A Simultaneous Determination of Third-Order Vibrational Anharmonicity Constants and Equilibrium Structure Molecular Structure of Non-linear HX Y type Molecules

Abstract

In order to eliminate ambiguities in spectroscopically determined molecular stiucture caused by intramolecular vibrations, a method has been developed which analyzes ground-state rotational constants and 'vibration-rotation constants of a sufficient number of isotopes simultaneously by the least-squares method using equilibrium structure parameters and thirdorder anharmonicity constants as adjustable parameters. The method has been applied to HNO/DNO and HOCl/DOCl, for both of which not all vibration-rotation constants, have been determined, preventing the equilibrium structure from being determined through a conventional procedure of calculating equilibrium rotational constants. The equilibrium structures thus obtained are r_e (H-N) =1.0628 (25) Å, r_e(N-O) =1.2058 (27) Å, and θ_e (HNO) =109.09(24)° for HNO and r_e(H-O)=0.9654(35)Å, r_e(O-C1) =1.6891(29)Å, and θ_e(HOCl)= 103.2 1(60)°for HOCl, with three standard deviations in parentheses. The analysis has also yielded some of the third-order anharmonicity constants, which are indispensable in analyzing vibrational changes of molecular constants and also in discussing the dynamical behavior of molecules. The “diagonal” third-order constants which are determined are F₁₁₁= -25.31(22) aJ A^-3, F₂₂₂-77(12) aJÅ^-3. and F₃₃₃= 1.05(15) aJ rad^-3 for HNO and F₁₁₁= 42.5 (10.4) aJ A^-3, F₂₂₂=-21.8(8.4) aJ Å. ^-3, and F₃₃₃= 0.42(1.14) aJ rad^-3 for HOCl, where the internal coorinates are numbered such that 1 for δr(H-X), 2 for δr(X-Y), and 3 for δθ(HXY), and the values in parentheses denote three standard deviations. It has also been shown that the method can be applied to molecules in an excited electronic state, using HNO in the A¹A¹¹ state as an example. The result is by no means satisfactory; the precision of the derived constants is not high. This is mainly ascribed to perturbations in the excited state, and the present analysis may provide us with chances of examining the interactions affecting the excited state. The method developed in the present paper will be applicable to a few other simple molecules such as bent XYZ-type molecules without involving any hydrogen/deuterium atoms and planar C_2v H₂XY-type, molecules.