Bending Vibrational Levels Research Articles

The 1.66 μm spectrum of the ethynyl radical, CCH

Frequency-modulated diode laser transient absorption spectra of the ethynyl radical have been recorded at wavelengths close to 1.66 μm. The observed spectrum includes strong, regular, line patterns. The two main bands observed originate in the ground X̃2Σ+ state and its first excited bending vibrational level of 2Π symmetry. The upper states, of 2Σ+ symmetry at 6055.6 cm−1 and 2Π symmetry at 6413.5 cm−1, respectively, had not previously been observed and the data were analyzed in terms of an effective Hamiltonian representing their rotational and fine structure levels to derive parameters which can be used to calculate rotational levels up to J = 37/2 for the 2Π level and J = 29/2 for the 2Σ one. Additionally, a weaker series of lines have been assigned to absorption from the second excited bending, (0 2 0), level of 2Σ symmetry, to a previously observed state of 2Π symmetry near 6819 cm−1. These strong absorption bands at convenient near-IR laser wavelengths will be useful for monitoring CCH radicals in chemical systems.

The electronic spectrum of the jet-cooled stibino (SbH2) free radical.

The Ã2A1-X̃2B1 electronic transition of the jet-cooled stibino (SbH2 and SbD2) free radical has been observed for the first time using laser induced fluorescence (LIF) detection. The radicals were produced by a pulsed electric discharge through a mixture of stibine (SbH3 or SbD3) in high pressure argon at the exit of a pulsed molecular beam valve. SbH2 exhibits only three LIF bands, assigned as 21 0, 00 0, and 20 1, with a fluorescence lifetime (τ), which decreases from ∼50 ns for 00 to <10 ns for 21. LIF transitions to the 00 (τ ∼ 2 µs), 21 (τ ∼ 400 ns), and 22 (τ ∼ 75 ns) upper vibronic states of SbD2 were also observed. High-resolution spectra exhibited large spin-rotation splittings and small resolved antimony hyperfine splittings due to a substantial Fermi contact interaction in the excited state. The experimentally determined rotational constants gave effective molecular structures of r0 ″ = 1.724(2) Å, θ0 ″ = 90.38(7)° and r0 ' = 1.693(6) Å, θ0 ' = 120.6(3)°. The ground state bending vibrational levels up to eight quanta (6404 cm-1) in SbH2 and 12 quanta (6853 cm-1) in SbD2 were measured from dispersed fluorescence spectra. All indications are that SbH2 undergoes a dissociative process at low vibrational energies in the excited electronic state.

Modelling the input and relaxation of vibrational energy in CO2 plasmas

A consistent theoretical analysis of a pulsed DC glow discharge operating at pressure of 5 Torr, current of 50 mA and plasma pulse of 5 ms in CO2 is presented. The model couples the electron Boltzmann equation to a rate balance equations involving ~70 individual vibrational states. The kinetic scheme and the corresponding e–V, V–T and V–V rate coefficients are validated via comparison between the model predictions and recent experimental data available in literature. The bending and symmetric vibrational levels show a continuous increase along the plasma pulse while the levels in the asymmetric mode present a maximum at around 0.7 ms. A corresponding maximum of the temperature of the asymmetric stretch vibration mode is observed as well at the start of the pulse reaching a value of about 900 K, well above the vibrational temperatures of the symmetric and bending modes, which remain always nearly equilibrated. A quick thermalization of the CO2 vibrational temperatures is always observed in the afterglow.

Qualitative models of intramolecular dynamics of acetylene: relation between the bending polyads of acetylene and perturbed Keplerian systems

ABSTRACTWe analyse qualitatively the bending vibrational polyads of the acetylene molecule (CH) in the approximation of the resonant oscillator with axial symmetry using an effective vibrational Hamiltonian which reproduces bending vibrational energy levels computed by Michel Herman and coworkers [M. Herman, A. Campargue, M.I.E. Idrissi, and J.V. Auwera, J. Phys. Chem. Ref. Data 32 (3), 921 (2003). doi: 10.1063/1.1531651]. We explain how the classical limit of this quantum system for the total vibrational angular momentum is equivalent to a reduced perturbed Keplerian system on the classical phase space , such as the hydrogen atom in external electric and magnetic fields in the Kustaanheimo–Stiefel formalism. In particular, bending vibrational -polyads of CH correspond to the n-shells of the perturbed hydrogen atom. Within this approach, using the techniques developed for the Keplerian systems and methods of the qualitative theory, we account concisely for all series of bifurcations of the classical nonlinear normal modes and their manifestations in the quantum energy level spectrum described by our predecessors [V. Tyng and M.E. Kellman, J. Phys. Chem. B 110 (38), 18859 (2006). doi: 10.1021/jp057357f]. In addition to local oscillator approximations near stable equilibrium points, notably the local modes discussed by Rose and Kellman [J. Chem. Phys. 105 (24), 10743 (1996). doi: 10.1063/1.472882] and Jacobson et al. [J. Chem. Phys. 109 (1), 121 (1998). doi: 10.1063/1.476529; J. Chem. Phys. 111, 600 (1999). doi: 10.1063/1.479341; J. Chem. Phys. 110, 845 (1999). doi: 10.1063/1.478052], we introduce two new global integrable approximations, and confirm them by constructing respective two regular complementary lattices of quantum states within one -polyad. From the stratification of the phase space, we uncover the geometrical meaning of the corresponding new good quantum numbers and define new kind of wavefunction localisation in the neighbourhood of two spheres in the four-dimensional space. Furthermore, we use our two approximate lattices to uncover quantum monodromy of the system through the evolution of an elementary quantum cell along a closed path in the images of the nearly integrable energy-momentum maps.

Analysis of the [formula omitted] bands of the ethynyl radical near 1.48 [formula omitted]m and re-evaluation of [formula omitted] state energies

We report the observation and analysis of spectra in part of the near-infrared spectrum of C2H, originating in rotational levels in the ground and lowest two excited bending vibrational levels of the ground X̃2Σ+ state. In the analysis, we have combined present and previously reported high resolution spectroscopic data for the lower levels involved in the transitions to determine significantly improved molecular constants to describe the fine and hyperfine split rotational levels of the radical in the zero point, v2=1 and the 2Σ+ component of v2=2. Two of the upper state vibronic levels involved had not been observed previously. The data and analysis indicate the electronic wavefunction character changes with bending vibrational excitation in the ground state and provide avenues for future measurements of reactivity of the radical as a function of vibrational excitation.

VIBRATIONALLY EXCITED C 4 H

Rotational spectra in four new excited vibrational levels of the linear carbon chain radical C4H were observed in the millimeter band between 69 and 364 GHz in a low pressure glow discharge, and two of these were observed in a supersonic molecular beam between 19 and 38 GHz. All have rotational constants within 0.4% of the ground vibrational state of C4H and were assigned to new bending vibrational levels, two each with and vibrational symmetry. The new levels are tentatively assigned to the and bending vibrational modes (both with symmetry), and the and combination levels ( symmetry) on the basis of the derived spectroscopic constants, relative intensities in our discharge source, and published laser spectroscopic and quantum calculations. Prior spectroscopic constants in the and levels were refined. Also presented are interferometric maps of the ground state and the level obtained with the Submillimeter Array (SMA) near 257 GHz which show that C4H is present near the central star in IRC+10216. We found no evidence with the SMA for the new vibrationally excited levels of C4H at a peak flux density averaged over a synthesized beam of Jy/beam in the 294–296 and 304–306 GHz range, but it is anticipated that rotational lines in the new levels might be observed in IRC+10216 when ALMA attains its full design capability.

Simplified Cartesian basis model for intrapolyad emission intensities in the bent-to-linear electronic transition of acetylene.

The acetylene emission spectrum from the trans-bent electronically excited à state to the linear ground electronic X̃ state has attracted considerable attention because it grants Franck–Condon access to local bending vibrational levels of the X̃ state with large-amplitude motion along the acetylene ⇌ vinylidene isomerization coordinate. For emission from the ground vibrational level of the à state, there is a simplifying set of Franck–Condon propensity rules that gives rise to only one zero-order bright state per conserved vibrational polyad of the X̃ state. Unfortunately, when the upper level involves excitation in the highly admixed ungerade bending modes, ν4′ and ν6′, the simplifying Franck–Condon propensity rule breaks down--as long as the usual polar basis (with v and l quantum numbers) is used to describe the degenerate bending vibrations of the X̃ state--and the intrapolyad intensities result from complicated interference patterns between many zero-order bright states. In this article, we show that, when the degenerate bending levels are instead treated in the Cartesian two-dimensional harmonic oscillator basis (with vx and vy quantum numbers), the propensity for only one zero-order bright state (in the Cartesian basis) is restored, and the intrapolyad intensities are simple to model, as long as corrections are made for anharmonic interactions. As a result of trans ⇌ cis isomerization in the à state, intrapolyad emission patterns from overtones of ν4′ and ν6′ evolve as quanta of trans bend (ν3′) are added, so the emission intensities are not only relevant to the ground-state acetylene ⇌ vinylidene isomerization, they are also a direct reporter of isomerization in the electronically excited state.

Studies of the Vibrational Energy Level of H2O by Algebraic and DFT Approaches

The molecular spectroscopy is a branch of physics that deals with the interaction of electromagnetic radiation with matter. Within new theoretical approaches, we have calculated the stretching and bending vibrational energy levels of a water molecule in fundamental and overtone modes. The present calculation not only predicts the higher overtones, but also shows good agreement with a few experimental data.

Vibrationally Hot Bands of the SiCN Ã 2Δ – X̃ 2Π System

We have generated SiCN in supersonic free jet expansions and observed the laser induced fluorescence (LIF) spectrum. In addition to the vibronic bands from the vibrationless level of the X̃ (2)Π state, the hot bands from the bending vibrational level, à (01(1)0) (2)Φ - X̃ (01(1)0) (2)Δ and à (01(1)0) (2)Π - X̃ (01(1)0) (2)Σ((-)), have been measured. The rotational energy levels were reasonably analyzed as those of the (2)K' - (2)K″ transitions, but their line intensities calculated from the Hönl-London factors derived in the intermediate case between Hund's case (a) and (b) could not reproduce the observed spectra. The Hönl-London factors derived in the (2)Λ' - (2)Λ″ ((2)Δ - (2)Π) transition reasonably reproduced the spectra. It indicates that coupling between the electronic orbital and vibrational angular momenta is weak in the SiCN (2)Δ - (2)Π system, and a basis set of |Λ v2 l Σ;J P MJ>, the so-called "l-basis", better describes the system than that of |Λ v2 K Σ;J P MJ>.

A laser-induced fluorescence study of the jet-cooled nitrous oxide cation (N2O+)

Laser-induced fluorescence and wavelength resolved emission spectra of the à (2)Σ(+) - X̃ (2)Π(i) electronic transition of the jet-cooled nitrous oxide cation have been recorded. The ions were produced in a pulsed electric discharge at the exit of a supersonic expansion using a precursor mixture of N(2)O in high pressure argon. Both spin-orbit components of the 0(0) (0) band were studied at high resolution and rotationally analyzed to provide precise molecular constants for the combining states. Emission spectra were obtained by laser excitation of the 0(0) (0), 2(0) (1), 3(0) (1), and 2(0) (2) absorption bands, providing extensive data on the ground state bending, stretching, and combination vibrational levels. These data were fitted to a Renner-Teller model including spin-orbit, anharmonic, and Fermi resonance terms. The observed energy levels and fitted parameters were found to be comparable to those in the literature predicted from an ab initio potential energy surface.

The ν2 bending vibrational structure of the $\tilde{X}$X̃ 2Σ+ state of MgNC

We have generated MgNC in supersonic free jet expansions and observed the laser induced fluorescence (LIF) of the Ã(2)Π-X̃(2)Σ(+) transition. We measured the LIF dispersed spectra from the single vibronic levels of the Ã(2)Π electronic state of MgNC, following excitation of each ν(2) bending vibronic band observed, i.e., the κ series of the (0,v(2)('),0)-(0,0,0), v(2)(') = 0, 1, 2, 4, and 6 vibronic bands. In the vibrational structure in the dispersed fluorescence spectra measured, the long progression of the ν(2) bending mode in the X̃(2)Σ(+) state is identified, e.g., up to v(2)('')=14 in the (0,6,0)-(0,v(2)(''),0) spectrum. This enables us to derive the potential curve of the ν(2) bending mode in the X̃(2)Σ(+) state. We used two kinds of models to obtain the potential curve; (I) the customary formula expressed in the polynomial series of the (v(2)('')+(d(2)/2)) term and (II) the internal rotation model. The potential curve derived from model (I) indicates the convergence of the bending vibrational levels at about 800 cm(-1) from the vibrationless level of MgNC, which may correspond to the barrier height of the isomerization reaction, MgNC ⇌ MgCN, in the X̃(2)Σ(+) state. Model (II) gives a simple picture for the isomerization reaction pathway with a barrier height of about 630 cm(-1) from the vibrationless level of the more stable species, MgNC. This shows that the v(2)('')=8 bending vibrational level of MgNC is already contaminated by the v(2)('')=2 bending vibrational level of the isomer, MgCN, and implies that the isomerization reaction begins at the v(2) ('')=8 level. The bending potential surface and the isomerization reaction pathway, MgNC ⇌ MgCN, in the X̃(2)Σ(+) state are discussed by comparing the potential derived in this study with the surface obtained by quantum chemical calculation.

The C3-bending vibrational levels of the C3–Kr and C3–Xe van der Waals complexes studied by their Ã−X̃ electronic transitions and by ab initio calculations

Fluorescence excitation spectra and wavelength-resolved emission spectra of the C(3)-Kr and C(3)-Xe van der Waals (vdW) complexes have been recorded near the 2(2-)(0), 2(2+)(0), 2(4-)(0), and 1(1)(0) bands of the Ã(1)Π(u)-X̃(1)Σ(g)(+) system of the C(3) molecule. In the excitation spectra, the spectral features of the two complexes are red-shifted relative to those of free C(3) by 21.9-38.2 and 34.3-36.1 cm(-1), respectively. The emission spectra from the à state of the Kr complex consist of progressions in the two C(3)-bending vibrations (ν(2), ν(4)), the vdW stretching (ν(3)), and bending vibrations (ν(6)), suggesting that the equilibrium geometry in the X̃ state is nonlinear. As in the Ar complex [Zhang et al., J. Chem. Phys. 120, 3189 (2004)], the C(3)-bending vibrational levels of the Kr complex shift progressively to lower energy with respect to those of free C(3) as the bending quantum number increases. Their vibrational structures could be modeled as perturbed harmonic oscillators, with the dipole-induced dipole terms of the Ar and Kr complexes scaled roughly by the polarizabilities of the Ar and Kr atoms. Emission spectra of the Xe complex, excited near the Ã, 2(2-) level of free C(3), consist only of progressions in even quanta of the C(3)-bending and vdW modes, implying that the geometry in the higher vibrational levels (υ(bend) ≥ 4, E(vib) ≥ 328 cm(-1)) of the X̃ state is (vibrationally averaged) linear. In this structure the Xe atom bonds to one of the terminal carbons nearly along the inertial a-axis of bent C(3). Our ab initio calculations of the Xe complex at the level of CCSD(T)∕aug-cc-pVTZ (C) and aug-cc-pVTZ-PP (Xe) predict that its equilibrium geometry is T-shaped (as in the Ar and Kr complexes), and also support the assignment of a stable linear isomer when the amplitude of the C(3) bending vibration is large (υ(4) ≥ 4).

Pulsed-field ionization zero electron kinetic energy spectrum of the ground electronic state of BeOBe+

The ground electronic state of BeOBe(+) was probed using the pulsed-field ionization zero electron kinetic energy photoelectron technique. Spectra were rotationally resolved and transitions to the zero-point level, the symmetric stretch fundamental and first two bending vibrational levels were observed. The rotational state symmetry selection rules confirm that the ground electronic state of the cation is (2)Σ(g)(+). Detachment of an electron from the HOMO of neutral BeOBe results in little change in the vibrational or rotational constants, indicating that this orbital is nonbonding in nature. The ionization energy of BeOBe [65480(4) cm(-1)] was refined over previous measurements. Results from recent theoretical calculations for BeOBe(+) (multireference configuration interaction) were found to be in good agreement with the experimental data.

VIBRATIONALLY EXCITED C 6 H

Rotational spectra in four new excited vibrational levels of the linear carbon chain radical C4H were observed in the millimeter band between 69 and 364 GHz in a low pressure glow discharge, and two of these were observed in a supersonic molecular beam between 19 and 38 GHz. All have rotational constants within 0.4% of the ground vibrational state of C4H and were assigned to new bending vibrational levels, two each with and vibrational symmetry. The new levels are tentatively assigned to the and bending vibrational modes (both with symmetry), and the and combination levels ( symmetry) on the basis of the derived spectroscopic constants, relative intensities in our discharge source, and published laser spectroscopic and quantum calculations. Prior spectroscopic constants in the and levels were refined. Also presented are interferometric maps of the ground state and the level obtained with the Submillimeter Array (SMA) near 257 GHz which show that C4H is present near the central star in IRC+10216. We found no evidence with the SMA for the new vibrationally excited levels of C4H at a peak flux density averaged over a synthesized beam of Jy/beam in the 294–296 and 304–306 GHz range, but it is anticipated that rotational lines in the new levels might be observed in IRC+10216 when ALMA attains its full design capability.

U (2) algebraic model applied to vibrational spectra of Nickel Metalloporphyrins

In this paper the highly excited stretching and bending vibrational energy levels of some Nickel Metalloporphyrin molecules are studied by U (2) algebraic model. Its application to Nickel Octaethyl Porphyrin, Nickel Tetra Phenyl Porphyrin and Nickel Porphyrin are presented with fewer algebraic fitting parameters. The highly excited stretching and bending vibrational energy levels of these molecules are showing the energy clustering spectrum.

Imaging Studies of the Photodissociation of NH3+ and ND3+ Cations

Velocity map ion imaging methods have been used to study the photofragmentation dynamics of state-selected NH3+ and ND3+ cations. The cations were prepared in selected nu2+ bending vibrational levels of the ground (x2A'') electronic state by two-photon resonant, three-photon ionization of NH3(ND3), via several different nu2' levels of the and ' Rydberg states. Subsequent excitation to the A2E state by absorption of a 207.6 nm photon resulted in N-H(D) bond fission and NH2+(ND2+) fragment ion formation. These fragments exhibit isotropic recoil velocity distributions, which peak at low kinetic energy but extend to the maximum allowed by energy conservation. Such findings accord with conclusions from earlier electron induced photoionization and photoelectron-photoion coincidence studies of NH3 at similar total energies (defined relative to the ground-state neutral) and, as previously, can be rationalized in terms of excitation to the Jahn-Teller distorted state, rapid radiationless transfer via one or more conical intersections linking the and state potential energy surfaces (PESs) and subsequent unimolecular decay on the latter PES. Weak NH2+ and NH+ fragment ion signals are also observed when exciting with the ionization laser only; imaging these fragment ions provides some insights into their likely formation mechanisms.

Rotational spectra of vibrationally excited CCH and CCD

The millimeter-wave rotational spectra of the lowest bending and stretching vibrational levels of CCH and CCD were observed in a low pressure discharge through acetylene and helium. The rotational, centrifugal distortion, and fine structure constants were determined for the (02(0)0) and (02(2)0) bending states, the (100) and (001) stretching levels, and the (011) combination level of CCH. The same pure bending and stretching levels, and the (110) combination level were observed in CCD. Apparent anomalies in the spectroscopic constants in the bending states were shown to be due to l-type resonances. Hyperfine constants, which in CCH are sensitive to the degree of admixture of the A 2Pi excited electronic state, were determined in the excited vibrational levels of both isotopic species. Theoretical Fermi contact and dipole-dipole hyperfine constants calculated by Peric et al. [J. Mol. Spectrosc. 150, 70 (1991)] were found to be in excellent agreement with the measured constants. In CCD, new rotational lines tentatively assigned to the (100) level largely on the basis of the observed hyperfine structure support the assignment of the C-H stretching fundamental (nu1) by Stephens et al. [J. Mol. Struct. 190, 41 (1988)]. Rotational lines in the excited vibrational levels of CCH are fairly intense in our discharge source because the vibrational excitation temperatures of the bending vibrational levels and the (110) and (011) combination levels are only about 100 K higher than the gas kinetic temperature, unlike the higher frequency stretching vibrations, where the excitation temperatures are five to ten times higher.

The bending vibrational levels of the acetylene cation: A case study of the Renner-Teller effect in a molecule with two degenerate bending vibrations

Forty three vibronic levels of C2H2+, X 2Pi u, with upsilon4 = 0-6, upsilon5 = 0-3, and K = 0-4, lying at energies of 0-3520 cm(-1) above the zero-point level, have been recorded at rotational resolution. These levels were observed by double resonance, using 1+1' two-color pulsed-field ionization zero-kinetic-energy photoelectron spectroscopy. The intermediate states were single rovibrational levels chosen from the A1Au, 4nu3 (K = 1-2), 5nu3 (K = 1), nu2+4nu3 (K = 0), and 47,206 cm(-1) (K = 1) levels of C2H2. Seven of the trans-bending levels of C2H2+ (upsilon4 = 0-3, K = 0-2) had been reported previously by Pratt et al. [J. Chem. Phys. 99, 6233 (1993)]; our results for these levels agree well with theirs. A full analysis has been carried out, including the Renner-Teller effect and the vibrational anharmonicity for both the trans- and cis-bending vibrations. The rotational structure of the lowest 16 vibronic levels (consisting of the complete set of levels with upsilon4 + upsilon5 < or = 2, except for the unobserved upper (2Pi u component of the 2nu4 overtone) could be fitted by least squares using 16 parameters to give an rms deviation of 0.21 cm(-1). The vibronic coupling parameter epsilon5 (about whose magnitude there has been controversy) was determined to be -0.0273(7). For the higher vibronic levels, an additional parameter, r45, was needed to allow for the Darling-Dennison resonance between the two bending manifolds. Almost all the observed levels of the upsilon4 + upsilon5 = 3 and 4 polyads (about half of the predicted number) could then be assigned. In a final fit to 39 vibronic levels with upsilon4 + upsilon5 < or = 5, an rms deviation of 0.34 cm(-1) was obtained using 20 parameters. An interesting finding is that Hund's spin-coupling cases (a) and (b) both occur in the Sigmau components of the nu4 + 2nu5 combination level. The ionization potential of C2H2 (from the lowest rotational level of the ground state to the lowest rotational level of the cation) is found to be 91,953.77 +/- 0.09 cm(-1) (3sigma).

The molecular potential energy surface and vibrational energy levels of methyl fluoride. Part II

New analytical bending and stretching, ground electronic state, potential energy surfaces for CH(3)F are reported. The surfaces are expressed in bond-length, bond-angle internal coordinates. The four-dimensional stretching surface is an accurate, least squares fit to over 2000 symmetrically unique ab initio points calculated at the CCSD(T) level. Similarly, the five-dimensional bending surface is a fit to over 1200 symmetrically unique ab initio points. This is an important first stage towards a full nine-dimensional potential energy surface for the prototype CH(3)F molecule. Using these surfaces, highly excited stretching and (separately) bending vibrational energy levels of CH(3)F are calculated variationally using a finite basis representation method. The method uses the exact vibrational kinetic energy operator derived for XY(3)Z systems by Manson and Law (preceding paper, Part I, Phys. Chem. Chem. Phys., 2006, 8, DOI: 10.1039/b603106d). We use the full C(3v) symmetry and the computer codes are designed to use an arbitrary potential energy function. Ultimately, these results will be used to design a compact basis for fully coupled stretch-bend calculations of the vibrational energy levels of the CH(3)F system.

First observation of the B̃A11 state of SiH2 and SiD2 radicals by optical-optical double resonance spectroscopy

The B1A1 state of SiH2 and SiD2 was observed by the optical-optical double resonance technique for the first time. The electronic band origin of the B state of SiD2 was determined to be 27 214.11 cm(-1). A very clear exclusive behavior depending on the even/odd value of the bending vibrational quantum number was observed in the spectra, representing a quasilinear behavior of the B state. The barrier height to linearity was estimated to be approximately 125 cm(-1) by the quasilinear analysis of the bending vibrational level structure of SiD2.