scholarly journals Proof and Use of the Method of Combination Differences for Analyzing High-Resolution Coherent Multidimensional Spectra

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 44
Author(s):  
Peter C. Chen ◽  
Jeffrey Ehme
Keyword(s):  
High Resolution ◽  
Quantum Number ◽  
Random Error ◽  
Energy Function ◽  
Special Form ◽  
Rotational Quantum Number ◽  
Simulated Data ◽  
Rotational Energy ◽  
Multidimensional Spectroscopy ◽  
3D Space

High-resolution coherent multidimensional spectroscopy is a technique that automatically sorts rotationally resolved peaks by quantum number in 2D or 3D space. The resulting ability to obtain a set of peaks whose J values are sequentially ordered but not known raises the question of whether a method can be developed that yields a single unique solution that is correct. This paper includes a proof based upon the method of combined differences that shows that the solution would be unique because of the special form of the rotational energy function. Several simulated tests using a least squares analysis of simulated data were carried out, and the results indicate that this method is able to accurately determine the rotational quantum number, as well as the corresponding Dunham coefficients. Tests that include simulated random error were also carried out to illustrate how error can affect the accuracy of higher-order Dunham coefficients, and how increasing the number of points in the set can be used to help address that.

scholarly journals The band spectra of helium and hydrogen at low temperatures

1926 ◽  
Vol 113 (763) ◽  
pp. 183-195 ◽  
Keyword(s):  
Angular Velocity ◽  
Quantum Number ◽  
Low Temperatures ◽  
Rotational Quantum Number ◽  
Rotational Energy ◽  
Normal Band ◽  
Maximum Intensity ◽  
Band Spectrum ◽  
First Line ◽  
Band Spectra

The theoretical effect on a band spectrum of a change in the temperature of the emitting gas or vapour is already well known. In a normal band the intensities of the component lines of a series at first increase with increasing values of the rotational quantum number ( m ), so that for some definite value of m (not necessarily integral) there is a maximum of intensity, after which the intensity gradually decreases to zero. A curve between the intensity and m should have the same general form as the curve of the Maxwellian distribution of the angular velocity, since the most important factor in the relative intensities of the components is the number of molecules in the different possible states of rotation. At low temperatures the number of molecules with large values of the rotational energy is reduced, with the result that band components with large values of m are reduced in intensity or disappear altogether. At the same timethe point of maximum intensity should be shifted to a lower value of m . Helium . In the present investigation the bands described by Curtis (1) in the spectrum of helium have been studied at the three temperatures given by surrounding the discharge tube with water, liquid air, and liquid hydrogen respectively. For certain series the change in the quantum number corresponding to the maximum intensity is very clearly shown, while for other series the first line is the most intense at all temperatures, and the lowering of the temperature has only the effect of reducing the relative intensity of the higher members of the series.

Effects of The Vibrational and Rotational Energy on Reaction Cross- Section in a Classical Trajectory Study of Atom-Diatomic Molecule Collisions

2008 ◽  
Vol 63 (10-11) ◽  
pp. 721-734
Author(s):  
Hamzeh M. Abdel-Halim ◽  
Sawsan M. Jaafreh
Keyword(s):  
Quantum Number ◽  
Diatomic Molecule ◽  
Cross Section ◽  
Reaction Cross Section ◽  
Equations Of Motion ◽  
Rotational Quantum Number ◽  
Reaction Rates ◽  
Classical Trajectory ◽  
Reaction Cross ◽  
Rotational Energy

Effects of the initial vibrational and rotational energy of a diatomic molecule on reaction rates of atom-diatomic molecule reactions have been studied using classical trajectory calculations. The reaction probabilities, cross-sections and rate constants were calculated using the three-dimensional Monte-Carlo method. Equations of motion, which predict the positions and momenta of the colliding particles after each step in the trajectory, have been integrated numerically by the Runge-Kutta-Gill and Adams-Moulton methods. Morse potential energy surfaces were used to describe the interaction between the atom and each atom in the diatomic molecule. Several atom-diatomic molecule systems were studied. Variation of the reaction cross-section with both vibrational and rotational quantum numbers has been studied. For all systems studied, it was found that the cross-section increases with the vibrational quantum number. However, the effect of rotational quantum number on cross-section varies from one system to another. Results obtained in the present work were compared with experimental data and/or with results obtained theoretically. Good agreements were observed with experimental and with theoretical results obtained by other investigators using different calculation methods.

A quasi-classical trajectory study of the reagent initial rotation quantum state effect on the reaction He + T2+ → HeT+ + T using an improved ab initio potential energy surface

2012 ◽  
Vol 90 (2) ◽  
pp. 230-236 ◽  
Author(s):  
Ningjiu Zhao ◽  
Yufang Liu
Keyword(s):  
Angular Momentum ◽  
Potential Energy ◽  
Potential Energy Surface ◽  
Quantum Number ◽  
Relative Velocity ◽  
Energy Surface ◽  
Rotational Quantum Number ◽  
Chem Phys ◽  
Classical Trajectory ◽  
Positive Direction

In this work, we employed the quasi-classical trajectory (QCT) method to study the vector correlations and the influence of the reagent initial rotational quantum number j for the reaction He + T2+ (v = 0, j = 0–3) → HeT+ + T on a new potential energy surface (PES). The PES was improved by Aquilanti co-workers (Chem. Phys. Lett. 2009. 469: 26–30). The polarization-dependent differential cross sections (PDDCSs) and the distributions of P(θr), P([Formula: see text]r), and P(θr, [Formula: see text]r) are presented in this work. The plots of the PDDCSs provide us with abundant information about the distribution of the product angular momentum polarization. The P(θr) is used to describe the correlation between k (the relative velocity of the reagent) and j′ (the product rotational angular momentum). The distribution of dihedral angle P([Formula: see text]r) shows the k–k′–j′ (k′ refers to the relative velocity of the product) correlation. The PDDCS calculations illustrate that the product of this reaction is mainly backward scatter and it has the strongest polarization in the backward and sideways scattering directions. At the same time, the results of the P([Formula: see text]r) demonstrate that the product HeT+ tends to be oriented along the positive direction of the y axis and it tends to rotate right-handedly in planes parallel to the scattering plane. Moreover, the distribution of the P(θr) manifests that the product angular momentum is aligned along different directions relative to k. The direction of the product alignment may be perpendicular, opposite, or parallel to k. Moreover, our calculations are independent of the initial rotational quantum number.

Effects of collision energy and rotational quantum number on stereodynamics of the reactions: H( 2 S) + NH( υ = 0, j = 0, 2, 5, 10)→N( 4 S) + H 2

2016 ◽  
Vol 25 (8) ◽  
pp. 083402 ◽  
Author(s):  
Wei Wang ◽  
Yong-Jiang Yu ◽  
Gang Zhao ◽  
Chuan-Lu Yang
Keyword(s):  
Quantum Number ◽  
Collision Energy ◽  
Rotational Quantum Number

State‐to‐state photoionization of VO: Propensity for large, positive changes in rotational quantum number

1992 ◽  
Vol 97 (4) ◽  
pp. 2809-2812 ◽  
Author(s):  
Joel Harrington ◽  
James C. Weisshaar
Keyword(s):  
Quantum Number ◽  
Rotational Quantum Number

scholarly journals How Identifying Circumgalactic Gas by Line-of-sight Velocity instead of the Location in 3D Space Affects O vi Measurements

2021 ◽  
Vol 923 (2) ◽  
pp. 137
Author(s):  
Stephanie H. Ho ◽  
Crystal L. Martin ◽  
Joop Schaye
Keyword(s):  
High Resolution ◽  
Density Profile ◽  
Column Density ◽  
Line Of Sight ◽  
Lower Mass ◽  
Star Forming ◽  
3D Space ◽  
High Incidence ◽  
High Incidence Rate ◽  
Stellar Masses

Abstract The high incidence rate of the O vi λλ1032, 1038 absorption around low-redshift, ∼L * star-forming galaxies has generated interest in studies of the circumgalactic medium. We use the high-resolution EAGLE cosmological simulation to analyze the circumgalactic O vi gas around z ≈ 0.3 star-forming galaxies. Motivated by the limitation that observations do not reveal where the gas lies along the line of sight, we compare the O vi measurements produced by gas within fixed distances around galaxies and by gas selected using line-of-sight velocity cuts commonly adopted by observers. We show that gas selected by a velocity cut of ±300 km s−1 or ±500 km s−1 produces a higher O vi column density, a flatter column density profile, and a higher covering fraction compared to gas within 1, 2, or 3 times the virial radius (r vir) of galaxies. The discrepancy increases with impact parameter and worsens for lower-mass galaxies. For example, compared to the gas within 2 r vir, identifying the gas using velocity cuts of 200–500 km s−1 increases the O vi column density by 0.2 dex (0.1 dex) at 1 r vir to over 0.75 dex (0.7 dex) at ≈ 2 r vir for galaxies with stellar masses of 109–109.5 M ⊙ (1010–1010.5 M ⊙). We furthermore estimate that excluding O vi outside r vir decreases the circumgalactic oxygen mass measured by Tumlinson et al. (2011) by over 50%. Our results demonstrate that gas at large line-of-sight separations but selected by conventional velocity windows has significant effects on the O vi measurements and may not be observationally distinguishable from gas near the galaxies.

scholarly journals Measurements of The Spectroscopic Properties of Hydrogen Iodide Molecules

2008 ◽  
Vol 5 (3) ◽  
pp. 446-448
Author(s):  
Baghdad Science Journal
Keyword(s):  
Absorption Spectrum ◽  
Quantum Number ◽  
Rotational Quantum Number ◽  
Spectroscopic Properties ◽  
Hydrogen Iodide

A calculation have been carried out for determination some of the spectroscopic properties of Hydrogen Iodide HI molecules such as, the intensity of the absorption spectrum as a function of the variation of the temperature ranging from 10 to 1000 K. This study shows that the populations and hence intensity of the molecule increased as the temperature increased. Another determination of the maximum rotational quantum number Jmax of N2 , CO , BrF AgCl and HI molecules has been carried out.

scholarly journals Rotation Effect in Morse Potential For K2 Molecule

2011 ◽  
Vol 8 (4) ◽  
pp. 968-971
Author(s):  
Baghdad Science Journal
Keyword(s):  
Quantum Number ◽  
Dissociation Energy ◽  
Effective Potential ◽  
Morse Potential ◽  
Rotational Quantum Number ◽  
Electronic States ◽  
Rotation Effect ◽  
Potential Curves

The rotation effect upon Morse potential had been studied and the values of the effective potential in potential curves had been calculated for electronic states (X2?+g , B ?u ) K2 molecule. The calculation had been computed for rotational quantum number (J = 5). Also, drawing potential curves for these systems had been done using Herzberg and Gaydon equations. It was found that the values of the dissociation energy which resulting from using Herzberg equation greater than that of Gaydon equation. Besides, it was found that the rotation effect for (X and B) electronic states in Morse potential is very small and in this case may negligible.

Quantum interference in H + HD → H2 + D between direct abstraction and roaming insertion pathways

Science ◽  
2020 ◽  
Vol 368 (6492) ◽  
pp. 767-771 ◽  
Author(s):  
Yurun Xie ◽  
Hailin Zhao ◽  
Yufeng Wang ◽  
Yin Huang ◽  
Tao Wang ◽  
...  
Keyword(s):  
Quantum Number ◽  
Quantum Interference ◽  
Chemical Reactivity ◽  
Rotational Quantum Number ◽  
Interesting Case ◽  
Phase Effect ◽  
Chemical Reaction Dynamics ◽  
Bohm Effect ◽  
Aharonov Bohm ◽  
Direct Abstraction

Understanding quantum interferences is essential to the study of chemical reaction dynamics. Here, we provide an interesting case of quantum interference between two topologically distinct pathways in the H + HD → H2 + D reaction in the collision energy range between 1.94 and 2.21 eV, manifested as oscillations in the energy dependence of the differential cross section for the H2 (v′ = 2, j′ = 3) product (where v′ is the vibrational quantum number and j′ is the rotational quantum number) in the backward scattering direction. The notable oscillation patterns observed are attributed to the strong quantum interference between the direct abstraction pathway and an unusual roaming insertion pathway. More interestingly, the observed interference pattern also provides a sensitive probe of the geometric phase effect at an energy far below the conical intersection in this reaction, which resembles the Aharonov–Bohm effect in physics, clearly demonstrating the quantum nature of chemical reactivity.

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