Lauri Halonen

Fermi resonances and local modes in water, hydrogen sulfide, and hydrogen selenide

A simple vibrational curvilinear internal coordinate Hamiltonian for bent H2X molecules is constracted by expanding the g matrix elements and the potential energy function in terms of the Morse variable y=1−exp(−ar) and retaining important local mode and Fermi resonance terms. The eigenvalues of this Hamiltonian are calculated variationally using Morse oscillator basis functions for the stretches and harmonic oscillator basis functions for the bend. The nonlinear least‐squares method is used to optimize the potential energy parameters. The model is applied to water, hydrogen sulfide, and hydrogen selenide. Experimental vibrational levels up to 18 500 cm−1 for five symmetrical isotopic species of water are reproduced with a standard deviation of about 4 cm−1. For both hydrogen sulfide and hydrogen selenide two symmetrical isotopic species were included in the optimization procedure and standard deviations of 1.0 and 0.66 cm−1 were obtained. The potential energy parameters obtained agree well with previous ...

A LOCAL MODE MODEL FOR TETRAHEDRAL MOLECULES

A three parameter coupled Morse oscillator model fitted to the known stretching vibrational energy levels is used to predict the energies of all stretching overtone bands with total quantum number ν ⩽ 5> for the molecules CH4, SiH4, GeH4 and their deuterium and 13C isotopic substituents. Close local mode degeneracies, with splittings of 3 cm-1 or less, are predicted at the highest energies for all molecules except CD4. Such degeneracies prevail at all excitation levels for SiH4 and GeH4, but those for ν ⩽ 3> are removed by deuterium substitution. The overtone splitting patterns of different molecules and the effects of isotopic substitution are rationalized by means of a correlation diagram, in which the ratio of bond anharmonicity to interbond coupling strength is used to rank the molecules on a scale running from local mode to harmonic normal mode limits. The ranking by local mode character is GeH4 > SiH4 > GeD4 > CH4 > SiD4 > CD4. A model intensity calculation for CH4 confirms the local mode picture wi...

Potential models and local mode vibrational eigenvalue calculations for acetylene

Two potential models for acetylene are developed and tested by comparison between variational calculations for the stretching vibrational term values and available spectroscopic data. The first model based on local bond potentials with harmonic interbond coupling gives root mean square deviations of 6 cm−1 for C2H2 and 3 cm−1 for C2D2. The second model is more ambitious, being designed to reproduce the dissociation characteristics of the molecules, and the calculated root mean square deviations from the experimental vibrational term values are larger, 32 cm−1 for C2H2 and 24 cm−1 for C2D2. The eigenvalue spectrum of C2H2 is shown to differ from that of C2D2 in showingmarked local mode features and this difference in behaviour is underlined by means of a correlation diagram. Finally it is shown how the known normal mode frequencies and anharmonic constants may be introduced into a simple model in order to predict the excited term values of C2H2, again with a root mean square deviation of 6 cm−1.

Reactivity of vibrationally excited methane on nickel surfaces

Four-dimensional variational calculations have been performed for modeling energy flow between methane (CH4) stretching vibrational energy states as the molecule adiabatically approaches a metallic surface. The model is based on a local mode Hamiltonian for an isolated CH4 molecule and a London-Eyring-Polanyi-Sato potential describing surface–molecule interactions. The results suggest the possibility of mode specific effects on chemical reactivity. Specifically, the symmetric A1 stretch fundamental adiabatically correlates with the localized excitation in the unique CH bond pointing towards the surface. Conversely, the antisymmetric F2 stretch fundamental excitation correlates with A and E vibrations in the CH3 radical, and therefore this degree of freedom is localized away from the reactive CH bond. Landau–Zener semiclassical analysis of nonadiabatic curve crossings predicts a significant velocity dependence to the state specific energy flow dynamics. Since excitation localized in active versus spectator...

Internal coordinate Hamiltonian model for Fermi resonances and local modes in methane

A vibrational model which is based on a Hamiltonian expressed in terms of curvilinear internal coordinates is applied to the overtone spectrum of methane, CH4. Symmetrized internal coordinates and their conjugate momenta are used as the bending variables. The stretching part of the Hamiltonian is expressed in an unsymmetrized form. Both the kinetic operator and the potential energy function are expanded as Taylor series around the equilibrium configuration. Symmetrized local mode basis functions for the stretches and symmetrized two- and three-dimensional harmonic oscillator basis functions in the Cartesian representations for bending degrees of freedom are used. Only resonance couplings are taken into account. Apart from some standard diagonal contributions harmonic oscillator matrix elements have been employed. This results in a simple block diagonal Hamiltonian model. The nonlinear least squares method is used to optimize model parameters for 12CH4. Observed vibrational term values up to 6050 cm−1 are ...

MOLECULAR ROTATIONS AND LOCAL MODES

Rotational energy level structures of stretching vibrational states have been investigated in the XH2, XH3, and XH4 type symmetrical hydrides. Transformations from standard vibration–rotation normal coordinate Hamiltonians are made to internal coordinate representations which explicitly give the terms responsible for rotational coupling between the different local mode states. It is shown that the local mode relations between the vibration–rotation parameters as given by Lehmann [J. Chem. Phys. 95, 2361 (1991)] and by Halonen and Robiette [J. Chem. Phys. 84, 6861 (1986)] make these Hamiltonians diagonal in the local mode basis. The effective vibration–rotation parameters of overtones are then proved to obey the local mode relations closer and closer as the vibrational excitation increases. A simple vibrational model accounts well for the vibrational dependencies of vibration–rotation constants in the case of SiH4, GeH4, and SnH4.

Rotational energy level structure of stretching vibrational states in some small symmetrical molecules

The vibrational dependence of various vibration–rotation parameters in XY2, XY3, and XY4 molecules with C2v, C3v, and Td point groups has been investigated between normal mode and local mode limits. The results at these two limiting cases differ drastically from each other. The rotational constants of the two lowest vibrational states in each overtone manifold (v=v1+v3=constant) are equal for v≥2 in the local mode limit. The effective Coriolis constants between these vibrational pairs disappear but the vibrationally off‐diagonal H22 resonance terms remain important as the local mode limit is approached. The vibrational dependence of the rotational constants of the stretching vibrational states in the symmetrically substituted acetylenes and in normal silane has been analyzed. It is shown that it is necessary to couple levels by quartic anharmonic resonance terms in the normal coordinate space in order to explain the vibrational behavior of the rotational constants.

HIGH DIMENSIONAL ANHARMONIC POTENTIAL ENERGY SURFACES : THE CASE OF METHANE

The overtone vibrational spectra of all Td symmetry isotopomers of methane have been analyzed simultaneously. A Hamiltonian expressed in internal curvilinear coordinates expanded to the fourth order has been employed, with a nine-dimensional basis of harmonic oscillator wave functions in symmetry coordinates. Near-resonant anharmonic interactions are treated to first order, while weaker interactions are handled as second order perturbations. A set of optimized Born–Oppenheimer force constants is obtained, which reproduces the observations up to 9500 cm−1 and shows an excellent agreement with the results of ab initio calculations.

Vibrational energy levels for symmetric and asymmetric isotopomers of ammonia with an exact kinetic energy operator and new potential energy surfaces

A new vibrational Hamiltonian operator for ammonia is presented. The potential energy part is expressed in terms of symmetrized bond-angle valence coordinates and an inversion coordinate, which is a function of the bond angles. In the exact kinetic energy operator, the stretching part is instead given in terms of unsymmetrized bond displacement coordinates. Six-dimensional ammonia potential energy surfaces are calculated using high-level ab initio tools, the CCSD(T) method with aug-cc-pVQZ and aug-cc-pVTZ basis sets. The potential energy functions are constructed in two, two-dimensional steps. The surfaces are expressed as a Taylor-type series with respect to the doubly degenerate asymmetric stretching and bending coordinates. This representation is given along a two-dimensional surface of the totally symmetric stretching and inversion coordinates of ammonia. Vibrational energies are calculated variationally in a finite basis representation. Employing successive basis set contractions, it is possible to o...

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...