Lifetimes Of Vibrational Levels Research Articles

Theoretical study of MgNa+ ionic system: potential energy curve, vibrational levels, dipole moments, radiative lifetimes and laser-cooling analysis

An extensive ab-initio quantum chemistry study and a discussion of the possible laser cooling and formation of the heteronuclear ionic MgNa+ molecule is presented in this paper. Our work is based on the use of non–empirical pseudo-potentials for the Mg2+ and Na+ cores, large Gaussian basis sets, parametrized l–dependent polarization potentials, and full valence configuration interaction calculations. We present here adiabatic potential energy curves of the ground and 44 low-lying excited electronic states of 1,3Σ+, 1,3Π, 1,3Δ symmetries, and their spectroscopic parameters (Re, De, Te, ωe, ωexe, and Be). Furthermore, numerous ionic – neutral avoided crossings, specially between higher adjacent electronic states of 1,3Σ+, 1,3Π symmetries, are identified and interpreted. The energy separations between these avoided crossings are also calculated. The electric dipole moment curves have been computed for a wide range of inter-nuclear distances. The vibrational energies are obtained by solving the nuclear Schrodinger equation, using the calculated potential energy curves. Thereafter, spontaneous and black-body radiation induced transition rates are calculated to obtain the ground and excited states vibrational level lifetimes. It has been observed that the lifetimes of the ground state vibrational levels are of the order of a second, while those of the excited states, mainly the 21Σ+ state, have the order of a nanosecond.

Vibrational energy transfer kinetics for quantitative species diagnostics using infrared laser-induced fluorescence

Infrared (IR) planar laser-induced fluorescence (LIF/PLIF) exploits the vibrational level transitions of small gas molecules to achieve spatially-resolved spectroscopic information of the species for combustion and flow-field studies. While typical LIF utilizes electronic excitations with ultraviolet or visible lasers, IR LIF presents an alternative for molecules that are not readily accessible with a conventional UV/visible excitation-collection system. In view of the complexities rooting from longer vibrational level lifetimes and more densely-spaced energy levels, a comprehensive vibrational energy transfer model is developed for state-to-state population evolution and transition process characterization, and a typical CO 2 /CO/H 2 O/O 2 /N 2 system relevant to combustion gas mixture is studied by considering a total of 265 energy states and 85,036 transition pathways. The resultant fluorescence signal is thereby studied, with quantitative dependence on local temperature, pressure, gas composition, as well as excitation laser parameters including wavelength, power level and linewidth. Further optimization of collection scheme can be achieved by considering the time-histories and major transition pathways pertaining species evolution on different energy levels. The study develops general modelling and methodology for characterizing the temporal and spectral behavior of a vibrationally-excited molecular system, and demonstrates the potential for quantitative, spatially-resolved diagnostics using IR LIF/PLIF.

Spectroscopic investigations of transition properties for the electronic states of PN+ correlating to two lowest dissociation limits

The PN+ cation is regarded as a candidate of ions which may exist in the interstellar medium. Accurate transition properties are desired to identify the spectra from astronomical observation. However, transition data of PN+ are relatively limited. In this work, the state-of-the-art ab initio calculations are carried out to investigate the low-lying electronic states of PN+ correlating to two lowest dissociation limits, its transition properties and its spin-orbit couplings. For the X2Σ+ and A2Π states, the calculated spectroscopic constants agree well with previous experimental data. For the other electronic states, the accuracy of the spectroscopic parameters is also ensured by comparing with previous theoretical results. Then, transition probabilities of dipole allowed transition systems are calculated. The radiative lifetimes of vibrational levels for the A2Π, 14Π, 14Δ, 14Σ−, and 24Π states are also evaluated. Such transition data can be used in the identification of PN+ in the laboratory or the interstellar space. Finally, the predissociation of 14Σ− (υ' = 1)→16Σ+, 14Σ− (υ' = 15)→16Π and 14Δ (υ'= 19)→16Π are analyzed with the help of spin-orbit coupling integrals.

Radiative lifetimes of vibrational levels and transition probabilities of spontaneous emissions of the six lowest-lying triplet states of AlN radical.

The potential energy curves of 23 states of AlN radical are calculated to accurately determine the first several lowest-lying singlet and triplet states. The calculations are done using the CASSCF method, which is followed by the valence internally contracted MRCI approach. The rotationless radiative lifetimes of the vibrational levels are approximately 10-7-10-8 s for the C3Π, D3Π, and E3Δ states, 101-10-4 s for the A3Σ- state, and 10-4-10-5 s for the B3Σ+ state. The origins of the vibronic bands and the radiative lifetimes agree well with the available experimental and other theoretical results. The Einstein coefficients of many vibronic emissions are large for the C3Π-X3Π, C3Π-A3Σ-, D3Π-X3Π, D3Π-A3Σ-, and E3Δ-X3Π transitions and therefore, these transitions are strong. The emissions of the E3Δ-D3Π system are so weak that it is difficult to measure them through spectroscopy. The spectral distribution of the vibronic emissions is evaluated for the transitions of 12 pairs of states. In terms of the radiative lifetimes and transition probabilities obtained here, several spectroscopic routines for observing these states via spectroscopy are proposed.

Spin-orbit calculations on the ground and excited electronic states of CdBr molecule

High-level configuration interaction method is used to calculate the 14 low-lying electronic states of CdBr. The spin-orbit coupling (SOC) effects are also taken into account. The potential energy curves (PECs) of the 14 Λ-S states, as well as those of 30 Ω states originating from those Λ-S states are determined. The spectroscopic constants of bound states are fitted based on the computed PECs, which agree well with previously available measurements. The predissociation of C2Π(ν′ ≥ 1)→B2Σ+is analyzed with the help of the SOC matrix elements. Finally, the lifetimes of vibrational levels ν′ = 0–5 of C2Π and B2Σ+states are calculated.

Transition Probabilities of Emissions and Rotationless Radiative Lifetimes of Vibrational Levels for the SiN Radical

Abstract The transition dipole moments of the SiN radical are calculated by the valence internally contracted multireference configuration interaction (icMRCI) approach with the aug-cc-pV6Z basis set. The transition probabilities of spontaneous emissions are computed between the eight lowest-lying doublet states. The vibrational band origins, Einstein coefficients, and Franck–Condon factors of all the spontaneous emissions involved are evaluated. The rotationless radiative lifetimes of the first 15 vibrational levels were determined to be approximately 10−3–10−5 s long for the A2Π state, 10−3–10−7 s long for the F2Π state, 10−6–10−7 s long for the C2Π state, 10−6 s long for the D2Σ− and E2Δ states, and 10−7 s long for the B2Σ+ and G2Δ states. It is observed that the rotationless radiative lifetimes quickly become shorter, with an increase in the vibrational level for the A2Π and F2Π states. The Einstein coefficients of many emissions are large for the B2Σ+–X2Σ+, B2Σ+–A2Π, C2Π–X2Σ+, C2Π–A2Π, D2Σ−–A2Π, E2Δ–A2Π, F2Π–X2Σ+, F2Π–A2Π, and G2Δ–A2Π systems. However, the emissions are very weak for the F2Π–D2Σ− system. The vibrational levels and rotational constants of each state are determined and the spectral range of each transition system is evaluated. The vibrational band origins are compared with the available experimental ones. The spectroscopic routines for detecting the unobserved states are proposed. These results can be employed to measure emissions, in particular those of interstellar clouds and stellar atmospheres.

Spectroscopic properties and transition probabilities of SiC+ cation

This study calculates the potential energy curves of 12 Λ-S and 27 Ω states, which belong to the first dissociation channel of SiC+ cation. The potential energy curves are computed with the complete active space self–consistent field method, which is followed by the valence internally multireference configuration interaction approach with the Davidson correction. The transition dipole moments are determined. Core-valence correlation and scalar relativistic correction, as well as extrapolation of the potential energies to the complete basis set limit are included. The spin-orbit coupling effect on the spectroscopic parameters and vibrational properties is evaluated. The vibrational band origins, Franck–Condon factors, and Einstein coefficients of spontaneous emissions are calculated. The rotationless radiative lifetimes of the vibrational levels are approximately 10−5 s long for the e2Π state. The partial radiative lifetimes of vibrational levels are approximately 10−7 s long for the 24Π and 24Σ− states, 10−5 to 10−6 s long for the 22Σ− state and the first well of the 14Π state, and very short for the second well of the 14Π state. Overall, the emissions are strong for the 22Σ−–c2Σ−, 24Σ−–X4Σ−, 24Π–X4Σ− transitions, and for the second well of the 14Π–14Σ+ transition. The spectral range of emissions is determined. In terms of the radiative lifetimes and transition probabilities obtained in this paper, some guidelines for detecting these states are proposed via spectroscopy. These results can be used to measure the emissions from the SiC+ cation, in particular, in interstellar clouds.

Transition Probabilities of Emissions and Rotationless Radiative Lifetimes of Vibrational Levels for the PO Radical

Abstract This work investigates the transition dipole moments (TDMs) and transition probabilities of electric dipole emissions between the X2Π, B2Σ+, B′2Π, D′2Π, C2Σ−, C′2Δ, F2Σ+, and P2Π states of the PO radical. The TDMs of 23 pairs of states are calculated by the internally contracted multireference configuration method with the aug-cc-pV6Z basis set. The vibrational band origins, Franck–Condon factors, and Einstein coefficients of all the spontaneous emissions are evaluated. The rotationless radiative lifetimes of the vibrational levels are approximately 10−7–10−8 s for the B2Σ+, C2Σ−, C′2Δ, P2Π, and F2Σ+ states; 10−4–10−5 s for the B′2Π state; and 10−1–10−2 s for the D′2Π state. The Einstein coefficients of many emissions are large for the B2Σ+–X2Π, B′2Π–X2Π, C′2Δ–X2Π, C2Σ−–X2Π, F2Σ+–X2Π, P2Π–X2Π, P2Π–B′2Π, and P2Π–D′2Π systems. Almost all the spontaneous emissions arising from the D′2Π state are very weak. The vibrational band origins of these emissions extend from the UV into the far-infrared spectra. The radiative lifetimes and vibrational band origins are compared with available experimental and theoretical values. According to the radiative lifetimes and transition probabilities obtained in this paper, some guidelines for detecting these states spectroscopically are proposed. The TDMs and transition probabilities reported here are considered to be reliable and can be used as guidelines for detecting similar transitions, especially those in interstellar space.

Charge symmetric dissociation of doubly ionized N2 and CO molecules.

We report a comparative study of the features in dissociative double ionization by high energy electron impact of N2 and CO molecules. The ratio of cross-section of charge symmetric dissociative ionization to non-dissociative ionization (CSD-to-ND ratio) and the kinetic energy release (KER) spectra of dissociation are experimentally measured and carefully corrected for various ion transmission losses and detector inefficiencies. Given that the double ionization cross sections of these iso-electronic diatomics are very similar, the large difference in the CSD-to-ND ratios must be attributable to the differences in the evolution dynamics of the dications. To understand these differences, potential energy curves (PECs) of dications have been computed using multi-reference configuration interaction method. The Franck-Condon factors and tunneling life times of vibrational levels of dications have also been computed. While the KER spectrum of N2 (++) can be readily explained by considering dissociation via repulsive states and tunneling of meta-stable states, indirect dissociation processes such as predissociation and autoionization have to be taken into account to understand the major features of the KER spectrum of CO(++). Direct and indirect processes identified on the basis of the PECs and experimental KER spectra also provide insights into the differences in the CSD-to-ND ratios.

Lifetime of vibrational levels from Fourier grid calculations: RbCs example

We present systematic calculations of the lifetimes of vibrational levels of excited Rb(5s)Cs(6p(1/2)) 0(+) electronic states. We show that a precise description of the variation with the internuclear distance of the transition dipole moment between electronic states is essential. It is also crucial to account precisely for the spin-orbit coupling between the Rb(5s)Cs(6p) A (1)Σ(+) and b (3)Π states. We describe the general trends of the probability of formation of stable molecules in the Rb(5s)Cs(6s) X (1)Σ(+) and a (3)Σ(+) electronic states, through radiative decay from the 0(+)v' levels, together with the branching ratios for the obtention of singlet or triplet molecules, stable with respect to dissociation. Furthermore, this analysis allows us to demonstrate the efficiency of the Mapped Fourier Grid Hamiltonian Representation method (MFGHR) to determine rigorously the energy variation, throughout the continuous part of the spectrum, of the density of an observable connecting bound vibrational levels and continuum states. The resolution in energy can be adapted to the studied problem through a judicious choice of the grid parameters.

Calculation of radiative parameters for the $$ {A^1}\sum\nolimits_u^{+} {{X^1}} \sum\nolimits_g^{+} {} $$ -transition of cesium dimer

Radiative parameters for vibrational bands (0 ≤ v′ ≤ 30, 0 ≤ v′′ ≤ 59) of the $$ {A^1}\sum\nolimits_u^{+} {{X^1}} \sum\nolimits_g^{+} {} $$ -electronic transition of a cesium dimer are calculated. These include vibronic band wavenumbers, Franck–Condon factors, Einstein coefficients for spontaneous emission, absorption band oscillator strengths, and radiative lifetimes for vibrational levels of the excited electronic state. Vibrational energies and wave functions for the ground and excited electronic states were found by a numerical solution of the radial wave equation based on potential curves plotted during the course of the study.

Dynamic study: Radiative and nonradiative lifetimes for vibrational levels of the A 1∑+ and C 1∑+ states of the alkali hydride KH

Newly calculated radiative transition probabilities for the A 1∑+ → X 1∑+ and C 1∑+ → X 1∑+ emission bands of KH are used to calculate the radiative and nonradiative lifetimes of the various vibrational levels (0 ≤ v ≤ 35) and (0 ≤ v ≤ 55) of A 1∑+ and C 1∑+ states of the diatomic potassium hydride, KH molecule. For higher vibrational levels, an estimate of the bound-to-free emission probability is also needed and included. Accurate positions and radiative and nonradiative lifetimes of states belonging to the adiabatic A and C states of KH molecule are estimated. The results come from a Fermi’s Golden Rule treatment in the coupling calculation. That confirms the accuracy reached in both approaches and also in the treatment of the diabatic-adiabatic transformation. It involves, in particular, an effective phase choice that is needed to properly estimate nonadiabatic couplings.

Electronic structure and fluorescence spectrum of the HeO+ cation

Quantum-mechanical calculations of the potential curves of the HeO+ ion are preformed which correlate with four lower dissociation limits and indicate the excimer type of the ion. The transition dipole moments of the 22Σ−→12Σ− and 24Σ−→14Σ − transitions are calculated. The energies and radiative lifetimes of vibrational levels are determined and structural and spectroscopic constants of the states 12Σ−, 22Σ−, 14Σ−, and 24Σ− are calculated. The fluorescence spectrum corresponding to the 22Σ−→12Σ− and 24Σ−→14Σ − transitions is also calculated. The possibility of lasing at these transitions is discussed.

Dissociative recombination of vibrationally excitedHD+: State-selective experimental investigation

measured. The method is based on using merged electron and molecular ion beams in a heavy-ion storage ring together with molecular fragment imaging techniques which allow us to probe the vibrational-state population of the stored beam as a function of time as well as the final state of the dissociation. The initial vibrational distribution of the stored ion beam ~from a Penning ion source! is found to be in good agreement with a Franck-Condon model of electron impact ionization, apart from slightly larger experimental populations found for low vibrational states; its time evolution in the storage ring reflects the predicted vibrational level lifetimes. Dissociative recombination measurements were performed with the electron and ion beams at matched velocities ~corresponding to average collision energies of about 10 meV!, and at several well-defined collision energies in the range of 3‐11 eV. The obtained vibrational-state specific recombination rate coefficients are compared with theoretical calculations and show that, although an overall agreement exists between experiment and theory, large discrepancies occur for certain vibrational states at low electron energy. @S1050-2947~99!09411-1# PACS number~s!: 34.80.Gs

The UV absorption of ClO Part 1. The A2Π–X2Π spectrum at wavelengths from 285–320 nm studied by cavity ring-down spectroscopy

The UV absorption of ClO at wavelengths between 285 and 320 nm has been investigated using cavity ring-down spectroscopy. This wavelength region spans the (0,0) to (7,0) bands of the A2Π3/2–X2Π3/2 and A2Π1/2–X2Π1/2 transitions. The previously unobserved A2Π3/2–X2Π3/2 (0,0) and (1,0) absorption bands have been recorded with rotational resolution, and spectra of the (2,0) to (6,0) bands of the A2Π1/2–X2Π1/2 transition are shown for the first time. Analysis of the spectra gives refined band origins and rotational constants for the A2Π v′ levels and reveals a strong v′ dependence in the linewidths of rotational features. The lifetimes of the A2Π3/2v′=0–2 and A2Π1/2v′=2–4 levels are revised from previous estimates, and the lifetimes of A2Π1/2v′=5 and 6 levels have been determined. The deduced predissociation rates for A2Π3/2v′=3–7 confirm earlier studies. The lifetimes of vibrational levels of the two spin–orbit components of the A2ΠΩ state are markedly different. No evidence of J′-dependence in the predissociation is found, in contrast to the corresponding A2Π3/2 state of the IO radical.

Experimental investigation of radiative lifetimes of vibrational levels at the electronic ground state of C2−

Radiative lifetimes of the vibrational levels v=2 to v=4 of the X 2Σg+ ground state of the C2− molecular ion have been experimentally investigated by photodetachment in a storage ring. The lifetime of the v=3 level was 0.32±0.02 s for 12C12C−, and 0.22±0.02 s for 12C13C−. For both ions, the lower limit for the v=2 lifetime was 5 s, and the upper limit for the v=4 level was ∼100 ms. The measured lifetime for v=3 of 12C12C− is a factor of 4 smaller than found in a calculation [P. Rosmus and H. Werner, J. Chem. Phys. 80, 5085 (1984)]. The results point to the existence of at least one bound vibrational level of the lowest 4Σu+ state.

Comment on “Lifetimes of vibrational levels in the B̃ 2A′ state of HCO”

Arguments are put forward that the quantum beats in the B̃ 2A′ electronic state of HCO attributed to a higher-order hyperfine perturbation by Tobiason and Rohlfing are most likely due to well-known hyperfine quantum beats. In contrast to Tobiason and Rohlfing's interpretation, hyperfine perturbations among bright and dark states are irrelevant for understanding such quantum beats.

Lifetimes of vibrational levels in the B̃ 2A′ state of HCO

We measure the fluorescence decays for low-lying rotational states in the first eight vibrational levels of HCO B̃ 2A′. Some long-lived decays exhibit weak quantum beats that we attribute to a higher-order hyperfine perturbation in the B̃ state. We estimate fluorescence quantum yields by combining measured fluorescence intensities and a calculated electronic transition moment. The estimated nonradiative decay rates increase with increasing vibrational excitation and exhibit mode specificity. We discuss possible vibronic coupling mechanisms, including spin-orbit coupling to quartet states and predissociation via the A ̃ 2 Π( 2 A″) and X̃ 2A′ states.

Lifetimes and Quenching of the Ā 2A′(υ3′ = 0 – 2) → X̄ 2A″ Fluorescence of HSO

AbstractFluorescence lifetimes of vibrational levels of the first electronically excited state (Ā 2 A′) of HSO, determined by the technique of discharge flow and laser‐induced fluorescence, are 81 ± 10, 74 ± 8, and 76 ± 14 μs for υ3′ = 0, 1 and 2, respectively. The rate coefficients of quenching of each level by He, N2, O2 and O3 were measured; the coefficients for HSO (Ā, υ3′ = 0 – 2) quenched by O3 arc 35–50 times as great as those of HSO by He.

Theoretical radiative transition probabilities of the CS + ion

The electronic transition moment functions for the A 2Π-X 2Σ +, B 2Σ +-X 2Σ +, B 2Σ +-A 2Π and C 2Δ-A 2Π transitions were calculated from highly correlated CASSCF CI electronic wavefunctions and used for the evaluation of the radiative lifetimes and absorption oscillator strengths. For the B 2Σ +, ν′=0 state the calculated lifetime of 364 ns is found to be in good agreement with the experimental value of 425 ± 25 ns. The variations of the radiative lifetimes with vibrational quantum number in the A, B and C states of CS + are predicted. These theoretical lifetimes are expected to be accurate w within about 20%. The dipole moment of the X 2Σ +, ν=0 state is calculated to be 0.509 ± 0.05 D. The radiative lifetimes of vibrational levels in the electronic ground state are also given. For the C 2Δ state spectroscopic constants are predicted.