asymmetry becomes very large near threshold. CCl3CN mostly forms Cl- in collisions slightly favoring the CCl3 end with a small energy dependence with the electron apparently entering the sigma* LUMO. CN- is formed in much smaller yield with a slight preference for the CN end. The parent negative ion CCl3CN- is observed, and a lower limit for its electron affinity is estimated to be 0.3 eV. Fragment ions CCl2CN- and CClCN- are also observed with upper limits for the quantity bond dissociation energy - electron affinity (BDE - EA) estimated to be 0.6 and 1.0 eV, respectively.     

Sulfur K-edge XAS and DFT studies on NiII complexes with oxidized thiolate ligands: implications for the roles of oxidized thiolates in the active sites of Fe and Co nitrile hydratase

S K-edge X-ray absorption spectroscopy data on a series of NiII complexes with thiolate (RS-) and oxidized thiolate (RSO2-) ligands are used to quantify Ni-S bond covalency and its change upon ligand oxidation. Analyses of these results using geometry-optimized density functional theory (DFT) calculations suggest that the Ni-S sigma bonds do not weaken on ligand oxidation. Molecular orbital analysis indicates that these oxidized thiolate ligands use filled high-lying S-O pi* orbitals for strong sigma donation. However, the RSO2- ligands are poor pi donors, as the orbital required for pi interaction is used in the S-O sigma-bond formation. The oxidation of the thiolate reduces the repulsion between electrons in the filled Ni t2 orbital and the thiolate out-of-plane pi-donor orbital leading to shorter Ni-S bond length relative to that of the thiolate donor. The insights obtained from these results are relevant to the active sites of Fe- and Co-type nitrile hydratases (Nhase) that also have oxidized thiolate ligands. DFT calculations on models of the active site indicate that whereas the oxidation of these thiolates has a major effect in the axial ligand-binding affinity of the Fe-type Nhase (where there is both sigma and pi donation from the S ligands), it has only a limited effect on the sixth-ligand-binding affinity of the Co-type Nhases (where there is only sigma donation). These oxidized residues may also play a role in substrate binding and proton shuttling at the active site.     

Theoretical investigation of the magnetic interactions of Ni9 complexes

On the basis of density-functional theory (DFT) calculations, a theoretical analysis of the exchange interactions in Ni9L2(O2CMe)8{(2-py)2CO2}4, was performed, where L is a bridging ligand, OH- (1) or N3- (2). Each magnetic interaction between the Ni spin centers is analyzed for 1 and 2 in terms of exchange integrals (J values), orbital overlap integrals (T values) and natural orbitals. It was found that a J3 interaction, which is a magnetic interaction via the bridging ligand orbitals, mainly controls the whole magnetic properties, and the dominant interaction is a sigma-type orbital interaction between Ni dz2 orbitals. Further investigations on the magnetostructural correlations are performed on the J3 interactions using simplest Ni-L-Ni models. These models reproduced the magnetic interactions qualitatively well not only for the Ni9 complexes but also for other inorganic complexes. Strong correlations have been found between the magnetic orbital overlaps (T values) and the Ni-L-Ni angle. These results revealed that the difference of the magnetic properties between OH- and N3- is caused by the orbital overlap integral (T values) of the sigma-type J3 interaction pathway. The magnetic interactions are also discussed from a Hubbard model by evaluating the transfer integral (t) and on-site Coulomb integrals (U), in relation to the Heisenberg picture.     

Investigating CN- cleavage by three-coordinate M[N(R)Ar]3 complexes

Three-coordinate Mo[N((t)Bu)Ar]3 binds cyanide to form the intermediate [Ar((t)Bu)N]3Mo-CN-Mo[N((t)Bu)Ar]3 but, unlike its N2 analogue which spontaneously cleaves dinitrogen, the C-N bond remains intact. DFT calculations on the model [NH2]3Mo/CN- system show that while the overall reaction is significantly exothermic, the final cleavage step is endothermic by at least 90 kJ mol(-1), accounting for why C-N bond cleavage is not observed experimentally. The situation is improved for the [H2N]3W/CN- system where the intermediate and products are closer in energy but not enough for CN- cleavage to be facile at room temperature. Additional calculations were undertaken on the mixed-metal [H2N]3Re+/CN- /W[NH2]3 and [H2N]3Re+/CN-/Ta[NH2]3 systems in which the metals ions were chosen to maximise the stability of the products on the basis of an earlier bond energy study. Although the reaction energetics for the [H2N]3Re+/CN /W[NH2]3 system are more favourable than those for the [H2N]3W/CN- system, the final C-N cleavage step is still endothermic by 32 kJ mol(-1) when symmetry constraints are relaxed. The resistance of these systems to C-N cleavage was examined by a bond decomposition analysis of [H2N]M-L1[triple bond]L2-M[NH2]3 intermediates for L1[triple bond]L2 = N2, CO and CN which showed that backbonding from the metal into the L1[triple bond]L2 pi* orbitals is significantly less for CN than for N2 or CO due to the negative charge on CN- which results in a large energy gap between the metal d(pi), and the pi* orbitals of CN-. This, combined with the very strong M-CN- interaction which stabilises the CN intermediate, makes C-N bond cleavage in these systems unfavourable even though the C[triple bond]N triple bond is not as strong as the bond in N2 or CO.     

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 Studies on the Spin Exchange Interaction in Copper(II) Complexes Coordinated with Nitronyl Nitroxide

In the recent years, a wide variety of transition metal complexes with the nitronyl radical ligands have been reported1,2. These systems display the various magnetic behaviors (ferro- or antiferro-magnetism) between the unpaired electrons on the radical ligands and on the paramagnetic metal ion center. However, few theoretical studies on the metal-radical complexes were reported and quite few are known about the nature of the exchange coupling interactions. In this work, we are interested i…     

Electronic structure of ferric heme nitrosyl complexes with thiolate coordination

The effect of trans thiolate ligation on the coordinated nitric oxide in ferric heme nitrosyl complexes as a function of the thiolate donor strength, induced by variation of NH-S(thiolate) hydrogen bonds, is explored. Density functional theory (DFT) calculations (BP86/TZVP) are used to define the electronic structures of corresponding six-coordinate ferric [Fe(P)(SR)(NO)] complexes. In contrast to N-donor-coordinated ferric heme nitrosyls, an additional Fe-N(O) sigma interaction that is mediated by the dz2/dxz orbital of Fe and a sigma*-type orbital of NO is observed in the corresponding complexes with S-donor ligands. Experimentally, this is reflected by lower nu(N-O) and nu(Fe-N) stretching frequencies and a bent Fe-N-O moiety in the thiolate-bound case.     

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.     

Discrepancy between the spin distribution and the magnetic ground state for a triaminoxyl substituted triphenylphosphine oxide derivative

The magnetic interaction and spin transfer via phosphorus have been investigated for the tri-tert-butylaminoxyl para-substituted triphenylphosphine oxide. For this radical unit, the conjugation existing between the pi* orbital of the NO group and the phenyl pi orbitals leads to an efficient delocalization of the spin from the radical to the neighboring aromatic ring. This has been confirmed by using fluid solution high-resolution EPR and solid state MAS NMR spectroscopy. The spin densities located on the atoms of the molecule could be probed since (1)H, (13)C, (14)N, and (31)P are nuclei active in NMR and EPR, and lead to a precise spin distribution map for the triradical. The experimental investigations were completed by a DFT computational study. These techniques established in particular that spin density is located at the phosphorus (rho=-15x10(-3) au), that its sign is in line with the sign alternation principle and that its magnitude is in the order of that found on the aromatic C atoms of the molecule. Surprisingly, whereas the spin distribution scheme supports ferromagnetic interactions among the radical units, the magnetic behavior found for this molecule revealed a low-spin ground state characterized by an intramolecular exchange parameter of J=-7.55 cm(-1) as revealed by solid state susceptibility studies and low temperature EPR. The X-ray crystal structures solved at 293 and 30 K show the occurrence of a crystallographic transition resulting in an ordering of the molecular units at low temperature.     

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.     

Theoretical study of exchange coupling in 3d-Gd complexes: large magnetocaloric effect systems

Polynuclear 3d transition metal-Gd complexes are good candidates to present large magnetocaloric effect. This effect is favored by the presence of weak ferromagnetic exchange interactions that have been investigated using methods based on Density Functional Theory. The first part of the study is devoted to dinuclear complexes, focusing on the nature and mechanism of such exchange interactions. The presence of two bridging ligands is found more favorable for ferromagnetic coupling than a triple-bridged assembly, especially for complexes with small M-O···O-Gd hinge angles. Our results show the crucial role of the Gd 5d orbitals in the exchange interaction while the 6s orbital seems to have a negligible participation. The analysis of the atomic and orbital spin populations reveals that the presence of spin density in the Gd 5d orbital is mainly due to a spin polarization effect, while a delocalization mechanism from the 3d orbitals of the transition metal can be ruled out. We propose a numerical DFT approach using pseudopotentials to calculate the exchange coupling constants in four polynuclear first-row transition metal-Gd complexes. Despite the complexity of the studied systems, the numerical approach gives coupling constants in excellent agreement with the available experimental data and, in conjunction with exact diagonalization methods (or Monte Carlo simulations), it makes it possible to obtain theoretical estimates of the entropy change due to the magnetization/demagnetization process of the molecule.     

NMR Investigation of beta-Substituted High-Spin and Low-Spin Iron(III) Tetraphenylporphyrins

The NMR spectra of a series of beta-substituted iron(III) tetraphenylporphyrin (2-X-TPP) complexes have been studied to elucidate the relationship between the electron donating/withdrawing properties of the 2-substituent and the (1)H NMR spectral pattern. The electronic nature of the substituent has been significantly varied and covered the -0.6 to 0.8 Hammett constant range. Both high-spin and low-spin complexes of the general formula (2-X-TPP)Fe(III)Cl and [(2-X-TPP)Fe(III)(CN)(2)](-) have been investigated. The (1)H NMR data for the following substituents (X) have been reported: py(+), NO(2), CN, CH(3), BzO (C(6)H(5)COO), H, D, Br, Cl, CH(3), NH(2), NH(3)(+), NHCH(3), OH, and O(-). The (1)H NMR resonances for low-spin dicyano complexes have been completely assigned by a combination of two-dimensional COSY and NOESY experiments. In the case of selected high-spin complexes, the 3-H resonance has been identified by the selective deuteration of all but the 3-H position. The pattern of unambiguously assigned seven pyrrole resonances reflects the asymmetry imposed by 2-substitution and has been used as an unique (1)H NMR spectroscopic probe to map the spin density distribution. The pyrrole isotropic shifts of [(2-X-TPP)Fe(III)(CN)(2)](-) are dominated by the contact term. In order to quantify the substituent effect, the dependence of isotropic shift of all low-spin pyrrole resonances and 3-H high-spin pyrrole resonance versus Hammett constants has been studied. The electronic effect is strongly localized at the beta-substituted pyrrole. The major change of the isotropic shift has also been noted for only one of two adjacent pyrrole rings, i.e., at 7-H and 8-H positions. These neighboring protons, located on a single pyrrole ring, experienced opposite shift changes when electron withdrawing/donating properties were modified. Two other pyrrole rings for all investigated derivatives revealed considerably smaller, substituent related, isotropic shift changes. A long-range secondary isotopic shift has been observed for [(2-D-TPP)Fe(III)(CN)(2)](-). The effect is consistent with a general spin density distribution mechanism due to beta-substitution. A fairly good correlation between the 3-H isotropic shift of (2-X-TPP)Fe(III)Cl and the Hammett constant has been found as well. The observed contact shift pattern of [(2-X-TPP)Fe(III)(CN)(2)](-) reflects spin pi delocalization into the highest filled MO equivalent to the unsubstituted porphyrin 3e(pi) orbital. To account for the substituent contribution, the semiquantitative Fenske-Hall LCAO method has been used to determine the molecular orbitals involved in the spin density delocalization. For low-spin complexes, (13)C pyrrole resonances of carbons bearing a proton have been identified by means of a (1)H-(13)C HMQC experiment. The reversed order of (13)C resonance patterns as compared to their (1)H NMR counterparts has been determined, e.g., the largest isotropic shift of 3-H has been accompanied by the smallest measured (13)C isotropic shift. Analysis of the isotropic shifts in (2-X-TPP)Fe(III)Cl and [(2-X-TPP)Fe(III)(CN)(2)](-) suggests that the observed regularities of the electronic structure modification due to the beta-substitution should apply to iron(III) natural porphyrin or geoporphyrin complexes.     

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.     

The effect of carbonyl group in the asymmetry of 3,4JCH coupling constants in norbornanones

A rationalization of the known difference between the 3,4JC4H1 and 3,4JC1H4 couplings transmitted mainly through the 7-bridge in norbornanone is presented in terms of the effects of hyperconjugative interactions involving the carbonyl group. Theoretical and experimental studies of 3,4JCH couplings were carried out in 3-endo- and 3-exo-X-2-norbornanone derivatives (X = Cl, Br) and in exo- and endo-2-noborneol compounds. Hyperconjugative interactions were studied with the natural bond orbital (NBO) method. Hyperconjugative interactions involving the carbonyl pi*(C2=O) and sigma*(C2=O) antibonding orbitals produce a decrease of three-bond contribution to both 3,4JC4H1 and 3,4JC1H4 couplings. However, the latter antibonding orbital also undergoes a strong sigmaC3--C4 --> sigma*(C2=O) interaction, which defines an additional coupling pathway for 3,4JC4H1 but not for 3,4JC1H4. This pathway is similar to that known for homoallylic couplings, the only difference being the nature of the intermediate antibonding orbital; i.e. for 3,4JC4H1 it is of sigma*-type, while in homoallylic couplings it is of pi*-type.     

Neutral carbene analogues of the heaviest Group 13 elements: consideration of electronic and steric effects on structure and stability

The neutral monovalent Group 13 beta-diketiminato complexes [CH{(CF3)2CN-2,6-iPr2C6H3}2In] and [CH{(Me)2CN-2,6-iPr2C6H3}2Tl] have been synthesised by analogous 'one-pot' procedures involving reaction of [KN(SiMe3)2] with the appropriate beta-imino-enamine and Group 13 iodide. The structure of the indium complex reveals that replacement of the ligand backbone methyl groups of the previously reported complex [CH{(Me)2CN-2,6-iPr2C6H3}2In] with trifluoromethyl substituents results in only minor modifications to the dimensions of the NCCCNIn metallacycle. The electronic structures of both indium species were interrogated by DFT calculations to reveal similar frontier molecular orbital schemes. In agreement with calculations performed previously on the aluminium and gallium complexes, [CH{(Me)2CN-2,6-iPr2C6H3}2Al] and [CH{(Me)2CN-2,6-iPr2C6H3}2Ga], the HOMO in both indium species comprises a metal-based sp-hybrid while the LUMO is a ligand-based orbital of pi symmetry. The vacant indium p-orbital is represented by the LUMO + 1. Although incorporation of the fluorinated substituents results in a stabilisation of the system overall, the stabilities and observed structural features of the complexes are reasoned to be primarily a result of the steric profile of the very bulky ligands and not through any redistribution of the electron density within the cyclic species. The thallium complex is isostructural to the analogous and previously reported aluminium, gallium and indium species. The greater stability of the monovalent state however is reflected in a reordering of the orbital energies and a stabilisation of the metal-based orbitals in the frontier region of the MO scheme.