Paul M. Parker

Asymmetric‐Top Vibration—Rotation Hamiltonians

From the general molecular vibration—rotation Hamiltonian in the Nielsen—Amat—Goldsmith formulation, Hamiltonians for asymmetric‐top molecules of the orthorhombic, monoclinic, and triclinic point group symmetries are deduced. These Hamiltonians are appropriate for the calculation of vibration—rotation energies to the fourth order of approximation.

Centrifugal‐Distortion Coefficients of the Nonlinear XYX Molecule

All coefficients of centrifugal distortion that are expected to contribute to the molecular vibration—rotation energies to fourth or lower orders of approximation are calculated for the nonlinear XYX molecule as functions of the fundamental molecular constants. The Nielsen—Amat—Goldsmith expansion of the vibration—rotation Hamiltonian forms the basis of this calculation.

Higher‐Order Centrifugal‐Distortion Effects in Asymmetric Rotators

The terms of the general molecular vibration—rotation Hamiltonian that are of the sixth power in the angular‐momentum components are studied. Those terms which are expected to contribute to the allowed energies in fourth order of approximation in the Nielsen—Amat—Goldsmith formulation are compiled. Nonlinear triatomic molecules are discussed as a special case.

Fourth‐Order Vibration–Rotation Hamiltonian of the Nonlinear XYX Molecule

Detailed expressions in terms of fundamental molecular parameters are given for the fourth‐order centrifugal distortion constants of the nonlinear XYX molecule. It is shown how these expressions can be used for the determination of the cubic potential constants of the XYX molecule if they are considered in conjunction with the reduced‐Hamiltonian theory of Watson. Three reduced Hamiltonians are treated in detail, and a generalization of Watsons theory is presented, and its need is justified.

Accidental Coriolis resonance in symmetric top molecules

Abstract A theoretical analysis of Coriolis interaction between a parallel vibration-rotation band and a perpendicular vibration-rotation band in polyatomic molecules with symmetry C 3 v is given. Computer techniques are used to explore the effects on the energy level structure of varying the relevant molecular parameters. The associated eigenvectors are also obtained. Parameters studied include a Coriolis coupling constant ζ nt 1 y , and a term Δ α B which accounts in an empirical way for the difference of rotational constant in the two interacting vibrational states.

Symmetry Properties of the Asymmetric‐Rotator Centrifugal‐Distortion Constants

The symmetry properties of the first‐order centrifugal‐distortion Hamiltonian for the asymmetric rotator have been studied. The number of independent distortion constants needed to interpret centrifugal‐distortion effects in microwave and infrared spectra of asymmetric top molecules is determined for the asymmetric‐rotator point groups and a number of relationships existing between these constants is given.

Sequential contact transformation formulation of asymmetric-rotator vibration-rotation Hamiltonian

Abstract The sequential contact transformation technique recently described in this journal by Niroomand-Rad and Parker is applied to the Amat-Nielsen expansion of the Darling-Dennison Hamiltonian of asymmetric rotator type molecules. The resulting formalism for the calculation of fourth-order Hamiltonian coefficients is significantly simpler than the conventional Amat-Nielsen contact transformation formalism. Therefore the eventual development of detailed expressions for fourth-order vibration-rotation interaction coefficients in terms of fundamental molecular constants now appears much more feasible.

A modified vibration-rotation contact transformation technique

Abstract A modification of the unitary operators used in conventional vibration-rotation contact transformation calculations is described and developed. It is shown that this modification leads to substantial and significant simplifications of the existing theory. The modified theoretical development is applied to the calculation of the sextic centrifugal distortion constants of asymmetric rotators, and the recent results of Aliev and Watson are duplicated.

Vibration-rotation theory and isotopic substitution in nonlinear triatomic molecules

Abstract In the interpretation of high-resolution data it is helpful to be able to relate the experimentally determined molecular constants, such as rotational constants, centrifugal distortion constants, and vibration-rotation interaction constants of a given molecule to those of its isotopically substituted variants. Results concerning the symmetric nonlinear triatomic molecule (XYX) have been given through the second order of approximation by previous workers. In this paper, extensions of the work to the fourth order of approximation and to the nonsymmetric nonlinear triatomic molecule (XYZ) are considered. These extensions are found to increase the algebraic complexity of the problem considerably, and results can generally be given in implicit form only. The approach used is one that emphasizes the isotopic invariants of the problem, i.e., those expressions which remain unchanged when applied to the various isotopic modifications of a given molecule under the assumption that the molecular force field and the molecular geometry remain unchanged under isotopic substitution.

Intensities of symmetric-top transitions in the presence of accidental coriolis resonance

Abstract A theoretical analysis of Coriolis interaction between a parallel vibration-rotationband and a perpendicular vibration-rotation band in polyatomic molecules with symmetry C 3 ν is continued. Computer techniques are used to explore the effects on the absorption transition intensities of varying the relevant molecular parameters. Parameters studied include a Coriolis coupling constant, a term which accounts in an empirical way for the difference of rotational constant in the two interacting vibrational states, and the ratio of the perpendicular to the parallel band dipole moment derivatives involved in the transition. A study of the energy level structure was given in an earlier publication in this journal by the same authors.