Esa Kauppi

A simple curvilinear internal coordinate model for vibrational energy levels

A simple curvilinear internal coordinate Hamiltonian model for vibrational term values of well bent XY2 molecules is developed. The stretching vibrations are described in the zero‐order picture by Morse oscillators and the bend by a harmonic oscillator. Coupling terms are approximated by harmonic oscillator formulas. Van Vleck perturbation theory is used to transform the Hamiltonian matrix to a block diagonal form. Analytical expressions for the matrix elements are derived. Fermi resonances between the stretches and the bend and local modes are taken into account by diagonalizing the block diagonal Hamiltonian matrix. Rotational parameters (α constants) are calculated with perturbation theory expressions. Potential energy parameters are optimized with the nonlinear least‐squares method using vibrational term values and α constants as data. The model is applied to five isotopic species of hydrogen sulfide and to two isotopic species of sulfur dioxide. The potential energy parameters obtained agree well wit...

Fermi resonances and local modes in pyramidal XH3 molecules: An application to arsine (AsH3) overtone spectra

A simple vibrational Hamiltonian expressed in terms of curvilinear internal coordinates has been used to model both stretching and bending vibrations in pyramidal XH3 molecules. The pure stretching part is expressed as harmonically coupled anharmonic oscillators and the pure bending part as harmonically coupled harmonic oscillators. The stretching and the bending modes are coupled with each other by Fermi resonance terms which contain contributions both from the kinetic and potential energy part of the full vibrational Hamiltonian. Only resonance couplings are included. The Hamiltonian matrices are symmetry factorized by employing symmetrized basis functions which consist of products of stretching oscillator and valence angle bending oscillator functions. This model is applied to observed vibrational term value data of arsine (AsH3). The least squares method is used to optimize potential energy parameters. The results obtained are in good agreement with ab initio calculations. All observed arsine overtone...

Fermi resonances between CH stretching and bending vibrations in CHF3, CHCl3, and (CF3)3CH

A simple vibrational curvilinear internal coordinate Hamiltonian is used to account for Fermi resonance interactions between CH stretching and bending vibrations in CHF3, CHCl3, and (CF3)3CH. The eigenvalues of the Hamiltonian are obtained variationally with a Morse oscillator basis set for the stretch and two‐dimensional harmonic oscillator basis set for the bend. Five or six potential energy parameters are found to describe well the experimental CH stretching and bending overtone levels of the studied molecules. In the case of CHF3 the potential energy surface obtained is in good agreement with ab initio surfaces. A bond dipole model is used to calculate infrared absorption intensities for the transitions from the ground state to the totally symmetric excited states.

Five‐dimensional local mode‐Fermi resonance model for overtone spectra of ammonia

A five‐dimensional local mode‐Fermi resonance model for overtone spectra of the ammonia molecule has been constructed. The model Hamiltonian is expressed in terms of curvilinear internal valence coordinates and it includes the three stretching vibrations and the doubly degenerate bending vibration. The symmetric bending vibration associated with the inversion motion has been excluded. Thus the model is useful for energy levels with the totally symmetric bending vibration on its ground state. Vibrational energy levels have been calculated using van Vleck perturbation theory. Nonlinear least‐squares method has been used to optimize potential energy parameters. Observed vibrational band origins for 14NH3, 14ND3, and 14NT3 have been employed as data. A fit with the standard deviation of 5.5 cm−1 has been obtained using one set of isotope invariant potential energy parameters. The optimised potential energy surface compare well with results of ab initio electronic structure calculations and with results of customary anharmonic force field calculations.

High-resolution photoacoustic overtone spectrum of acetylene near 570 nm using a ring-dye-laser spectrometer

Abstract A high-resolution vibration—rotation spectrum of acetylene has been obtained in the wavenumber region 17360–17560 cm −1 with a new ring-dye-laser spectrometer where an intracavity photoacoustic detection method has been used. The spectra obtained show large signal-to-noise ratios. Five new very weak bands have been observed and successfully analyzed to provide a set of vibrational term values and rotational constants.

High‐resolution photoacoustic Ti:sapphire/dye ring laser spectrometer

A high‐resolution photoacoustic Ti:sapphire/dye ring laser spectrometer with a high level of automation is described. It produces high quality Doppler‐limited overtone spectra. The performance of the spectrometer has been demonstrated by measuring both low‐ and high‐resolution spectra of acetylene in the wave number regions 10850–12900 cm−1 and 11500–11650 cm−1, respectively. The spectra show large signal‐to‐noise ratios (≳7000) for strong absorption peaks. Some strong absorption lines have been compared with published FTIR spectral data.

Potential energy surface and vibrational analysis along the stretching vibrations of the ArHAr+ ion

Abstract An ab initio calculated potential energy surface along the stretching coordinates of the linear ArHAr + ion presented. The potential surface has been obtained using the MP2/15s11p3d1f/7s2p1d level of the ab initio electronic structure calculation theory. Qualitatively the potential is characterised by a development of double minimum structure at elongated Ar---Ar distances at higher vibrational energies and by a large amplitude for the motion of the hydrogen atom. The stretching vibrational energy levels and wavefunctions have been calculated variationally using harmonic oscillator basis functions. The vibrational analysis indicated extensive mixing of the zeroth-order harmonic oscillator vibrational states already at the bottom of the well giving rise to strong absorption “progression” starting at 1208 cm −1 . The Einstein A coefficients for spontaneous emission transitions have also been calculated and the IR emission spectrum is predicted to be particularly rich in the 1100–1900 cm −1 spectral region.

Potential energy surface and vibrational analysis along the stretching vibrations of XeHXe+ ion

An analytical potential energy surface (PES) along the stretching coordinates of a linear XeHXe+ ion is presented. Ab initio calculations within the effective core potential approach are used as input for the PES. The present vibrational analysis indicates extensive mixing of the zeroth‐order harmonic oscillator vibrational states, and a rather complete collapse of the normal mode picture already near the bottom of the potential well. At higher vibrational energies, and elongated Xe–Xe distances, development of a double minimum in the PES is observed. The simulated absorption spectrum consists of a strong vibrational progression near 1000–1700 cm−1, and is in qualitative agreement with the previous matrix isolation data. The intensity distribution of the vibrational progression is mostly due to the potential terms rather than nonlinear contributions in the Taylor series expansion of the electric dipole moment. Due to the highly anharmonic potential, and subsequent breakdown of selection rules, the emissio...

Fermi resonances in overtone spectra of bromoform, CHBr3

A curvilinear internal coordinate Hamiltonian is used to analyze Fermi resonances between CH stretching and bending vibrations in bromoform. Besides the usual Fermi resonance terms, cubic and quartic kinetic and potential energy terms in bending variables are included in the Hamiltonian. The eigenvalues are obtained variationally with a Morse oscillator basis set for the stretch and a two‐dimensional harmonic oscillator basis set for the bend. The potential energy parameters are optimized with the nonlinear least squares method. A bond dipole model is used to calculate infrared absorption intensities. The model reproduces well the observed vibrational term values and infrared absorption intensities.

High-resolution photoacoustic study of the 4ν1 band system of monofluoroacetylene using a titanium : sapphire ring laser

Abstract A titanium : sapphire ring laser has been used in intracavity experiments to obtain high-resolution photoacoustic overtone spectra of monofluoroacetylene in the wavenumber region 12200–13800 cm −1 . The spectra obtained show very large signal-to-noise ratios (> 1000) for strong absorption peaks. Two band systems, 4ν 1 and 4ν 1 + ν 5 , have been observed. Both of these contain several individual bands which often seem to be severely perturbed. Altogether seven bands in the 4ν 1 band system have been assigned rotationally.