Variational Calculations of Rovibrational Energies for CO(2)

A two-step quadrature-based variational calculation of ro-vibrational levels and wavefunctions of CO2 using a bisector-x molecule-fixed frame

In this paper, we propose a new two-step strategy for computing ro-vibrational energy levels and wavefunctions of a triatomic molecule and apply it to CO2. A two-step method [J. Tennyson and B. T. Sutcliffe, Mol. Phys., 1986, 58, 1067] uses a basis whose functions are products of K-dependent "vibrational" functions and symmetric top functions. K is the quantum number for the molecule-fixed z component of the angular momentum. For a linear molecule, a two-step method is efficient because the Hamiltonian used to compute the basis functions includes the largest coupling term. The most important distinguishing feature of the two-step method we propose is that it uses an associated Legendre basis and quadrature rather than a K-dependent discrete variable representation. This reduces the cost of the calculation and simplifies the method. We have computed ro-vibrational energy levels with J up to 100 for CO2, on an accurate available potential energy surface which is known as the AMES-2 PES and present a subset of those levels. We have converged most levels up to 20 000 cm-1 to 0.0001 cm-1.

A Spectroscopic Description of Asymmetric Isotopologues of CO2

A polyad-conserving algebraic model applied to vibrational excitations of asymmetric isotopologues of CO2 is presented. First, the problem of vibrational excitations is studied by taking into account only the minimum subspace of states to characterize the Fermi interaction. This analysis allows an estimation of the force constants as well as the feasibility of describing the system in a local mode scheme, in terms of SU(2) operators associated with Morse ladder operators for the stretches. This description together with the algebraic U(3) for the bends establishes the dynamical group SU1(2) × U(3) × SU2(2) for a series of isotopologues. Six isotopologues are considered, namely, 16O12C18O, 16O12C17O, 16O13C18O, 16O13C17O, 17O13C18O, and 17O12C18O in their electronic ground states. For isotopologues 16O12C18O, 16O12C17O, 17O12C18O, and 16O13C18O, the vibrational description was carried out using a Hamiltonian involving 14 parameters. For this series of isotopologues with a number of energy terms 90, 57, 42, and 40, the deviations obtained were rms = 0.15, 0.10, 0.06, and 0.07 cm-1, respectively. For 16O13C17O, with 28 experimental energies and involving 13 parameters, the deviation was rms = 0.05 cm-1, while for 17O13C18O, a different strategy was proposed since only 12 experimental energy levels. In all cases, the polyad scheme P212 = 2(ν1 + ν3) + ν2 was considered. In addition, a new criterion of locality/normality degree is proposed, embracing the case of molecules with normal mode behavior, in particular, the isotopologues of CO2.

Classical and quantum-mechanical plane switching in CO2

Classical plane switching takes place in systems with a pronounced 1:2 resonance, where the degree of freedom with the lowest frequency is doubly degenerate. Under appropriate conditions, one observes a periodic and abrupt precession of the plane in which the doubly degenerate motion takes place. In this article, we show that quantum plane switching exists in CO(2). Based on our analytical solutions of classical Hamilton's equations of motion, we describe the dependence on vibrational angular momentum and energy of the frequency of switches and the plane switching angle. Using these results, we find optimal initial wave-packet conditions for CO(2) and show, through quantum-mechanical propagation, that such a wave packet indeed displays plane switching at energies around 10 000 cm(-1) above the ground state on time scales of about 100 fs.

Dissociation energies of six NO2 isotopologues by laser induced fluorescence spectroscopy and zero point energy of some triatomic molecules

We have measured the rotationless photodissociation threshold of six isotopologues of NO2 containing 14N, 15N, 16O, and 18O isotopes using laser induced fluorescence detection and jet cooled NO2 (to avoid rotational congestion). For each isotopologue, the spectrum is very dense below the dissociation energy while fluorescence disappears abruptly above it. The six dissociation energies ranged from 25 128.56 cm(-1) for 14N16O2 to 25 171.80 cm(-1) for 15N18O2. The zero point energy for the NO2 isotopologues was determined from experimental vibrational energies, application of the Dunham expansion, and from canonical perturbation theory using several potential energy surfaces. Using the experimentally determined dissociation energies and the calculated zero point energies of the parent NO2 isotopologue and of the NO product(s) we determined that there is a common De = 26 051.17+/-0.70 cm(-1) using the Born-Oppenheimer approximation. The canonical perturbation theory was then used to calculate the zero point energy of all stable isotopologues of SO2, CO2, and O3, which are compared with previous determinations.

CO2 molecule as a quantum realization of the 1:1:2 resonant swing-spring with monodromy

We consider the wide class of systems modeled by an integrable approximation to the 3 degrees of freedom elastic pendulum with 1:1:2 resonance, or the swing-spring. This approximation has monodromy which prohibits the existence of global action-angle variables and complicates the dynamics. We study the quantum swing-spring formed by bending and symmetric stretching vibrations of the CO2 molecule. We uncover quantum monodromy of CO2 as a nontrivial codimension 2 defect of the three dimensional energy-momentum lattice of its quantum states.

Spectroscopy and Intensity Measurements of the 3nu(1)+3nu(3) Tetrad of (12)CO(2) and (13)CO(2)

Three of the four components of the 3nu(1)+3nu(3) tetrad of (12)C(16)O(2) and (13)C(16)O(2), labeled 30031, 30032, and 30033 in HITRAN notation, have been observed by intracavity laser absorption spectroscopy in the 10 450- to 11 000-cm(-1) region. The rotational analysis has yielded the rovibrational parameters of the vibrational states. The experimental values are found to be in very good agreement with the rovibrational energies recently predicted from variational calculations and reduced effective Hamiltonians. The absolute band intensity of these extremely weak transitions have been measured. The study of the relative intensities within the 3nu(1)+3nu(3) tetrad suggests that part of the oscillator strength is carried by the (22(0)3) state. Copyright 2001 Academic Press.