An efficient method for the calculation of generalized overlap amplitudes for core photoelectron shake-up spectra

Using a Gelfand-Tsetlin N-electron basis and a graphical unitary group approach, an efficient method is derived for the calculation of generalized overlap amplitudes of the formX⁽ⁿ⁾_p = < Ψ⁽ⁿ⁾)(N-1) ¦ψa_p¦ψ⁽⁰⁾ (N) >, whereψ⁽ⁿ⁾(N-1) and ψ⁽⁰⁾(N) denote complete active space wavefunctions and p is a core orbital index. Using this method the computational effort to obtain Xⁿ_p is negligible compared to the wavefunction optimization.     

Dissociation of symmetry-adapted local modes studied by FFT-propagation of bond-adapted wavefunctions

The time evolutions ψ₊(t) and ψ_?(t) of dihydrides' near degenerate local modes with + and ? symmetry may be evaluated by Fast Fourier Transform (FFT) propagation of a single bond-adapted wavefunction ψ _a = 2^?1/2 (ψ₊?ψ_?). This economic technique is demonstrated by model simulations of fast dissociations of highly excited local stretches of H₂O.     

Intramolecular dynamics: time evolution of superposition states in the regular and irregular spectrum

The time evolution of wavefunctions ψ(t) is compared in two systems, one with a regular energy spectrum and one with an irregular spectrum. The behavior of P(t) = {|[ψ(O)|ψ(y]}|² is found to be the same in both systems, P(t) decay is insensitive to the coupling between the degrees of freedom.     

Open-Shell coupled-cluster method: Variational and nonvariational calculation of ionization potentials

A hermitian, variational open-shell coupled-cluster method is described and applied to the calculation of H₂O and N₂ ionization potentials in the _T ≈ T₂ approximation. A nonvariational calculation is also carried out, with the inclusion of T₁ and T₃ in addition to T₂. Both methods give fair agreement with experiment when only T₂ is taken into account. T₃, which is included at present in the nonvariational scheme only, has a considerable effect on the results and gives good agreement with experiment.     

The wavefunction of non-stationary states in terms of complex coordinates and a related variational principle

The wavefunction of a decaying state is expressed in terms of complex coordinates as ψ(p) = a(θ)ψ _o(p) + b(θ)x(p), where the square integrable θ_o(p) and x(p) contain the localized and asymptotic information respectively. From Fano theory, we derive the relationship of a(?) and b(?) to the energy and width of the resonance state. This forms the basis for a new variatfonal principle for optimization of trial functions in the complex coordinate—energy plane.     

The role of radicals and clusters in thermal plasma flash evaporation processing

The prominent features of plasma flash evaporation may be caused by cluster deposition under high net flux of radicals. In order to clarify such features quantitatively, the atomic oxygen flux (Γ _o ) and cluster size (d) in 200 Torr RF thermal Ar-O₂ plasma were measured on the substrate. It was found that Γ _o higher than 10¹⁹ atoms/cm²·s can be easily acheived in this processing and this value corresponds to frozen atomic oxygen fraction 7 %. The cluster size of YBCO was estimated to be about 0.3 to 10 nm. 0.8 nm cluster deposition under Γ _o higher than 6 × 10¹⁸ atoms/cm²·s made it possible to deposit fine epitaxial YBCO films with Tc = 90K on SrTiO₃ (100) with extremely high deposition rate around 2.2 μm/min.     

The unattainability of a unified E.M.F. series for molten salts the relation between the temperature coefficient of isothermal cells and the thermoelectric coefficients of thermocells

It is shown that the e.m.f. of a cell (T₁) A¦AX¦BX¦B (T₂) can not be split unambiguously into a combination of an isothermal cell A¦AX¦BX¦B either at T₁ or at T₂ and a thermocell either B¦BX¦B or A¦BX¦A between T₂ and T₁. The difference Δ in e.m.f. of both possible combinations is equal to FΔ/(T₂ - T₁) = ^*S(X^? in AX) - ^*S(X^? in BX).In examples given for molten silver and cuprous halides this difference in transported entropies is 1–2 cal mol^?1 K^?1 or Δ equal to 17.5–35 mV for T₂ - T₁ = 400 K. It is impossible to obtain unambiguously a unified e.m.f. series. The same qualitative conclusion is reached on the basis of the second law of thermodynamics from a discussion of an irreversible cyclic process involving the four cells mentioned.     

Utilisation du calcul des modes normaux de vibration pour la détermination de la conformation de la glycylglycine et de la triglycine en solution aqueuse

The valence force field of α-glycylglycine was applied to different G matrices calculated for several values of the dihedral angles ψ₁, φ₂ and ψ₂. The relations v_i = ?(ψ_i,φ_i) obtained for different isotopic species were compared with the experimental frequencies of the aqueous solution thereby giving the absolute value of the angles. A complementary study by means of depolarised light scattering led to the determination of their sign. These relations were then used in the conformational analysis of triglycine in aqueous solution. The conformation of glycylglycine differs strongly in aqueous solution from that in the solid state, especially concerning the relative positions of the peptide and carboxylic group (φ₂ = ?70° and ?160°). For triglycine, we showed the existence of a chelated ring “C₇” similar to that observed for the acetylated dipeptides.     

Marron-weare variational computation of energy differences for motions of C2H6, B2H6, CH3CH inf2 sup+ , and CH3BH2

The passage of D_3dC₂H₆ and B2H6 toward a D₂ h bridged structure, and the motion of a methyl proton maintaining C symmetry in C₂H _inf5 ^sup+ and CH₃BH₂ are described by integral Hellmann-Feynman computations in a Frost floating spherical Gaussian basis. Marron and Weare's variational corrections to the integral Hellmann-Feynman formula forAE between statesA andB are evaluated with variational functions of the form η(ψ_A/S_AB-ψ_B)) used to refine the stateB. An analogous function ξ(ψ_B/S_AB-ψ_A) refines state A. Both η and ξ are chosen variationally to minimize Marron and Weare's functional. No obvious advantage of the variational method became apparent in this simple application.     

Open circuit potential measurements with Ti/TiO2 electrodes

The open circuit potential (OCP) vs pH response of Ti/TiO₂ electrodes prepared by thermal and electrochemical oxidation of metallic titanium was measured in KNO₃ aqueous solutions in order to establish whether the slopes of the OCP-pH curves can be used as a measure of the variation of surface potential (ψ_o) of TiO₂ with the pH of the aqueous solution. For comparison purposes, ψ_o—pH slopes were also evaluated from surface charge-pH data obtained by acid-base potentiometric titrations of TiO₂ dispersions.Ti/TiO₂ electrodes showed a linear OCP-pH response in the range of ph 5–10 with slopes of −0.039 ± 0.005 V ph⁻¹. The OCP-pH dependence of Ti/TiO₂ electrodes was lower than that predicted thermodynamically. According to the triple-layer model, used to describe the oxide/aqueous solution interface, the OCP-pH slopes obtained for Ti/TiO₂ electrodes cannot be identified with the variation of ψ_o with the pH. Calculations with this model indicated that neither the single nor the double extrapolation methods used to evaluate the intrinsic ionization constant of oxide surface sites render realistic values of these parameters for the TiO₂ surface.The analysis of surface charge—pH data and the use of the triple-layer model to predict experimental values indicated that the ψ_o—pH slopes of TiO₂ surfaces must be greater (in absolute magnitude) than 0.041 V pH⁻¹.     

b1Σ+ Emissions from group V–VII diatomic molecules. b 0+ → X1 0+, X2 1 emissions of AsI and SbI

Chemiluminescence from the b 0⁺ → X₁ 0⁺ band system of AsI and of the b 0⁺ → X₁ 0⁺, X₂ 1 systems of SbI in the near-infrared spectral region has been observed in a discharge flow system. Analysis of the spectra led to the spectroscopic constants (in cm^?1) of AsI: ω_e(X₁, X₂) = 257 ± 2, ω_ex_e(X₁, X₂) = 0.82 ± 0.2, T_e(b 0⁺) = 11738 ± 5, ω_e(b 0⁺) = 271 ± 2, ω_ex_e(b 0⁺) = 0.66 ± 0.2, and of SbI: T_e(X₂ 1) = 965 ± 10, ω_e(X₁, X₂) = 206 ± 6, T_e(b 0⁺) = 12328 ± 10, ω_e(b 0⁺) = 211 ± 6. The intensity ratio of the two sub-systems b 0⁺ → X₂ 1 and b 0⁺→ X₁ 0⁺ was found to be ≈0.013 in the case of SbI and ? 0.01 for AsI.     

Conformational structure of peptides containing dehydroalanine: Formation of β‐bend ribbon structure

α,β‐Unsaturated amino acids (dehydroamino acids) have been found in naturally occurring antibiotics of microbial origin and in some proteins. Due to the presence of the C_αC_β double bond, the dehydroamino acids influence the main‐chain and the side‐chain conformations. The lowest‐energy conformational state of the model tripeptides, Ac–X–ΔAla–NHMe, (X=Ala, Val, Leu, Abu, or Phe) corresponds to ϕ₁=−30°, ψ₁=120° and ϕ₂=ψ₂=30°. This structure is stabilized by the hydrogen bond between CO of the acetyl group and the NH of the amide group, resulting in the formation of a 10‐membered ring. In the model heptapeptide containing ΔAla at alternate position with Ala, Abu, and Leu, the lowest‐energy conformation corresponds to ϕ=−30° and ψ=120° for all the Ala, Abu, and Leu residues and ϕ=ψ=30° for all ΔAla residues. A graphical view of the molecule in this conformation reveals the formation of three hydrogen bonds involving the CO moiety of the ith residue and the NH moiety of the i+3th residue, resulting in a 10‐membered ring formation. In this structure, only alternate peptide bonds are involved in the intramolecular hydrogen‐bond formation unlike the helices and it has been named the β‐bend ribbon structure. The helical structures were predicted to be the most stable structures in the heptapeptide Ac–(Aib–ΔAla)₃–NHMe with ϕ=±30°, ψ=±60° for Aib residues and ϕ=ψ=±30° for ΔAla residues. The computational results reveal that the ΔAla residue does not induce an inverse γ‐turn in the preceding residue. It is the competitive interaction of small solvent molecules with the hydrogen‐bonding sites of the peptide which gives rise to the formation of an inverse γ‐turn (ϕ₁=−54°, ψ₁=82°; ϕ₂=44°, ψ₂=3°) in the preceding residue to ΔAla. The computational studies for the positional preference of ΔAla in the peptide containing one ΔAla and nine Ala residues reveals the formation of a 3₁₀ helical structure in all the cases with the terminal preferences for ΔAla, consistent with the position of ΔAla in the natural antibiotics. The extended structures is found to be the most stable for poly‐ΔAla. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 15–23, 1999     

Microwave spectrum of the s-trans form of 3-pyridinecarbaldehyde

The microwave spectra of the ground state and one excited state of the ON s-trans form of 3-pyridinecarbaldehyde have been measured and assigned. The ground state rotational constants and dipole moment components are: A = 5417.8, B = 1583.289, C = 1225.389 (in MHz) and ¦μ_a¦ = 1.35, ¦μ_b¦ = 0.5 (in debye). The excited state most probably belongs to the C₃C torsion, for which the vibrational frequency is estimated to be 135 ± 30 cm^?1.     

Zeeman experiments on the 3Eu α 1A1g transition of platinum porphein in an n-alkane single crystal at 4.2

We report absorption spectra from the ground state to the photoexcited triplet state of platinum porphin (PtP) in single crystals of n-octane (C₈) and n-decane (C₁₀) at 4.2 K, with and without a magnetic field. For PtP in C₁₀ the same transition was studied in emission. From the experiments, values are derived of the spin-orbit coupling parameter Z, the crystal field splitting δ and the orbital angular momentum A for PtP in the two hosts: Z = 76 ± 2 cm^?1 (C₈, C₁₀), δ = 71 ± 1 cm^?1 (C₈), 55 ± 1 cm^?1 (C₁₀) and A = 1.6 ± 0.1 (C₈, C₁₀). For the ratio of the in-plane and the z-polarized electric dipole transition moments we obtain ¦Mx,y¦/¦Mz¦=76± 0.3 (C₈).     

Stereochemical leakage mechanisms for tricarbonyl(dienyl)iron cations

ψ-Endo to ψ-exo leakage during solvolysis of a ψ-endo-dienol—Fe(CO)₃ dinitrobenzoate ester does not proceed via a syn, syn-cis-dienyl—Fe(CO)₃ cation. The most probable leakage mechanism involves non-stereospecific ionization of the dinitrobenzoate ester. syn,syn-cis-Dienyl—Fe(CO)₃ cations are formed from ψ-exo-dienol—Fe(CO)₃ complex during chromatography on grade I neutral alumina.     

The molecular structure of gaseous tetrachloro-p-benzoquinone and tetrachloro-o-benzoquinone by electron diffraction

The structures of tetrachloro-p-benzoquinone and tetrachloro-o-benzoquinone (p- and o-chloranil) have been investigated by gas electron diffraction. The ring distances are slightly larger and the carbonyl bonds slightly smaller than in the corresponding unsubstituted quinones. The molecules are planar to within experimental error, but small deviations from planarity such as those found for the para compound in the crystal are completely compatible with the data. Values for the geometrical parameters (r_a distances and bond angles) and for some of the more important amplitudes (l) with parenthesized uncertainties of 2σ including estimated systematic error and correlation effects are as follows. Tetrachloro-p-benzoquinone: D_2h symmetry (assumed); r(CO) = 1.216 Å(4), r(CC) = 1.353 Å(6), r(C-C) = 1.492 Å(3), r(C-Cl) = 1.701 Å(3), ∠C-C-C = 117.1° (7), ∠CC-C1 = 122.7° (2), l(CO)= 0.037 Å(5), l(CC) = l(C-C) - 0.008 Å(assumed) = 0.049 Å(7), and l(C-Cl) = 0.054 Å(3). Tetrachloro-o-benzoquinone: C_2v symmetry (assumed); r(CO) = 1.205 Å(5), r(CC) = 1.354 Å(9), r(C_cl-C_cl) = 1.478 Å(28), r(Co-C_cl) = 1.483 Å(24), r(C_o-C_o) = 1.526 Å(2), r(C-Cl)= 1.705 Å(3), <C_o-CO = 121.0° (22), ∠C-C-C = 117.2° (9), ∠C_co, ClC-Cl = 118.9° (22), ∠C_ccl, ClC-Cl = 122.2°(12), l(CO) = 0.039 Å(5), and l(C_cl-C_cl) = l(C_o-C_cl) = l( Co-Co) = l(CC) + 0.060 Å(equalities assumed) = 0.055 Å(9). Vibrational'shortenings (shrinkages) of a few of the long non-bond distances have also been measured.     

Electronic structures and stabilities of sodium clusters: jellium-sphere dimer calculation

Bonding properties of sodium-cluster dimers, (X ₄)₂ and (X ₈)₂, whereX _n is a jellium sphere corresponding to a cluster ofn atoms, were investigated by the linear-combination-of-jellium-orbitals method with local-spin-density-functional approximation. The stability ofn=8 clusters, observed in the experiment, is discussed in relation to the binding properties of dimers. We have found that (1) the (X ₄)₂ bonding has a covalent character, which makes theX ₈ formation favorable, and (2)X ₈ has an inert property because the force between jellium spheres in (X ₈)₂ is due to a weak dispersion force.     

Thermodynamics of the URuC system

Thermodynamic measurements by the electromotive force method were made on the binary intermetallic phases URu₃ and U₃Ru₅ and on the ternary carbides URu₃C_0.7 and U₂RuC₂ of the URu and the URuC systems between 950 and 1200 K using galvanic cells with CaF₂ single crystal electrolytes: U, UF₃¦CaF₂¦UF₃, URu₃, Ru; U, UF₃¦CaF₂¦UF₃, U₃Ru₅, URu₃; Ru, URu₃, UF₃¦CaF₂¦UF₃, URu₃C_0.7, Ru, C; U, UF₃¦CaF₂¦UF₃, URu₃C_0.7, U₂RuC₂, C. The Gibbs energies of formation of URu₃, U₃Ru₅, URu₃C_0.7 and U₂RuC₂ were evaluated from the measured electromotive force which give ^fΔG^o〈URu₃〉 = −199 100 + 35.9 T J mol^−1fΔG^o〈U₃Ru₅〉 = −398 600 + 43.6 T J mol^−1fΔG^o〈URu₃C_0.7〉 = −192 600 + 2.5 T J mol^−1fΔG^o〈U₂RuC₂〉 = −380 200 + 52.5 T J mol⁻¹ The implications of these thermodynamic data for the behaviour of the fission product ruthenium in irradiated carbide fuels are discussed.     

A fast CI method for closed shells

A variational method for closed shells derived from MBPT is proposed. The method consists in the diagonalization of the hamiltonian in the subspace generated by the HF ground state |φ_HF) and f_i(H_o) V_res|φ_HF) (i = 1,2,… m) where H_o is the HF hamiltonian, V_res is the residual potential and the f_iti are arbitrary functions. Test calculations performed on H₂O give 97% of the double excitations CI limit with very short computer time.     

Spatial correlation of atomic electrons: He

For any two-electron wavefunction whose angular dependence is given in terms of the spherical harmonics of the individual electrons and/or o₁₂, where o₁₂ is the interelectronic angle. a transformation is generated which reduces |ψ(r₁, r₂, o₂, o₁, o₁₂ )|² to |ψ(r₁, r₂, o₁₂)|². Geometric aspects of electron correlation are analyzed in terms of this resulting three-coordinate function, with specific application to a number of wave functions for doubly-excited helium. Angular correlation has been studied by integrating |ψ(r₁, r₂, o₁₂)|² over its radial dependence to yield p(o₁₂), the probability density function for the interelectronic angle. Trends of p(o₁₂) for doubly-excited states of the helium atom are related to a number of quantities including energies and autoionization widths. These trends can be rationalized in terms of a simple classical model. The full spatial correlation involving |ψ(r₁, r₂, o₁₂)|² is explored by the use of three-dimensional graphs for some of these states.