Rovibrational Wave Functions Research Articles

Absolute Line Intensities in the Bands ν2 and ν5 and the Transition Dipole Moments of CH3F

The absolute intensities of 188 vibration-rotational spectral lines of transitions to the vibrational states ν2 = 1 and ν5 = 1 of 12CH3F have been measured with a diode laser. By taking into account the mixing of the rovibrational wavefunctions of both vibrational states by Coriolis and l-type interactions (Papoušek, Papoušková, Ogilvie, Pracna, Civiš, and Winnewisser. J. Mol. Spectrosc.153, 145-166 (1992 )), the values of the vibrational transition moments and their relative signs were determined by a least squares fit to the experimental data: 〈0, 00|μz| 1, 00〉 = ϵ × (0.01106 ± 0.00017)D and〈0, 00|μx|0, 1±1〉 = ϵ × (0.02173 ± 0.00005)D where ϵ = ±1.

Ab initio calculation of nuclear quadruple coupling constants of rovibrational levels of 11B 2H, 10B 1H 10B 1H in the double-minimum B 1Σ + electronic state

The 11B, 10B, and 2H quadrupole coupling constants of rovibrational levels of 11B 2H, 10B 2H, and 10B 1H in their B 1Σ + state were calculated from molecular wavefunctions which explicitly describe nuclear displacement. The electric field gradient as a function of the internuclear distance was computed by use of the multi-reference configuration interaction approach, the radial rovibrational wavefunctions were obtained by the Fourier grid Hamiltonian method. The double—minimum character of the potential is seen to markedly influence the rovibrational dependences of the boron and deuteron coupling constants. The quadrupole hyperfine structrure of all vibrational levels of 11B 2H and 10B 2H isotopomer is essentially determined by the relatively strong boron coupling which is perturbed by the deuteron coupling.

A Refined Quartic Forcefield for Acetylene: Accurate Calculation of the Vibrational Spectrum

It is now possible to calculate the nine-dimensional rovibrational wavefunctions of sequentially bonded four-atom molecules variationally without dynamical approximation. In the case of HCCH, the simplest such molecule, many hundreds of rovibrational (J = 0, 1, 2) levels can be converged to better than 1.5 cm −1. Variational calculations of this kind are used here systematically to refine the well-known quartic valence-coordinate forcefleld of Strey and Mills [J.Mol. Spectrosc.59, 103-115 (1976)] against experimental term values up to three C-H stretch quanta for the principal and two deuterated isotopomers, yielding a new surface that reproduces the energies of all the known Σ, Π, and Δ states of these species up to the energy of two C-H stretch quanta with an rms error of 3 cm−1 . The refined forcefield is used to study the resonances associated with the accidental degeneracies (ν2 + ν4 + ν5, ν3) and (ν2 + 2ν5, ν1) in the principal isotopomer, leading to a clarification of the assignment of she experimentally detected states in the 2ν3 and 3ν3, polyads, and to the finding that vibrational Coriolis (kinetic energy) terms, rather than quartic anharmonicities in the potential, are the primary cause of the resonant interactions. Using a new cubic ab initio electric dipole field to calculate IR absorption coefficients, 24 undetected Σ and Π states of 1H12C12C1H and 5 undetected Σ states of D12C12CD are identified as candidates for experimental study, and their calculated energies and assignments are given.

Efficient calculation of rovibrational eigenstates of sequentially bonded four-atom molecules

A new efficient and fully symmetry-adapted finite-basis variational method for calculating the rovibrational eigenstates (J≥0) of any sequentially bonded four-atom molecule is presented. The exact kinetic-energy operator T̂VR in valence coordinates is used in a scheme of successive basis-set contractions. The success of the method is demonstrated with new results for the molecules HCCH, HOOH, and HCNO, respectively linear, nonlinear, and quasilinear. The complexity of T̂VR contributes little to the computational cost, yielding a Hamiltonian matrix whose elements can all be cheaply calculated from products of arbitrarily accurate one-dimensional integrals; the dominant cost is that of matrix diagonalization. Matrices of up to 6000×6000 are used to obtain low-lying levels converged to small fractions of 1 cm−1, even for the difficult case of HOOH. The generalization to J≥0 allows the calculation of Π states for HCCH and HCNO and effective rotational constants for HCCH, all usefully converged. For the first time nine-dimensional rovibrational wave functions for four-atom systems are calculated without dynamical approximation and with basis sets well completed in all degrees of freedom. For HCCH it is straightforward to obtain hundreds of rovibrational (J=0,1,2) levels converged to better than 1.5 cm−1, opening up the possibility of the systematic refinement of the nuclear potential function V̂N.

Variational calculation of the ro-vibrational states of Na3+

An ab initio variational ro-vibration calculation has been performed for the ground electronic state of Na3 +. A discrete potential energy surface was generated using the configuration interaction ansatz, within the frozen-core approximation. An analytical surface was generated from a Pade approximate expansion, which utilized a Dunham expansion variable. The force field was embedded in the Eckart-Watson Hamiltonian from which ro-vibrational wavefunctions and eigenenergies were variationally calculated for the low-lying ro-vibrational states.

The interaction of rotation and local mode tunneling in the overtone spectra of symmetric hydrides. II. The spatial properties of the XH4 eigenstates

The matrix elements of the XH4 rotation-tunneling Hamiltonian are given for basis states with all of the vibrational excitation in a single bond. A basis set of symmetrized rovibrational wave functions is given that are eigenfunctions in the limit in which the local mode tunneling rate is much smaller than the rotational precession rate. Using this basis, it is demonstrated that, in this limit, vibrational tunneling occurs with a simultaneous reorientation of the molecule, such that the spatial properties of the excited bond are the same as if tunneling did not take place at all. A resonant two-photon dissociation experiment is proposed that could observe this effect. It is found that as one moves away from this limit, the polarization properties of the F2 symmetry vibrational state retain much of the symmetric top structure.

Bands of H 3+ up to 4 ν2: Rovibrational transitions from first principles calculations

Band origins and Einstein A coefficients are presented for transitions linking all the vibrational levels of H 3 + up to 4 ν 2( l = 4). The importance of these data for astrophysical modeling is discussed. For H 3 +, rovibrational wavefunctions and energy levels are obtained for J up to 16. These are used to synthesize sample rovibrational spectra with particular emphasis on the ν 1 + 2 ν 2( l = 2) ← 0 and 4 ν 2( l = 2) ← 0 bands, which would appear to be good candidates for laboratory observation.

Linestrengths for the electric quadrupole fundamental band of the oxygen molecule with rotation-vibration interaction corrections

The effect of rotation-vibration interaction on the rovibrational wavefunctions belonging to a 3Σ electronic state is investigated in the harmonic approximation. The results are used to obtain the Herman-Wallis type corrections to the branch linestrengths of the quadrupole fundamental band of O 2. The usefulness of the refined linestrength formulas and their limiting forms for Hund's case (b) are discussed.

Double-minimum B 1∑+ electronic state of BH: rovibrational dependence of the ab initio boron quadrupole coupling constant

The 11B quadrupole coupling constants of rovibrational levels of 11B1H in its B1∑+ state have been computed from molecular wavefunctions which explicitly describe nuclear displacement. The necessary radial rovibrational wavefunctions were obtained by the Fourier-grid-Hamiltonian method. The double-minimum character of the potential is seen to influence profoundly the rovibrational dependence of the boron quadrupole coupling constant. The quadrupole hyperfine patterns are predicted to be markedly different from those corresponding to the previously studied ∑+ states of diatomic molecules represented by single-minimum potentials.

Rovibrational spectra of open-shell van der Waals complexes: Ar–OH(X 2Π)

The infrared spectrum of Ar(1S0)–OH(X 2Π) has been predicted using an ab initio potential-energy surface. We assume that the electronic spin and orbital angular momenta remain coupled to the rotational motion of the diatom in a van der Waals complex. The rovibrational energies and wave functions are calculated using a basis-set method involving expansion of the rovibrational wave function in terms of a product basis of optimized radial and angular wave functions. Unusual features are observed due to the nonzero electronic angular momentum of the diatom in the rovibrational levels. The effect of deuterium substitution on the predicted spectra has also been studied.

Calculation of van der Waals spectra for H2HF, D2HF, and H2DF

Calculations of spectra for the excitation of the van der Waals modes in the weakly bound complexes H2HF, D2HF, and H2DF are reported. An ab initio potential energy surface has been computed using the coupled electron pair approximation with a large basis set. The rovibrational bound states for the complexes are calculated using a variational method. A self-consistent field approach is used to optimize the basis sets for bending and stretching motion in the van der Waals complex. The calculated spectra compare very well with those measured in near-infrared experiments. The computations provide a systematic analysis of the relative stability and rigidity of the different complexes, the very large zero-point energy effects, and the unusual nature of the rovibrational wave functions in these van der Waals molecules. The predicted spectra contain some new bands with surprisingly large intensities that might be detectable in experiments.

Exact solvable quantum models of rotating-vibrating triatomic molecules

Quantum models of rotating-vibrating triatomic molecules are presented. They are specified by model potential functions written in local or collective internal coordinates. For these models the exact rovibrational (RV) wavefunctions and energy levels are calculated for low values of the angular momentum quantum number J. For some states with high J approximate analytic formulae for energy levels are given. The proposed models are realistic and describe correctly the main features of RV states. New physical effects which occur in molecules due to strong rotation-vibration interaction are discussed.

Calculations of the ro-vibrational absorption transition probabilities in triatomic molecules

The variational method is used to determine ro-vibrational wavefunctions for triatomic molecules from ab initio potential energy functions. These wavefunctions are then used, in conjunction with ab...

Self-consistent approach to the bending-rotation interactions in the H 2O molecule

Approximate separation methods for the calculation of rovibrational wavefunctions and energy levels of a molecule are considered. Two kinds of molecular models with some frozen internal motions are studied. These are the rigid and static models. They are compared for the H 2O and D 2O molecules. The static models can be obtained in the framework of a self-consistent theory. This theory is applied to separate the bending and rotation motions of the H 2O molecule. The self-consistent approach allows for a clear interpretation of physical effects occurring in a vibrating-rotating molecule.

Hartree theory for rovibrational states of molecules

A new method for the calculation of rovibrational wavefunctions and energy levels of molecules is presented. In this method the Hartree separation scheme is applied in order to reduce the rovibrational Schrodinger equation to coupled vibrational and rotational equations. They are solved in a self-consistent way. The method allows the determination of a centrifugal potential describing the influence of rotations on the internal motions in a molecule. The theory presented is tested on the formaldehyde molecule which is nonrigid in the A 1 A 2 electronic state. The results obtained indicate that our approach is more effective and accurate than the standard variational approach.

Two particles on a sphere as a rigid-bender model of the helium atom

The model of two particles on a sphere is considered from the viewpoint of the body frame. The exact ro-vibrational (RV) wavefunctions and energy levels are calculated for the realistic model potential. The obtained results shed a new light on double excited states of the helium atom (He ∗∗).

The calculation of the vibration-rotation energies of triatomic molecules using scattering coordinates

Department of Physics and Astronomy, University College London, Gower Street, London WCIE 6BT, England Received 25 January 1986 This paper is a review of work I have been involved with concerning the calculation of ro-vibrational energy levels and wavefunctions, mainly of triatomic systems. The method reviewed is that of Tennyson and Sutcliffe for the calculation of spectra of triatomics as atom-diatom collision complexes, which is particularly ap- propriate for molecules with one or more large amplitude vibrational mode. The method uses polynomial basis functions to carry the nuclear motions and is variational for a given potential. Hamiltonians for four different sets of body-fixed axes are derived. The computational implementation of the method is discussed, including improvements to some published algorithms. The use of a two step (secondary) variational procedure for highly-excited rotational states is discussed and sample results given. Extensions to non-Born-Oppenheimer problems, transition intensities and polyatomic molecules are also considered. Comparisons are made with other techniques for calculating ro-vibrational spectra with some specific molecular examples.

Dissociation on ground-state potential-energy surfaces

Two new techniques allowing for the resolved spectral study of dissociation on ground-state potential-energy surfaces are presented. First, Stark level-crossing spectra of highly vibrationally excited ground-state formaldehyde (S*0) characterize the initial rovibrational wavefunctions of dissociative formaldehyde states. Individual S*0 D2CO states are resolved near the barrier to dissociation but broaden and overlap at higher energies. Neighbouring resolvable states possess enough individual vibrational character to vary by over one order of magnitude in lifetime. A potential barrier height of 78.0–81.1 kcal mol–1 has been determined for H2CO → H2+ CO dissociation. Second, photofragment excitation (PHOFEX) spectra probe the production of correlated fragment states from ketene photodissociation. Molecular-beam PHOFEX spectra show that ketene possesses no observable rotational structure and only weak vibrational structure. The PHOFEX spectrum of an individual rotational state of the lowest vibronic state of singlet methylene gives the energetic threshold for formation of that state along with ground-state CO. The threshold for the combination with each successive CO(v″= 0, J″) channel is clearly resolved. A statistical calculation reproduces the main features of the PHOFEX spectra. Analysis of the PHOFEX spectra gives a H2CCO →1CH2+ CO dissociation threshold of 30 102 ± 15 cm–1. Finally, the effect of a potential barrier in the dissociation coordinate on statistical vs. dynamical control of dissociation is discussed.

A b i n i t i o dipole surfaces, vibrationally averaged dipole moments, and infrared transition intensities for KCN and LiCN

Using the rovibrational wave functions which have been obtained from ab initio potentials and making analytic fits to the ab initio calculated dipole surfaces, we have evaluated the dipole (transition) moments of KCN and LiCN for several vibrational states (for J=0 and 1). The ‘‘exact’’ rotational transition intensities of the a-type transitions in (triangular) KCN and those of (linear) LiNC and LiCN can be rather accurately reproduced by a rigid rotor model with the vibrationally averaged dipole moments; for the (weak) b-type transitions in KCN this model breaks down, however. Although the bending motions in these cyanides have large amplitudes, the vibrational transition intensities in LiNC and LiCN conform to the harmonic oscillator model. In KCN, where the large amplitudes of the bending modes and their coupling with the K–CN stretch leads to significant anharmonic shifts in the transition frequencies, the harmonic intensity pattern is perturbed by Fermi resonances, for instance, between the stretch fundamental and the second bending overtone. We have also calculated the lifetime for radiative decay of (metastable) LiCN into LiNC: 24 s for the ground state, much less for vibrationally excited states.

Effect of Phase Choices in Rovibrational Wavefunctions on the Labeling of K-and l-Type Doubling in Molecular Energy Levels

Abstract The change in phase factor of the wavefunction does not affect the absolute value of the matrix element, but does change the phase factor of the off-diagonal matrix element. This phase dependence causes a serious confusion in the sign of some parameters in the molecular Hamiltonian, which appear only in the off-diagonal matrix element; for example, the sign of the l-type doubling constant q of a linear or a symmetric-top molecule. In the present paper, the energy eigenvalues, symmetry species, and labeling of the eigenfunctions are discussed for the K-type doubling of asymmetric-top molecules and for the l-type doubling of linear or symmetric-top molecules in relation to the choices of phases in the basis wavefunctions.