Relative intensities in x-ray photoelectron spectra

An experimental determination of the relative intensities of X-ray photoelectron lines corresponding to the inner levels of elements with Z ? 20, and calculations of the total photo-ionization cross-sections for all shells of these elements with the Hartree—Fock—Slater potential are reported. The experimental and theoretical values agree well for the 1s levels while marked discrepancies are revealed for the 2p levels. The theoretical values of the cross sections for the atomic valence levels are used to calculate the relative intensities of molecular levels in CF₄, BF₄^?, BeF₄^2?, LiF, NO₃^?, CO₃^2?, CO, N₂, CO₂, H₂O and C₄H₅N. The results of the calculations agree satisfactorily with experiment.     

Relative intensities in x-ray photoelectron spectra. Part VI. The spectra of He(I), He(II), Y Mζ and Zr Mζ

The 2s- and 2p-electron photoionization cross-sections at photon energies up to 190 eV have been calculated, using the RPAE method for averaged configurations of the C, N, O and Ne atoms. The RPAE method ensures a more accurate relation between the cross-sections, 2s/2p, than that obtained using the Hartree—Fock method. Within the framework of the Gelius—Siegbahn model, but with the use of theoretical atomic cross-sections, we have calculated the photoionization cross-sections for He(I), He(II), Y Mζ, Zr Mζ for CH₄, C₂H₆, C₃H₈, C₂H₄, C₂H₂, NH₃, H₂O, CN^?, N₂, CO, CO₂, N₂O and NO₂^? molecules. For CO, N₂, CO₂, N₂O and H₂O molecules, a comparison is made between the theoretical and experimental cross-sections for hν < 60 eV. The calculated absolute and relative values of the molecular-orbital cross-sections are in reasonable agreement with experiment, especially at hν ? 40 eV. The calculations correctly reproduce the change in intensities under the transition He(I) → He(II). We have shown that our calculations have a significant advantage over those performed using the PW and OPW approximations. It is shown for NO, N₂, CO, H₂O, CH₄, NH₃ and N₂O molecules that the total photoionization cross-section calculated taking into account the real structure of the molecular orbitals is in better agreement with the experimental photoabsorption cross-section than is the sum of the cross-sections for the atoms in a molecule.     

Relative intensities in x-ray photoelectron spectra. Part II

Experimental data on the relative intensities of X-ray photoelectron lines of some elements with 22 ? Z ? 56, and the calculations for the photoionization cross-sections for inner levels of some elements with 21 ? Z ? 63 are reported. The relationship between photoionization relative cross-sections and line relative intensities is examined. Theoretical values of the photoionization cross-sections were used in the calculations of relative intensities of molecular valence levels for AO₄^x? (A = Cl, S, P, Se, As), AF₆^x? (A = S, Si, Al), COS, CS₂ and H₂S.     

The concentration dependence of the proton chemical shift and the deuterium quadrupole coupling parameter for binary solutions of ethanol

Concentration dependent experimental measurements of the ethanol hydroxyl proton chemical shift σ_H for binary solutions were carried out. The solvents used were carbon tetrachloride (CCl₄), benzene, chloroform, acetonitrile, acetone and dimethylsulphoxide (DMSO). The chemical shift values range from 0.69 ppm (relative to TMS) for dilute ethanol (extrapolated to infinite dilution) in CCl₄ to 5.34 ppm for neat liquid ethanol. Ab initio calculations of the ethanol-solvent hydrogen bond energies show a correlation with the values for the chemical shift. The hydrogen bond energies for ethanol-solvent dimers range from 0.63 kcal mol^?1 for ethanol-CCl₄ to 9.34 kcal mol^?1 for ethanol-DMSO. Theoretical calculations show a linear correlation between the deuterium quadrupole coupling parameter XD ^ar d the isotropic proton chemical shift σ_H: X_D(kHz) = 291.48 ? 14.96 σ_H, where σ_H is the proton chemical shift in ppm relative to TMS (R ² = 0.99). Using the concentration dependent chemical shift data and this equation, X_D ia observed to range from 280 kHz for very dilute concentrations in CCl₄, where the primary species is ethanol monomer, to 210 kHz for the neat liquid that is comprised primarily of cyclic pentamers.     

Electric field dissociation of H+ 2: close-coupled scattering calculations

Close-coupling scattering calculations have been carried out to predict the magnitude of electric fields required to dissociate specific vibration—rotation levels in H⁺ ₂. Results for electric fields up to 40 kV cm^?1, which may dissociate levels up to 25 cm^?1 below the dissociation limit, are presented. The results are used to simulate spectra which are compared with experimental spectra. A method for extracting the eigenphase sum from a coupled channel scattering calculation is described in the appendix and used in the calculations.     

Repulsion parameters of ions and radicals—Application to perovskite structures

The compressible ion approach to repulsion which has been shown to work well for the alkali halides (J. Phys. Chem. Solids37, 395 (1976) ; Curr. Sci. 46, 359 (1977)) has been extended to other cubic ionic crystals. Repulsion parameters have been refined for a number of ions and radicals viz., Cu⁺, Ag⁺, Tl⁺, Mg²⁺, Ca²⁺, Sr²⁺, Ba²⁺, Zn²⁺, Cd²⁺, Hg²⁺, Mn²⁺, Fe²⁺, Co²⁺, Ni²⁺, Sm²⁺, Eu²⁺, Yb²⁺, Pb²⁺, H^?, O^2?, S^2?, Se^2?, Te^2?, NH₄⁺, SH^?, SeH^?, BrO₃^?, ClO₃^?, ClO₄^?, CN^?, NH₂^?, NO₃^?, BH₄^?, BF₄^?, SO₄^2?, NH^2?. Using these parameters, calculations have been made on the lattice spacings and compressibilities of a number of perovskite-like crystals of the form A⁺B²⁺C₃^?. The predicted values agree well with experiment. In the case of four crystals viz., LiBaF₃, LiBaH₃, LiEuH₃ and LiSrH₃, there were large discrepancies between the calculated and observed lattice spacings. When these crystals were assumed to be of the inverse perovskite structure, calculations showed good agreement with the experimental data.     

Accurate ab initio anharmonic force field and heat of formation for silane

From large basis set coupled cluster calculations and a minor empirical adjustment, an anharmonic force field for silane has been derived that is consistently of spectroscopic quality (±1 cm^?1 on vibrational fundamentals) for all isotopomers of silane studied. Inner-shell polarization functions have an appreciable effect on computed properties and even on anharmonic corrections. From large basis set coupled cluster calculations and extrapolations to the infinite-basis set limit, we obtain TAE₀ = 303.80 ± 0.18 kcal mol^?1, which includes an anharmonic zero-point energy (19.59 kcal mol^?1), inner-shell correlation (—0.36 kcal mol^?1), scalar relativistic corrections (— 0.70 kcal mol^?1) and atomic spin-orbit corrections (—0.43 kcal mol^?1). In combination with the recently revised ΔH ^o _{f, o}[Si(g)], we obtain ΔH ^o _f.o[SiH₄(g)] = 9.9 ± 0.4 kcal mol^?1 in between the two established experimental values.     

Variational calculation of low-lying and excited vibrational levels of the water molecule

The variational method of calculating vibrational energy levels for triatomic molecules has been extended to determine the lowest 22 levels for H₂O, using an analytic form for the potential surface developed by Sorbie and Murrell. In addition, complete ab initio calculations of the fundamental frequencies for H₂O have been carried out using extensive configuration interaction forms for the potential. They are predicted to be 3720, 1629, and 3807 cm^?1, to be compared with experimental values of 3656, 1597, and 3754 cm^?1. Also discussed is how the variational method may be extended to allow the calculation of vibrational energy levels for larger molecules.     

Vibrationally inelastic scattering of H∼ ions from H2, N2, O2 and CO2

State-resolved measurements are presented for vibrational excitation of H₂, N₂, O₂ and CO₂ by H^? impact in the collision energy rangeE _cm=20–180 eV and for scattering in the forward direction (0±0.5°). The data obtained from the measurements are the relative intensities and differential cross sections for vibrational excitation up toν′=4, the transition probabilitiesP _0→ν′ and the vibrational energy transferΔE _vib. For the systems H^?-H₂, N₂, O₂ the vibrational inelasticity increases in the order H₂-N₂-O₂. The mechanism for vibrational excitation in these systems is due to transient charge transfer from the H^? ion into antibonding orbitals of the target molecule which provides a bond stretching force during the collision. For H₂ and N₂, the results are compared with corresponding measurements for H⁺ scattering where the interaction mechanism is quite different. In the case of CO₂, vibrational excitation in forward scattering is caused primarily by the long-range dipole interaction. The spectra are very similar for H^?-CO₂ and H⁺-CO₂. Finer details are attributed to the influence of transient charge transfer and valence interactions.     

Twenty-parameter eigenfunctions and energy values of the 23 S States of He and He-like Ions

Twenty-parameter calculations of the energies and wave functions of the first excited states 2³ S of He, Li⁺, Be⁺⁺, B⁺⁺⁺, O⁶⁺, Ne⁸⁺, Mg¹⁰⁺, have been carried out using Hylleraas' method. The energy values have been corrected for mass polarization. The coefficients of the best wave functions are listed. Similar calculations for the 2³ S state of the H^? ion yield an energy value which cannot be distinguished from the energy of a free H atom. For He and Li⁺, in addition, forty-parameter calculations have been carried out. The results compare well with the recent calculations of Pekeris using a somewhat different method. Even after the inclusion of the relativistic correction, the theoretical energy values deviate slightly from the observed. The differences, ?0·10±0·05 cm^?1 for He and ?1·07±0·10 cm^?1 for Li⁺, represent observed values of the Lamb shifts in the 2³ S states. These values agree within their uncertainties with the values predicted from quantum electrodynamics.     

Intensity studies in Raman effect

The dependence of the relative intensities of Raman lines, having different polarisation characters, on the mode of excitation has been studied using unpolarised, horizontally and vertically polarised incident light. Standard intensities have been obtained in the cases of CCl₄, CHCl₃, C₆H₆, C₂Cl₄, C₂H₂Cl₂, C₂H₄Cl₂, C₆H₅Cl, C₆H₅CH₃ and C₆H₅CH₂OH with the intensity of the 458 cm^?1 line of CCl₄ as standard and from these, the values ofα′, the derived polarisability, have been obtained in the case of total symmetric lines characteristic of particular bonds and certain conclusions regarding the intensity variations of corresponding lines in the different liquids have been arrived at. Values of derived anisotropy have also been obtained in the case of the depolarised lines relative to that of 313 cm^?1 line in CCl₄.     

Shift of the centers of H<Subscript>2</Subscript>O absorption lines in the region of 1.06 μm

The shift coefficients for the lines of the ν₁ + ν₂ + ν₃ and ν₂ + 2ν₃ bands of H₂O in the region from 9403 to 9413 cm^?1 are measured and calculated. The measurements are performed using an intracavity laser spectrometer based on a neodymium laser with a determination error of the line center of 0.003–0.004 cm^?1. The Ar, Kr, and Xe noble gases, as well as nitrogen, oxygen, and hydrogen were used as buffer gases. The coefficients of shifts in eight H₂O absorption lines induced by oxygen, nitrogen, and atmospheric air pressures fall into the region from ?0.004 to ?0.069 cm^?1/bar. The calculations are performed by a semiempirical method using variational wave functions, which, in contrast to other studies, correctly takes into account intramolecular interactions. The calculated values agree satisfactorily with experimental data.     

Additivity and non-additivity of dissociation energies in intermolecular interactions. Theoretical studies on (H2)n,n = 2-8, (CO2)n,n = 2-6 and (HF)n,n = 2-8

CCSD(T) and MP2 results using the aug-cc-pV5Z basis set are reported for chain, cyclic and other structures of the clusters (H₂)_n, n?=?2-8, (CO₂)_n, n?=?2-6 and (HF)_n, n?=?2-8. In chain-like structures of (H₂)_n and (CO₂)_n, with the bonding type of the dimer maintained, the dissociation energy D_e of the dimer doubles for the trimer, triples for the tetramer, and so on. Due to these systems being dominated by short-range forces, interactions are essentially restricted to neighbouring monomers. For other types of (H₂)_n and (CO₂)_n structures, the multipliers relative to the dimerisation energy can be much higher. Dissociation energies for the hexamers in S₆ symmetry of both H₂ (379?cm^?1) and CO₂ (4925?cm^?1) are over ten times the respective dimerisation energies. For the chain-like trimer of HF, however, D_e is in excess of double the dimer value. Mainly due to longer-range dipolar forces, the interactions reach beyond the neighbouring monomers. The interaction energy between HF monomers in chains follows an approximate R^?2 (R being the F–F distance) relationship, The calculated dissociation energies of the HF octamer are 15,985?cm^?1 (factor of 10.4) for the chain, and 21,003?cm^?1 (factor of 13.7) for the C_6h cyclic structure.     

Condensation Product of 1-Naphthaldehyde and 3-Aminophenol: Fluorescent “on” Probe for Ce3+and “off” Probe for Dichromate (Cr2O72−)

A new probe (Z)-3-((naphthalen-1-ylmethylene)amino)phenol has been synthesized by condensation reaction between 1-naphthaldehyde and 3-aminophenol for the fluorescent sensing of Ce³⁺ by “on” mode and dichromate (Cr₂O₇^2?) by “off” mode. Metal ions—Ag⁺, Al³⁺, As³⁺, Ba²⁺, Ca²⁺, Cd²⁺, Ce⁴⁺, Co²⁺, Cr³⁺, Cr⁶⁺, Cu²⁺, Fe²⁺, Fe³⁺, Hg²⁺, K⁺, La⁺, Li⁺, Mg²⁺, Mn²⁺, Na⁺, Ni²⁺, Pb²⁺, Zn²⁺and anions Br^?, C₂O₄^2?, CH₃COO^?, Cl^?, CO₃^2?, F^?, H₂PO₄^?, HCO₃^?, HF₂^?, HPO₄^2?, I^?, MnO₄^?, NO₃^?, OH^?, S^2?, S₂O₃^2?, SCN^?, SO₄^2? do not interfere. The limit of detection (LOD) for sensing Ce³⁺ and Cr₂O₇^2? ions are 1.286?×?10^–7 M and 6.425?×?10^–6 M, respectively.

     

Semiempirical molecular orbital calculations of anisotropic 1H, 13C and 19F hyperfine coupling constants in hydrocarbon and fluorocarbon radicals

The anisotropic hyperfine coupling constants (AHCC) from the electron spin resonance (E.S.R.) spectra of a variety of atoms in organic radicals have been calculated by means of semiempirical molecular orbital wavefunctions in the INDO approximation. Hyperfine tensors involving ¹H, ¹³C and ¹⁹F nuclei are obtained for the ?H, ?H₃, CH₃?H₂, (CH₃)₃? hydrocarbon radicals, malonic acid radical, ?H₂F, ?F₂H, ?F₃ and CF₃?H₂ radicals. The calculated values are compared with available experimental, non-empirical and semiempirical values for these radicals. All integrals of the operator entering the electronic contributions have been evaluated over Slater type orbitals. The introduction of deorthogonalized wavefunctions gives generally better calculated results. In particular, the tensor components of the ¹⁹F AHCC are in good agreement with the experimental results without the necessity of readjusting the effective nuclear charges.     

Polarizabilities of confined two-electron systems: the 2-electron quantum dot,the hydrogen anion,the helium atom and the lithium cation

The static dipole polarizabilities of two-electron systems confined by a spherical harmonic-oscillator potential?ω?have been calculated by the coupled-cluster CCSD method. The combined effect of the confining potential?ω?and the central electrostatic field on the polarizabilities of the quantum dot, and the confined systems, H^?, He and Li⁺, respectively, have been investigated. The polarizabilities of the quantum dot can be calculated analytically. The polarizability?α?of the 2-electron quantum dot for ω?=?0.01 is calculated to be 19?996?au, in perfect agreement with the exact value, 20?000?au. Already medium confinement, ω?=?1.0, reduces?α?to 2.00?au. The decrease of the polarizability is smaller for H^? (α?=?216.1?au for ω?=?0.0 and 0.985 au for ω?=?1.0), and much smaller for He and Li⁺ (1.3819 and 0.3813?au for He for ω?=?0.0 and ω?=?1.0, respectively, and 0.1921 and 0.128?au for Li⁺). The theoretical polarizabilities for unconfined (ω?=?0.0) H^?, He and the Li⁺ cation are in very good agreement with the best published theoretical and/or experimental data. Our final polarizability for H^?, 216.0±0.5?au, appears to be one of the most accurate values published so far. The optimization procedures of basis sets applicable to calculations of polarizabilities of systems confined by a spherical harmonic-oscillator potential are presented.     

Shock compression of simple molecules

A simple approach is developed to calculate shock compression of simple molecules. This approach is based upon an accurate analytic representation of the Lennard-Jones fluids in conjunction with the Enskog theory, which is used to calculate the molecular diameter as a function of temperature along the Hugoniot. The model permits rapid, yet reliable calculations. It is applied to N₂, O₂, H₂, D₂, CH₄, CO, and CO₂. The results are tested by the comparison with experimental data and with other calculations. The computed Hugoniots agree reasonably with experimental results for many (but not all) simple molecules and are comparable to those of more complicated models.     

Water vapor line shifts in the range 5000–5600 cm<Superscript>−1</Superscript> induced by the pressure of different buffer gases

The coefficients of the water vapor line shifts induced by the pressure of oxygen, nitrogen, and argon are measured and calculated in the spectral range from 5000 to 5600 cm^?1. The experimental data are obtained from the analysis of the absorption spectra of H₂O-O₂, H₂O-N₂, and H₂O-Ar mixtures measured on a Fourier spectrometer with a resolution of 0.007 cm^?1 in a wide pressure range of buffer gases at room temperature for an optical path length of 84.05 m. The calculations are performed according to the Anderson impact theory of broadening with the use of only one adjustable parameter—the effective mean dipole polarizability of the upper vibrational state. The shifts of one and the same lines induced by the pressure of different buffer gases are compared; the role played by different terms of the intermolecular potential in the formation of the shifts is analyzed.     

F<Stack> <Subscript>3</Subscript> <Superscript>−</Superscript> </Stack> molecular ions in fluoride crystals

The UV absorption spectra of F₃^? molecular ions in LaF₃, SrF₂, CaF₂, and BaF₂ crystals doped with rare-earth elements are studied. Comparison of radiation-colored and additively colored crystals reveals the absorption bands of F₃^? hole centers in the region near 6 eV. Nonempirical calculations of optical transitions agree well with experimental results.     

New analysis of the ν2, ν3, ν4, and ν6 bands of formaldehyde H2 CO line positions and intensities in the 5-10 μm spectral region

This work, besides its fundamental interest is mainly motivated by the atmospheric importance of formaldehyde. The 10-μm region is indeed a possible spectral domain for the detection of this molecule in the atmosphere and no line parameters are presently available in the atmospheric databases for H₂CO in this spectral range. Using the experimental data available in the literature for the ν₃, ν₄, and ν₆ bands [J. Chem. Phys. 91 (1989) 646 and references therein] and for the ν₂ band [J. Mol. Spectrosc. 96 (1982) 353 and references therein] and adequate theoretical models it proved possible to reproduce satisfactorily the experimental data and to generate a list of line positions and intensities for the 5-10 μm region. The Hamiltonian model accounts for the various Coriolis-type resonances which perturb the energy levels of the 3¹, 4¹, and 6¹ vibrational states as well as for the weaker anharmonic resonances coupling the 2¹ and 3¹ energy levels. This is also the case for the line intensity calculations which allow one to reproduce satisfactorily the line by line intensity measurements as well as the integrated intensities available in the literature.