Molecules with high rotational angular momentum: a generalized ab initio approach

Abstract

An outline is given of a systematic and automated computational procedure based upon our successful ab initio approach to the theoretical study of centrifugal distortions of rotating molecules and their associated energy stabilizations. Such a generalized procedure permits the ready evaluation of the centrifugal distortion spectroscopic constants for moderate-sized molecules of low or no symmetry; these molecules represent cases for which the older version of our computational procedure is unwieldy. More broadly, we explore the energies and geometries of molecules in those regions of nuclear coordinate hyperspace which are accessible by such distortions from the equilibrium geometry. A method is outlined for optimizing the geometry of a molecule in the presence of a centrifugal field which is parametrically dependent upon the rotational angular momentum. The field is not fixed for a given angular momentum, but is coupled with the geometry via the moment of inertia tensor. This development should prove to be of major benefit to both computational chemists and molecular spectroscopists, as it will advance the interplay of theoretical and experimental studies of molecular structure.

Rotational energy dispersions: Analytic descriptions

“…If desired, the various series and PadC approximant forms may be augmented by J-dependent Z PE contributions based on the analytic E" expressions in Table I and illustrated by the MO and L.JO Z PE series in Eqs. (4) and ( 5 ) . Results for the LJO are of particular interest since the LJO serves as a model for van der Waals complexes.…”

“…Results were presented in our first study ( I ) for Hi, NH,, CH4, BFs, and SF6. More detailed studies followed (2-4) of H20, 03, and PH3, as well as an outline of a generalized extension of the method (5). The procedure is structurally oriented, that is, it focuses on the question of the size and shape of molecules with nonzero rotational angular momentum.…”

“…4. Plot of LJO reduced effective quartic constant a4Ac/b0yz = (1 -f)/y vs y'12 = a[J(J + l)] 'I': (a) exact, (b) Pad6 approximant [ 1 / 1 ] (Table IV), (c) series approximation to n = 3.LJO 2 PE may be obtained as a function of y from the reduced force constant and the series reversion of y( z) or y(x), and is given in units of 6@:" byZPE(y)/ZPE(O)= 1 -9y -65y2/2 -1795y3/28 005y4/8 -1 103 533y5/24 + --- (5).…”