Momentum dependence of π–π∗ excitations of benzene rings in condensed phases

Hayashi, Hisashi; Watanabe, Noboru; Udagawa, Yasuo; Kao, Chi Chang

doi:10.1016/s0368-2048(00)00266-8

Cited by 3 publications

(6 citation statements)

References 14 publications

(8 reference statements)

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“…The IXS ( I c3 ) spectra obtained in this study for liquid water and benzene are shown in Figure a,b, respectively. For both liquids, the IXS intensity decreased with decreasing q , as has been found previously. , The count rates of these IXS spectra were ∼10 times higher than the rates reported in previous measurements, ,, which indicates a marked improvement in both the S/N ratios and the reliability of the IXS profiles.…”

Section: Resultssupporting

confidence: 84%

“…The obtained OOS data for liquid water and liquid benzene are tabulated in the second column of Tables and and are shown in Figure a,b, respectively, in addition to the previous IXS-derived OOS data (for benzene, the previous OOS was calculated from the IXS data in ref ). The OOS values obtained using the Bethe sum rule (eq ) are absolute and not relative, with units of eV –1 .…”

Section: Resultsmentioning

confidence: 99%

“…Optical oscillator strength distributions for (a) liquid water and (b) liquid benzene. For comparison, previous IXS results obtained from refs and (“Previous IXS”) are also plotted.…”

Section: Resultsmentioning

confidence: 99%

“…In this case, the spatial average of the matrix element in eq reduces to ( q 2 /3)|⟨ f |∑ j r j |i⟩| 2 , which is exactly the same as the matrix element for photoabsorption. ,, This type of IXS is sometimes called X-ray Raman scattering ,, and is employed mainly to study excitations of core electrons (generally having small values of r e ), where the condition qr e ≪ 1 is fulfilled over a wide range of q . For valence electrons of molecular condensates ( r e ≈ 1), the condition qr e ≪ 1 is realized for small values of q or 2θ (for q ≤ ∼0.3 au). , Therefore, under the dipole approximation, the functions for which q = 0 [e.g., S (0, E ), d f (0, E )/d E , ε(0, E ), and Im(−1/ε(0, E ))] can be deduced from the small-angle IXS spectra. Hereafter, the 0 is omitted when the “optical” dielectric functions are expressed [e.g., ε( E )].…”

Section: Introductionmentioning

confidence: 96%

“…In our previous studies, ,, we pointed out that inelastic X-ray scattering (IXS) (for which the double-differential cross-section (∂ 2 σ/∂Ω∂ E ) for isotropic samples is given by (∂ 2 σ/∂Ω∂ E ) = (∂σ/∂Ω) Th S ( q , E ), where (∂σ/∂Ω) Th is the Thomson scattering cross section) is free from the difficulties inherent to VUV and EELS measurements; in particular, no vacuum is required. Subsequently, through IXS measurements using second-generation synchrotron X-ray sources, d f ( q , E )/d E and its related functions for several volatile liquids were obtained over a wide range of q and E values. ,,,− …”

Section: Introductionmentioning

confidence: 99%

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Accurate Measurements of Dielectric and Optical Functions of Liquid Water and Liquid Benzene in the VUV Region (1–100 eV) Using Small-Angle Inelastic X-ray Scattering

Hayashi

Hiraoka

2015

J. Phys. Chem. B

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Using a third-generation synchrotron source (the BL12XU beamline at SPring-8), inelastic X-ray scattering (IXS) spectra of liquid water and liquid benzene were measured at energy losses of 1-100 eV with 0.24 eV resolution for small momentum transfers (q) of 0.23 and 0.32 au with ±0.06 au uncertainty for q. For both liquids, the IXS profiles at these values of q converged well after we corrected for multiple scattering, and these results confirmed the dipole approximation for q ≤ ∼0.3 au. Several dielectric and optical functions [including the optical oscillator strength distribution (OOS), the optical energy-loss function (OLF), the complex dielectric function, the complex index of refraction, and the reflectance] in the vacuum ultraviolet region were derived and tabulated from these small-angle (small q) IXS spectra. These new data were compared with previously obtained results, and this comparison demonstrated the strong reproducibility and accuracy of IXS spectroscopy. For both water and benzene, there was a notable similarity between the OOSs of the liquids and amorphous solids, and there was no evidence of plasmon excitation in the OLF. The static structure factor [S(q)] for q ≤ ∼0.3 au was also deduced and suggests that molecular models that include electron correlation effects can serve as a good approximation for the liquid S(q) values over the full range of q.

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Section: Resultssupporting

confidence: 84%

Section: Resultsmentioning

confidence: 99%

“…Optical oscillator strength distributions for (a) liquid water and (b) liquid benzene. For comparison, previous IXS results obtained from refs and (“Previous IXS”) are also plotted.…”

Section: Resultsmentioning

confidence: 99%