Stable and efficient algorithms for Xα multiple scattering calculations

Solutions to some practical problems that arise in multiple scattering calculations on large molecules are discussed. (1) Numerical instabilities near the zero of energy can be removed by rescaling the secular matrix. (2) The calculation of structure factors can be made much more efficient by the application of symmetry projection operators. (3) An energy search procedure is described that ensures that no states are inadvertently neglected. Test calculations incorporating these changes illustrate the improved numerical stability, and show decreases in computation time of 30–60%, when compared to previous codes. The procedures suggested here are applicable to both relativistic and nonrelatitistic calculations.     

Atomic Xα calculations based on EHFS(α) = Eexp

The total energies and one-electron energies for first- and second-row atoms were calculated by using the Hartree–Fock and the Hartree–Fock-Slater Hamiltonian with X_α orbitals, u_i(α_exp); α was parametrized from E^HFS (α_exp) = E^exp. The E^HF (α_exp) total energies are always higher than the Hartree–Fock energies for the atoms. The relation of the calculated ionization potential to the experimental ionization potential depends on the α used to define u_i(α), α_exp, or α_HF.     

The α and α parameters for spin polarized Hartree–Fock–Slater calculations

α and α are derived for use in spin polarized Hartree–Fock–Slater programs. They are assumed to depend only on the number of up and down spin electrons in the atom. The calculated eigenvalues show a slight improvement only for carbon, nitrogen, and oxygen.     

Incidence of the relativistic corrections in electronic properties of 5d compounds: MS–Xα Calculations on hexachloroiridates (III and IV) and tungsten trioxide

Multiple-scattering–X_α (MS –X_α) calculations have been performed on IrCl, IrCl, and WO clusters. Relativistic calculations have been performed by the inclusion of the approximation of Wood and Boring in the MS –X_α method, i.e., mass–velocity and Darwin terms are taken into account self-consistently, while the effects of the spin–orbit operator are estimated by first-order perturbation theory. The strong contraction of s and p orbitals can be seen on selected displays of radial wave functions and significant changes in the energy diagrams between the nonrelativistic and the relativistic calculations can be obtained. The comparison with photoemission spectra clearly shows the necessity of including relativistic corrections in the calculations. The calculated spin–orbit parameters are in agreement with experiment for core levels, while a strong dependence of the spin–orbit parameters on the one electron energies is pointed out; this dependance is unconnected from the atomic contributions to the molecular orbitals.     

Generalized Hellmann–Feynman theorem in the Xα method

In the Xα method a generalized Hellmann–Feynman theorem has been derived, and its most important applications are presented. A formula for electronegativity using the definition of electronegativity given by Iczkowski and Margrave and the magnetic nuclear shielding factor and its relation to the electronegativity have been obtained. The virial theorem of the Xα method has also been derived with the aid of the Hellmann–Feynman theorem.     

The MTXαR method. The determination and use of “molecular” α values in molecular multiple scattering Xα calculations

A semiempirical approach is used to fix the α value for use in the extraatomic regions in multiple-scattering (MS Xα) calculations which retain the muffin-tin treatment of the potential. Such a “molecular” α value for an atom is determined by requiring the corresponding homonuclear diatomic molecule to have its minimum at the experimentally determined equilibrium separation; hence they are called α _R. Molecular α _R values are determined for the ground state Li₂ and F₂ molecules and are tested in a calculation of the ground state LiF potential curve. We find a binding energy at the calculated equilibrium separation to be within 1% of the experimental value. The LiF curve based entirely on the ordinary atomic α values is substantially inferior. The present MT Xα _R approach appears to be competitive with others which are intended to improve the muffin-tin version of MS Xα calculations.     

Studies of unoccupied orbitals of BF3 and BCL3 by electron transmission spectroscopy and multiple scattering Xα calculations

Electron transmission spectroscopy (ETS ) and bound-state and continuum multiple-scattering Xα (MS -Xα) calculations are employed to characterize the unoccupied a′₂, a′₁ and e′ orbitals of BF₃ and BCl₃. The a′₂ orbital of BF₃, which produces a peak about 7 eV below threshold in the x-ray absorption spectrum (XAS ), generates a scattering resonance at 3.5 eV in ETS. Similarly, the e′ orbital that lies about 2 eV above threshold in XAS occurs about 13?16 eV above threshold in ETS . Dissociation of F^? from BF₃ due to electron attachment is attributed to a core-excited shape resonance involving an e″ → a″₂ excitation and electron capture into the a′₂ orbital. In BCl₃ all the unoccupied orbitals lie at lower energy than in BF₃ and are closely spaced, making definitive spectral assignments difficult. Both Hartree-Fock (HF ) and MS -Xα methods apparently underestimate the stability of the unoccupied e′ orbital of BCl₃. Vibronic coupling due to out-of-plane bending may significantly affect the spectral intensities. Feshbach resonances are observed for BCl₃ at energies close to those observed in the vacum-UV absorption spectrum. The lower energies of the unoccupied orbitals of BCl₃ are consistent with their stronger bonding to nucleophiles.     

MSW–SCF–Xα studies of some silicon compounds. I. Iminosilicon (HNSi)

MSW –SCF –Xα calculations have been carried out to obtain ionization potentials (via Slater's transition state concept) and charge distributions for HNSi. The results are interpreted and compared with previous ab initio and CNDO /2 studies.     

EPR study of selected gadolinium complexes: β-diketonates and polycarboxylates

The gadolinium chelates with: acetylacetone—Gd(acac)₃ · 3H₂O, thenoyltrifluoroacetone—Gd(TTA)₃ · 2H₂O, benzoylacetone—Gd(BAC)₃ · 2H_2O, ethylenediaminetetraacetate Gd(EDTA) and diglycolate Gd(DGA)₃ have been chosen for EPR study (X band). The EPR spectra of these complexes were obtained in the form of badly separated signals and thus were difficult to interpret. In order to improve the spectra resolution a computer analysis based on Fourier transform was applied. This analysis permitted a considerable increase in resolution of the spectra and revealed the fine structure of Gd³⁺ ion in the condensed phase.     

Three zinc iodide complexes based on phosphane ligands: syntheses,structures, optical properties and TD–DFT calculations

Three zinc iodide complexes based on phosphane ligands, namely diiodidobis(triphenylphosphane‐κP)zinc(II), [ZnI₂(C₁₈H₁₅P₂)₂], ( 1 ), diiodidobis[tris(4‐methylphenyl)phosphane‐κP]zinc(II), [ZnI₂(C₂₁H₂₁P₂)₂], ( 2 ), and [bis(diphenylphosphoryl)methane‐κ²O,O′]zinc(II) tetraiodidozinc(II), [Zn(C₂₅H₂₂O₂P₂)₃][ZnI₄], ( 3 ), have been synthesized and characterized. Single‐crystal X‐ray diffraction revealed that the structures of ( 1 ) and ( 2 ) are both mononuclear four‐coordinated ZnI₂ complexes containing two monodentate phosphane ligands, respectively. Surprisingly, ( 2 ) spontaneously forms an acentric structure, suggesting it might be a potential second‐order NLO material. The crystal structure of complex ( 3 ) is composed of two parts, namely a [Zn(dppmO₂)₃]²⁺ cation [dppmO₂ is bis(diphenylphosphoryl)methane] and a [ZnI₄]²⁻ anion. The UV–Vis absorption spectra, thermal stabilities and photoluminescence spectra of the title complexes have also been studied. Time‐dependent density functional theory (TD–DFT) calculations reveal that the low‐energy UV absorption and the corresponding light emission both result from halide‐ligand charge‐transfer (XLCT) excited states.     

Ab initio Hartree–Fock and multiple-scattering Xα calculation of the g factors for CuF2

Ab initio Hartree–Fock and multiple-scattering wave functions are calculated for linear CuF₂. These wave functions are used to calculate the spin–orbit coupling in a new way where the neglect of two- and many-center terms is avoided and where experimental or calculated spin–orbit coupling constants for the atomic ions are used. The calculated value of g is too small by the MS Xα method and too large by the ab initio method, indicating too much 3d–L interaction in the MS Xα case and too little in the ab initio case.     

γ–α Solid–solid transition of isotactic polypropylene

X-ray diffraction patterns have been taken as a function of time and temperature on a sample of polypropylene held under high pressure (4.14 kbar) for 180 hr. at a temperature of 248°C. and subsequently cooled to room temperature. The molded sample initially crystallizes in the triclinic γ–phase but transforms to the γ–phase at elevated temperatures. The rate of conversion from γ to α is a function of time and temperature and tends to approach a constant value with increasing time. The nature of the thermal changes occurring in the sample was also studied by differential scanning calorimetry. It appears that at low scan speeds, there is a solid–solid transformation from the α-phase to the γ–phase, but at high scan speeds, the γ–phase melts without conversion to the α-phase.     

Computational insight into asymmetric uranyl‐salophen coordinated with α, β‐unsaturated aldehydes and ketones

The study of the catalytic activity and activation mechanism of asymmetric uranyl‐salophens with α, β‐unsaturated aldehydes or α, β‐unsaturated ketones, is a research hotspot. In this paper, the complexes of the uranyl–salophen(U‐S) modified by unilateral benzene, coordinated with cyclohexenone, cyclopentenone and acrolein, were investigated using density functional theory calculations at the level of B3LYP/6‐311G(d, p) basis set. The results showed that the uranyl‐salophen(U‐S) weakened the large π bond between C = C and C = O of the α, β‐unsaturated aldehydes and ketones, making the unsaturated aldehydes and ketones activated. In addition, the molecular‐recognition selectivity of the asymmetrical uranyl‐salophen for cyclohexenone and cyclopentenone were much higher than for acrolein.     

Study on improving the accuracy of the total energy calculated by the DV–Xα method

The effect of the truncation errors resulting from the numerical integration on the accuracy of the calculation results in the DV –Xα method is analyzed and it is shown that evaluating the overlap integrals analytically or adopting orthogonalized basis sets can reduce the errors on the density matrices to the second order. An approach to improve the calculation accuracy of the total energy is proposed based on the error analysis. The calculation results for several molecules are presented to demonstrate the conclusion. © 1994 John Wiley & Sons, Inc.     

Infrared and Raman spectra of (η6-mesitylene)M(CO)3 complexes (MCr,Mo or W): An insight into metal–arene bonding

Infrared and Raman spectra of mesitylene complexes of chromium, molybdenum and tungsten tricarbonyls have been studied. Bands have been assigned and intesities calculated for a number of important modes. The intensities are related to the polarities and polarizabilities of individual bonds within the molecules. Variations of bond properties with change of metal M in the (η⁶-mesitylene)M(CO)₃ complexes have been examined. The results are interpreted in terms of the relative importance of π-donation from the arene to the metal and of δ-backbonding. A molecular orbital scheme is proposed which accounts for the changes observed in the degree of π-and δ-bonding within the group of complexes studied.     

Cobalt(II)–metformin complexes containing α‐diimine/α‐diamine as auxiliary ligand: DNA binding properties

The cobalt(II) complexes [Co(Cl)₂(met)(o‐phen)] ( 1 ), [Co(Cl)₂(en)(met)] ( 2 ) and [Co(Cl)₂(met)(opda)] ( 3 ) (met = metformin, o‐phen = ortho‐phenanthroline, en = ethylenediamine, opda = ortho‐phenylenediamine) were synthesized and characterized using liquid chromatography–mass spectrometry, elemental analysis, molar conductance measurements, thermal analysis, infrared spectroscopy, magnetic moment measurements, electronic spectroscopy and X‐ray diffraction. The metal centre was found to be in an octahedral geometry. UV–visible absorption, fluorescence and viscosity measurements were conducted to assess the interaction of the complexes with calf thymus DNA. The complexes showed absorption hyperchromism in UV–visible spectra with DNA. The binding constants from UV–visible absorption studies were 1.38 × 10⁵, 2.1 × 10⁵ and 3.1 × 10⁵ M^?1 for 1 , 2 and 3 , respectively, and Stern–Volmer quenching constants from fluorescence studies were 0.146, 0.176 and 0.475, respectively. Viscosity measurements revealed that the binding of the complexes with DNA could be surface binding, mainly due to groove binding. The activities of the complexes in DNA cleavage decrease in the order 3 > 2 > 1 . The complexes were docked into DNA topoisomerase II using Discovery Studio 2.1 software.     

An unexpected transformation of benzyl carbamates into α-azidobenzeneacetamides

Successive treatment of benzyl carbamates 5 (Z-protected secondary amines) with lithium diisopropylamide (LDA), diphenyl phosphorochloridate (DPPC1), and NaN 3 yielded the corresponding ã-azidobenzeneacetamides 6 in 45–50% yield (Schemes 2 and 3). In the case of Z-protected diisopropylamine 5b , the phosphate 7 was isolated as a minor product. A reaction mechanism for this unexpected transformation is proposed in Scheme 4, the key step being the ring closure of a benzylic anion to give an oxirane intermediate B. In cursory experiments, it was demonstrated that ã-azidobenzeneacetamides 6 can be used as 2-phenylglycine synthons in the formation of dipeptides by using a phosphine-mediated coupling (Scheme 5).     

Singlet–triplet splittings as obtained from the Xα-scattered wave method: A theoretical analysis

The theoretical determination of singlet–triplet splittings of the excited states of closed-shell molecules is discussed with emphasis on the use of the Xα–scattered wave method. With this method, splittings can be computed in two independent ways. Both will have corrections due to orbital relaxation effects. The singlet–triplet splittings obtained with the Xα–scattered wave method for several large organic molecules are reviewed. It is seen that the results using the two splitting formulas differ by a large amount; in fact, they differ by the magnitude of the computed splitting. We provide a criterion for choosing the results obtained with one method over the other by showing that they both give upper bounds to the best result obtainable within the framework of the model. However, because of the large differences between the two methods, the quantitative value of the splitting should be viewed with caution.     

Thermal properties and morphology of α-methylstyrene-butadiene-α-methylstyrene triblock copolymer

Poly(α-methylstyrene-butadiene-α-methylstyrene) (mSBmS) was synthesized by two stages living anionic polymerization. Sodium naphthalene was used as initiator and HMPT as promoter to accelerate cross-over reactions. The microstructure and composition of mSBmS were identified by infrared and nuclear magnetic resonance spectroscopes. The domain size was roughly calculated from TEM observation. It was observed that the morphology changed with the composition. The mSBmS exhibited two T_g^s, ?4 and 172°C, that associated with polybutadiene and poly-α-methylstyrene, respectively. Comparing stress relaxation behaviors of mSBmS and styrene-butadienestyrene (SBS) at various temperatures, mSBmS showed a better thermal stability and degradation resistance than SBS. From the thermal gravimetric analysis, at 200°C, mSBmS gave a weight loss less than 1%, which provided a further evidence of better thermal stability of this material than of SBS.     

Stereochemical analysis of the 3α‐ and 3β‐hydroxy metabolites of tibolone through NMR and quantum‐chemical investigations. An experimental test of GIAO calculations

The configuration at C‐3 of the 3α‐ and 3β‐hydroxy metabolites of tibolone was studied by extensive application of one‐ and two‐dimensional ¹H and ¹³C NMR spectroscopy combined with molecular modeling performed at the B3LYP/6–31G(d) level. Using HF and DFT GIAO methods, shielding tensors of the two molecules were computed; comparison of the calculated NMR chemical shifts with the experimental values revealed that the density functional methods produced the best results for assigning proton and carbon resonances. Although steroids are relatively large molecules, the present approach appears accurate enough to allow the determination of relative configurations by using calculated ¹³C resonances; the chemical shift of pairs of geminal α/β hydrogen atoms can also be established by using calculated ¹H resonances. Copyright © 2002 John Wiley & Sons, Ltd.