Predissociation Widths Research Articles

Formation of the CH/CD molecules through radiative association of C with H/D

ABSTRACT Reaction rate constants have been calculated for the formation of CH and CD molecules through radiative association of C and H/D atoms in their ground states. Quantum mechanical and semiclassical/classical methods were used to obtain the reaction cross-sections. Shape resonances and inverse pre-dissociation are accounted for with Breit–Wigner theory. The potential, permanent/transition dipole moment curves and experimental pre-dissociation widths are taken from the literature. The resulting reaction rate constants were fitted to the Kooij formula for use in astrochemical modelling. Our rate constant is 3.5 × 10−17 cm3 s−1 at 100 K and it peaks at 20 K, where it is 8.0 × 10−17 cm3 s−1. These values are larger than what has been obtained in earlier studies but not large enough to account for the interstellar abundance of CH.

Predissociation and pressure dependence in the low frequency far wing of the Wulf absorption band of ozone near 1.2 µm

The weak low frequency tail of the ozone Wulf band is newly studied by high sensitivity cavity ring down spectroscopy (CRDS) in the 7920–8700 cm−1 range. Although strongly obscured by impurity lines, the ozone absorption signature shows up in the recorded spectra as two mostly unresolved absorption bands. These two bands with maximum near 8154 and 8450 cm−1 are hot bands from the (020) and (100) ground state vibrational levels reaching the same predissociated 3A2(000) upper state of 16O3. The observed bands include a mostly structureless continuum and lines exhibiting a clear broadening due to the predissociation of the 3A2(000) upper state. On the basis of assignments of the rotational structure available in the literature for the 3A2(000)-X1A1(000) cold band centered near 9553 cm−1, seventy-four relatively narrow lines could be rotationally assigned to the 3A2(000)-X1A1(020) and 3A2(000)-X1A1(100) hot bands. A line shape analysis, performed using a Voigt profile, provided the width of the Lorentzian component. Additional recordings performed at various pressures for 18 lines allowed to disentangle the pressure and predissociation contributions to the fitted Lorentzian widths. As a result, the newly derived pressure broadening coefficients of the considered rovibronic transitions are found to be similar to those of the rovibrational infrared bands. All the lines studied are affected by significant predissociation due the spin-orbit coupling between the 3A2(000) level and high lying dissociative vibrational levels of the X1A1 electronic ground state. The resulting set of predissociation widths for sixty lines ranges between 9 × 10−3 and 0.2 cm−1 corresponding to upper state lifetime of 560 and 25 ps, respectively. The reported results are discussed in relation with previous experimental and theoretical studies.

Nonrelativistic energies and predissociation widths of quasibound states in the Li3+-dμ molecular ions

Muonic molecular ions 6Li3+dμ and 7Li3+dμ are studied numerically. Using the complex coordinate rotation method we found six rotational states (three for each isotope), which are resonant states with the life-time of an order of picoseconds. These molecular systems may be of interest for studying low-energy fusion reactions. A key quantity, , the wave function squared at the coalescence point of the nuclei is calculated for S states for both isotopes with a precision better than 3%.

Predissociation of the B Σu−3 state of S2: A coupled-channel model

A coupled-channel Schrödinger equation model of predissociation in the B Σu-3 state of S2 is developed and optimized by comparison with recent photoabsorption spectra of the B Σu-3-X Σg-3(v,0) bands for 11 ≤ v ≤ 27, covering the energy range 35 800-41 500 cm-1. All bands in this range exhibit varying degrees of diffuseness, with corresponding predissociation linewidths Γ ≈ 4-60 cm-1 full-width at half-maximum. Model comparisons with both low-temperature (T = 370 K) and high-temperature (T = 823 K) spectra indicate, for many bands, significant dependence of the linewidth on both the rotational quantum number J and the fine-structure component Fi. Just as in the analogous case of O2, the B(v)-state predissociation in S2 is caused principally by spin-orbit interaction with 3Πu, 1Πu, 5Πu, and Σu+3 states. The inner-limb crossing with B″3Πu is responsible for the predissociation of B(v = 11) and provides a significant slowly varying contribution for B(v ≥ 12). The outer crossings with the 1Πu, 5Πu, and 2 Σu+3 states are responsible for oscillatory contributions to the predissociation widths, with first peaks at v = 13, 20, and 24, respectively, and the 5Πu contribution dominant. Prior to the photodissociation imaging study of Frederix et al. [J. Phys. Chem. A 113, 14995 (2009)], which redefined the dissociation energy of S2, the prevailing paradigm was that only the 1Πu interaction was responsible for the B(v = 11-16) predissociation: this view is not supported by our model.

VUV spectroscopic study of the state of H2

Spectral lines, probing rotational quantum states J′ = 0, 1, 2 of the inner well vibrations (υ′ ≤ 8) in the state of molecular hydrogen, were recorded in high resolution using a vacuum ultraviolet Fourier transform absorption spectrometer in the wavelength range 73–86 nm. Accurate line positions and predissociation widths are determined from a fit to the absorption spectra. Improved values for the line positions are obtained, while the predissociation widths agree well with previous investigations.

Spectroscopy above the ionization threshold: Dissociative recombination of the ground vibrational level of ${\rm N}_{\rm 2}^{\rm + }$N2+

Comprehensive theoretical calculations are reported for the dissociative recombination of the lowest vibrational level of the N(2)(+) ground state. Fourteen dissociative channels, 21 electron capture channels, and 48 Rydberg series including Rydberg states having the first excited state of the ion as core are described for electron energies up to 1.0 eV. The calculation of potential curves, electron capture and predissociation widths, cross sections and rate constants are described. The cross sections and rate constants are calculated using Multichannel Quantum Defect Theory which allows for efficient handling of the Rydberg series. The most important dissociative channel is 2(3)Π(u) followed by 4(3)Π(u). Dissociative states that do not cross the ion within the ground vibrational level turning points play a significant role in determining the cross section structure and at isolated energies can be more important than states having a favorable crossing. By accounting for autoionization, the interactions between resonances, between dissociative states, and between resonances and dissociative states it is found that the cross section can be viewed as a complex dissociative recombination spectrum in which resonances overlap and interfere. The detailed cross section exhibits a rapid variation in atomic quantum yields for small changes in the electron energy. A study of this rapid variation by future high resolution storage ring experiments is suggested. A least squares fit to the calculated rate constant from the ground vibrational level is 2.2(+0.2)/(-0.4) × 10(-7) × (T(e)/300)(-0.40) cm(3)/sec for electron temperatures, T(e), between 100 and 3000 K and is in excellent agreement with experimentally derived values.

The D1Πu state of HD and the mass scaling relation of its predissociation widths

Absorption spectra of HD have been recorded in the wavelength range of 75–90 nm at 100 K using the vacuum ultraviolet Fourier transform spectrometer at the Synchrotron SOLEIL. The present wavelength resolution represents an order of magnitude improvement over that of previous studies. We present a detailed study of the D1Πu–X1Σ+g system observed up to v′ = 18. The Q-branch transition probing levels of Π− symmetry are observed as narrow resonances limited by the Doppler width at 100 K. Line positions for these transitions are determined to an estimated absolute accuracy of 0.06 cm−1. Predissociation line widths of Π+ levels are extracted from the absorption spectra. A comparison with the recent results on a study of the D1Πu state in H2 and D2 reveals that the predissociation widths scale as μ−2J(J + 1), with μ being the reduced mass of the molecule and J the rotational angular momentum quantum number, as expected from an interaction with the B′1Σ+u continuum causing the predissociation.

VUV Spectroscopic Study of the D 1Π u State of Molecular Deuterium

The D 1Π u – absorption system of molecular deuterium has been re-investigated using the VUV Fourier-Transform (FT) spectrometer at the DESIRS beamline of the synchrotron SOLEIL and photon-induced fluorescence spectrometry (PIFS) using the 10 m normal incidence monochromator at the synchrotron BESSY II. Using the FT spectrometer absorption spectra in the range 72–82 nm were recorded in quasi static gas at 100 K and in a free flowing jet at a spectroscopic resolution of 0.50 and 0.20 cm−1 respectively. The narrow Q-branch transitions, probing states of Π− symmetry, were observed up to vibrational level v = 22. The states of Π+ symmetry, known to be broadened due to predissociation and giving rise to asymmetric Beutler–Fano resonances, were studied up to v = 18. The 10 m normal incidence beamline setup at BESSY II was used to simultaneously record absorption, dissociation, ionization and fluorescence decay channels from which information on the line intensities, predissociated widths, and Fano q-parameters were extracted. R-branch transitions were observed up to v = 23 for J = 1–3 as well as several transitions for J = 4 and 5 up to v = 22 and 18 respectively. The Q-branch transitions are found to weakly predissociate and were observed from v = 8 to the final vibrational level of the state v = 23. The spectroscopic study is supported by two theoretical frameworks. Results on the Π− symmetry states are compared to ab initio multi-channel-quantum defect theory (MQDT) calculations, demonstrating that these calculations are accurate to within 0.5 cm−1. Furthermore, the calculated line intensities of Q-lines agree well with measured values. For the states of Π+ symmetry a perturbative model based on a single bound state interacting with a predissociation continuum was explored, yielding good agreement for predissociation widths, Fano q-parameters and line intensities.

The predissociation of the 2σ u −1 (c 4Σ u − , v states of the oxygen molecular ion

The dynamics of predissociation of the 2σu−1(c4Σu−), v vibrational states of the O2+ ion was studied theoretically using the method of coupled differential equations. The main equations describing the vibrational motions of nuclei in the adiabatic and diabatic approximations are given. The applicability scope of approximate methods for solving these equations was studied. The predissociation widths for the v = 0 and 1 vibrational levels were found to be Γ0 = 0.054 meV and Γ1 = 9.71 meV. This substantiated the results of recent observations of neutral fragments formed after the dissociation of the O2 molecule. About 99% of the O2+ ions in the 2σu−1(c4Σu−), v states were found to decompose to the O(1D) + O+(4S) dissociation products.

Study of the B″B¯Σu+1 state of H2: Transition probabilities from the ground state, dissociative widths, and Fano parameters

The transition probabilities, the dissociation widths, and the associated Fano parameters for rovibronic lines with J"=0,...,3 of the absorption bands of the B"B 1Sigmau+ state out of the X 1Sigmag+ v"=0 ground state were measured over the complete vibrational progression, showing clearly that only the inner-well state with B" 4psigma character can absorb vuv light and predissociate efficiently. The absolute values of these transition probablities, predissociation widths, and Fano parameters were found to agree well with ab initio calculations if one takes into account that the calculations neglect nonadiabatic couplings.

Investigation of photoionization and photodissociation of an oxygen molecule by the method of coupled differential equations

The photoionization and photodissociation of an oxygen molecule are investigated theoretically by the method of coupled differential equations. The molecular orbitals of the core are calculated in the MO LCAO approximation. The molecular orbitals of a photoelectron in the discrete and continuous spectra are determined by the single-center method. The wave functions of vibrational motion of the oxygen molecule are obtained within the diabatic approach. The described method is used for calculating the predissociation and autoionization widths of the 2σ u −1 (c 4Σ u − )n/σg, v Rydberg states of the oxygen molecule. The total cross sections of the resonant photoionization and neutral predissociation calculated for the oxygen molecule in the excitation energy range 20.6–24.8 eV are in good agreement with the available experimental data.

Theoretical study of nonadiabatic interactions, radiative lifetimes and predissociation lifetimes of excited states of BH

Ab initio multireference configuration interaction calculations have been carried out on the lower-lying electronic states of BH and their nonadiabatic interactions. The ab initio data have been included in subsequent calculations involving solution of the complex eigenvalue Schrödinger equation to determine predissociation widths and lifetimes of vibrational-rotational levels of these states. Secondly, previously calculated ab initio data on the Rydberg states and their nonadiabatic interactions have been included in multi-state vibrational calculations on the 3p and 3d complexes in BH and BD. The results are in good agreement with the experimental analysis of the 3p and 3d spectra in BH and BD. Furthermore, interaction of the 3d states with the neighbouring 4s state is also found to be important.

Pressure broadening and fine-structure-dependent predissociation in oxygen BΣu−3, v=

Both laser-induced fluorescence and cavity ring-down spectral observations were made in the Schumann-Runge band system of oxygen, using a novel-type ultranarrow deep-UV pulsed laser source. From measurements on the very weak (0,0) band pressure broadening, pressure shift, and predissociation line-broadening parameters were determined for the B 3sigma(u)-, v = 0,F(i) fine-structure components for various rotational levels in O2. The information content from these studies was combined with that of entirely independent measurements probing the much stronger (0,10), (0,19), and (0,20) Schumann-Runge bands involving preparation of vibrationally excited O2 molecules via photolysis of ozone. The investigations result in a consistent set of predissociation widths for the B 3sigma(u)-, v = 0 state of oxygen.

General complex rotated finite-element method for predissociation studies of diatomic molecules: An application on the(1–6)Σg+1states ofH2

An exterior complex rotated finite element method was applied on the diabatic multichannel Schr\"odinger equation in order to compute and compare rovibronic energy structures, predissociation widths, and nonradiative lifetimes for levels in the (1--4), (1--5), and $(1\text{--}6)^{1}\ensuremath{\Sigma}_{g}^{+}$ manifolds of ${\mathrm{H}}_{2}$. The rotationless $(v,J=0)$ levels are found to be more or less shifted relative to each other when comparing the results for these three manifolds. The existence of homogeneous spectroscopic perturbations was investigated by studying the rovibronic $(v,J=0\ensuremath{-}10)$ sequences for energies and level widths. Known experimental and theoretical radiative lifetimes were used to estimate present levels that might be spectroscopically measurable. The computed level widths for the $EF$, $GK$, and $H$ electronic levels were generally found to be about two orders of magnitude larger than previously reported [P. Quadrelli, K. Pressler, and L. Woiniewicz, J. Chem. Phys. 93, 4958 (1990)], indicating a somewhat stronger predissociation.

Observation of the long-range potential well of the $\mathsf{(6)^1\Sigma^+_g(3s+5s)}$ state of Na $\mathsf{_2}$

We report on the first observation of the outer well of the \((6)^1\Sigma^+_g\) state of Na2 molecule. The levels are populated in a molecular beam experiment with a three step laser excitation. The fact that these levels predissociate allows an almost background free detection by the appearance of atomic fluorescence. With this method almost all vibrational levels of the outer well are observed. The corresponding predissociation line widths show an oscillating behaviour. The theoretical description of the predissociation is presented in the framework of mapped Fourier grid Hamiltonian representation with optical potential, involving two coupled electronic states. Combining the spectroscopic information on energy positions and predissociation widths, a Rydberg-Klein-Rees potential curve is given for the outer well. Such a state could offer a reliable path for photoassociation of cold Na atoms and formation of ultracold Na2 molecules.

Theoretical ab initio study of the electronic states of KrH and KrH+: Quantum defect and complex coordinate calculations on the Rydberg states of KrH

Potential energy curves have been calculated for the ground and excited electronic states of KrH and the cation KrH+ by ab initio configuration interaction calculations using effective core potentials for Kr. Quantum defect functions have been determined from the ab initio potentials of the low-lying Rydberg states of KrH and potential energy curves have been generated for higher n (s,p,d) Rydberg states. The resulting bound–bound transition energies are in excellent agreement with experimental data. The interaction of the 5p B 2Π state with the 5s and 5p A 2Σ and C 2Σ+ states and their predissociation by X 2Σ+ has been treated by multistate complex scaling calculations for both KrH and KrD. Much larger predissociation widths are obtained in KrH than in KrD, in agreement with experimental observations.

Calculating quasi-bound rotation-vibrational states of HOCl using massively parallel computers

We calculate positions and predissociation widths for quasi-bound states of HOCl with total angular momentum of J=0 and J=3. An ab initio potential energy surface is used in conjunction with a complex absorbing potential (CAP). These calculations are performed by diagonalising a complex symmetric Hamiltonian using our discrete variable representation (DVR) based parallel code, PDVR3D, and a truncation and diagonalisation algorithm. The resonances are identified as those states in the continuum, which are stable with respect to CAP and basis set parameters. Test on the resonances are carried out using over 90 different absorbing potential heights. Resonances of both Feshbach (vibrational trapping) and shape (rotational trapping) are identified.

Nonadiabatic Predissociation Studies of the (1-3) 3Π g System of Al 2 by Means of a Complex Rotated Finite Element Method

A general numerical Runge–Kutta–Fehlberg based diabatization procedure for electronic states in diatomics was applied to the adiabatic (1-3) 3Π g system of Al 2 in order to obtain a strictly diabatic basis. Using an exterior complex rotated finite element method, adiabatic Born–Oppenheimer (BO) as well as diabatic rovibronic term energy values and predissociation widths for the (2) 3Π g ; ( v, N)=(0−50, 0−25) and (3) 3Π g ; ( v, N)=(0−17, 0−25) levels were computed. Comparing rotationless BO and diabatic energies, differences between 10 and 25 cm −1 are found for the (2) 3Π g levels while the (3) 3Π g levels display an almost constant shift ∼12 cm −1. From the widths, the nonradiative lifetime for each rovibronic level was calculated. Based on existing rotationless radiative lifetimes, an estimation of an upper limit of about 50 ns was used to determine a number of rovibronic (2, 3) 3Π g levels which may be experimentally observed.

Predissociations in u+ and 1g states of K2

Recently Wang, Gould, and Stwalley [Phys. Rev. Lett. 80, 476 (1998)] showed by exciting atomic fragments that predissociation occurs in the 1g and 0u+ states of K2. In this study, we supplement the interpretation given in the original report with a more detailed discussion. The calculations presented here use discrete variable representation, close coupling, and semiclassical methods, and incorporate an ab initio calculation of diagonal and off-diagonal spin–orbit elements. The predicted predissociation widths for the 1g state are too narrow to be observed directly, but may be correlated with the strength of the spectral lines observed by exciting atomic fragments. The missing v=90 level of the 1g state in the observed fragmentation spectrum, where the predissociation rate is calculated to be nearly maximum, is attributed to a node in the absorption line strength close to this vibrational level. Since the available information on K2 electronic states (despite recent progress) gives inadequate information on the inner walls of the A state and especially of the b state, calculations of predissociation in the 0u+ state can give only a range of possible widths. We fit widths to 0u+ spectral lines observed by monitoring trap loss. The fitted experimental widths are significantly larger than the maximum calculated predissociation widths, suggesting that there was line broadening associated with the laser power required for the observation.

Formation of Cs $ \mathsf {_2}$ molecules via Feshbach resonances stabilized by spontaneous emission: theoretical treatment with the Fourier grid method

This paper proposes a general method to investigate Feshbach resonances in atomic collisions similar to Cs(6 s ) + Cs(6 p ) in the thermal or cold regime. In order to compute the predissociation widths of the C 1 Π u (6 s + 5 d ) bound vibrational levels of Cs2, coupled both with the (2) 3 Σ + u (6 s + 6 p ) continuum and with the (2) 3 Π u (6 s + 5 d ) vibrational series, a Fourier grid method is implemented, with an optical potential. A convenient way of optimizing the latter is proposed. A large number of resonances are found and calculations of their cross-sections for stabilization into ground state molecules show that the rate may be important. This confirms the interpretation of Lintz and Bouchiat [Phys. Rev. Lett. 80, 2570 (1998)] who observed dimer formation in cell experiments. Possible generalization to the cold regime relies on the possibility to tune the position of a resonance to coincide with the maximum of the collisional energy distribution.