Molecular Orbital Coefficients Research Articles

EPR and optical absorption studies of vanadyl impurity in zinc potassium phosphate hexahydrate single crystal

Electron paramagnetic resonance (EPR) study of VO 2+ doped zinc potassium phosphate hexahydrate single crystal is carried out. The angular variation of the spectra is studied in the three crystallographic planes. The principal value of spin Hamiltonian parameters g and A and the direction cosines which principal axes make with the crystallographic axes are determined. The observed values are site I: g ∥ =1.9664±0.0002, g ⊥ =1.9973±0.0002, A ∥ =150±2×10 −4 , A ⊥ =60±2×10 −4 cm −1 ; site II: g ∥ =1.9276±0.0002, g ⊥ =1.9921±0.0002, A ∥ =155±2×10 −4 and A ⊥ =62±2×10 −4 cm −1 . By comparison of direction cosines of g from EPR with the direction cosines of different bonds obtained from crystal structure data it is ascertained that the VO 2+ ion occupies Zn 2+ substitutional sites. The optical absorption study of the crystal at room temperature is also carried out. The bands observed in the optical absorption spectrum are attributed to d–d transitions. The EPR results together with the optical data are employed to estimate the molecular orbital (MO) coefficients. These MO coefficients (also called bonding coefficients) are further used to discuss the nature of bonding of VO 2+ ion with different ligands in the crystal.

Studies of the g factors and the superhyperfine parameters for Ni3+ in the fluoroperovskites

The g factors and the ligand superhyperfine parameters A' and B' for Ni(3+) in KMgF(3), CsCaF(3) and RbCaF(3) are theoretically studied from the formulas of these parameters for a 3d(7) ion under octahedral environments in the weak field scheme. The unpaired spin densities for the fluorine 2s, 2p, and 2p, orbitals are quantitatively determined from the molecular orbital and configuration interaction coefficients based on the cluster approach. The calculated results show good agreement with the experimental data, based on only one adjustable parameter (i.e., the proportionality factor p related to the ligand s- and p-orbitals). The superhyperfine parameters for the axial and planar ligands in RbCaF(3):Ni(3+) are satisfactorily interpreted from the different impurity-ligand distances due to the elongation of the ligand octahedron during cubic-to-tetragonal phase transition.

Investigations on the EPR Parameters for the Square Planar Cu2+ Centers in K2PdX4 (X = Cl, Br)

The EPR parameters g factors g||, g⊥ and the hyperfine structure constants A|| and A⊥ for the square planar Cu2+ centers in K2-PdX4 (X = Cl, Br) are theoretically investigated from the perturbation formulas of these parameters for a 3d9 ion under tetragonally elongated octahedra. In these formulas, not only the contributions from the conventional crystal-field (CF) mechanism, but also those from the charge-transfer (CT) mechanism are taken into account. The related molecular orbital coefficients are uniformly determined from the cluster approach, and the tetragonal field parameters Ds and Dt are obtained from the superposition model and the local structures of the systems. Based on only one adjustable parameter, the present results are in reasonable agreement with the observed values. Importance of the charge-transfer contributions is more significant for ligand Br than that for Cl due to the stronger covalency and much larger spin-orbit coupling coefficient of the former.

EPR and optical absorption studies of VO2+ doped l-alanine (C3H7NO2) single crystals

Abstract VO 2+ doped l -alanine (C 3 H 7 NO 2 ) single crystals and powders are examined by electron paramagnetic resonance (EPR) and optical absorption spectroscopy. Three magnetically different sites are resolved from angular variations of l -alanine single crystal EPR spectra. In some specific orientations each VO 2+ line splits into three superhyperfine lines with intensities of 1:2:1 and maximum splitting value of 2.23 mT. The local symmetries of VO 2+ complex sites are nearly axial. The optical absorption spectra show three bands. Spin Hamiltonian parameters are measured and molecular orbital coefficients are calculated by correlating EPR and optical absorption data for the central vanadyl ion.

Theoretical studies of the spin Hamiltonian parameters for the tetragonal Rh2+ centers in MgO and CaO

The spin Hamiltonian parameters (the anisotropic g factors, the hyperfine structure constants and the ligand superhyperfine parameters) for the tetragonal Rh2+ centers in MgO and CaO are theoretically studied from the perturbation formulae of these parameters for a 4d7 ion in tetragonally elongated octahedra. In these formulae, the related molecular orbital coefficients as well as the ligand unpaired spin densities are determined quantitatively from the cluster approach in a uniform way. The above centers are attributed to Rh2+ occupying divalent cation sites in MgO (and CaO), associated with a relative elongation of 0.5% (and 1.4%) along the [001] (or C4) axis due to the Jahn–Teller effect. The calculated spin Hamiltonian parameters based on the Jahn–Teller elongations are in good agreement with the observed values. The local structures of the impurity centers are discussed.

Mixed alkali effect in Cu2+ doped boroarsenate glasses—EPR and optical absorption studies

The local structure around Cu 2+ ion has been examined by means of electron paramagnetic resonance and optical absorption measurements in x K 2 O–(40− x )Na 2 O–50B 2 O 3 –10As 2 O 3 (0⩽ x ⩽40) glasses. The site symmetry around Cu 2+ ions is found to be tetragonally distorted octahedral and the ground state of Cu 2+ is d x 2 - y 2 . The spin-Hamiltonian parameter g || goes through a minima whereas A ∥ goes through a maxima around R K =0.5, showing the mixed alkali effect. The glass exhibited broad absorption band centred 12,239 cm −1 corresponding to the transition 2 B 1g → 2 B 2g . By correlating the EPR and optical absorption data, the molecular orbital coefficients α 2 and β 1 2 are evaluated for the present glass system. The IR studies show that the glass system contains BO 3 and BO 4 units in the disordered manner.

EPR and optical absorption studies on VO 2+ ions in sodium citrate single crystals

X-band electron paramagnetic resonance (EPR) studies of VO 2+ ions in sodium citrate single crystals have been done at room temperature. Detailed EPR analysis indicates the presence of two magnetically inequivalent VO 2+ sites. Both the vanadyl complexes are found to take up substitutional position. The angular variation of the EPR spectra in three planes ba*, bc and ca* are used to determine principal g and A tensors. For the two sites the spin Hamiltonian parameters are, Site I: g x = 1.9680, g y = 2.0053, g z = 1.9124, A x = 79, A y = 76, A z = 185; Site II: g x = 1.9650, g y = 2.0067, g z = 1.9418, A x = 78, A y = 70, A z = 186 × 10 −4 cm −1. The optical absorption study is also carried out at room temperature and absorption bands are assigned to various transitions. The theoretical band positions are obtained using energy expressions and a good agreement is found with the experimental values. By correlating EPR and optical data different molecular orbital coefficients are evaluated and the nature of bonding in the crystal is discussed.

Synthesis, characterization, crystal structure and ab initio studies on 5-ethoxycarbonly-6-methyl-4-phenyl-2-thioxo-1,2,3,4-tetrahydropyrimidine

The title compound, 5-ethoxycarbonly-6-methyl-4-phenyl-2-thioxo-1,2,3,4-tetrahydropyrimidine, has been synthesized and characterized by elemental analysis, IR, UV–vis and X-ray single crystal diffraction. Ab initio calculations have been carried out for the title compound by using B3LYP and HF methods at 6-31G* basis set. The calculated results show that the predicted geometries can reproduce the structural parameters, although the intermolecular interactions have some influences on the molecular geometry in the solid state. Predicted vibrational frequencies by two methods are consistent with each other. They have been assigned and compared with experimental IR spectra. The theoretical electronic absorption spectra have been calculated by both TD-DFT and HF-CIS methods, and the results indicate that only the former can approximately predict the electronic spectra for the title compound. Molecular orbital coefficients analyses suggest that the electronic transitions are mainly assigned to n → π* and π → π* electronic transitions. On the basis of vibrational analyses, the thermodynamic properties of the title compound at different temperatures have been calculated, revealing the correlations between C p , m 0 , S m 0 , H m 0 and temperatures.

One‐Electron‐Reduced and ‐Oxidized Stages of Donor‐Substituted 1,1,4,4‐Tetracyanobuta‐1,3‐dienes of Different Molecular Architectures

A series of monomeric and oligomeric donor-substituted 1,1,4,4-tetracyanobuta-1,3-dienes (TCBDs) with various topologies have been synthesized by means of thermal [2+2] cycloaddition between tetracyanoethylene (TCNE) and donor-substituted alkynes, followed by retro-electrocyclization. One-electron-reduced and -oxidized stages of the donor-substituted TCBDs were generated by chemical methods. The obtained radical anions and radical cations were studied by using electron paramagnetic resonance/electron nuclear double resonance (EPR/ENDOR) spectroscopy, supported by density functional theory (DFT) calculations. The extent of pi-electron delocalization in the paramagnetic species was investigated in terms of the EPR parameters. Despite favorable molecular orbital (MO) coefficients, the EPR results suggest that in radical anions the spin and charge are confined to the electron-withdrawing TCBD moieties on the hyperfine EPR timescale. The observed spin localization is presumably caused by an interplay between the nonplanarity of the studied pi systems, limited pi-electron conjugation, and very likely counterion effects. In radical cations, an analogous spin and charge localization confined to the electron-donating N,N-dialkylaniline moieties was found. In this case, an efficient electron delocalization is disabled by small MO coefficients at the joints between the donor and acceptor portions of the studied TCBDs.

EPR and optical absorption studies on VO 2+ ions in l-asparagine monohydrate single crystals

X-Band electron paramagnetic resonance (EPR) studies of VO 2+ ions in l-asparagine monohydrate single crystals have been done at room temperature. Detailed EPR analysis indicates the presence of two magnetically inequivalent VO 2+ sites. Both the vanadyl complexes are found to take up interstitial position. The angular variation of the EPR spectra in three planes ab, bc and ca are used to determine principal g and A tensors. For the two sites the spin Hamiltonian parameters are, site I: g x = 1.9633, g y = 2.0274, g z = 1.9797, A x = 88, A y = 61, A z = 161 × 10 −4 cm −1; site II: g x = 1.9627, g y = 1.9880, g z = 1.9425, A x = 90, A y = 66, A z = 167 × 10 −4 cm −1. The optical absorption study is also carried out at room temperature and absorption bands are assigned to various transitions. The theoretical band positions are obtained using energy expressions and a good agreement is found with the experimental values. By correlating EPR and optical data different molecular orbital coefficients are evaluated and the nature of bonding in the crystal is discussed.

Interfacial Behavior of Cysteine between Mild Steel and Sulfuric Acid as Corrosion Inhibitor

Interfacial behavior of cysteine (Cys) between mild steel and sulfuric acid solution as a corrosion inhibitor has been studied with electrochemical AC (alternating current) and DC (direct current) techniques at (25.0±0.1) °C. The AC impedance results were evaluated using equivalent circuits in which a constant phase element (CPE) has been replaced with double layer capacitance ( C dl) to represent the frequency distribution of experimental data. Changes in impedance parameters (charge transfer resistance and double layer capacitance) indicated that cysteine molecules acted by accumulating at the metal/solution interface. The fractional coverage of the metal surface (ϑ) was determined using AC impedance results and it was found that the adsorption of cysteine on the mild steel surface followed a Langmuir isotherm model with a standard free energy of adsorption (ΔG 0 ads) of −35.1 kJ·mol −1. To clarify the type of interaction between mild steel surface and cysteine molecules with a molecular orbital approach, electronic properties, such as, the highest occupied molecular orbital (HOMO) energy, the lowest unoccupied molecular orbital (LUMO) energy, and the frontier molecular orbital coefficients have been calculated. Energy gaps for the interaction of mild steel surface and cysteine molecules ( E LUMO Fe− E HOMO Cys and E LUMO Cys− E HOMO Fe) were used to determine whether cysteine molecules acted as electron donors or electron acceptors when they interacted with the mild steel surface. The local reactivity was evaluated through the condensed Fukui indices. Theoretical calculations were carried out using the density functional theory (DFT) at B3LYP level with the 6-311++G(d,p) basis set for all atoms by Gaussian 03W program.

Theoretical investigations of the hyperfine interactions for Co 2+ in the fluoroperovskites

The hyperfine structure constant A of central ion and the superhyperfine parameters A′ and B′ of ligands for Co 2+ in LiBaF 3, KMgF 3, KZnF 3 and CsCdF 3 are theoretically studied from a cluster approach based on the weak field scheme. The unpaired spin densities for the fluorine 2s, 2pσ and 2pπ orbitals are quantitatively calculated from the molecular orbital and mixing interaction coefficients based on the cluster approach. The experimental A, A′ and B′ as well as the g factor for Co 2+ in these fluoroperovskites are satisfactorily explained in a uniform way. The results are discussed.

Molecular orbital propagation to accelerate self-consistent-field convergence in an ab initio molecular dynamics simulation

Based on the idea of molecular orbital (MO) propagation, we propose a novel effective method for predicting initial guesses for the self-consistent-field calculations in direct ab initio molecular dynamics (AIMD) simulations. This method, called LIMO, adopts the Lagrange interpolation (LI) polynomial technique and predicts initial MO coefficients at the next AIMD step by using several previous results. Taking into account the crossing and/or mixing of MOs leads to orbital invariant formulas for the LIMO method. We also propose a simple method for determining the optimal degree of the LI polynomial, which corresponds to the number of previous steps. Numerical tests confirm that this proposed method is both effective and feasible.

Theoretical study of the superhyperfine parameters for Cu2 + in K2PdX4 (X = Cl, Br)

The superhyperfine parameters T(j) (j = x, y, z) for Cu(2+) in the square-planar K(2)PdX(4) (X = Cl, Br) are theoretically studied from the perturbation formulas of these parameters for an octahedral 3d(9) cluster, by considering both the contributions from the crystal-field and charge-transfer mechanisms. The related molecular orbital coefficients are determined from the cluster approach in a uniform way. Based on one adjustable proportional factor rho for the orbital admixture coefficients, the calculated results of present work show reasonable agreement with the observed values.

A pentacene intermediate via formal intramolecular photoredox of a 6,13-pentacenequinone in aqueous solution

The formal intramolecular photoredox reaction (or tandem phototautomerizations) of aromatic ketones in aqueous solution discovered in our laboratory has been extended to a number of acenequinones. In particular, we were interested in whether the photoredox reaction could be applied to 2-(hydroxymethyl)-6,13-pentacenequinone (4), which would result in 2-formyl-6,13-dihydroxypentacene (10) and hence offer a photochemical method for synthesizing a pentacene derivative. Whereas a number of acenequinones displayed a range of photoredox reactivity, photolysis of 4 in acidic aqueous solution (pH < 3) resulted in a clean intramolecular photoredox reaction, via an enol intermediate, to give 10 (green compound; Φ ~ 0.2 at pH 1), which was too reactive for isolation or trapping by standard ArOH trapping agents such as acetic anhydride. These reactions may be viewed as a one-way photochemical intramolecular “redox switch” from quinone to hydroquinone with concurrent oxidation of an attached hydroxymethyl (alcohol) moiety. Without the attached alcohol moiety, these acenequinones are photostable in aqueous solution. The trend in observed relative reactivity may be partially rationalized by examining changes in molecular orbital coefficients observed in the calculated HOMOs and LUMOs (at the AM1 level).Key words: pentacene, acenequinones, photoredox, enol, acid catalysis.

Substituent effects in the intramolecular photoredox reactions of benzophenones in aqueous solution

A number of α-hydroxy-3-benzylbenzophenones 7–11 have been synthesized for the purpose of studying the effect of a phenyl substituent on the intramolecular photoredox reaction of 3-(hydroxymethyl)benzophenone (5) discovered in our laboratory. This latter compound was found to undergo a unimolecular (formal) intramolecular redox reaction upon photolysis in aqueous acid that results in clean reduction of the benzophenone ketone (to secondary alcohol) and oxidation of the alcohol to aldehyde. Three of the phenyl-substituted compounds with simple phenyl (7), p-methylphenyl (8), and p-methoxyphenyl (9) were found to undergo the acid-catalyzed intramolecular photoredox reaction with the observation that 9 also undergoes a residual photoredox reaction that is not acid-mediated and may involve initial photoinduced electron transfer, which is supported by LFP data. The m-methoxyphenyl (10) compound did not undergo the reaction. The trend in observed relative reactivity may be partially rationalized by examining changes in molecular orbital coefficients observed in the calculated HOMOs and LUMOs. The photoredox reaction has also been applied twice in succession in a single compound 11, demonstrating that the photoredox reaction may be useful for sequential photoredox reactions in a multifunctional compound.Key words: intramolecular photoredox, acid catalysis, meta effect, benzophenone photochemistry.

Unravelling the Origin of Intermolecular Interactions Using Absolutely Localized Molecular Orbitals

An energy decomposition analysis (EDA) method is proposed to isolate physically relevant components of the total intermolecular interaction energies such as the contribution from interacting frozen monomer densities, the energy lowering due to polarization of the densities, and the further energy lowering due to charge-transfer effects. This method is conceptually similar to existing EDA methods such as Morokuma analysis but includes several important new features. The first is a fully self-consistent treatment of the energy lowering due to polarization, which is evaluated by a self-consistent field calculation in which the molecular orbital coefficients are constrained to be block-diagonal (absolutely localized) in the interacting molecules to prohibit charge transfer. The second new feature is the ability to separate forward and back-donation in the charge-transfer energy term using a perturbative approximation starting from the optimized block-diagonal reference. The newly proposed EDA method is used to understand the fundamental aspects of intermolecular interactions such as the degree of covalency in the hydrogen bonding in water and the contributions of forward and back-donation in synergic bonding in metal complexes. Additionally, it is demonstrated that this method can be used to identify the factors controlling the interaction of the molecular hydrogen with open metal centers in potential hydrogen storage materials and the interaction of methane with rhenium complexes.

Lagrangian approach to molecular vibrational Raman intensities using time-dependent hybrid density functional theory

The authors propose a new route to vibrational Raman intensities based on analytical derivatives of a fully variational polarizability Lagrangian. The Lagrangian is constructed to recover the negative frequency-dependent polarizability of time-dependent Hartree-Fock or adiabatic (hybrid) density functional theory at its stationary point. By virtue of the variational principle, first-order polarizability derivatives can be computed without using derivative molecular orbital coefficients. As a result, the intensities of all Raman-active modes within the double harmonic approximation are obtained at approximately the same cost as the frequency-dependent polarizability itself. This corresponds to a reduction of the scaling of computational expense by one power of the system size compared to a force constant calculation and to previous implementations. Since the Raman intensity calculation is independent of the harmonic force constant calculation more, computationally demanding density functionals or basis sets may be used to compute the polarizability gradient without much affecting the total time required to compute a Raman spectrum. As illustrated for fullerene C60, the present approach considerably extends the domain of molecular vibrational Raman calculations at the (hybrid) density functional level. The accuracy of absolute and relative Raman intensities of benzene obtained using the PBE0 hybrid functional is assessed by comparison with experiment.

An EPR and optical absorption study of VO 2+ ions in di-ammonium hydrogen citrate [(NH 4) 2C 6H 6O 7] single crystals

Single crystal and powder EPR studies of VO 2+ doped di-ammonium hydrogen citrate [(NH 4) 2C 6H 6O 7] are carried out at room temperature. The angular variation of the EPR spectra show three different VO 2+ complexes that are located in different chemical environment, and each environment contains two magnetically inequivalent VO 2+ sites in distinct orientations occupying substitutional positions in the lattice. Crystalline field around the VO 2+ ion is nearly axial. The optical absorption spectrum shows two bands centred at 16,949 and 12,345 cm −1. Spin Hamiltonian parameters and molecular orbital coefficients are calculated from the EPR and optical data, and results are discussed.

Synthesis, characterization, crystal structure and DFT studies on 1-acetyl-3-(2,4-dichloro-5-fluoro-phenyl)-5-phenyl-pyrazoline

The title compound, 1-acetyl-3-(2,4-dichloro-5-fluoro-phenyl)-5-phenyl-pyrazoline, has been synthesized and characterized by elemental analysis, IR, UV–vis and X-ray single crystal diffraction. Density functional (DFT) calculations have been carried out for the title compound by using B3LYP method at 6-31G* basis set. The calculated results show that the predicted geometry can well reproduce the structural parameters. Predicted vibrational frequencies have been assigned and compared with experimental IR spectra and they are supported each other. The theoretical electronic absorption spectra have been calculated by using TD-DFT method. Molecular orbital coefficients analyses suggest that the above electronic transitions are mainly assigned to n → π* and π → π* electronic transitions. On the basis of vibrational analyses, the thermodynamic properties of the title compound at different temperatures have been calculated, revealing the correlations between C p , m 0 , S m 0 , H m 0 and temperatures.