Mean amplitudes of vibration for biphenylene

A normal coordinate analysis for the in-plane vibrations of biphenylene was performed. Calculated values of mean amplitudes of vibration for all interatomic distance types in biphenylene and biphenylene-d₈ are given.With 2 Figures     

Mean amplitudes of vibration and related quantities for methyl cyanide

Mean amplitudes of vibration for CH₃CN and CD₃CN have been calculated from spectroscopic data and a normal coordinate analysis. The linear shrinkage effects and perpendicular amplitude correction coefficients are also reported.     

Mean amplitudes of vibration for cyclohexene from spectroscopic data

A normal coordinate analysis is performed for cyclohexene (C₆H₁₀). The calculated frequencies for C₆H₁₀ and C₆D₁₀ are reported. The mean amplitudes of vibration for all types of interatomic distances in these two molecules were also computed. Those of the bonded distances and nonbonded C?C distances in C₆H₁₀ are compared with the corresponding data from election diffraction.     

Mean amplitudes of vibration for cyclobutane and cyclobutane-d8 from spectroscopic data

Mean amplitudes of vibration for cyclobutane and cyclobutane-d₈ are calculated on the basis of spectroscopic data. Results for the bonded distances are compared with data from electron diffraction, and a good agreement is found.     

Mean amplitudes of vibration for CH3SO2F and CH3SO2Cl from spectroscopic data

A tentative assignment of vibrational frequencies for CH₃SO₂F and CH₃SO₂Cl is established. The available spectral data from literature were supplemented by new infrared measurements in the liquid phase. A normal coordinate analysis was performed on the basis of the assigned frequencies. Calculated mean amplitudes of vibration from this analysis are reported. The results are compared with mean amplitudes from recent gas electron diffraction data.     

Mean amplitudes of vibration of molecules and ions with interhalogen bonds and related species

Mean amplitudes of vibration of molecules and ions containing interhalogen bonds are reviewed and critically analyzed. The presented information comprises pure interhalogen compounds as well as oxohalides. Correlations between mean amplitude values and structural and bond properties are discussed. Comparisons with data of related - specially isoelectronic - species are also performed. Characteristic ranges for the mean amplitudes of vibration for halogen-halogen and halogen-oxygen bonds could be established. The presented and discussed results are also of central importance for the analysis and interpretation of electron diffraction studies.     

Mean amplitudes of vibration for PMo12O40 3− and its fragments

Mean amplitudes of vibration () are calculated for all 80 distance types in PMo₁₂O₄₀ ^3–. The values are discussed and some of them compared with the corresponding values calculated for, five different fragments of the structure. Reasonable values (<0.12 Å at 298 K) are found even for extremely long distances, e.g. 0.078 Å at 298 K for the longest oxygen-oxygen distance (10.4 Å). The values for bonded distances as well as a number of nonbonded distances have comparable magnitudes in the fragments and the whole structure; in other cases the fragment values are substantially higher.

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Mittlere Schwingungsamplituden für PMo₁₂O₄₀ ^3– und Fragmente

Zusammenfassung Mittlere Schwingungsamplituden () für alle 80 Typen von Abständen in PMo₁₂O₄₀ ^3– wurden berechnet. Die Werte werden diskutiert und einige werden mit denen von fünf verschiedenen Fragmenten der untersuchten Struktur verglichen. Es wurden auch für extrem große Distanzen plausible -Werte (<0,12 Å bei 298 K) gefunden (z. B. 0,078 Å bei 298 K für die größte, O–O-Distanz 10,4 Å). Die, -Werte für Bindungslängen und auch für einige Abstände von nicht aneinander gebundenen Atomen weisen in den Fragmenten und in der Gesamtstruktur vergleichbare Größe auf; in anderen Fällen sind die Fragment-Werte allerdings bedeutend höher.

     

Mean amplitudes of vibration and perpendicular amplitude correction coefficients for 1,2,4,5-hexatetraene and 1,2,4-pentatriene

Mean amplitudes of vibration (u) and perpendicular amplitude correction coefficients (K) for 1,2,4,5-hexatetraene and 1,2,4-pentatriene were computed from spectroscopic data. Values at 298°K for all interatomic distances are given and discussed.     

Mean amplitudes of vibration of the XF+4 interhalogen cations

Mean amplitudes of vibration for the cations ClF⁺₄, BrF⁺₄ and IF⁺₄ have been calculated using the ‘Method of the Characteristic Vibrations’ and recently revised spectroscopic data. The results are briefly discussed and some comparisons with isoelectronic molecules and other related species are made.     

Mean-square amplitudes of vibration and shrinkage effects from mindo/2 calculations

MINDO/2 semi-empirical molecular orbital theory can be used to calculate mean-square amplitudes of vibration and shrinkage effects. Calculated values for ethylene and benzene deviate from spectroscopic values by an average of 4 %. The force field calculations can be carried out conveniently in Cartesian coordinates.     

Condensed values of mean and amplitudes of vibration

Calculated mean amplitudes of vibration for all types of distances in light and heavy naphthalene and benzene are represented (in 10⁻³ Å units) on figures. Some comments are made on the partially deuterated compounds.     

Mean amplitudes of vibration of the ClF6, BrF6 and IF6 anions

Mean amplitudes of vibration for the title hexafluoroanions were calculated on the basis of its vibrational-spectroscopic and structural data in the temperature range between 0 and 1000 K. The results are briefly discussed in comparison with those of other related species.     

Ab initio and density functional calculations of mean-square amplitudes of vibration for benzene and cubane

Mean-square amplitudes of vibration were calculated using ab initio and density functional methods for benzene and cubane. Both 6-31G^* and 6-311G^** basis sets were employed. It was found that significant improvements were achieved when electron correlation was introduced, even if only at the local density functional level. The mean-square amplitudes calculated were not effected by the basis set used for benzene and slightly improved for the highly strained cubane molecule when the larger basis set was used. An attempt was also made to improve the calculated mean-square amplitudes by making use of scale factors found in the literature, which were developed to improve the calculated frequencies. It was found that only the SCF mean-square amplitudes were significantly improved.     

Mean amplitudes and shrinkages for SiH3NCO and SiH3NCS

Mean amplitudes and shrinkages are calculated from spectroscopic data for SiH₃NCO, SiD₃NCO, SiH₃NCS and SiD₃NCS. The lowest frequency (ν₁₀) in each of the molecules is uncertain, and its influence on the calculated amplitude parameters is investigated. The results are compared with electron diffraction studies.     

Potential energy constants,mean-square amplitudes of vibration and rotational distortion constants for C2F4, C2Cl4 and C2Br4

By adopting the potential energy function of G.V.F.F. type the principal force constants for each of the perhaloethylenes C₂F₄, C₂Cl₄ and C₂Br₄ were refined through a best-fit iteration process. The carbon—carbon and carbon—halogen stretching force constants are discussed considering the possible effects of halogen atoms on the molecular structure. The mean-square parallel and perpendicular amplitudes of vibration at 298·16°K were computed. The rotational distortion constants were evaluated on the basis of a first-order perturbation method.     

A new,practical method of computing mean amplitudes of vibration and perpendicular amplitude correction coefficients

A new approach for calculating mean amplitudes of vibration (u), perpendicular amplitude correction coefficients (K) - used in the calculation of R_α structures and shrinkage effects - and related quantities are presented. The method is based on an expansion of interatomic distances in terms of the cartesian displacement coordinates. This leads to a practical way of calculating the u and K values, which is convenient for computer solution. Only a short subroutine is necessary in addition to a normal coordinate program by W.D. Gwinn in order to perform these calculations.     

Theory of a new method of computing mean amplitudes of vibration and perpendicular amplitude correction coefficients

Some theoretical aspects of the calculations of mean amplitudes of vibration (l) and perpendicular amplitude correction coefficients (K) are treated. A recipe for practical computations of the l and K values is given. In contrast to the conventional methods the proposed computation of K circumvents the calculation of mean-square perpendicular amplitudes.     

Relations between mean amplitudes of vibration and corresponding internuclear distances : II. Bonded carbon-carbon distances

The empirical relation u(CC_bond) = −0.071856 + 0.124162 r − 0.028974 r² was established from a statistical treatment of 57 electron diffraction measurements (1.2086 r 1.549, where r is the bond distance, and u is the mean amplitude of vibration; both in Å units). The agreement between observed and calculated u values is significantly improved when compared with the corresponding treatment of bonded and non-bonded CC distances taken together.