Grid of expressions related to the Einstein coefficients

Sturm, James E.

doi:10.1021/ed067p32

Cited by 12 publications

(5 citation statements)

References 2 publications

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“…In this approximation, which has been found to give a fairly accurate quantitative description of several different molecular systems, − the coupling between two CN-stretch modes a and b is given by J a b = 1 4 normalπ normalε 0 [ true normalμ false→ a · true normalμ false→ b r a b 3 − 3 false( r⃗ a b · true normalμ false→ a false) false( r⃗ a b · true normalμ false→ b false) r a b 5 ] where μ⃗ a , b are the CN-stretch transition dipoles and r ⃗ ab is the distance vector between the two transition dipoles. The magnitude of the CN-stretch transition-dipole moment can be determined from the integrated absorption coefficient, and from the experimental FTIR spectrum (Figure ), we obtain |μ⃗| = 0.089 D. Using the geometrical parameters of the polyisocyanide helix ( r = 2.3 Å, ∠(μ⃗ i , μ⃗ i +1 ) = 90°, ∠(μ⃗ i , r ⃗ i , i +1 ) = 56°), we find J 1 = 7 cm −1 . This implies an ω A − ω E frequency splitting of 14 cm −1 , which agrees reasonably well (both in sign and magnitude) with the experimental value of 8 cm −1 , thus confirming our assigment of the strong absorption band to the E mode and of the shoulder to the A mode.…”

Section: Resultsmentioning

confidence: 85%

Direct Access to Polyisocyanide Screw Sense Using Vibrational Circular Dichroism

et al. 2010

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We show that the screw sense of polyisocyanide helices can be determined in a simple manner from the vibrational circular dichroism (VCD) of their CN-stretching mode. The relation between VCD and molecular structure is obtained using the coupled-oscillator approximation. It is shown that since the CN groups point approximately radially outward from the helical axis, the CN-stretch region of the VCD spectrum of a polyisocyanide helix consists of a single couplet, the sign of which is directly related to the screw sense of the helix. We use this method to determine the screw sense of poly(R)-2-isocyanooctane and poly(S)-2-isocyanooctane from their VCD spectrum.

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Section: Resultsmentioning

confidence: 85%

Direct Access to Polyisocyanide Screw Sense Using Vibrational Circular Dichroism

et al. 2010

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“…[a] Notation: q m —monolayer capacity (molecule number); K L , K SV —binding constants from the Langmuir isotherm and the Stern–Volmer equation, respectively; Δ G L , Δ G SV —free Gibbs energies calculated based on the value of K L and K SV in accordance with the equation Δ G =− RT Ln( K ); the value of dipole transition moment μ in RhB, taken for the calculation of α , was established from the UV/Vis spectra: it is 15.227 D.…”

Section: Resultsmentioning

confidence: 99%

Fundamental Aspects of Xanthene Dye Aggregation on the Surfaces of Nanocluster Polyoxometalates: H‐ to J‐Aggregate Switching

Fazylova

Shevtsev

Михайлов

et al. 2020

Chemistry A European J

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The induced aggregation of the xanthenedye rho-damineB (RhB) on metal oxide centers belonging to the highly symmetric surfaces of precise nanoscale templates with Keplerate (Mo 132 )o rtoroidal (Mo 138 )s tructures has been studied. With the joint use of the Langmuir isotherma nd full Stern-Volmer models, the thermodynamic reasons for dye adsorption on the nanocluster surface, such as amixture of monomer,H -aggregate (H-dimer), and J-aggregate forms (which can coexist or switch one into another under the exact conditions), were established:t his was shown through UV/Vis and fluorescence spectroscopies. By using the frame-work of the excitonm odel, it is shownt hat the angle( a)b etweent he transition dipole moments of RhB is very sensitive to surface strain inside the dye sub-monolayer.A saresult, it is possible to switch from H-to J-aggregates by the postfunctionalization of polyoxometalate (POM)-RhB associates by the surfactant bilayer shell, which allows the surface strain to grow.R ecommendations are provided for managing the appearance of H-or J-aggregates on metal oxide (or polyelectrolyte) surfacesd uring photovoltaico rb ioimaging applications.[a] V. Fazylova, N. Shevtsev,S .M ikhailov, Prof. [b] G. Kim Institute of Organic Synthesis Ural Branch of the Russian Academyo fSciences 22 AkademicheskayaS t.,6 20990 Ekaterinburg (Russia) Supporting information and the ORCID identification number(s) for the author(s) of this article can be found under: https://doi.

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“…First of all, the integrated absorption coefficient (IAC) can be extracted. 58 This extinction coefficient is defined in terms of the optical density, IAC = R e dn, where n denotes the wave number. The IAC can be computed as the area under optical density (expressed in terms of dm 3 mol À1 cm À1 ) as a function of the wave number.…”

Section: Deconvolution Of the Visible Spectrummentioning

confidence: 99%

Color prediction from first principle quantum chemistry computations: a case of alizarin dissolved in methanol

et al. 2012

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The electronic spectrum of alizarin (AZ) in methanol solution was measured and used as reference data for color prediction. The visible part of the spectrum was modelled by different DFT functionals within the TD-DFT framework. The results of a broad range of functionals applied for theoretical spectrum prediction were compared against experimental data by a direct color comparison. The tristimulus model of color expressed in terms of CIE XYZ and CIE Lab parameters was applied both to experimental and predicted spectra. It was found that the HSE03 method along with the 6-31G(d,p) basis set provides the most accurate color prediction, much better than other commonly used functionals such as B3LYP, CAM-B3LYP or PBE0. Besides, the influence of potential errors, introduced by theoretical predictions on color estimation, was examined for different wavelengths. The obtained results showed that color prediction is significantly dependent on the type of basis set and functional applied. The proposed methodology provides a simple, straightforward and more reliable way of theoretical protocols validation than just a comparison of experimental and estimated values of maximum absorbance wavelength.

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Grid of expressions related to the Einstein coefficients

Abstract: The following is a collection of all of the relations of Einstein coefficients.

Cited by 12 publications

References 2 publications

Direct Access to Polyisocyanide Screw Sense Using Vibrational Circular Dichroism

Direct Access to Polyisocyanide Screw Sense Using Vibrational Circular Dichroism

Fundamental Aspects of Xanthene Dye Aggregation on the Surfaces of Nanocluster Polyoxometalates: H‐ to J‐Aggregate Switching

Color prediction from first principle quantum chemistry computations: a case of alizarin dissolved in methanol

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