Kinematical evaluation of force constants: application to trihalides of phosphorus and arsenic

The F-matrix elements for the two-dimensional symmetry species are dependent on one arbitrary parameter in addition to the vibrational frequencies. This parameter has been chosen as an angle � (0 ≤ � ≤ 2π) and the F-matrix elements for the A1- and the E-species of trihalides of phosphorus and arsenic have been studied as functions of �. It is found that the best values of the force constants obtained from Coriolis 1; constants can be correlated with those values of the angle ξ for which the bending force constant exhibits a minimum.

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Ein Iterationsverfahren zur Berechnung von Kraftkonstanten aus Grundschwingungsfrequenzen

Zeitschrift für Naturforschung A ◽

10.1515/zna-1970-8-917 ◽

1970 ◽

Vol 25 (8-9) ◽

pp. 1274-1280

Author(s):

W. Hüttner

Keyword(s):

Least Squares ◽

Force Constant ◽

Vibrational Frequencies ◽

Force Constants ◽

Normal Equations

Abstract A method for the adjustment of force constants from vibrational frequencies is presented. It re-presents an alternative to the various types of least-squares procedures which are widely used in force constant calculations, and avoids some of the well-known divergence difficulties which may occur in such least-squares iterations. Solving a system of normal equations is replaced by two simpler operations which cannot become ill-conditioned by singularities. The method applies preferably to cases where the number of excess data is small or zero.

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CHARACTERISTIC VIBRATIONAL FREQUENCIES OF OXYGEN COMPOUNDS OF SILICON, PHOSPHORUS, AND CHLORINE: CORRELATION OF STRETCHING FREQUENCIES AND FORCE CONSTANTS WITH BOND LENGTHS AND BOND ORDERS

Canadian Journal of Chemistry ◽

10.1139/v63-443 ◽

1963 ◽

Vol 41 (12) ◽

pp. 3021-3033 ◽

Cited By ~ 65

Author(s):

E. A. Robinson

Keyword(s):

Bond Length ◽

Force Constant ◽

Chlorine Atom ◽

Silicon Atom ◽

Vibrational Frequencies ◽

Force Constants ◽

Bond Orders ◽

Present Treatment ◽

Bond Lengths ◽

Linear Correlations

For oxygen compounds of chlorine, phosphorus, and silicon, respectively, correlations are established between stretching frequencies and force constants of Cl—O, P—O, and Si—O bonds, and their bond lengths.By deducing bond orders on the assumption that only [Formula: see text]and [Formula: see text] orbitals on the central chlorine, phosphorus, or silicon atom are utilized in the formation of double bonds with lone pairs of electrons on oxygen, linear correlations between bond orders and force constants are established.The present treatment leads to the conclusion that the presence of a maximum of 12 electrons in the valency shells of chlorine, phosphorus, and silicon is required to best explain the bond length and force constant data, when highly electronegative ligands such as oxygen or fluorine are attached to the central silicon, phosphorus, or chlorine atom.

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Vibrational Spectra of the Hexacarbonyl Manganese(I) Cation

Canadian Journal of Chemistry ◽

10.1139/v74-035 ◽

1974 ◽

Vol 52 (2) ◽

pp. 213-215 ◽

Cited By ~ 16

Author(s):

R. A. N. McLean

Keyword(s):

Force Constant ◽

Raman Spectra ◽

Vibrational Spectra ◽

Vibrational Frequencies ◽

Force Constants ◽

Infrared And Raman Spectra

The infrared and Raman spectra of the hexacarbonylmanganese cation as Mn(CO)6+ PF6− were assigned by comparison with other hexacarbonyl species. The CO stretching force constants for Mn(CO)6+ and Re(CO)6+ as indicated by the CO stretching vibrational frequencies are not significantly different. However, the Mn—C force constant in Mn(CO)6+ is likely to be considerably less than the Cr—C force constant in Cr(CO)6, whereas Re(CO)6+ and W(CO)6 have similar values. It is postulated that, although Mn(CO)6+ has equal metal–carbon σ bonding to Re(CO)6+, the metal-carbon σ bonding is less for Mn(CO)6+.

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Bonded Force Constant Derivation of Lysine-Arginine Cross-linked Advanced Glycation End-Products

10.26434/chemrxiv.5891602.v2 ◽

2018 ◽

Author(s):

Anthony Nash ◽

Nora H de Leeuw ◽

Helen L Birch

Keyword(s):

Molecular Dynamics ◽

Force Constant ◽

Computational Study ◽

Force Constants ◽

Quantum Mechanical ◽

Advanced Glycation ◽

Partial Charges ◽

Cross Links ◽

Complete Set ◽

Dynamics Simulations

<div> <div> <div> <p>The computational study of advanced glycation end-product cross- links remains largely unexplored given the limited availability of bonded force constants and equilibrium values for molecular dynamics force fields. In this article, we present the bonded force constants, atomic partial charges and equilibrium values of the arginine-lysine cross-links DOGDIC, GODIC and MODIC. The Hessian was derived from a series of <i>ab initio</i> quantum mechanical electronic structure calculations and from which a complete set of force constant and equilibrium values were generated using our publicly available software, ForceGen. Short <i>in vacuo</i> molecular dynamics simulations were performed to validate their implementation against quantum mechanical frequency calculations. </p> </div> </div> </div>

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RAMAN SPECTRA OF TITANIUM DI-, TRI-, AND TETRA-CHLORIDES

International Journal of Modern Physics B ◽

10.1142/s021797920100886x ◽

2001 ◽

Vol 15 (28n30) ◽

pp. 3865-3868 ◽

Cited By ~ 2

Author(s):

H. MIYAOKA ◽

T. KUZE ◽

H. SANO ◽

H. MORI ◽

G. MIZUTANI ◽

...

Keyword(s):

Force Constant ◽

Raman Spectra ◽

Normal Mode ◽

Raman Band ◽

Normal Mode Analysis ◽

Force Constants ◽

Mode Analysis ◽

Oxidation Number

We have obtained the Raman spectra of TiCl n (n= 2, 3, and 4). Assignments of the observed Raman bands were made by a normal mode analysis. The force constants were determined from the observed Raman band frequencies. We have found that the Ti-Cl stretching force constant increases as the oxidation number of the Ti species increases.

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Berechnung kinetischer Isotopeneffekte für die Reaktion von Methyljodid mit Cyanid-Ion

Zeitschrift für Naturforschung A ◽

10.1515/zna-1966-0909 ◽

1966 ◽

Vol 21 (9) ◽

pp. 1377-1384

Author(s):

A. V. Willi

Keyword(s):

Transition State ◽

Secular Equation ◽

Isotope Effects ◽

Force Constants ◽

Bond Breaking ◽

Bending Force ◽

A Value ◽

Order Of Magnitude ◽

Deuterium Isotope Effects ◽

The Difference

Kinetic carbon-13 and deuterium isotope effects are calculated for the SN2 reaction of CH3I with CN-. The normal vibrational frequencies of CH3I, the transition state I · · · CH3 · · · CN, and the corresponding isotope substituted reactants and transition states are evaluated from the force constants by solving the secular equation on an IBM 7094 computer.Values for 7 force constants of the planar CH3 moiety in the transition state (with an sp2 C atom) are obtained by comparison with suitable stable molecules. The stretching force constants related to the bonds being broken or newly formed (fCC, fCC and the interaction between these two stretches, /12) are chosen in such a way that either a zero or imaginary value for νʟ≠ will result. Agreement between calculated and experimental methyl-C13 isotope effects (k12/ k13) can be obtained only in sample calculations with sufficiently large values of f12 which lead to imaginary νʟ≠ values. Furthermore, the difference between fCI and fCC must be small (in the order of 1 mdyn/Å). The bending force constants, fHCI and fHCC, exert relatively little influence on k12/k13. They are important for the D isotope effect, however. As soon as experimental data on kH/kD are available it will be possible to derive a value for fHCC in the transition state if fHCI is kept constant at 0.205 mdynA, and if fCI, fCC and f12 are held in a reasonable order of magnitude. There is no agreement between experimental and calculated cyanide-C13 isotope effects. Possible explanations are discussed. — Since fCI and fCC cannot differ much it must be concluded that the transition state is relatively “symmetric”, with approximately equal amounts of bond making and bond breaking.

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