Assignment Of Fundamental Frequencies Research Articles

Anti-k-labeling of graphs

It is well known that the labeling problems of graphs arise in many (but not limited to) networking and telecommunication contexts. In this paper we introduce the anti-k-labeling problem of graphs which we seek to minimize the similarity (or distance) of neighboring nodes. For example, in the fundamental frequency assignment problem in wireless networks where each node is assigned a frequency, it is usually desirable to limit or minimize the frequency gap between neighboring nodes so as to limit interference.Let k ≥ 1 be an integer and ψ is a labeling function (anti-k-labeling) from V(G) to {1,2,…,k} for a graph G. A no-hole anti-k-labeling is an anti-k-labeling using all labels between 1 and k. We define wψ(e)=|ψ(u)−ψ(v)| for an edge e=uv and wψ(G)=min{wψ(e):e∈E(G)} for an anti-k-labeling ψ of the graph G. The anti-k-labeling number of a graph G, λk(G), is max {wψ(G): ψ}. In this paper, we first show that λk(G)=⌊k−1χ−1⌋, and the problem that determines the anti-k-labeling number of graphs is NP-hard. We mainly obtain the lower bounds on no-hole anti-n-labeling number for trees, grids and n-cubes.

Study of Coordination Characteristics of some Metal Complexes of 2-Thiouracil by Infrared Spectroscopy

The infrared spectra of 2-Thiouracil (Thu) have been recorded in the region 4000-400 cm-1. The assignments of fundamental frequencies have been proposed on the basis of assignments in related molecules. Correlation of vibrational assignments with those of related molecules have been pointed out. The metal ion interactions of Thu with Cd (II), Hg (II), Cu (II), and Zn (II) bromides have been investigated by infrared spectroscopy. The results are consistent with the bonding of ligands through sulphur in all the complexes. The vibrational frequencies of metal complexes of 2-Thiouracil are correlated with the spectral data of other structurally related pyrimidine thione complexes.

Study of Coordination Characteristics of some Metal Complexes of 2-Thiouracil by Infrared Spectroscopy

The infrared spectra of 2-Thiouracil (Thu) have been recorded in the region 4000-400 cm-1. The assignments of fundamental frequencies have been proposed on the basis of assignments in related molecules. Correlation of vibrational assignments with those of related molecules have been pointed out. The metal ion interactions of Thu with Cd (II), Hg (II), Cu (II), and Zn (II) bromides have been investigated by infrared spectroscopy. The results are consistent with the bonding of ligands through sulphur in all the complexes. The vibrational frequencies of metal complexes of 2-Thiouracil are correlated with the spectral data of other structurally related pyrimidine thione complexes.

Theoretical anharmonic Raman and infrared spectra with vibrational assignments and NBO analysis for 2,3,4,5,6-pentafluoroaniline

2,3,4,5,6-Pentafluoroaniline (PFA) is a very attractive object to theoretical study of fluorine interaction with an aromatic ring. Two major opposite effects are observed in PFA: interaction of the σ–π electron donating amino group, promoting electrophilic substitution at the ortho/para position by increasing the electron density at the ortho/para carbons versus fluorine substituents. This very strongly withdraws electron density from the aromatic system through the σ bond (inductive effect) and donates electron density through the π system (resonance effect). The stability of PFA arising from hyper conjugative interaction is investigated with natural bond orbital (NBO) analysis. The influences of the fluorine atoms on the geometrical and electronic properties as well as the detailed interpretation of vibrational spectra and potential energy distribution (PED) are also reported. The assignment of fundamental frequencies is confirmed by the qualitative agreement between the observed and calculated wavenumbers.

Rotational analysis of bands in the high-resolution infrared spectra of the three species of butadiene-1,4- d2; refinement of the assignments of the vibrational fundamentals

Samples of trans, trans and cis, cis forms of butadiene-1,4- d 2 have been synthesized and found to contain useful amounts of the cis, trans species as a contaminant. Assignments of fundamental frequencies for the three isotopomers of butadiene-1,4- d 2 have been extended and improved from investigations of their Raman spectra as well as their infrared (IR) spectra. High-resolution IR spectra have been recorded for the three isotopomers, and a rotational analysis has been completed for strong bands of each species. Ground state and some upper state rotational constants have been fit. Corresponding ground state moments of inertia compare favorably with equilibrium moments of inertia obtained from B3LYP/6-311++G** theory. Two 13C isotopomers are being prepared, and an improved structural analysis of butadiene will soon be available to assess how π-electron delocalization affects its structure.

Spectra and structure of polyamine-copper(II) complexes. Infrared spectrum and normal coordinate calculations of mono(diethylenetriamine) copper(II) nitrate

The infrared spectrum of mono(diethylenetriamine)copper(II) nitrate has been obtained in the frequency range 4000-80 cm −1. Assignments of fundamental frequencies in the coordination site, as well as in the free and bonded nitrates, were performed regarding the structure of the complex. Also, a normal coordinate analysis based on a simplified model, was carried out in order to distinguish the frequency position of some normal modes, such as the three different ν(CuN) and the two different ν(CuO) modes.

Theoretical study on the assignment of fundamental frequencies of o-benzyne

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTTheoretical study on the assignment of fundamental frequencies of o-benzyneRuifeng Liu, Xuefeng Zhou, and Peter PulayCite this: J. Phys. Chem. 1992, 96, 21, 8336–8339Publication Date (Print):October 1, 1992Publication History Published online1 May 2002Published inissue 1 October 1992https://doi.org/10.1021/j100200a024RIGHTS & PERMISSIONSArticle Views94Altmetric-Citations20LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (558 KB) Get e-Alerts

Geometry, force field, and fundamental frequencies of 4a,4b-dihydrophenanthrene, a scaled quantum-mechanical force field study

Geometries of both cis- and trans-4a,4b-dihydrophenanthrene are optimized by restricted Hartree—Fock method with 4–21G basis. At this level of theory, the trans-conformer is predicted 8.0 kcal/mol lower in energy than the cis one. The quadratic force field of the trans-conformer obtained from empirical scaling of the ab initio force constants reproduced the observed frequencies with mean deviation of about 10 cm −1. Based on the calculation an earlier assignment of two observed frequencies is confirmed and assignment of the rest of the observed frequencies is given. The observed frequencies at 1555 and 1534 cm −1 are concluded not to be fundamental frequencies of the subject molecule. This study shows again the practical value of the scaled quantum-mechanical force field method in the assignment of fundamental frequencies and identification of reaction products.

Crystal Structure and Spectroscopic Investigation of 1,3-Dichloro-1,3-Diazetidine-2,4-Dione and 1,3 - Bis(Trimethylsilyl) -1,3- Diazetidine- 2,4- Dione

Abstract Crystal structures of 1,3-dichloro-1,3-diazetidine-2,4-dione (1) and 1,3-bis(trimethylsilyl) -'1,3-diazetidine-2,4-dione (2) have been determined by X-ray crystallography, and new infrared and Raman data of 1 have been recorded in the solid state, leading to revised and complete fundamental frequency assignments. Both compounds show a planar ring with a trans-configuration of the substituents X [X = -Cl, -Si(CH3)3]. The angles between the C-N-C plane and the exocyclic N-X bond are quite different: 32.5(1)° in 1 and 2.5(2)° and 0.8(2)° in 2. These values are extremes referring to the known structural data of 1,3-diazetidine-2,4-diones. A normal coordinate analysis together with ab initio and semi-empirical calculations have been performed for 1 in order to support the vibrational assignments. The general valence force field confirms the revised frequency assignments. For discussion of the coupling phenomena in this molecule, the normal modes of vibration are plotted in terms of atomic displacements.

Vibrational spectra and force constants of ClNCCl 2

New infrared and Raman data have been obtained on gas, liquid, and solid phase samples of three isotopic species of N-chloro-isocyanid dichloride, namely, ClNCCl 2, Cl 15NCCl 2, and ClN 13CCl 2, leading to revised fundamental frequency assignments. Special attention was paid to the deformation vibrations for which wrong assignments exist in the literature. The general valence force field confirming the revised frequency assignments has been determined using presently available electron diffraction data and reflects the somewhat unusual electronic situation in the molecule.

Electronic and vibrational spectra and thermodynamic functions of 3- and 4-methoxy benzonitriles

The i.r. absorption spectra of 3- and 4- methoxy benzonitriles have been recorded on a Perkin—Elmer 521 spectrophotometer, while the Raman spectrum of 4-methoxybenzonitrile was recorded on CODERG Raman spectrometer T800 triple monochromator. The near ultraviolet absorption spectra of both the molecules in vapour phase have been recorded on Medium Quartz Hilger spectrograph and that of 4-methoxybenzonitrile on DK-2A ratio recording spectrophotometer also. The assignment of fundamental frequencies to various modes of vibration have been proposed and on the basis of free internal rotation and assigned vibrational frequencies, the thermodynamic functions of the molecules have been computed on a VAX-11/780 computer. The analysis of the electronic spectra has been given in terms of fundamentals, their combinations and overtones. 4-Methoxy benzonitrile has exhibited two band systems corresponding to 1 A 1 g - 1 B 2 u (2600 Å) and 1 A 1 g - 1 B 1 u (2100 Å) system of benzene, while 3-methoxybenzonitrile exhibited only the former system. The red shift of 0,0 bands has been discussed.

Vibrational spectrum and thermodynamic functions of para methylbenzonitrile molecule

Raman spectrum of para methylbenzonitrile (CH 3C 6H 4CN) has been recorded on a Russian model ESP-51 three prism glass spectrograph with a linear dispersion of 19 Å/mm at 4000 Å using 4358 Å line of a low pressure 3 A Hg-arc as the exciting line. The i.r. spectrum of the molecule has been recorded in the region 4000-250 cm −1 on a Perkin—Elmer model 521 spectrophotometer. Assuming C 2 v symmetry a complete assignment of fundamental frequencies to various modes of vibration of the molecule has been proposed. On the basis of free internal rotation with six-fold symmetry and assigned vibrational frequencies thermodynamic functions of the molecule have been computed on a TDC 316 computer.

Infrared and Raman spectra of [(CH3)3C]2PF and [(CH3)3C]2PCl

Abstract The liquid state infrared spectra of bis(t-butyl) fluorophosphine and bis(t-butyl) chlorophosphine were recorded from 3100 to 33 cm−1. Corresponding Raman displacements are reported as well as polarization data. Assignments of fundamental frequencies are consistent with Cs symmetry for the skeletal framework and local C3v for the t-butyl groups. The assignments are compared with those of the related t-butyl-dihalophosphines reported earlier.

Thermodynamic properties of oxalyl fluoride from 13°K to its boiling point

The saturated molar heat capacity has been measured from 13°K to its normal boiling point, 270.13°K, for a sample of 99.94 mole% purity. The molar heat of fusion was found to be 3204 cal/mole at the triple-point temperature of 260.73°K. The molar heat of vaporization at the normal boiling point was found to be 6753 cal/mole. The vapor pressure of the solid in the range from 234°K to the triple point of 260.73°K is represented by the equation lnP(torr)=115.38986 − 8720.5964/T − 13.623524 lnT. The vapor pressure of the liquid from the triple point to the boiling point of 270.13°K is represented by the equation lnP(torr)=185.93601 − 10 317.218/T − 25.202996 lnT. The standard entropy of oxalyl fluoride gas at the normal boiling point was found to be 73.01± 0.16 cal/mole·° K. Neither of the two fundamental frequency assignments reported in the literature when used in the statistical entropy calculation gives satisfactory agreement with the calorimetric entropy. It is believed that the discrepancy results from the uncertainty in the assignment of one or more of the low frequency Raman-active modes of the molecule.

Etude par spectroscopie de vibration des interactions des halogenures d'antimoine et des halogenures de gallium — III Spectroscopie de vibration des trihalogenures de gallium cristallises

Vibrational spectroscopic study of the gallium trihalides allows to state precisely the assignments of fundamental frequencies of these compounds. The influence of crystalline field with internal vibrations of dimer molecules Ga 2 X 6 in the unit cell, then is interpreted, from crystallographic data of literature (Ga 2Cl 6) or obtained within this work (Ga 2Br 6 and Ga 2I 6).

Vibrational Spectra of IOF5, OsOF5, and ReOF5

Raman spectra of IOF5, OsOF5, and ReOF5, and the infrared spectra of OsOF5 and ReOF5 are presented, all for the gaseous state. Complete assignments of fundamental frequencies are made, and these confirm the expected C4ν symmetry. Fundamental frequencies in cm−1 in the order, 4a1, 2b1, b2, and 4e, are: for IOF5, 927.0, 680.4, 640.2, 362.9, 647, 307, ∼ 330, 710.3, 372.2, 343, and 204.8; for OsOF5, 962.6, 716.4, 644, 280.5, 644, 210, 332, 700.6, 263, 367, and 164; and for ReOF5, 989.8, 738.6, 643, 309, 652, 234, 334, 713.0, 260, 365, and 125 cm−1.

Lattice Dynamics of Methanol: Hydrogen Bonding and Infrared Absorption

Mathematical methods of treating lattice dynamics of solids have been applied to interpret the infrared spectrum of crystalline CH3OH and CH3OD. New spectra were recorded in the near-infrared region for crystalline CH3OH, CH3OD, and of mixed crystals at various concentrations. The far-infrared spectrum is also reported. Attempts were made to find spectral evidence of the two crystalline modifications of CH3OH. A valence force field has been derived by a least squares fitting on the k = 0 modes of both molecules; the assignments of fundamental frequencies are discussed. Based on this derived force field, phonon dispersion curves and one-phonon and two-phonon densities of states have been calculated in the single-chain approximation. These are used in the interpretation of the infrared spectrum. The vibrational spectra of mixed crystals of CH3OH and CH3OD reveal unusual features which suggest that the breadth of absorption bands due to the hydrogen-bonded atoms is not a property of a single hydrogen bond but arises from cooperative effects with similar neighbors in the chain. The broadness seems to be a function of the chain length.

Raman Spectra of MoF6, TcF6, ReF6, UF6, SF6, SeF6, and TeF6 in the Vapor State

Raman spectra of MoF6, TcF6, ReF6, UF6, SF6, SeF6, and TeF6 have been observed for the gaseous state using laser excitation. Some assignments of fundamental frequencies have had to be revised from previously accepted values. The overtone 2ν6 was observed for all these gaseous hexafluorides and several other overtones were observed for some of the molecules. Considerable broadening of the eg and f2g fundamentals was observed for TcF6 and for ReF6. This broadening is attributed to dynamic Jahn–Teller coupling. The best currently available measured values of fundamental frequencies for all 15 hexafluoride molecules of known Oh symmetry are tabulated.

Microwave spectra of nitryl fluoride in excited vibrational states and its application to vibrational assignment

Microwave spectra of nitryl fluoride in the v 3 = 1 and v 6 = 1 states were identified. The rotational constants, vib-rot interaction constants and inertia defects in these states were determined. Large inertia defects and large vib-rot interaction constants α C and their signs in the excited vibrational states indicate that the ν 3 and ν 6 vibrations are nearly degenerate and further that the frequency of ν 3 is larger than that of ν 6. The inertia defects were combined with the calculated Coriolis coupling constants to estimate the frequency difference ν 3 - ν 6 = 8 cm −1, which gave a definite discrimination among possible assignments of fundamental frequencies already proposed.

The Chemistry of Trifluoroamine Oxide. IV. The Infrared Spectra of F314 NO and F315 NO

The infrared spectra of trifluoroamine oxide and its 15N analogue have been measured from 4000 to 260 cm−1. Fundamental frequency assignments (based upon C3ν symmetry) made from the 14N spectrum are: ν1( a1) = 1689, ν2( a1) = 740, ν3( a1) = 528, ν4( e) = 880, and ν6( e) = 398 cm−1. Normal coordinate calculations support the assignment of the remaining fundamental ν5( e) to a band system appearing as a shoulder, about 558 cm−1, on the intense ν3( a1) fundamental.