Semiempirical local spin: Theory and implementation of the ZILSH method for predicting Heisenberg exchange constants of polynuclear transition metal complexes

The local spin formalism ( 3 ) for computing expectation values 〈S_A · S_B〉 that appear in the Heisenberg spin model has been extended to semiempirical single determinant wave functions. An alternative derivation of expectation values in restricted and unrestricted cases is given that takes advantage of the zero differential overlap (ZDO) approximation. A formal connection between single determinant wave functions (which are not in general spin eigenfunctions) and the Heisenberg spin model was established by demonstrating that energies of single determinants that are eigenfunctions of the local spin operators with eigenvalues corresponding to high‐spin radical centers are given by the same Heisenberg coupling constants {J_AB} that describe the true spin states of the system. Unrestricted single determinant wave functions for transition metal complexes are good approximations of local spin eigenfunctions when the metal d orbitals are local in character and all unpaired electrons on each metal have the same spin (although spins on different metals might be reversed). Good approximations of the coupling constants can then be extracted from local spin expectation values 〈S_A · S_B〉 energies of the single determinant wave functions. Once the coupling constants are obtained, diagonalization of the Heisenberg spin Hamiltonian provides predictions of the energies and compositions of the spin states. A computational method is presented for obtaining coupling constants and spin‐state energies in this way for polynuclear transition metal complexes using the intermediate neglect of differential overlap Hamiltonian parameterized for optical spectroscopy (INDO/S) in the ZINDO program. This method is referred to as ZILSH, derived from ZINDO, Davidson's local spin formalism, and the Heisenberg spin model. Coupling constants and spin ground states obtained for 10 iron complexes containing from 2 to 6 metals are found to agree well with experimental results in most cases. In the case of the complex [Fe₆O₃(OAc)₉(OEt)₂(bpy)₂]⁺, a priori predictions of the coupling constants yield a ground‐state spin of zero, in agreement with variable‐temperature magnetization data, and corroborate spin alignments proposed earlier on the basis of structural considerations. This demonstrates the potential of the ZILSH method to aid in understanding magnetic interactions in polynuclear transition metal complexes. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Dissociation and IVR pathways for the CF3H(H2O)3 cluster

Classical trajectory simulations are used to study the intramolecular dynamics of isolated CF₃H and the CF₃H(H₂O)₃ cluster, by either exciting the CH stretch local mode to then=6 level or by adding an equivalent amount of energy to an OH stretch normal mode. Energy transfer from the CH local mode is statistically the same for CF₃H(H₂O)₃ as for isolated CF₃H, and agrees with previous experimental studies. Clusters excited with 6 quanta in the CH local mode are remarkably stable. Though the CF₃H-(H₂O)₃ intermolecular potential is only 1.5 kcal/mol, only 1 of 26 clusters excited with 6 quanta in the CH local mode dissociate within 10 ps. The absorption linewidth for the CH local mode in CF₃H(H₂O)₃ is related to IVR within CF₃H and not to the unimolecular lifetime of the cluster. When an OH stretch normal mode of the cluster is excited, energy transfer to CF₃H is negligible and nearly one half of the clusters dissociate within 10 ps.     

Theoretical studies of the g factors and local structures of the Ni3+ centers in Na2Zn(SO4)2·4H2O and K2Zn(SO4)2·6H2O crystals

The local structures and the g factors g_i (i = x, y, z) for Ni³⁺ centers in Na₂Zn(SO₄)₂·4H₂O (DPPH) and K₂Zn(SO₄)₂·6H₂O (PHZS) crystals are theoretically studied by using the perturbation formulas of the g factors for a 3d⁷ ion with low spin (S = 1/2) in orthorhombically compressed octahedra. In these formulas, the contributions to g factors from both the spin-orbit coupling interactions of the central ion and ligands are taken into account, and the required crystal-field parameters are estimated from the superposition model and the local geometry of the systems. Based on the calculations, the Ni-O bonds are found to suffer the axial compression δz (or Δz) of about 0.111 Å (or 0.036 Å) along the z-axis for Ni³⁺ centers in DPPH (or PHZS) crystals. Meanwhile, the Ni-O bonds may experience additional planar bond length variation δx (≈0.015 Å) along x- and y-axes for the orthorhombic Ni³⁺ center in DPPH. The theoretical g factors agree well with the experimental data. The obtained local structural parameters for both Ni³⁺ centers are discussed.     

Use of X-Ray Absorption Spectra as a “Fingerprint” of the Local Environment in Complex Chalcogenides

The local environment of tin, titanium, iron, and sulfur in spinel compounds Cu₂FeSn₃S₈ and Cu₂FeTi₃S₈ was studied by X-ray absorption spectroscopy (XAS) at the titanium, iron, sulfur K edges, and the tin L_I-edge. As detailed calculations of the electronic structure of these compounds are difficult to carry out due to the large number of atoms contained in the unit cell, the XAS spectra of the spinels are compared to those of relatively simple binary sulfides like SnS₂, TiS₂, and FeS. Indeed, the metal environments in these binary compounds are very similar to those in the spinels, and they can be considered good model compounds allowing the interpretation of electronic transitions observed in the spectra of quaternary phases. In the latter, the bottom of the conduction band is mainly formed by Sn 5s–S 3p, Sn 5p–S 3p antibonding states for the tin-based compounds and by Ti 3d_t2g–S 3p, Ti 3d_eg–S 3p antibonding states for the titanium-based compounds. It it shown that the local environment of iron atoms remains unchanged when substituting tin with titanium atoms, according to a topotactic substitution.     

Microdomains, Solid Solutions and the "Defect Fluorite" to C-Type Sesquioxide Transition in CeO2-RO1.5 and ZrO2-RO1.5 Systems

Satellite dark field (SDF) imaging is used to show that there is a definite change in symmetry on moving across the two-phase region separating the so-called "defect fluorite" and C-type sesquioxide solid solution regions in (1 - x)CeO₂ · xRO_1.5 and (1 - x )ZrO₂ · xRO_1.5 systems. SDF images of the "defect fluorite" side of the two-phase region are characterized by a microdomain texture on the 100-200 Å scale and the local symmetry within any one of these microdomains is shown to be lower than cubic. Corresponding SDF images of the C-type sesquioxide side of the two-phase region are by contrast homogeneous and consistent with Ia3 space group symmetry. The nature of the local oxygen vacancy distribution on either side of the two-phase region is discussed and a possible model for the "defect fluorite" side of the two-phase region proposed.     

Application of many-body perturbation theory in the localized representation for the all-trans conjugated polyenes

Ab initio self-consistent field (SCF ) calculations are performed with the standard 6-31G* basis set for all-trans conjugated oligomers C_2n+2H_2n+4. The canonical occupied and virtual molecular orbitals (MO s) are separately localized by unitary transformations. Due to the localization, the perturbation operator is partitioned into two-particle and into single-particle terms; the MBPT is, therefore, a double-perturbation expansion in this case. By using the localized representation of the MBPT , the correlation energy contributions can be partitioned into local and nonlocal effects. It can be shown that the local effects are very important and well transferable, which makes possible the calculation of the correlation energy of larger molecules if the localized molecular orbitals (occupied and virtual) of smaller related molecules are known. © 1994 John Wiley & Sons, Inc.     

A local spin evaluation into the active site models of [2Fe2S] ferrodoxin [Fe<Subscript>2</Subscript>S<Subscript>2</Subscript>(SR)<Subscript>4</Subscript>]<Superscript>2−</Superscript> (R=—H, —CH<Subscript>3</Subscript>)

To test the feasibility of local spin theory of Davidson and Clark for ferrodoxin clusters, the models [Fe₂S₂(SR)₄]²⁻ (R=—H, —CH₃) are chosen for evaluation. This purpose is realized by calculating the local spin expectation values 〈S _A·S _B〉, 〈S _A ² 〉, and m _A and discussing the connection between these expected values and the Heisenberg spin model (HSM) and the Noodleman broken-symmetry approach. In practical calculation, the spin-unrestricted Hartree-Fock (UHF) and spin-polarized density functional theory (DFT) are used and the calculational qualities of these two methods are also discussed. In addition, the theoretical magnetic coupling constants J _AB of these models are calculated by various computational schemes for comparison with both theoretical and experimental results previously reported. Supported by the Doctorial Initial Foundations of Hainan Normal University (Grant No. 13140252)     

A [4π+4π] intramolecular photocyclomer of 9‐anthroic anhydride: 5,6,11,12‐tetrahydro‐5,12;6,11‐di‐o‐­benzenodibenzo[a,e]cyclooctene‐5,6‐dicarboxylic anhydride

The title compound, C₃₀H₁₈O₃, was obtained by light irradiation of a di­chloro­ethane solution of 9‐anthroyl chloride and 9‐anthroic acid. The mol­ecules, which possess approximately mm2 local symmetry, are packed in columns, the oxy­genated moieties facing each other according to the symmetry of a monoclinic lattice. The space group of the crystal is P2₁/c, with a whole mol­ecule as the asymmetric unit. The structure is compared with those of similar dianthracene derivatives.     

“Expanded” local mode approach for XY2 (C2v) molecules

For XY₂ (C_2v symmetry) molecules, the local mode method is modified on the basis of a careful analysis of the transformation coefficients l_Nαλ and the properties of the intramolecular potential function, and an expanded local mode approach is derived. It is shown that relationships between known spectroscopic parameters, found in the spectroscopic literature, can be improved. New relationships between the centrifugal distortion coefficients are obtained. It is shown that knowledge of the centrifugal distortion coefficients of the ground vibrational state allows the possibility of predicting values of both the band centres and the spectroscopic parameters of deformational bands, even under conditions of a total absence of initial information on these deformational bands. The prediction possibility of the derived expanded local mode approach is analyzed.     

Studies on the EPR parameters and local angular distortion for the tetragonal Cu2+ center in CaWO4 crystal

The electron paramagnetic resonance (EPR) parameters—g factors g_i (i = || and ⊥) and hyperfine structure constants A_i (M) and A_i(N), with M and N belonging to isotopes ⁶³Cu²⁺ and ⁶⁵Cu²⁺—and local structure of Cu²⁺ ion occupying W⁶⁺ site in CaWO₄ crystal are theoretically studied based on the perturbation formulas of these parameters for a 3d⁹ ion under tetragonally elongated tetrahedra. In these formulas, the ligand orbital (LO) and spin–orbit coupling (SOC) contributions are included due to the shorter impurity-ligand distance R (≈1.83 Å) and hence the strong covalency of the studied [CuO₄]⁶⁻ cluster, and the related molecular orbital coefficients are quantitatively determined from the cluster approach in a uniform way; meanwhile, the required crystal field (CF) parameters for the tetragonally distorted tetrahedron (TDT) are estimated from the superposition model and the local structure of the impurity Cu²⁺ center. According to the calculation, the bond angle θ between the four equivalent Cu²⁺-O²⁻ bonds and the C₄ axis in the CaWO₄:Cu²⁺ is found to be about 2.1° smaller than that (θ₀ ≈ 54.74°) for an ideal tetrahedron due to the Jahn–Teller (JT) effect and the size mismatch. The fitted results agree well with the observed values, and the validity of the present assignment for the local structure of the Cu²⁺ center is also discussed.     

Applications of the MBPT in the localized representation

Diagrammatic formulation of the MBPT is applied when the occupied and the virtual canonical orbitals are separately localized by unitary transformations. In this localized representation, due to the off-diagonal Fock matrix elements, the perturbation operator contains extra terms generating the so-called localization corrections. These corrections enter the perturbation energy in third and higher orders. Their magnitude depends on the type of localization, but they represent only a small fraction of the canonical corrections. The calculation of the localization corrections, however, does not need a significant amount of extra computer time. It is shown that by introducing an “order of neighborhood” local and nonlocal effects of the electron correlation can be separated and the contribution of the nonlocal effects can be neglected to a good approximation. Ab initio calculations have been carried out for the normal saturated hydrocarbons: C_2n+1H_4n+4 and for the all-trans conjugated polyenes C_2n+2H_2n+4. As to the ratio of the local and nonlocal corrections, it is shown that there is only a quantitative difference for these two kinds of systems (strongly or weakly localizable). Neglecting nonlocal effects, considerable amount of computer time can be saved.     

A theoretical study of electronic effects in alkyne‐linked reactive intermediates: (nitrenoethynyl)methylenes, (nitrenoethynyl)silylenes,and (nitrenoethynyl)germylenes

Acetylene‐linked reactive intermediates of (nitrenoethynyl)‐X‐methylenes, (nitrenoethynyl)‐X‐silylenes, and (nitrenoethynyl)‐X‐germylenes are almost experimentally unreachable (X–M–C≡C–N; X=H ( 1 ), CN ( 2 ), OH ( 3 ), NH₂ ( 4 ), NO₂ ( 5 ), and CHO ( 6 ); M=C, Si, and Ge). The effects of the electron‐donating and electron withdrawing groups were compared and contrasted at seven levels of theory. All singlet species as ground states with one local open‐shell singlet carbene subunit (π¹π¹) and another local open‐shell singlet nitrene subunit (π¹π¹) were found to be more stable than their corresponding triplets including one local open‐shell singlet carbene (δ¹π¹) (or one local closed‐shell singlet carbene [δ²π⁰]) and another local triplet nitrene subunit (π¹π¹) with 45.94–77.996 kcal/mol singlet–triplet energy gap (ΔE_s‐t). Their relative silylenes and germylenes made reduction of ΔE_s‐t, so the triplet ground states were found for species 3 _Si , 4 _Si , 5 _Si , 2 _Ge , 3 _Ge , 4 _{Ge ,} and 5 _Ge . All the singlet silylenes/germylenes formed by one local closed‐shell singlet silylenes/germylenes (δ²π⁰) and one local closed‐shell singlet nitrene subunit (π²π⁰). Also, one local closed‐shell singlet silylene/germylene subunit (δ²π⁰) and one local triplet nitrene subunit (π¹π¹) were observed for triplet silylenes/germylenes. The singlet and triplet species 3 _Si , 4 _Si , 3 _Ge , and 4 _Ge , due to their electrophilic (Si₄/Ge₄) and nucleophilic (X₅) centers, could be identified as intermediates in chemical reactions.     

Ab initio studies of internal rotation barriers and vibrational frequencies of (C2H2)2, (CO2)2, and C2H2-CO2

We have performed large-scaleab initio calculations using second order Møller-Plesset perturbation theory (MP2) on the three van der Waals dimers formed from acetylene and carbon dioxide. Intermolecular geometrical parameters are reliably computed at this level of theory. Calculations of vibrational frequencies of the van der Waals modes, currently unobtainable by experimental means, give important information about the intermolecular potential and predict significant large-amplitude motion. Zero point energy contributions are shown to be vital in assessing the relative stability of conformations which are close in energy. Our studies suggest that the barrier to interconversion tunnelling in (CO₂)₂ is significantly smaller than previously inferred and is approximately the same as in (C₂H₂)₂. The reason for the rigidity of (CO₂)₂ is the difference in monomer centre-of-mass separation between ground state and transition state. We also show that, in addition to the previously observedC _2v form, the collinear form of C₂H₂-CO₂ is a local minimum on its potential energy surface.     

Carbon Dioxide Capture and Release by Anions with Solvent‐Dependent Behaviour: A Theoretical Study

Recently, Clyburne and co‐workers [Science, 2014 , 344, 75–78] reported the novel synthesis of the elusive cyanoformate anion, NCCO₂^?. The stability of this anion is dependent on the dielectric constant of the local environment (polarity‐switchable solvent): it is stable in low‐polarity media and unstable in high‐polarity solvents; hence, capturing and then releasing CO₂. The possibility of extending such behaviour to other anions is explored herein. Specifically, the CO₂ capture process is studied for 26 anions in the gas phase and 3 distinct solvents (water, tetrahydrofuran, and toluene) by using the polarisable continuum model. Calculations are performed with the M06‐2X and B3LYP‐D3 density functionals and the aug‐cc‐pVTZ basis set. The design of new CO₂ complexes with the anion, which can be formed or destroyed on demand by changing the solvent, is possible; the results for the alkoxylate and thiolate anions are especially promising. The nature of the substituents connected to the atom that bonds to CO₂ in the anion is crucial in modulating the relative stability of the products—a key point for reversibility in the CO₂ capture process. A moderate interaction for the anion–CO₂ adduct—about 10 kcal mol^?1 relative free energy with respect to the isolated reactants in the gas phase—and a relevant effect in the dielectric constant of the local environment are also key ingredients to achieve solvent dependency.     

On the relationship between the electron-pair distribution function and the correlation energy of an atom

The pair distribution function h(r₁₂;r₁, γ) and the virial theorem are used to derive a general expression for the local contributions to the total correlation energy of an atom. A direct link between correlation effects and the correlation energy is obtained by use of G(r₁, γ) and Γ(r₁, y). The former is the probability associated with a given choice of r₁ and γ, while the latter describes the local contribution to the correlation energy. Explicit calculations for the ground state of helium indicate that the angular dependence of the local contribution to the correlation energy is essentially independent of r₁, whereas the local correlation energy shows a strong r₁ dependence. The maximum contribution to the correlation energy occurs at intermediate values of γ where there is close agreement between the Hartree–Fock and exact densities.     

The photoelectron spectra of D2d and C2ν hydrocarbons containing two norbornadiene or quadricylane groups

The photoelectron spectra of the hydrocarbons 1 to 4 have been recorded and interpreted by qualitative correlation with the spectra of their subsystems norbornadiene, quadricyclane, allene and cyclopropane. It has been shown that the interactions of the symmetry adapted orbitals of the subsystems are governed not only by their symmetry behaviour with respect to D_2d in 1 and 2 , or C_2ν in 3 and 4 , but also by the local symmetry at the points of attachment of the subsystems.     

Site Preference of Cations and Structural Variation in MgAl2–xGaxO4 (0 ≤ x ≤ 2) Spinel Solid Solution

The crystal structures of MgAl_2–xGa_xO₄ (0 ≤ x ≤ 2) spinel solid solutions (x = 0.00, 0.38, 0.76, 0.96, 1.52, 2.00) were refined using ²⁷Al MAS NMR measurements and single crystal X‐ray diffraction technique. Site preferences of cations were investigated. The inversion parameter (i) of MgAl₂O₄ (i = 0.206) is slightly larger than given in previous studies. It is considered that the difference of inversion parameter is caused by not only the difference of heat treatment time but also some influence of melting with a flux. The distribution of Ga³⁺ is little affected by a change of the temperature from 1473 K to 973 K. The degree of order‐disorder of Mg²⁺ or Al³⁺ between the fourfold‐ and sixfold‐coordinated sites is almost constant against Ga³⁺ content (x) in the solid solution. A compositional variable of the Ga/(Mg + Ga) ratio in the sixfold‐coordinated site has a constant value through the whole compositional range: the ratio is not influenced by the occupancy of Al³⁺. The occupancy of Al³⁺ is independent of the occupancy of Ga³⁺, though it depends on the occupancy of Mg²⁺ according to thermal history. The local bond lengths were estimated from the refined data of solid solutions. The local bond length between specific cation and oxygen corresponds with that expected from the effective ionic radii except local Al–O bond length in the fourfold‐coordinated site and local Mg–O bond length in the sixfold‐coordinated site. The local Al–O bond length in the fourfold‐coordinated site (1.92 Å) is about 0.15 Å longer than the expected bond length. This difference is induced by a difference in site symmetry of the fourfold‐coordinated site. The nature that Al³⁺ in spinel structure occupies mainly the sixfold‐coordinated site arises from the character of Al³⁺ itself. The local Mg–O bond length in the sixfold‐coordinated site (2.03 Å) is about 0.07 Å shorter than the expected one. Difference Fourier synthesis for MgGa₂O₄ shows a residual electron density peak of about 0.17 e/ų in height on the center of (Ga_0.59 Mg_0.41)–O bond. This peak indicates the covalent bonding nature of Ga–O bond on the sixfold‐coordinated site in the spinel structure.     

Effect of Anion Position on the Electronic Energy Structure of CuGaS2 and AgGaS2

The effect of the anion displacement parameter (u) on the local partial and total densities of electronic states is investigated for two chalcogenides of A^IB^IIIC ₂ ^VI type: CuGaS₂ and AgGaS₂. The forbidden gap (E_g) of the compounds is estimated. The calculations were performed in the framework of the cluster version of the local coherent potential approximation. It is established that E_g is a linear function of u. The curves of the local partial densities of states permit the estimation of the dependence of the splitting of the characteristic maxima on the chosen value of u; this dependence is also linear.     

Geometry,Vibrational and NMR Spectra of Icosahedral 1-Methylazacloso-dodecaborane

Geometry, vibrational and NMR spectra of the icosahedral aza-closo-dodecaborane MeNB₁₁H₁₁ are calculated by ab initio methods. The results are compared with experimental data. They are in accord with local C_5v symmetry of the cluster unit and local C_3v symmetry of the methyl group. The boron atoms B7–B11 are coupled to B12 by the small constant ¹J (¹¹B, ¹¹B) = 12 Hz.     

Investigations of the local distortions and EPR parameters for Cu2+ in xNa2O‐(30–x)K2O‐70B2O3 (5 ≤ x ≤ 25 mol%) glasses

The local distortions and electron paramagnetic resonance parameters for Cu²⁺ in the mixed alkali borate glasses xNa₂O‐(30–x)K₂O‐70B₂O₃ (5 ≤ x ≤ 25 mol%) are theoretically studied with distinct modifier Na₂O compositions x. Owing to the Jahn–Teller effect, the octahedral [CuO₆]¹⁰⁻ clusters show significant tetragonal elongation ratios p ~19% along the C₄ axis. With the increase of composition x, the cubic field parameter Dq and the orbital reduction factor k exhibit linearly and quasi‐linearly decreasing tendencies, respectively, whereas the relative tetragonal elongation ratio p has quasi‐linearly increasing rule with some fluctuations, leading to the minima of g factors at x = 10 mol%. The composition dependences of the optical spectra and the electron paramagnetic resonance parameters are suitably reproduced by the linear or quasi‐linear relationships of the relevant quantities (i.e., Dq, k, and p) with x. The above composition dependences are analyzed from mixed alkali effect, which brings forward the modifications of the local crystal‐fields and the electronic cloud distribution around Cu²⁺ with the variation of the composition of Na₂O.