Mean-square Perpendicular Amplitudes Research Articles

ChemInform Abstract: SHRINKAGES OF THE INTERNUCLEAR DISTANCES IN SOME HEXAFLUORIDES OF OCTAHEDRAL SYMMETRY

AbstractEine kurze Analyse der Verkürzung der interatomaren Abstände in molekularen Systemen durch thermische Bewegungen wird gegeben.

Spectroscopic studies of potential energy constants, root-mean-square amplitudes, coriolis coupling coefficients and shrinkages of chemical bonds in mercurous halides

A brief vibrational and structural analysis of mercurous halides possessing a linear symmetrical configuration with the symmetry point groupD∞h has been made. On the basis of group theoretical considerations, potential energy constants have been evaluated by employing a five-constant valence force field. Mean-square amplitudes and root-mean-square amplitudes for both bonded and nonbonded atom pairs have been computed at the temperatures 298 °K and 500 °K. The Coriolis coupling coefficients have been, in terms of the symmetrized force constants, computed. The generalized mean-square amplitudes (mean-square parallel amplitudes, mean-square perpendicular amplitudes, and mean cross products) have been evaluated from the symmetrized mean-square amplitudes, and used to calculate the shrinkages of chemical bonds. The results have been discussed in relation to the nature of the two characteristic bonds of these three molecular systems.

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.

Shrinkages of the internuclear distances in some hexafluorides of octahedral symmetry

A brief analysis of the shrinkages or shortening of the internuclear distances in many molecular systems has been made. Analytical expressions for the linear shrinkage and nonlinear shrinkage have been derived in terms of the meansquare perpendicular amplitudes. Analytical expressions for the generalized mean-square amplitudes (mean-square parallel amplitudes, mean-square perpendicular amplitudes, and mean cross products) for an octahedralXY6 molecule have been given in terms of the mean-square amplitude matrices. The linear and nonlinear shrinkages for the hexafluorides of sulfur, selenium, tellurium, molybdenum, technetium, ruthenium, rhodium, tungsten, rhenium, osmium, iridium, platinum, uranium, neptunium, and plutonium have been computed at 298°K and 500°K, and the results have been briefly discussed.

Mean amplitudes of vibration in some tetrahedral tetrahalogeno complexes

The Cyvin method, utilizing symmetry coordinates, has been employed here to compute the mean-square amplitude quantities, generalized mean-square amplitudes (mean-square parallel amplitudes, mean-square perpendicular amplitudes and mean cross products) and mean amplitudes of vibration for the bonded as well as non-bonded atom pairs at the temperaturesT=298°K andT=500°K for the tetrahedral tetrahalogeno complexes of zinc, cadmium, gallium, indium, thallium and arsenic. The non-linear behaviour of the mean amplitudes of vibration in terms of the electronegativities of the central atoms has been discussed, followed by a discussion on the replacement of peripheral atoms.

Mean Amplitudes of Vibration of Some Tetrahedral XY4 Type Molecules‐Part I

AbstractThe general theory of mean‐square amplitude matrices has been briefly applied to the tetrahedral XY4 type molecule. The expressions for the twelve mean‐square amplitude quantities as linear combinations of the symmetrized mean‐square amplitude matrix elements have been given. The secular equations for the normal frequencies involving symmetry force constants and symmetrized mean‐square amplitude matrix elements have been obtained. The expressions for the generalized mean‐square amplitudes (mean‐square parallel amplitudes, mean‐square perpendicular amplitudes, and mean cross products) in terms of the Σ matrix elements have been given. For the molecules SiF4, OsO4, RuO4, CH4, CD4, CD4 and Cl4, the computed values of (1) mean‐square amplitude quantities, (2) generalized mean‐square amplitudes and (3) mean amplitudes of vibration at the temperatures T=O and T=298°K have been reported.

Vibrational mean-square amplitude matrices—XII

Expressions are given for the generalized mean-square amplitudes (mean-square parallel amplitudes, mean-square perpendicular amplitudes, and mean cross products) in terms of the Σ matrix elements for the following molecular models: (i) linear YXZ, (ii) regular trigonal X3, (iii) plane square X4, (iv) tetrahedral X4, (v) linear symmetrical XY2, (vi) bent symmetrical XY2, (vii) planar symmetrical XY3, and (viii) tetrahedral XY4. Numerical values of the mentioned quantities are reported for 12CO2, 13CO2, 14CO2, OCS, OCSe, CS2, SCSe, CSe2, SCTe, P4, 14NO2,15NO2, 11BF3, 11BCl3, 11BBr3, and 11BI3.