VIBRATIONAL ANALYSIS OF SUBSTITUTED AND PERTURBED MOLECULES. I. EXACT ISOTOPE RULES FOR MOLECULES

Author Institution: North American Aviation Science CenterGreen's function and partitioning techniques are applied to molecular systems. A general theory is developed which results in exact and explicit formulas for the vibrational frequencies of isotopically substituted molecules without recourse to a force constant model. The construction of the Green's function from the symmetry coordinates and experimental frequencies is discussed. It is shown that the mixing of the symmetry coordinates of the unperturbed molecules is determined uniquely from the experimental data. The product rule obtained does not involve the moments of inertia and in many cases depends only upon mass ratios

VIBRATIONAL ANALYSIS OF SUBSTITUTED AND PERTURBED MOLECULES. IV. FORCE CONSTANTS FOR BORON TRIHALIDES

Author Institution: North American Aviation Science CenterUsing the Green's function, we have generated the cartesian force constants for the in-plane vibrations of planar $XY_{3}$ molecules. These force constants are linear combinations of internal coordinate symmetry force constants, and the transformation may be easily obtained. The result is four explicit expressions for the independent force constants which determine the zero-order vibrational frequencies Heretofore, three of the force constants have appeared as unknown parameters in a set of two simultaneous non-linear equations, limiting the accuracy conveniently attainable. For $XY_{3}$ planar molecules, it is possible to determine the six valence force constants of the complete quadratic potential function. Comparison of our results with those of previous calculations indicates that we have obtained greater accuracy with significantly less effort. Variations in the force constants with small changes in frequencies indicate the desirability of utilizing the Green's function approach, and bypassing the force constant model, wherever possible

VIBRATIONAL ANALYSIS OF SUBSTITUTED AND PERTURBED MOLECULES. II. PLANAR XY3XY_{3} MOLECULES: APPLICATION TO BCl3,HBCl2BCl_{3}, HBCl_{2}, AND DBCl2DBCl_{2}

Author Institution: North American Aviation Science CenterThe vibrational frequencies of isotopically substituted planar $XY_{3}$ molecules have been obtained using the Green's function and partioning techniques. Taking $HBCl_{2}$ as an ``isotopic'' species of $BCl_{3}$, we have calculated its spectrum, without invoking a force constant model. The excellent agreement between predicted and observed spectra indicates that even the force constant changes may be neglected as a first approximation. Using the information provided by the calculations, we have observed and identified five of the six $HBCl_{2}$ fundamentals: $\nu_{1}=762$ and $740 cm^{-1}, B^{10}-$ and $B^{11}-Cl$ symmetric stretches; $\nu_{2}=2617 cm^{-1}$, B-H stretch (no splitting); $\nu_{4}=1100$ and $1089 cm^{-1}, B^{10}-$ and $B^{11}-Cl$ asymmetric stretch; $\nu_{5}=892 cm^{-1} (B^{11}$ only), in-plane H deformation; and $\nu_{4}=795$ and $784 cm^{-1}$, out-of-plane deformation. Frequencies observed and identified for the deuterated compound are: $\nu_{2}=1969 cm^{-1}, B-D$ stretch; and $\nu_{6}=661$ and $645 cm^{-1}, B^{10}-B^{11}$ splitting. The calculations also indicate that the other frequencies we have not observed are hidden by $BCl_{3}$ bands, and that $\nu_{3}$, a $B-Cl$ bending mode is at $\approx 285-290 cm^{-1}$, outside the range of our instrument