JOURNAL OF MOLECULAR SPECTROSCOPY 178, 93–98 (1996) ARTICLE NO. 0161 A Breakdown of the Watson-Type Hamiltonian for Some Asymmetric-Top Molecules: The Case of the Spin-Multiplet State K. Yokoyama,* W. C. Lineberger,* and K. M. T. Yamada² * JILA, University of Colorado and NIST, and Department of Chemistry and Biochemistry, University of Colorado, Boulder, Colorado 80309-0440; and ² National Institute for Advanced Interdisciplinary Research, Tsukuba, Ibaraki 305, Japan Received February 9, 1996; in revised form April 24, 1996 A breakdown of the standard Watson-type rotational Hamiltonian was suggested for a molecule with H 2 XYZ structure [S ˇ . Urban and K. M. T. Yamada, J. Mol. Spectrosc. 160, 279–288 (1993)]. This breakdown is due to a near-resonant interaction between the ground state rotational levels and rotational levels in an excited vibrational state. This interaction has been observed in the excited electronic state of H 2 CCC 0 ( 2 A 1 state ) by high-resolution autodetachment spectroscopy. The centrifugal distortion coupling term and nonvanishing matrix elements for electronic spin doublet and triplet states are described using Hund’s case ( b ) basis sets. The results are used to interpret the centrifugal distortion couplings between the n 6 and n 9 modes and the vibrational ground states in H 2 CCC 0 . Centrifugal distortion coupling constants C ac 6 Å 1.0723(2) 1 10 04 and C ab 9 Å01.5397(5) 1 10 05 were obtained for this system.  1996 Academic Press, Inc. INTRODUCTION 0 and a nearby CCC out-of-plane bending mode ( n 6 ) and between £ Å 0 and CCC in-plane bending mode ( n 9 ) in the excited electronic state ( 2 A 1 state) of H 2 CCC 0 ( 4, 5 ). The Watson-type Hamiltonian ( 1 ) is commonly used to This observation motivated us to rederive the centrifugal model the rotational levels of the vibrational ground state distortion coupling term for use with spin-multiplet states. of polyatomic molecules. However, Yamada ( 2 ) found that In this paper, the conditions that lead to the breakdown of the validity of the Watson-type Hamiltonian breaks down the standard Watson-type Hamiltonian are reviewed, and the when it is applied to the interaction between the vibrational centrifugal distortion coupling term is used to account for the ground state and n 5 of HNCO. The breakdown that Yamada breakdown discussed for spin-multiplet states. Nonvanishing discovered can be understood as a nonnegligible centrifugal matrix elements are obtained for doublet and triplet states distortion coupling between the rotational levels of vibra- of a C 2£ molecule. The results are used to interpret the auto- tionally excited states and nearby rotational levels of the detachment spectrum of H 2 CCC 0 . vibrational ground state. Although the vibrationally excited states reside far from vibrational ground levels in many THEORY cases, the energies of vibrationally excited states can be compared to the ground vibrational state rotational levels The effective centrifugal distortion operator can be de- for molecules that have small rotational moments of inertia. rived from a rotation – vibration Hamiltonian expanded in An entire class of such molecules includes those with an normal vibrational coordinates by using a standard perturba- H 2 XYZ-type structure. Urban and Yamada ( 3 ) have demon- tion treatment. This is usually carried out in the harmonic strated that the effective rotational Hamiltonian in its stan- oscillator ( H 20 ) basis ( 1, 6 ) and includes quartic, sextic, and dard power-series expansion converges only within a limited higher-order terms. In the notation used in the following range of rotational quantum numbers for such molecules. discussion, the first subscript indicates the order of the vibra- They demonstrated the effects of the centrifugal distortion tional operator and the second subscript indicates the order coupling contributions for some rotational constants for of the rotational operator. In this perturbation approach, the H 2 CCO and H 2 CNN and predicted that the divergence of quartic centrifugal distortion operator H 04 is obtained from this power series occurs at K ú 20. Unfortunately, molecules H 12 , with this amount of rotational excitation (e.g., 4000 cm 01 ) are difficult to prepare in sufficient concentration for spectro- scopic detection. H O 12 Å0 ∑ s q s v s ∑ a,b C ab s J O a J O b . [1] An exception to this trend is propadienylidene, H 2 CCC. The lowest energy H 2 CCC vibrational mode is much lower Here s is the normal mode and a and b represent two than that for either H 2 CCO or H 2 CNN, and a recent study Cartesian coordinates ( x , y , or z ) . The dimensionless param- with high-resolution autodetachment spectroscopy revealed that the centrifugal distortion coupling occurs between n Å eter, C ab s , is given by 93 0022-2852/96 $18.00 Copyright  1996 by Academic Press, Inc. All rights of reproduction in any form reserved. AID JMS 7052 / 6t0d$$$$21 06-27-96 18:23:08 mspal AP: Mol Spec