High resolution rotation–vibration Raman spectra of benzene. I. The totally symmetric bands of C6H6

1978 ◽  
Vol 56 (7) ◽  
pp. 974-982 ◽  
Author(s):  
A. B. Hollinger ◽  
H. L. Welsh
Keyword(s):  
Raman Spectrum ◽  
High Resolution ◽  
Least Squares ◽  
Raman Spectra ◽  
Multiple Reflection ◽  
Slit Width ◽  
Linear Least Squares ◽  
Raman Cell ◽  
Least Squares Minimization

The Raman spectrum of benzene vapour was excited in a multiple reflection Raman cell by an Ar+ laser and was photographed with a spectral slit width of ~0.17 cm−1. All seven Raman-active fundamentals were observed. Analyses of the totally symmetric ν1 and ν2 bands are given in this article. About 150 maxima were observed for ν2 (C—C stretching) and ~100 for ν1 (C—H stretching); the latter was to some extent obscured by the ν15 band. These partially resolved rotational structures were analyzed by setting up suitable schemes of approximate assignments for the maxima and calculating the band constants by a linear least-squares minimization.

High resolution rotation–vibration Raman spectra of benzene. II. The doubly degenerate bands of C6H6

1978 ◽  
Vol 56 (11) ◽  
pp. 1513-1525 ◽  
Author(s):  
A. B. Hollinger ◽  
H. L. Welsh
Keyword(s):  
Raman Spectrum ◽  
High Resolution ◽  
Computer Program ◽  
Raman Spectra ◽  
Multiple Reflection ◽  
Slit Width ◽  
Molecular Constants ◽  
Raman Cell

The Raman spectrum of benzene vapour was excited in a multiple reflection Raman cell by an Ar+ laser and was photographed with a spectral slit width of ~ 0.15 cm−1. The results for the five doubly degenerate Raman-active fundamentals are given in this communication. More than 150 maxima were resolved in the ν17 band and the spectrum was analyzed with a computer program to give ν17 = 1177.776(10) cm−1, B1 – B0 = 1.00(4) × 10−4, C1 – C0 = −0.50(2) × 10−4 cm−1, and ζ17 = 0.010(1). About 60 maxima were recorded in the ν18 band; molecular constants were determined but with less precision than for ν17. The ν15 band (partially overlapped by ν1) and the (ν16, ν2 + ν18) Fermi diad showed resolved structure but no detailed analyses were possible. The ν11 band showed no resolved structure.

High resolution rotation–vibration Raman spectra of benzene. III. The spectrum of C6D6

1979 ◽  
Vol 57 (5) ◽  
pp. 767-774 ◽  
Author(s):  
A. B. Hollinger ◽  
H. L. Welsh ◽  
K. S. Jammu
Keyword(s):  
Raman Spectrum ◽  
High Resolution ◽  
Least Squares ◽  
Raman Spectra ◽  
Multiple Reflection ◽  
Slit Width ◽  
Molecular Constants ◽  
Least Squares Fit

The Raman spectrum of benzene-d6 vapour was excited in a multiple reflection cell by an Ar+ laser and was photographed with a spectral slit width of ~0.15 cm−1. Extensive structure (164 maxima) was observed for the ν2 (C—C stretching) fundamental but only the S branch (39 maxima) of the ν1 (C—D stretching) band was well-resolved. These totally symmetric bands were analysed and molecular constants determined from a least-squares fit. Three doubly degenerate bands were observed; ν15 and ν16 were unresolved, and in ν17 only 19 lines could be measured. Consequently, no detailed analyses were possible but the values of some molecular constants were estimated.

High resolution rotation–vibration Raman spectra of acetylene. I. The spectrum of C2H2

1980 ◽  
Vol 58 (4) ◽  
pp. 534-543 ◽  
Author(s):  
E. Kostyk ◽  
H. L. Welsh
Keyword(s):  
Raman Spectrum ◽  
High Resolution ◽  
Raman Spectra ◽  
Gas Pressure ◽  
Multiple Reflection ◽  
Slit Width ◽  
Lower State ◽  
Vibrational States ◽  
Band Origin ◽  
Raman Cell

The Raman spectrum of gaseous acetylene was excited in a multiple-reflection Raman cell by a single-moded Ar+ laser and recorded photographically; the gas pressure was 380 Torr and the spectral slit-width ~0.1 cm−1. The three Raman-active fundamentals ν1, ν2, and ν41 of C2H2 were analyzed to give the band origin, ν0, and the upper state constants, B1 and D1; accurate infrared values of the lower state constants, B0 and D0, were assumed in the analysis. The values of the constants for the ν2 band illustrate the accuracy obtained: ν0 = 1974.317(2), B1 = 1.170419(14), D1 = 1.579(18) × 10−6 cm−1. Five difference bands originating in transitions from the low-lying ν4 = 1 and ν5 = 1 vibrational states were also measured and analyzed.

High resolution rotation–vibration Raman spectra of acetylene. II. The spectra of C2D2 and C2HD

1980 ◽  
Vol 58 (6) ◽  
pp. 912-920 ◽  
Author(s):  
E. Kostyk ◽  
H. L. Welsh
Keyword(s):  
High Resolution ◽  
Raman Spectra ◽  
Ground State ◽  
Multiple Reflection ◽  
Acetylene Molecule ◽  
Band Origin ◽  
Infrared Studies ◽  
Internuclear Distances ◽  
Raman Cell ◽  
Gas Pressures

The Raman spectra of gaseous C2D2 and C2HD were excited in a multiple-reflection Raman cell by a single-moded Ar+ laser and recorded photographically; the gas pressures were in the range, 130–200 Torr, and the spectral slit width was ~ 0.1 cm−1. The ν1, ν2, and ν41 bands of C2D2 and the ν1 and ν2 bands of C2HD were recorded. These were analyzed to give the band origin, ν0, and the upper state constants, B1 and D1; accurate infrared values of the ground state constants, B0 and D0, were assumed in the analyses. Values of the rotation–vibration interaction constants, αi, assembled from Raman and infrared studies of C2H2, C2D2, and C2HD, were used to calculate the equilibrium internuclear distances for the acetylene molecule: re(C—H) = 1.06250 ± 0.00010 and re(C≡C) = 1.20241 ± 0.00009 Å.

Quantitative HREM using non-linear least-squares methods

1994 ◽  
Vol 52 ◽  
pp. 716-717
Author(s):  
Wayne E. King ◽  
Michael A. O’Keefe ◽  
Geoffrey H. Campbell
Keyword(s):  
High Resolution ◽  
Grain Boundary ◽  
Least Squares ◽  
Atomic Structure ◽  
Linear Least Squares ◽  
Electron Microscopic ◽  
Atomic Column ◽  
Imaging Parameters ◽  
Non Linear ◽  
Experimental Image

Non-linear least-squares methods have been coupled with high resolution image simulation to determine the critical electron microscopic imaging parameters, such as thickness and defocus, from an experimental image. The method has been extended to include the optimization of atomic column positions and occupancy to determine atomic structure. As an example, the method has been applied to the refinement of the atomic structure of a Σ5(310)/[001] grain boundary in Nb.In the past, high resolution electron microscopy has been applied in a primarily qualitative manner through the visual comparison of experimental images with simulated images. The potential for more quantitative analysis has been pointed out and recently, increasing attention is being given to more quantitative matching of experiment with simulation. Emphasis is being placed on the deduction of imaging parameters and/or the refinement of atomic structures from experimental images.In this paper, we describe an approach to the optimization of the critical electron-optical imaging parameters of an experimental image and the atomic structure of a crystalline defect, namely a grain boundary.

THE RAMAN SPECTRA OF LIQUID AND SOLID H2, D2, AND HD AT HIGH RESOLUTION

1962 ◽  
Vol 40 (1) ◽  
pp. 9-23 ◽  
Author(s):  
S. S. Bhatnagar ◽  
Elizabeth J. Allin ◽  
H. L. Welsh
Keyword(s):  
Raman Spectrum ◽  
High Resolution ◽  
Raman Spectra ◽  
Vibrational Frequencies ◽  
Dispersion Forces ◽  
Present Communication ◽  
Linear Dispersion ◽  
Vibrational Coupling

The Raman spectra of liquid (~18° K) and solid (~2° K) n-H2, p-H2, n-D2, o-D2(80%), and HD were photographed with a reciprocal linear dispersion of 3 to 6 cm−1 per mm. The S0 rotational lines show broadening of a few cm−1 but the Q1 vibrational lines are very sharp. The S0(0) transition of p-H2 and o-D2 is a triplet of sharp lines, but the corresponding transition in HD is not split. The vibrational frequencies in the liquid are lowered by 7 to 9 cm−1 and in the solid by 8 to 11 cm−1 from the gas values. The Raman spectrum of p-H2 has been discussed in detail by Van Kranendonk. In the present communication the vibrational shifts in the various solids are correlated by representing them as the sums of shifts due to dispersion forces, overlap forces, and vibrational coupling.

Maximum Likelihood Estimation and Non-Linear Least Squares Fitting Implementation in FPGA Devices for High Resolution Hodoscopy

2013 ◽  
Vol 60 (5) ◽  
pp. 3578-3584 ◽  
Author(s):  
Jose M. Blasco ◽  
Enrique Sanchis ◽  
Vicente Gonzalez ◽  
Jose D. Martin ◽  
Francisco J. Egea ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
High Resolution ◽  
Maximum Likelihood Estimation ◽  
Least Squares ◽  
Likelihood Estimation ◽  
Linear Least Squares ◽  
Least Squares Fitting ◽  
Non Linear

Quantitative HREM using non-linear least-squares methods

1996 ◽  
Vol 54 ◽  
pp. 94-95
Author(s):  
Wayne E. King ◽  
Geoffrey H. Campbell
Keyword(s):  
High Resolution ◽  
Least Squares ◽  
Yttrium Aluminum Garnet ◽  
Linear Least Squares ◽  
Electron Microscopic ◽  
Simulated Image ◽  
Optical Images ◽  
Non Linear ◽  
Experimental Image ◽  
Image Position

Non-linear least-squares methods have been coupled with high resolution image simulation to determine the critical electron microscopic imaging parameters, such as thickness and defocus, from experimental high resolution electron optical images of yttrium aluminum garnet (YAG). For a quantitative fit between experimental and simulated images we seek to minimize the residual image fi(x) at each pixel,(1)where is the intensity value of the ith pixel in the experimental image, is the intensity value of the ith pixel in the simulated image based on the image model x, and W is the image that represents the uncertainty associated with measurement of the ith pixel in the experimental image.

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