Glyn Cooper

Absolute scale determination for photoabsorption spectra and the calculation of molecular properties using dipole sum-rules

An assessment of the absolute scales of photoabsorption differential oscillator strength (df/dE) spectra which were originally normalized using valence shell TRK (i.e. S(O)) sum-rule normalization is presented for a series of dipole (e,e) measurements for 5 noble gases and 52 small molecules. This comprehensive data set involves previously published absolute high resolution dipole (e,e) spectra of the valence shell discrete region combined with very wide range low resolution measurements in the ionization continuum for each atom or molecule. The absolute scales established for the dipole (e,e) spectra using the S(O) sum-rule in the originally published works (data available on the world wide web at ftp://chem.ubc.ca/pub/cooper or by anonymous ftp - see end of present paper for more details) are assessed by deriving static dipole polarizabilities for each atom and molecule using the S(−2) sum-rule. These values are found to be highly consistent with experimental and theoretical literature values of the static dipole polarizability and in almost all cases well within the estimated ±5% accuracy of the originally published TRK sum-rule normalized absolute photoabsorption differential oscillator strength spectra. Significant errors of 8% and 19% in the previously published absolute oscillator strength scales for CCl4 (G.R. Burton, W.F. Chan, G. Cooper, C.E. Brion, Chem. Phys. 181 (1994) 147) and SiF4 (X. Guo, G. Cooper, W.F. Chan, G.R. Burton, C.E. Brion, Chem. Phys. 161 (1992) 453, 471) respectively are revealed by the dipole polarizability analysis and approproate corrections are recommended. Alternative methods of absolute scale determination for photoabsorption spectra using static or dynamic dipole polarizabilities from refractive index or dielectric constant measurements are also considered. These are found to be particularly useful especially where data are restricted to lower photon energies (< 60 eV) or where phenomena such as low lying inner shells, continuum shape resonances or Cooper minima preclude the use of the valence shell TRK sum-rule. As a result of the assessment of the absolute scales for the published dipole (e,e) spectra and since polarizabilities and refractive index data can typically be obtained with even higher precision (+-1%), these data have been used to further refine the measured differential oscillator strength scales. On this basis, dipole oscillator strength sums S(u) (u = −1, −2, −3, −4, −5, −6, −7, −10) and L(u) (u = −1, −2, −3, −4, −5, −6) are obtained from the df/dE spectra. For many of the systems considered, the presently reported dipole sums are derived molecular properties are more accurate than previously reported values. In fact, for 28 of the 52 small molecules these sum-rule values represent the only available values. The dipole sums can be used to calculate normal Verdet constants which are involved in the Faraday effect. It is also shown that accurate values of the rotationally averaged C6(A,B) dispersion coefficients for the long-range interaction of all possible pairs of atomic and/or molecular species can be obtained from the measured differential oscillator strength spectra. Alternatively, an approximation to C6(A,B), requiring only the S(−2) and L(−2) sums, is shown to provide very reliable estimates of C6(A,B).

Absolute optical oscillator strengths for discrete and continuum photoabsorption of molecular nitrogen (11–200 eV)

Abstract Absolute optical oscillator strengths for the photoabsorption of molecular nitrogen in the energy region 11–200 eV have been determined using low resolution (1 eV fwhm) dipole (e, e) spectroscopy. The absolute scale was obtained by TRK sum-rule normalization. High resolution (0.048 eV fwhm) dipole (e, e) spectroscopy has been used to measure the absolute optical oscillator strengths for the excitation of molecular nitrogen in the valence shell discrete region. The measurements are free of the “line saturation” (bandwidth) effects which complicate direct photoabsorption studies using the Beer-Lambert law. Absolute optical oscillator strengths for excitation to individual vibronic bands of the b 1 Π u and b′ 1 Σ + u valence excited states, the c 1 Π u , c′ 1 Σ + u and o 1 Π u Rydberg states and also the e 1 Π u and e′ 1 Σ + u states have been obtained. The present results are compared with previously published experimental data and theoretical calculations.

The electronic spectrum of water in the discrete and continuum regions. Absolute optical oscillator strengths for photoabsorption (6–200 eV)

Abstract The electronic excitation spectrum and the associated absolute optical oscillator strengths for the photoabsorption of water have been determined in the energy region 6–200 eV using low resolution dipole (e, e) spectroscopy and TRK sum-rule normalization. In addition, detailed studies of the absolute photoabsorption oscillator strengths for the valence shell discrete electronic transitions of water have been made using high resolution dipole (e, e) spectroscopy (0.048 eV fwhm), from the first excitation threshold up to 30 eV. The present results are free of “line saturation” (i.e. bandwidth/linewidth interaction) effects which can lead to serious errors when absolute intensity measurements are made using conventional Beer-Lambert law photoabsorption methods.

Absolute optical oscillator strengths for discrete and continuum photoabsorption of carbon monoxide (7-200 eV) and transition moments for the X 1Σ+ → A 1Π system

Abstract Absolute optical oscillator strengths for the photoabsorption of carbon monoxide have been determined in the energy region 7–200 eV using low resolution dipole (e, e) spectroscopy and TRK sum-rule normalization. High resolution dipole (e, e) spectroscopy has been used to measure the absolute optical oscillator strengths for the photoabsorption of carbon monoxide in the valence shell discrete region from the first excitation threshold to 21 eV. Values of the absolute optical oscillator strengths for excitation of the vibrational levels of the A 1 Π, C 1 Σ + , B 1 Σ + and E 1 Π excited electronic states are reported. The variation of transition moment with internuclear distance is investigated for the vibronic bands of the X 1 Σ + → A 1 Π transition.

Absolute photoabsorption and photoionization of formaldehyde in the VUV and soft X-ray regions (3–200 eV)

Abstract The absolute photoabsorption spectrum of the valence shell of formaldehyde has been measured using dipole (e,e) spectroscopy from ≈3–200 eV photon energy. Long range absolute oscillator strength (cross section) measurements have been performed at ≈1 eV fwhm resolution, while the low energy discrete structured region (3–20 eV) has been examined in more detail at ≈50 meV fwhm resolution. Absolute oscillator strenghts for many of the individual discrete vibronic transitions have been obtained. In addition, dipole (e,e + ion) coincidence spectroscopy has been used to study the ionic photofragmentation of formaldehyde. Photoion branching ratios, absolute partial photoionization oscillator strenghts and photoionization efficiencies have been obtained from the first IP up to 80 eV photon energy. A dipole induced breakdown scheme for formaldehyde has been derived using the present results in combination with previously published photoelectron-photoion coincidence measurements (R. Bombach et al., Int. J. Mass Spectrum. Ion Phys. 40 (1981) 275) and experimental (D.M.P. Holland, Chem. Phys. 133 (1989) 453) and theoretical (P.W. Langhoff et al., J. Chem. Phys. 69 (1978) 4689) valence shell photoelectron branching ratios. From this breakdown analysis, electronic ion state partial photoionization oscillator strengths for formaldehyde from 14–30 eV photon energy have been derived.

The electronic absorption spectrum of NH3 in the valence shell discrete and continuum regions. Absolute oscillator strengths for photoabsorption (5–200 eV)

Abstract The electronic spectrum and the absolute photoabsorption oscillator strengths (cross sections) for the valence shell of NH 3 have been measured using high- (0.048 eV fwhm) and low-resolution (≈ 1 eV fwhm) dipole (e, e) spectroscopy in the photon energy ranges 5.0–31 and 5.5–200 eV, respectively. The high-resolution data have been obtained at vibrational resolution and have been used to determine the integrated oscillator strengths of several vibronic transitions in the discrete absorption region below the first ionization potential. The oscillator strength data are compared with previously published absolute measurements obtained using direct optical techniques and electron impact spectroscopy. Criteria are discussed for estimating the corrections for Pauli-excluded transitions required for the normalization of relative photoabsorption spectra when using the partial Thomas-Reiche-Kuhn sum rule.

The electronic spectrum of carbon dioxide. Discrete and continuum photoabsorption oscillator strengths (6–203 eV)

Abstract The recently developed high resolution dipole (e,e) method, which is free of Beer—Lambert law “line saturation” errors, has been used to determine absolute photoabsorption oscillator strengths for the discrete electronic excitation of carbon dioxide in the energy region 6–30 eV. Low resolution dipole (e,e) measurements (1 eV fwhm) have also been made in the equivalent photon energy range 8.5–203 eV. The absolute scale of the present measurements was obtained by TRK sum-rule normalization.

Absolute oscillator strengths for the photoabsorption, photoionization and ionic photofragmentation of silicon tetrafluoride. I. The valence shell

Abstract Absolute photoabsorption oscillator strengths (cross sections) for the valence shell of silicon tetrafluoride have been measured using dipole (e, e) spectroscopy in the equivalent photon energy range 10–100 eV at an energy resolution of ≈ 1 eV fwhm. A high-resolution (0.048 eV fwhm) photoabsorption oscillator strength spectrum of silicon tetrafluoride has also been determined using a high-resolution dipole (e, e) spectrometer in the equivalent photon energy range 10–50 eV. Absolute oscillator strengths for the discrete features in the pre-ionizatin edge region of the high resolution spectrum have been obtained and their spectral assignments are discussed. Photoionization time-of-flight mass spectra have been collected using dipole (e, e + ion) coincidence spectroscopy from the first ionization potential up to 100 eV. Photoion branching ratios and photoionization efficiencies have been determined from the TOF mass spectra, and these have been used along with the measured absolute photoabsorption oscillator strengths to obtain the absolute partial photoionization oscillator strengths for production of the molecular and dissociative fragment ions. The ionic photofragmentation branching ratios differ substantially from previously published results (Lablanquie et al., J. Chem. Phys. 90 (1989) 7078; Imamura et al., J. Chem. Phys. 94 (1991) 4936). Absolute electronic state partial photoionization oscillator strengths have also been derived using the measured absolute photoabsorption oscillator strengths and photoionization efficiencies along with photoelectron branching ratios for the electronic states of silicon tetrafluoride reported in an earlier PES study (Yates et al., J. Chem. Phys. 83 (1985) 4906). The results are compared with MS-Xα calculations. The dipole induced breakdown for silicon tetrafluoride is also discussed.

Absolute optical oscillator strengths (11–20 eV) and transition moments for the photoabsorption of molecular hydrogen in the Lyman and Werner bands

Abstract The recently developed high resolution dipole (e, e) method has been used to measure the absolute optical oscillator strengths for discrete and continuum transitions for the photoabsorption of molecular hydrogen throughout the valence shell region, in the energy range 11–20 eV. Absolute optical oscillator strengths for the vibrational transitions of the Lyman and Werner bands are determined and compared with available experimental and theoretical data. The variation of the electronic transition moment with internuclear distance is studied for the Lyman and Werner bands. The present oscillator strengths and transition moments are in excellent agreement with the highest levels of theory. Finally the dipole strengths of both bands at the equilibrium internuclear distance (0.741 A) are also reported.

Absolute optical oscillator strengths for the photoabsorption of molecular oxygen (5-30 eV) at high resolution

Abstract Absolute optical oscillator strengths for the photoabsorption of molecular oxygen in the valence shell discrete electronic excitation region have been measured in the energy range 5–30 eV using high resolution dipole (e, e) spectroscopy. Absolute intensities for the Schumann-Runge continuum region and for the discrete bands below the first ionization potential are reported and compared with available experimental and theoretical data.