Quasibound Vibrational Levels Research Articles

Metastable homonuclear diatomic trications [formula omitted] for elements X from the first three rows of the periodic table

Motivated by a systematic stability scan of the homonuclear diatomic systems with elements from hydrogen to argon, we investigated in detail the ensuing five candidates for metastable trications, viz., O23+, P23+, S23+, Cl23+, and Ar23+ by multireference configuration interaction computations. Each of these tricationic systems exhibits a barrier in its ground state potential energy curve leading to quasi-bound nuclear motion. The resulting lifetimes vary drastically; while S23+ and Cl23+ in their lowest vibrational states can be regarded as practically stable, the predicted lifetimes of O23+ and Ar23+ are too short to allow a mass spectroscopic detection of these systems by current experimental capabilities. In the case of Ar23+, the theoretically predicted existence of quasibound vibrational levels also depends on whether or not relativistic corrections are taken into account.

A dissociative photoionization study of the c4Σu− state in O+2 using the TPEPICO technique

In the dissociative photoionization (DPI) process, hν + O2 → O + O+ + e−, ionisation and dissociation both occur (either as a direct or indirect process) following photoabsorption. The Threshold Photoelectron Photoion Coincidence (TPEPICO) technique, i.e. measuring the coincidence yield between threshold photoelec-trons and photoions is a powerful way of studying the dynamics involved. The c4Σu− state in O+2 at ~ 24.56 eV has a shallow minimum in its potential that supports two distinct quasi-bound vibrational levels (v = 0, 1). We have investigated the angular distributions of 2 eV O+(4S) ions produced from DPI of O +2 c4Σu− (v = 0, 1) using the TPEPICO technique.

State-specific dissociation modeling with multiquantum vibration-translation transitions

An efficient state-specific model of dissociation using a quadrature approach is proposed by considering multiquantum vibration-translation (VT) transitions (between bound and quasibound vibrational levels) according to the forced harmonic oscillator theory. Application of this model to a pure N₂ gas flow behind a plane shock wave shows that dissociation has a large influence on intermediate and higher vibrational levels and is characterized by state-specific incubation distances, before which VT energy exchanges remain the dominant mechanism just behind the shock.

Dynamical insights into π1σ∗ state mediated photodissociation of aniline

This article reports a comprehensive study of the mechanisms of H atom loss in aniline (C(6)H(5)NH(2)) following ultraviolet excitation, using H (Rydberg) atom photofragment translational spectroscopy. N-H bond fission via the low lying (1)pi sigma(*) electronic state of aniline is experimentally demonstrated. The (1)pi sigma(*) potential energy surface (PES) of this prototypical aromatic amine is essentially repulsive along the N-H stretch coordinate, but possesses a shallow potential well in the vertical Franck-Condon region, supporting quasibound vibrational levels. Photoexcitation at wavelengths (lambda(phot)) in the range 293.859 nm > or = lambda(phot) > or = 193.3 nm yields H atom loss via a range of mechanisms. With lambda(phot) resonant with the 1(1)pi pi(*) <-- S(0) origin (293.859 nm), H atom loss proceeds via, predominantly, multiphoton excitation processes, resonantly enhanced at the one photon energy by the first (1)pi pi(*) excited state (the 1(1)pi pi(*) state). Direct excitation to the first few quasibound vibrational levels of the (1)pi sigma(*) state (at wavelengths in the range 269.513 nm > or = lambda(phot) > or = 260 nm) induces N-H bond fission via H atom tunneling through an exit barrier into the repulsive region of the (1)pi sigma(*) PES, forming anilino (C(6)H(5)NH) radical products in their ground electronic state, and with very limited vibrational excitation; the photo-prepared vibrational mode in the (1)pi sigma(*) state generally evolves adiabatically into the corresponding mode of the anilino radical upon dissociation. However, as the excitation wavelength is reduced (lambda(phot) < 260 nm), N-H bond fission yields fragments with substantially greater vibrational excitation, rationalized in terms of direct excitation to 1(1)pi pi(*) levels, followed by coupling to the (1)pi sigma(*) PES via a 1(1)pi pi(*)/(1)pi sigma(*) conical intersection. Changes in product kinetic energy disposal once lambda(phot) approaches approximately 230 nm likely indicate that the photodissociation pathways of aniline proceed via direct excitation to the (higher) 2(1)pi pi(*) state. Analysis of the anilino fragment vibrational energy disposal-and thus the concomitant dynamics of (1)pi sigma(*) state mediated photodissociation-provides a particularly interesting study of competing sigma(*) <-- pi and pi(*) <-- pi absorption processes and develops our appreciation of the photochemistry of aromatic amines. It also allows revealing comparisons with simple amines (such as ammonia and methylamine) as well as the isoelectronic species, phenol. This study yields a value for the N-H bond strength in aniline, D(0)(H-anilino) = 31630+/-40 cm(-1).

Theoretical study of the ground and first excited singlet state potential energy surfaces of disulphur monoxide (S2O)

An extended region of the ground state potential energy surface (PES) in the vicinity of the experimentally observed isomer of disulphur monoxide (S2O) has been characterized using second-order generalized Van Vleck perturbation theory (GVVPT2) and the cc-pVDZ basis set. The corresponding region of the PES of the first excited singlet state, [Ctilde] 1A′, was analysed in order to elucidate the nature of the experimentally observed dissociation of the excited state S2O. Our calculations support experimental results suggesting the existence of several quasi-bound vibrational energy levels on the excited state PES. The second excited singlet state, [Dtilde] 1A′, was also examined. Our results corroborate the hypothesis that the cause of the predissociation of excited state S2O into its ground state dissociation products is due to the interaction of the lowest two excited state PESs at elongated S-S bond distances. Additional GVVPT2 calculations for the ground and excited state equilibrium structures were performed with the cc-pVTZ basis, and are in good agreement with experimental and CI results.

TPEsCO spectra of HCl 2+ and DCl 2+: experiment and theory

Vibrationally resolved threshold photoelectrons in coincidence (TPEsCO) spectra of the X 3Σ − and a 1Δ states of HCl 2+ and DCl 2+ are compared with ab initio simulations. The four resonances observed in the TPEsCO spectra of both the X 3Σ − and a 1Δ states of HCl 2+ are assigned as three quasi-bound vibrational levels and one continuum resonance with an energy greater than the potential barrier maximum. The four clearly identified resonances observed in the TPEsCO spectra of both the X 3Σ − and a 1Δ states of DCl 2+ are assigned as quasi-bound vibrational levels.

A first principle effective Hamiltonian for including nonadiabatic effects for H2+ and HD+

We compute nonadiabatic corrections for all bound and long-lived quasi-bound vibrational levels of H2+ and HD+ for selected rotational levels. This is done using the Bunker and Moss formalism with the correction factors computed from ab initio wave functions. The electronic wave functions are expanded in terms of nuclear centered Gaussian basis functions. The agreement with accurate calculations is very good: for H2+, the root-mean-square error in the computed dissociation energies is 0.0006 cm−1, and, furthermore, most transition frequencies are predicted to within about 0.0001 cm−1. For HD+, the results are not quite as good due to the uncertainties in the adiabatic correction. This paves the way for using these techniques to accurately predict the nonadiabatic effects for more complicated molecules.

Analysis and transition probabilities of the B1Π u→ X1Σ g+ band system of Na 2 excited by the 4579 Å Ar + laser line

The fluorescence spectrum of Na 2 induced by the 4579.35 Å line of an argon ion laser has been analyzed with special emphasis on determination of accurate relative intensities and on the observation of higher vibrational levels in the B 1Π u excited state close to the dissociation limit. We have observed seven fluorescence series for the B 1Π u→ X 1Σ g + band system corresponding to the excitation transitions: v′=27, J′=31←v″=7, J″=31; v′=28, J′=43←v″=7, J″=43; v′=24, J′=3←v″=6, J″=3; v′=15, J′=55←v″=0, J″=55; v′=31, J′=42←v″=8, J″=42; v′=29, J′=25←v″=8, J″=24 and v′=23, J′=39←v″=5, J″=38 . Some series are reported for the first time. Dunham coefficients and Franck–Condon factors valid for all quasibound vibrational energy levels v′=28–33 of the B 1Π u excited electronic state are also reported. The radiative transition probabilities and radiative lifetimes for the observed fluorescence series were calculated by using hybrid potential energy curves for the B 1Π u and X 1Σ g + states constructed up to last vibrational levels and a transition dipole moment function. The transition probabilities and lifetimes agree with the observed measurements usually within the experimental uncertainty. A very weak rotational satellite structure with jumps with Δ J′=±1,±2,…,±20 for some bands of most intense fluorescence series Q(31) at v′=27 was also analyzed.

Optical-optical double resonance and Fourier transform spectroscopy: The Rb 2 B 1Πu electronic state up to the quasibound energy levels

Nearly all quasibound vibrational energy levels of the Rb 2 B 1Π u state were accessed via a double resonance excitation scheme. A resonant excitation process, X 1 Σ g + → A 1 Σ u + → (2) 1 Π g has been used to populate single ro-vibrational levels of the upper (2) 1Π g state. Spectra of the (2) 1 Π g → B 1 Π u infrared fluorescence were recorded by high resolution Fourier transform spectroscopy. Taking account of previously studied B 1 Π u → X 1 Σ g + fluorescence spectra led to accurate effective molecular constant for the B 1Π u state. The line broadening due to the tunneling effect was observed for the uppermost vibrational levels. The barrier height was found to be /2~ 205 cm −1 above its asymptotic limit ( 5S 1 2 + 5P 3 2 ) at 9.14Å.

A pseudopotential hole-particle treatment of neutral rare gas excimer systems. II. The Rydberg states of the Ar*2 dimer

A pseudopotential hole-particle model (corresponding to the formalism introduced in paper I) is applied to the determination of the Rydberg states of the Ar2* excimer with and without spin–orbit coupling. All the Λ–Σ Rydberg states (without spin–orbit coupling) adiabatically dissociating into Ar+Ar* (4s,4p,3d,5s,5p,4d), are investigated and all Ω states adiabatically dissociating into Ar+Ar*(4s,4p) have been determined including spin–orbit coupling. The calculation also includes at short distance attractive molecular configurations diabatically correlated with higher atomic asymptotes. The nature of the Λ–Σ states is analyzed and assigned with reference to the Rydberg orbitals of the Kr* united atom limit. Extensive comparison with previous calculations and experiments is carried on. For the lowest ungerade states (1)1u, 0−u, (1)0+u, and (2)0+u, good quantitative agreement is found with experimental high resolution studies. Several members of Rydberg series are calculated and assigned, yielding intra-Rydberg transition energies (1)3Σ+u((1)1u,0−u)→m 3Πg or m 3Σ+g in good correspondence with recent intra-Rydberg spectroscopy experiments. In particular the present calculation provides a likely interpretation of the infrared spectra of Ar2* as due to (1)3Σ+u→(1)3Σ+g transitions with an upper corresponding Ω state (1)1g,0−g containing quasi-bound vibrational levels.

Extended ab Initio Study of the Vibrational Dynamics of H +5 and D +5 Including All Vibrational Modes

The full nine-dimensional vibrational problem of the H + 5 complex is investigated: (i) using a model Hamiltonian which is based on the approximation that apart from the energy barrier for the internal propeller-like rotation motion all the other barriers on the potential energy hypersurface of the complex are assumed to be infinitely high, and (ii) applying an adiabatic approximation by which the nine-dimensional vibrational model Hamiltonian Schrödinger equation can be separated into three smaller subsystems. The relevant sections of the potential energy surface which are needed to describe all the vibrational modes and the major couplings between them are determined by ab initio calculations at the configuration interaction level of theory, and an analytic potential energy function is obtained by fitting to the ab initio data. The calculated energies of the low-lying bound and quasi-bound vibrational levels of the H + 5 and D + 5 ions allow a complete assignment of all the vibrational bands which have been observed in the photodissociation spectra of H + 5 and provide dissociation energies D 0 for the H + 5 and D + 5 ions which are in good agreement with the most recent experimental data.

First observation of the quasibound levels and tunneling line broadening in the 3 1Πg state of Na2 using an ultrasensitive ionization detector

All quasibound vibrational energy levels v=27 and 28 of the Na2 3 1Πg state were accessed by using optical–optical double resonance and detected with a shielded ionization detector. The line broadening due to the tunneling effect was observed to be larger than 1 cm−1 at the rovibrational level v=28, J=31. The potential curve has been determined by the Rydberg–Klein–Rees method and modified using Jeung’s calculation for the large distance barrier and comparison of the calculated and the measured line widths. The barrier height was found to be ∼126 cm−1 above its asymptotic limit (3s+4p) at 5.98 Å. There also exists an unobserved shallow outer well with depth ∼35 cm−1 at 9.5 Å according to our modification of Jeung’s calculated potential. One way to possibly probe this outer well is also discussed.

A three-dimensional time-dependent wavepacket calculation for bound and quasi-bound levels of the ground state of HCO: resonance energies, level widths and CO product state distributions

A newly developed scheme for treating poiar angle coordinates has been used in the solution of the time-dependent Schrodinger equation for a triatomic system in Jacobi coordinates. This has been applied to calculations of the energies of bound vibrational levels and quasi-bound resonances of HCO in its ground electronic state. Initial wavepackets have been chosen to simulate the B 2A′–X 2A′ emission spectrum of HCO (the ‘hydrocarbon flame bands’), and to represent dissociation on the X2A′ surface following Renner–Teller-induced internal conversion from the A2A″ state. A revised geometry rCH= 1.12 A, rco= 1.37 A and αHCO= 107A has been derived for the B;state by comparison of theoretical and experimental Franck–Condon factors. The out-going waves have been analysed to yield vibration–rotation population distributions at all energies for the CO dissociation product. The wavefunctions for selected quasi-bound vibrational levels have been generated by resonant driving of the time-dependent equation, and graphically illustrate the vibrational redistribution accompanying dissociation.The pattern of lifetimes and product state distributions is in good qualitative agreement with the available experimental data, and is found to be correlated with empirical vibrational quantum numbers for the quasi-bound resonances. The dissociation dynamics are significantly different for states with high v2 from those for high v3. These variations are discussed in relation to the nature of the ab initio potential-energy surface and of the vibrational motion for each state.

Metastable 3Σ−g ground state of F++2 and the bonding in molecular dications

Large multireference configuration interaction (MR-CI) calculations on the F++2 ion predict a 3Σ−g ground state, metastable with respect to tunneling into the F++F+ nuclear continuum. The potential energy curve displays a 0.40 eV barrier at Rb=1.607 Å, between the local potential minimum (Re=1.289 Å) and the 3Pg(F+)+3Pg(F+) asymptote at 7.69 eV lower energy. The potential barrier traps four quasibound vibrational levels, with a tunneling lifetime of 16 ms for v=0. A Dunham analysis at the well minimum gives ωe=919.4 cm−1, ωexe=16.31 cm−1, Be=1.073 cm−1, and αe=0.0316 cm−1. In a departure from an earlier viewpoint, the origin of the barrier in this and other dications is interpreted as a sum of the e2/R Coulomb repulsion and the ordinary chemical bonding of the constituent ions. This model also explains the purely repulsive character found for the valence-excited 1Δg and 1Σ+g states.

Spin-forbidden decay of the dication HS2+

The lifetimes of the low-lying vibrational levels of the X2Π state of the recently identified dication HS2+ [Miller et al., Int. J. Mass Spectrom. Ion Proc. 100, 505 (1990)] are considered. The stability of this state is attributable to a barrier formed from the avoided crossing of 2Π states asymptotically characterized as H++S+ and H+S2+. As a result of this barrier, the nonrelativistic X2Π potential energy curve supports several quasibound vibrational levels that are long lived with respect to tunneling. However, this is not the principal decay mechanism. We show that the lifetimes of the low-lying vibrational levels, v=0−4, are controlled entirely by the spin–orbit induced perturbation, 14Σ−∼X2Π, and the corresponding allowed crossing of the X2Π potential energy curve by the dissociative 14Σ− potential energy curve which correlates with the ground state asymptote H++S+(4S).

The potential energy barrier of the Na2 B 1Πu state

The technique of modulated gain spectroscopy has provided detailed information about the shape of the Na2 B 1Πu state potential barrier to dissociation. By measuring the rotation–vibration energies (to ±0.006 cm−1) of all (v′=27–33) quasibound vibrational levels and the rotation-dependent tunneling rates (as obtained from linewidth measurements) of the highest quasibound vibrational level, v′=33, we have been able to characterize this barrier. Our studies show that the barrier height is U(rmax,J=0)=375.2±3.9 cm−1, relative to the center of gravity of the Na(3s)+Na(3p) atomic limit, and the barrier maximum is located at rmax=6.85±0.02 Å.

Ab initio investigation of low-lying 2Σ + and 2Π states of NO 2+

Exploratory calculations have been carried out for the three lowest 2Σ + and 2Π states of NO 2+ using full-valence MC SCF plus first-order CI techniques. Potential-energy curves are reported for more than thirty internuclear distances between 1.6 and 40 a 0. These are discussed in terms of the extensive experimental investigations of this ion, including the recent observation of an emission. Many of the adiabatic states are characterized by potential wells lying above their asymptotic limits, supporting several quasibound vibrational levels.

Observation of the quasibound energy levels and tunnelling lifetimes in the Na 2 B 1Π u state

All quasibound vibrational energy levels υ′= 27–33 of the Na 2 B 1 Π u state are accessed via a triple resonance excitation scheme: cw modulated gain spectroscopy (MGS). Two independent analyses involve a Padé-type near-dissociation representation of the observed energies and non-linear least-squares fits to the lineshapes. The results are values for the barrier height (379.3 ±2.3 cm −1 above the center of gravity of the 3s + 3p separated atom limit), the total number of quasibound, rotationless energy levels (υ′max = 33), and tunnelling lifetimes for υ′= 33, J = 3–17 (τ = 93.5 ± 2.8 ps-18.3 ± 1.1 ps).

Laser predissociation spectroscopy of the f 4Πg state of O2+

Two quasibound vibrational levels of the f 4Πg state have been observed by monitoring O+ photofragments resulting from absorption of laser radiation by the a 4Πu state. The first spectroscopic constants for the f state have been derived from rotational and isotopic analyses. Measurements of the predissociation linewidths and photofragment kinetic energies have been used to refine estimates of the barrier in the f state potential curve and to identify likely predissociation mechanisms.

Ab initio calculation of the X 2Σ +u state of He +2 and adjustment governed by translational spectroscopic measurements

Results of ab initio CI calculations are presented for the ground state potential energy curve of He + 2. In addition all possible quasibound vibrational rotational levels have been calculated. A comparison with experimentally observed levels for all isotopic combinations of He + 2 at first showed relatively large discrepancies, especially for the level widths (one order of magnitude). Using several tentative assignments of vibrational and rotational quantum numbers to the observed levels, a procedure was developed to adjust the ab initio potential to fit the experimental data on both energy and lifetimes of the levels. The change in the dissociation energy necessary to accomplish this is 15 meV; moreover, in the bonding region between 1.3 and 3.5 bohr the analogous changes were everywhere than 1.0 meV.