331 research outputs found
MOLECULAR BOND STRENGTHS, BOND ENERGIES, AND FORCE CONSTANTS
No full textAuthor Institution: Physics Department, Illinois Institute of Technology``Bond Strength'' is a term which is much used but seldom (if ever) defined. A possible definition would be that the bond strength is the average force S required to do 99.99 per cent of the work necessary to produce infinite separation of the atoms X and Y in the bond. That is ""[FIGURE]"" \begin{equation}S= \int^{R}_{r_{v}} f(r)\ dr/ \int^{R}_{r_{e}}dr,\end{equation} where is the force at the internuclear separation is the separation at equilibrium, and R is that value of r at which the potential energy being the dissociation energy (or bond energy). Using the Morse potential energy function, with and , one finds that , where a is the constant in the Morse function that determines the curvature of the potential energy curve near . Using this, and replacing the first integral in Eq. (1) by 0.9999 , gives \begin{equation}S=0.1010\ a\ W_{De}\end{equation} If a is not known, one can use the stretching force constant f for the X-Y bond. This is given by . Using the value of a obtained from this, Eq. (2) becomes \begin{equation}S=0.07142 (f\ W_{De})^{1/2},\end{equation} or \begin{equation}S=9.0419\ \mu\ dyn (f\ W_{De})^{1/2}\end{equation} when f is in microdynes per picometer and is in electron-volts. Previously, L. Pokras obtained for , the values dyn/pm, 5.2933 eV, for , and 51.194, 5.3211, for . Using these, and . Values of S for other bonds, calculated from less reliable values of are: and . It is interesting to note that the S values of , and are in the ratio 1 to 1.9 to 2.9
FORCE CONSTANTS FROM RYDBERG-KLEIN-REES POTENTIAL ENERGY CURVES.
No full textAuthor Institution: Physics Department, Illinois Institute of TechnologyWe have calculated equilibrium force constants internuclear separation, U = potential energy, e = equilibrium] from the Rydberg-Klein-Rees potential energy curves for 11 diatomic molecules. The results are in good agreement with the values previously calculated from , which was derived from the harmonic potential energy function [c = speed of light in vacuum, classical vibrational frequency in cycles/sec for infinitesimal amplitudes, reduced mass]. This is as it should be since the force per unit displacement at should be the same for any valid potential energy curve. The values of for isotopes of these molecules were nearly the same as for the ordinary molecules. For HCI, the values were: microdynes/picometer. If the molecule were a harmonic oscillator, the force derivative function would be the same for all values of r, but for the actual molecule the values of this function vary with r. At ; at is the value of r at the inflection point i on the potential energy curve]. The average value of for the vibrational state v can be taken as the effective force constant in that vibrational state. We have calculated values of from the R-K-R curve of for several values of v. As v increases from 0 to 9, decreases from to . Effective force constants and for and were calculated for the 11 molecules. In all cases, and were larger than and smaller than observed wave number in cycles/cm]. For , the values are:
Depolarization Factors of Raman Lines
No full textAuthor Institution: Department of Physics, Lynchburg CollegePresentations without an abstract printed in the proceedings do not have an abstract (image or text) in the Knowledge Bank record
POTENTIAL ENERGY CONSTANTS FOR SOME HALOMETHANES FROM MOLECULAR PARAMETERS
No full textAuthor Institution: Department of Physics, Illinois Institute of TechnologyA theory is presented for the calculation of the potential energy constants (f’s) of some halomethane molecules. The potential energy function is assumed to be that of a harmonic oscillator with interactions between pairs of internal displacement coordinates. The f for the stretching of a bond is assumed to be a linear function of the charge density. It is assumed that a small amount of charge may be transferred between bonds. The shape of the bonds is assumed to be that of a prolate spheroid. The total amount of charge for bonding present in a molecule is assumed to be constant. An angle deformation is viewed as the bending of two bonds. The f for the bending of a bond is assumed to be a fraction of the f for the stretching of that bond. The interaction f’s between the different coordinates are assumed to arise from changes in the charge densities of the bonds involved. The f’s are used in a Wilson FG matrix normal coordinate treatment. A set of computer programs facilitated the investigation of the values of the empirical constants introduced in the theory. One program calculated the f’s which reproduced the experimental spectrum by use of an iteration procedure. The molecules investigated were , , , and . The average difference between the f’s from theory and those from experimental data for the stretching f’s is {\AA}, that for the bending f’s is , that for the stretching-stretching interaction f’s is {\AA}, that for the stretching-bending interaction f’s is , and that for the bending-bending interaction f’s is {\AA}. Calculations are continuing
INTRODUCTORY PAPER ON RAMAN SPECTROSCOPY
No full textAuthor Institution: Spectroscopy Laboratory, Department of Physics, Illinois Institute of Technology, Chicago, IllinoisTHE RAMAN effect was discovered in 1928 and since that time an average of 125 papers per year on this subject have appeared. Our Raman spectrograms are obtained by use of two cylindrical, horizontal, low-pressure, Pyrex Hg arcs. Raman-displacement spectrograms are obtained with a 2-prism spectrograph having a dispersion of 33 \AA/mm and depolarization-factor spectrograms with a hilger E518 spectrograph having a dispersion of 63 \AA/mm, both at 4500 \AA. Relative intensities are obtained with a microdensitometer and a microphotometer. A reliable single-exposure method (J. Chem. Phys. 13, 101 (1945) is used for the depolarization factors because short-cut methods can lead to erroneous conclusions about molecular structure. Since some vibrations are not observable in Raman spectra, an infrared spectrometer is a necessary supplement. Infrared data are especially needed from 100 to and with greater resolution above . Group theory selection rules predict the spectra that should result for various assumed structures of the molecule (Am. J. Phys. 11, 239 (1943)). Comparison with experimental data may thus enable one to determine the structure. Dangerous assumptions-frequently made-are that all of the observed Raman lines are fundamentals, and that fundamentals correspond only to strong bands. Hence, a reliable assignment of the fundamentals is necessary. Dr. Meister suggests that an anharmonicity treatment, even if incomplete, may provide useful additional checks upon the assignments. Another important check is a normal coordinate treatment, using the most general potential-energy expression possible (Am. J. Phys. 14, 13 (1946)). Even this, however, does not always lead to an unambiguous assignment for all lines, especially when two fundamentals fall close together. The final decision on the assignment of the fundamentals must be a matter of considered judgment in which all the possible tests are taken into account. When the fundamentals have been reliably assigned, and their degeneracies determined, one can then calculate thermodynamic properties for the ideal gaseous state, provide the product of the three principal moments of inertia, or the bond distances and interbond angles, are known (Chem. Rev. 27, 17 (1940))
Vibrational Spectrum of Di-iodoacetylene
No full textAuthor Institution: Illinois Institute of TechnologyPresentations without an abstract printed in the proceedings do not have an abstract (image or text) in the Knowledge Bank record
BOND STRENGTHS, DISSOCIATION AND ZERO-POINT ENERGIES, AND FORCE CONSTANTS FOR 49 DIATOMIC MOLECULES AND 24 SUBSTITUTED METHANES
No full textAuthor Institution: Department of Physics, Illinois Institute of TechnologyUsing the spectroscopic constants , and , the equilibrium internuclear distance , the bond energy , and the reduced mass , one can calculate for a diatomic molecule the band origin of the 1-0 band, the force constants and the constant the zero-point energy , the equilibrium dissociation energy , the constant , the bond strength S, and the constant in the Morse function for the potential energy U. For different molecules of the same bond type, the values of and are nearly constant, and one can therefore establish average values and for each bond type. Such calculations were made for 49 diatomic molecules having the bond types B-A, B-B, B-C, B-D, and B-E. When and are not known, these values of and can be used with and to calculate good approximate values of and S. This was done for all the 49 diatomic molecules to determined values was remarkably good. Similar calculations were made for the bonds C-H, C-F, C-Cl, C-Br, and C-I (which include the same bond types) in 24 substituted methanes, using , and or for the stretching vibration. For , there was good agreement between our values of and the corresponding w values reported by Dennison; by King, Mills, and Crawford; and by Aldous and Mills
Raman Spectra of Hydrocarbons IV. 2,5-Dimethyl-1,5-Hexadiene and 2,5-Dimethyl-2,4-Hexadiene
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