Xiao-Gang Wang

A nine-dimensional perturbative treatment of the vibrations of methane and its isotopomers

The vibrations of methane isotopomers with Td, C3v, and C2v symmetry are studied by means of high order Van Vleck perturbation theory. The vibrational states up to 9000 cm−1 are investigated by combining the ab initio force field of Lee, Martin and Taylor [J. Chem. Phys. 95, 254 (1995)] with a fourth order perturbative treatment based on curvilinear normal coordinates. Implementation of the perturbation theory using both analytical and numerical expression of the kinetic energy operator is considered. The quadratic and select cubic and quartic force constants are refined via a nonlinear least squares fit to experimental data The fit force constants reproduce 130 experimental band centers with a root mean squares deviation of 0.70 cm−1. The choice of polyad quantum number is discussed with respect to different molecules. The convergence of the energy levels is discussed by carrying out the perturbation calculation up to eighth order.

Anharmonic force field and vibrational frequencies of tetrafluoromethane (CF4) and tetrafluorosilane (SiF4)

Accurate quartic anharmonic force fields for CF4 and SiF4 have been calculated using the CCSD(T) method and basis sets of spdf quality. Based on the ab initio force field with a minor empirical adjustment, the vibrational energy levels of these two molecules and their isotopomers are calculated by means of high order Canonical Van Vleck Perturbation Theory (CVPT) based on curvilinear coordinates. The calculated energies agree very well with the experimental data. The full quadratic force field of CF4 is further refined to the experimental data. The symmetrization of the Cartesian basis for arbitrary combination bands of Td group molecules is discussed using the circular promotion operator for the doubly degenerate modes, together with tabulated vector coupling coefficients. The extraction of the spectroscopic constants from our second order transformed Hamiltonian in curvilinear coordinates is discussed, and compared to a similar procedure in rectilinear coordinates.

High resolution spectroscopic study of arsine: 3ν1 and 2ν1+ν3 dyad: The tendency of symmetry reduction

The high resolution spectrum of AsH3 3ν1 and 2ν1+ν3 stretching overtone dyad was recorded and analyzed. The major vibration‐rotation parameters of these overtones were obtained. The result indicates that these overtone vibrational states are close to the local mode limit and the rotational levels show the tendency to approach an asymmetric top.

A perturbative calculation of the rovibrational energy levels of methane

The rovibrational energy levels of methane are determined from a quartic ab initio potential energy force field where the expansion coordinates are the Morse coordinates for the stretches and extension coordinates for the bends. Energies are calculated using canonical Van Vleck perturbation theory. Results are obtained for both rotation-vibration Hamiltonians expressed as functions of curvilinear and rectilinear normal coordinates. Second, fourth, and sixth order curvilinear results are compared with experimental results, and fourth order results for the rectilinear and curvilinear Hamiltonian are compared to each other. The calculated rovibrational levels are in good agreement with the experimental values for low J levels. The calculated rotational level splittings are in even better agreement with the experiment. In particular, the ground state tetrahedral splittings, which are as small as 10(-4) cm(-1), are well reproduced by our calculations at sixth order.

Vibration–rotational spectroscopy of XH2 and XH3 type molecules near the local mode limit

Present work studies the effective rotational Hamiltonians and their vibration–rotational parameters for XH2 and XH3 type molecules near the local mode limit by including the diagonal matrix elements of coordinate operators when the bond anharmonicity is significant. An improved ‘‘α relation’’ is given for the local mode limit by taking the anharmonic bond oscillator wave function as the basis function. Then the rotational tunneling approach is extended to model the effect of nonzero interbond coupling for XH2 and XH3 type molecules, which provides a dynamical view of the rovibrational structure of the local mode states.

A nine-dimensional high order perturbative study of the vibration of silane and its isotopomers

The vibrations of silane isotopomers with Td, C3v, and C2v symmetry are studied by means of high order canonical Van Vleck perturbation theory (CVPT). Transforming the quartic ab initio force field of Martin, Baldridge, and Lee [Mol. Phys. 95, 254 (1999)] into curvilinear normal coordinates, CVPT is used to calculate energies that agree well with experimental data. Both low energy stretch–bend combination bands and high energy stretch local mode bands of silane up to 12 000 cm−1 are well reproduced. The choice of polyad quantum number is discussed with respect to different molecules. Comparing sixth- to eighth-order level of theory, most of the levels agree to within 0.1 cm−1. Spectroscopic constants are given for all the major isotopomers. The construction of the full cubic and quartic resonance operators for symmetric top species are summarized. The Si–H and Si–D stretch modes of Td and C3v symmetry species are studied with a 4D stretch variational model using both the fitted three-parameter potential a...

HIGH RESOLUTION SPECTROSCOPIC STUDY OF H2SE (40+, 0) A1 AND (40-, 0) B2 STRETCHING STATES : NORMAL MODE AND LOCAL MODE ANALYSIS

High resolution spectra of the coupled and degenerate (40+, 0) A1 and (40-, 0) B2 (the local mode pair) states of H2Se are reported. The vibration–rotation transitions of H2 n Se (n = 80,78) were assigned by using the ground state combination differences and least-squares fits to yield the rotational and coupling constants for the two stretching states with degenerate band origins: υ0 (40+, 0) = 8894·504cm-1; υ0 (40-, 0) = 8894·504cm-1. Several striking local 0 0 mode limit effects and the formation of fourfold rovibrational energy clusters are observed and discussed.

Exact vibration-rotation kinetic energy operators in two sets of valence coordinates for centrally connected penta-atomic molecules

The exact vibration-rotation quantum mechanical kinetic energy operator (KEO) for centrally-connected penta-atomic molecules such as methane and its isotopomers is derived for two sets of internal valence coordinates: the polyspherical coordinates and the bond-angle valence coordinates. The vibrational KEO including the pseudo-potential term is discussed for two forms of the modified Jacobian. For the rotational and vibration-rotation coupling KEO, results for two schemes of embedding the body-fixed coordinate system are presented: the bond embedding and the bisector embedding. Full expressions for the bisector embedding are too complicated to give in detail, but the working connection between the two embedding schemes is given. The future applications, including the perturbative and variational calculation of the vibrations and/or rotations for centrally connected penta-atomic molecules using the vibration-rotation KEO expressions derived in this work, are discussed.

High resolution spectroscopic study of CH3D in the region 5900–6100 cm−1

The vibrational overtone band of monodeuterated methane (CH3 in the region 5900–6100 cm−1 was recorded by a high resolution Fourier transform spectrometer. Rotational analyses were performed separately for the parallel 2v 4(A1) and perpendicular 2v 4(E) bands, whose origins were found to be 5980.41 cm−1 and 6022.21 cm−1, respectively. The A1 band displays J-resolved rotational structure while the K structure is resolved only at higher J values. A resonance Hamiltonian with the polyad number P = 2n 1 + 2n 4 + n 5 is derived using the fourth order Canonical Van Vleck Perturbation Theory (CVPT) to show that the 2v 4(A1 and 2v 4(E) are vibrationally perturbed by Fermi and Darling—Dennison resonances. The observation of rotational l-resonance in the 2v 4(E) band is a consequence and evidence of the mixing of the vibrational states with different l values.

The ab initio calculated dipole moment surface and overtone relative intensities of CH chromophore in CHCl3

Relative absorption intensities of the Fermi resonance polyads of isolated CH chromophore for the CHCl3 molecule were calculated with one-dimensional and two-dimensional dipole moment surfaces, which are obtained by the ab initio density functional method. The calculation showed an unusual strong absorption at the second Fermi resonance polyad, which agrees well with the experimental data. Such an intensities anomaly can be attributed to the nonlinearity of the dipole moment surface in the vicinity of the equilibrium configuration. By taking advantage of the two-dimensional dipole moment surface where both CH stretching and bending vibrations are taken into consideration, the ν1 and 2ν4 bands which constitute the first Fermi resonance polyad and have little wave function mixture, are found to be of almost equal intensity. Such a calculation agrees with observations.