Vibrational Level Spacings Research Articles

Perturbation effects in photoassociation spectra of ultracold Cs2

We present perturbations in photoassociation spectra of ultracold caesium. High-precision photoassociation spectra up to 54 cm−1 below the Cs (6S1/2)+Cs(6P1/2) asymptote revealed perturbations related to resonant coupling between electronic states of the same symmetry but belonging to different asymptotes. The perturbations, which are manifested as irregularities in vibrational level spacings, are most pronounced for the 0u+ state, but to some extent present in the 1g and 0g− states, which are also affected by predissociation. We have performed theoretical calculations of perturbations for all three states and found qualitative agreement with the experimental results.

Theoretical study of the CsH molecule: adiabatic and diabatic potential energy curves and dipole moments

For nearly all states dissociating below the ionic limit, we perform an adiabatic and diabatic study for 1Σ+ and 3Σ+ electronic states dissociating into Cs (6s, 6p, 5d, 7s, 7p, 6d, 8s and 4f) + H (1s). Furthermore, we present the adiabatic results for the 1–5 1,3Π and 1–3 1,3Δ states. The calculations rely on an ab initio pseudopotential, semi-empirical operator core-valence correlation and full valence CI approaches, combined to an efficient diabatization procedure. For the low-lying states, our spectroscopic constants and vibrational level spacing are in very good agreement with the available experimental data. Diabatic potentials and dipole moments are analysed, revealing the strong imprint of the ionic state in the 1Σ+ adiabatic states. The H electron affinity correction was accounted for by the use of the efficient diabatization method. This leads to a better agreement with the available experimental data. Experimental suggestions are also given for the higher excited states based on their unusual behaviour.

A vibrational level spacing analysis of the LiK + lowest electronic states: Long-range behavior and evaluation of Li and K polarizabilities

A vibrational level spacing analysis of the lowest electronic states of the LiK + ionic molecule dissociating into Li(2s, 2p, 3s, 3p, 3d, 4s and 4p) + K + and Li + + K(4s, 4p, 5s, 3d, 5p, 4d, 6s) has been performed using the usual WKB semiclassical approximation. Accurate long-range potentials have been determined and allowing for the determination of all vibrational levels near the dissociation limit, the Li and K atomic polarizabilities, the number of trapped vibrational levels, and the vibrational turning points. The extracted polarizabilities for the ground levels of Li and K atoms have been compared with the available theoretical and experimental values. A very good agreement has been shown for them. The obtained atomic polarizabilites have been used to reproduce the long-range potential energy curves showing the good agreement between the ab initio calculated and the analytical potentials. A systematic generation of the missed Numerov vibrational levels and their turning points near the dissociation limit was done for all the LiK + electronic states.

Theory of the photodissociation of ozone in the Hartley continuum; effect of vibrational excitation and O(1D) atom velocity distribution

The effect of vibrational excitation on the photodissociation cross section of ozone in the Hartley continuum is examined. The calculations make use of newly computed potential energy and transition dipole moment surfaces. The initial vibrational states of the ozone are computed using grid based techniques and the first few ab initio computed vibrational energy level spacings agree to within 10 cm(-1) with experimental values. The computed total absorption cross sections arising from different initial vibrational states of ozone are discussed in the light of the nature of the transition dipole moment surface. The computed cross section for excitation from the ground vibrational-rotational state is in good agreement with the experimentally measured cross section. Excitation of the asymmetric stretching vibration of ozone has a marked effect on both the form and magnitude of the photodissociation cross section. The velocity distributions of highly reactive O(1D) atoms arising from the photodissociation process in different wavelength ranges is also presented. The results show that the O(1D) atoms travel with a most probable translational velocity of 2.030 km s(-1) corresponding to a translational energy of 0.342 eV or 33.0 kJ mol(-1).

Photoassociation spectroscopy of ultracold Cs below the 6P1/2 limit.

We have performed high precision photoassociation spectroscopy of ultracold cesium gas. Using trap-loss fluorescence detection and controlling the background cesium pressure we were able to photoassociate atoms into excited states of ultracold molecules with large detunings up to 56 cm(-1) below the Cs(6S(1/2)) + Cs(6P(1/2)) atomic asymptote. Vibrational progressions are assigned to 0(g)(-), 0(u)(+), and 1(g) long-range states. By fitting the spectral data to the LeRoy-Bernstein expression, the effective coefficients of the leading long-range interactions and the vibrational quantum number at dissociation are obtained. In addition we have observed spectral perturbations between states of the same symmetry belonging to different asymptotes (6P(1/2) and 6P(3/2)). The perturbations are manifested through irregular vibrational level spacings and are especially pronounced in the 0(u)(+) symmetry. Many observed rotational levels indicate d- and higher partial wave contributions to the photoassociation cross section in the presence of trapping laser light, while spectral regions with only weak features suggest nodes in the lower state wave functions corresponding to the two ground state atoms asymptote.

Effect of Pump and Probe Light Field on Picosecond Time-Resolved Resonance Raman Spectra of S1 trans-Stilbene. Disagreement between Stokes- and Anti-Stokes Scattering Frequencies

Abstract Picosecond time-resolved spontaneous resonance Raman spectra of the first excited singlet (S1) state of trans-stilbene were measured with various power densities of pump or probe light, for both the Stokes and anti-Stokes scattering regions. Careful calibration of the peak positions of the 285 cm-1 Raman bands reveals that the Stokes scattering band and the anti-Stokes scattering band shift to the same direction in absolute wavenumber, or to the opposite directions in Raman shift, when the pump or probe power density is increased. The direction of the wavenumber shift caused by the pump light field is opposite to that caused by the probe. Because of these apparent peak shifts, the Stokes Raman band and the anti-Stokes Raman band are recorded at different Raman shifts. The intrinsic change of the vibrational level spacing and the apparent peak shift caused by the pump or probe light field can be clearly separated by calculating the “symmetric” and “anti-symmetric” components from the Stokes and anti-Stokes peak positions. The experimental results are not explained by the optical Stark effect in its simplest form. Possible mechanisms to account for the results are discussed.

Ab initioadiabatic and diabatic energies and dipole moments of the RbH molecule

For nearly all the states dissociating below the ionic limit [i.e., Rb $(5s,$ $5p,$ $4d,$ $6s,$ $6p,$ $5d,$ $7s,$ and $4f)+\mathrm{H}$ $(1s)]$ in ${}^{1}{\ensuremath{\Sigma}}^{+}$ and ${}^{3}{\ensuremath{\Sigma}}^{+}$ symmetries, we present an adiabatic and diabatic study. Adiabatic results are also reported for ${}^{1}\ensuremath{\Pi},$ ${}^{3}\ensuremath{\Pi},$ ${}^{1}\ensuremath{\Delta},$ and ${}^{3}\ensuremath{\Delta}$ symmetries. The ab initio calculations rely on pseudopotential, operatorial core-valence correlation, and full valence configuration-interaction approaches, combined to an efficient diabatization procedure. For the low-lying states, our vibrational level spacings and spectroscopic constants are in good agreement with the available experimental data. Diabatic potentials and dipole moments are analyzed, revealing the strong imprint of ionic state in the ${}^{1}{\ensuremath{\Sigma}}^{+}$ adiabatic states while improving the results. As for LiH, vibrational spacing of the A state is bracketed by our results, with and without the improvement, taking into account the diabatic representation. Experimental suggestions are also given.

Ab initio adiabatic and diabatic energies and dipole moments of the KH molecule

An ab initio adiabatic and diabatic study of the KH molecule is performed for all states below the ionic limit [i.e., K (4s, 4p, 5s, 3d, 5p, 4d, 6s, and 4f)+H(1s)] in 1Σ+ and 3Σ+ symmetries. Adiabatic results are also reported for 1Π, 3Π, 1Δ, and 3Δ symmetries. The ab initio calculations rely on pseudopotential, operatorial core valence correlation, and full valence CI approaches, combined to an efficient diabatization procedure. For the low-lying states, our vibrational level spacings and spectroscopic constants are in very good agreement with the available experimental data. Diabatic potentials and dipoles moments are analyzed, revealing the strong imprint of the ionic state in the 1Σ+ adiabatic states while improving the results. The undulations of the diabatic curves and of the triplet–singlet diabatic energy difference which we found positive, as in Hund’s rule, are related to the Rydberg functions. As for LiH, the vibrational spacing of the A state is bracketed by our results with and without the improvement taking into account the diabatic representation. Experimental suggestions are also given.

Improvement of the Spectroscopic Constants of the PF(A3Π) State and Assignment of the PF(A–X) Transition Dipole Function

High-resolution laser-excitation spectra were acquired for the v′=3–7 levels of the PF(A3Π0,1,2←X3Σ−) transition from PF(X3Σ−) molecules generated in a discharge flow reactor. These results were combined with lower resolution excitation spectra for the v′=8–11 levels and with existing high-resolution data in the literature for v′=0 and 1 to assign improved spectroscopic constants for PF(A3Π0,1,2). The abnormal vibrational energy level spacings for all spin components of the PF(A3Π) state are evidence for a homogeneous interaction with another 3Π state. The Λ-doublet separation in the PF(3Π0) substate increases with vibrational level, which is taken as evidence for interaction with the PF(b1Σ+) state. Laser-induced fluorescence spectra from individual v′=0–5 levels were used to obtain vibrational band intensities of the A–X transition. The strong dependence of the transition dipole on the r-centroid is consistent with the reduction in the radiative lifetimes with increasing v′ level. The similarity between the isovalent PF(A3Π) and SO(A3Π) states is noted and the bond dissociation energy of PF(X3Σ−) is discussed.

Time resolved coherent anti-Stokes Raman scattering of I2 isolated in matrix argon: Vibrational dynamics on the ground electronic state

Time-resolved, electronically resonant, coherent anti-Stokes Raman scattering is used to prepare and interrogate vibronic coherences of molecular iodine in matrix Ar. Coherences that involve evolution on the excited B(3Π0u) state, first- and third-order coherences, decay in less than one vibrational period (τ<300 fs). In contrast, as many as 200 vibrational periods of motion can be observed for Raman-prepared wave packets consisting of zero-phonon vibrational superpositions on the ground electronic state (second-order coherence). Packets consisting of v=4, 5 and v=3, 4, 5 on the X(1Σg) state decay with a half-life of 10±1 ps at 31 K, allowing a more accurate measure of vibrational level spacings and decoherence time than has been possible in frequency domain. The harmonic frequency of the molecule is reduced by 1.5 cm−1 (0.7%) in the matrix. The lack of recurrence in the excited electronic state ensures that the resonant anti-Stokes scattering arises only from the negative momentum component of the Raman packet. This momentum filter, which should be ubiquitous in condensed media, leads to a signal with deeper modulation than in the gas phase.

Guiding, focusing, and cooling of atoms in a strong dipole potential

* (doughnut) modes for atomic beam manipulation. A slow atomic beam is guided over up to 0.3 m and focused down to 6.5 μm radius. The doughnut mode is used as a strong mesoscopic dipole potential with vibrational level spacings up to the photon recoil energy. Polarization gradient cooling in this system generates a bimodal momentum distribution with a narrow component momentum width of 4 ?k.

Statistical analysis of the recoil energy distributions in the products of the unimolecular dissociations of NO 2 and C 2O

Recoil energy distributions in the products of the barrierless unimolecular dissociations NO 2 → NO+O and C 2O → C+CO are derived within the framework of phase space theory (PST) in both cases where the reactant beam is supersonic or thermalized. The strong fluctuations observed experimentally in the distributions are rationalized in terms of vibrational level spacings, angular momentum constraints and the fact that the density of states corresponding to a given rotational energy of the nascent diatomic diverges when this energy tends to zero. Up to now, these fluctuations have not been considered as being compatible with a statistical process.

Modeling vibrational energy exchange of diatomic molecules using the Morse interatomic potential

A model of dissociation of diatomic molecules in intermolecular collisions, for use in Direct Simulation Monte Carlo (DSMC) calculations, has been proposed by Lord. This model, is a development of the exact available energy or vibrationally linked chemistry model of Bird, which models dissociation and chemical reactions directly via Borgnakke–Larsen type energy redistributions between translation and internal modes, dissociation being assumed to occur whenever the vibrational energy of a molecule exceeds its dissociation energy. The model employs the correct energy level scheme of a Morse oscillator and has been shown to yield equilibrium dissociation rate constants for N2 which are in excellent agreement with published values. A shortcoming of the model, however, is that it is purely classical, the molecular vibrational energy being assumed to be continuously distributed. Although this is not a serious defect for the prediction of dissociation, since the dissociation energy is normally many times the largest vibrational energy level spacing, it means that the model is unsuitable for describing vibrational energy exchange at lower collision energies where quantization effects are significant and must be taken into account in a way which satisfies detailed balance at equilibrium. The present paper describes a quantized extension of the earlier model which satisfies this requirement and can therefore be used in conjunction with it. It is shown that the two models become identical at high collision energies.

CΣ+ State of 7LiH

The 7LiH C1Σ+ excited electronic state has been observed for the first time by pulsed optical−optical double resonance fluorescence depletion spectroscopy. Several rovibrational levels of the A1Σ+ excited electronic state have been selected as the intermediate states. Among 10 vibrational states of the C1Σ+ electronic state 81 rovibrational levels have been observed. The spectral assignment is identified from the observed rotational structures, term values, and vibrational level spacings and from a comparison with recent accurate ab initio calculations of Boutalib and Gadea [J. Chem. Phys. 1992, 97, 1141].

Ab initio study of the LiH+ molecule, electronic interaction analysis and LiH UV photoelectron spectrum

Abstract All adiabatic curves of LiH + dissociating into Li(2s, 2p, 3s, 3p, 3d) + H + and Li + + H (1s, 2s, 2p) are determined by an ab initio approach involving a non-empirical pseudopotential for the Li(ls 2 ) core and core valence correlation corrections. The resulting spectroscopic constants and vibrational level spacings of all these states are presented. From the usual semiclassical approximations an analysis of the high energy vibrational level spacing is performed allowing for accurate long range extrapolations. For the lowest curves dissociating into Li + + H (1s) and Li (2s) + H + an analysis of the main electronic interactions is carried out from a diabatic model and reveals the importance of the binding charge delocalisation effects versus the polarisation (charge localised) ones. In addition the LiH photoelectron spectrum is calculated. An interesting feature of that spectrum is that both bound-bound and bound-free transitions coexist due to the particular shape of the LiH and LiH + potential energy curves.

Pure Sequence Vibrational Spectra of Small Polyatomic Molecules

Highly excited (0<E<4 eV) vibrational levels in the electronic ground state of small, gas phase, polyatomic molecules can be examined by a variety of Franck-Condon controlled laser spectroscopic schemes: one-laser (Dispersed Fluorescence: DF), two-laser (Stimulated Emission Pumping: SEP) and three-laser (IR-SEP). The DF spectra contain patterns of vibrational level spacings and transition intensities that can provide a basis for assigning nonrigorous quantum numbers to individual eigenstates or feature states (which consist of clusters of unresolved eigenstates) or refining a superpolyad fit model. The SEP spectra contain a quantity (∼103) of features sufficient to invite application of a variety of statistical measures. Rigorously pure sequences (same total symmetry, same J) can be constructed. The > 103: 1 dynamic range of these spectra combined with the ability to vary systematically the electronically excited rovibronic level from which these spectra emanate, can produce nearly complete pure sequences. Low resolution spectra correspond to early time, localized dynamics. Such spectra often contain fully resolved Franck-Condon bright feature states, each of which can be unambiguously assigned to a set of normal mode vibrational quantum numbers. Sometimes, such assignments can only be secured by high resolution detective work. Viewed at higher resolution, feature states often split up, revealing several layers of underlying structure. The hierarchy of splittings in the frequency domain corresponds to sequential spreading of the initially localized excitation in the time domain. Elaborate but traditional multi-resonance superpolyad effective Hamiltonian (ℌeff) matrix fit models can describe the coarse structure in the spectrum and the early time intramolecular dynamics. Since the superpolyad model is based on matrix elements of a relatively small number of anharmonic coupling terms (e.g., k122Q1Q22) evaluated in a normal mode, harmonic oscillator, product basis set, the superpolyad model is readily scaled to higher energy. The superpolyad model provides an accurate and refinable model for early time sequential Intramolecular Vibrational Redistribution (IVR) processes. Upon scaling to higher energy, the model provides testable predictions as the early time dynamics becomes more rapid and more complex. The most informative, reliable, and robust statistical measures applicable to polyatomic molecule vibrational spectra are those based on the well characterized initial localization and its early time dynamics, as described by a superpolyad ℌeff model. Superpolyad models describe how the remnants of regular dynamics are encoded in the spectrum at both high and low resolution. The models predict characteristic patterns of frequency separations and relative intensities which will be approximately replicated many times in the spectrum. The Extended Autocorrelation (XAC) pattern recognition method allows these patterns to be detected and located in the spectrum. Another scheme is based on the appearance in the spectrum of fine permutation splittings superimposed on a much coarser manifold of vibrational levels. These identical atom permutation splittings become resolvable when a molecule begins to tunnel between different chemically bonded networks on a time scale comparable to the inverse of the spectral resolution (1/δν). A third technique, tree-based hierarchical analysis (e.g., parsimonious trees) can reveal, without an a priori specified model, a hierarchy of coupling matrix elements (or delocalization rates). Spectroscopic detective work can identify the approximately conserved quantities that are destroyed by each of the hierarchical couplings. Because of the wide variety of approximately conserved quantities and coupling mechanisms responsible for the sequential destruction of these quantities, it is likely that the usual statistical measures developed by “quantum chaologists” for locating a system on the Poisson (regular, localized) ↔GOE (chaotic, delocalized) continuum, are too inflexible and reductionistic to yield useful insights into polyatomic molecule rotation-vibration dynamics. We believe that the important question is not whether molecules ever achieve the “bag of atoms limit”, but how they approach this limit. How fast does the initially localized excitation decay? Where does the energy go? What are the mechanisms that cause the energy to flow?

Ab initio adiabatic and diabatic potential-energy curves of the LiH molecule

For nearly all states below the ionic limit [i.e., Li(2s, 2p, 3s, 3p, 3d, 4s, and 4p)+H] we perform the first adiabatic and diabatic studies. This treatment involves a nonempirical pseudopotential for Li and a full configuration-interaction treatment of the valence-electron system. Core–valence correlation is taken into account according to a core-polarization-potential method. We present an analysis of the diabatic curves and introduce appropriate small corrections accounting for basis-set limitations. For the low-lying states, our vibrational level spacings and spectroscopic constants are in excellent agreement with the available experimental data and with the best all-electron results. Experimental suggestions are given for the higher states.

The multiconfiguration time-dependent Hartree–Fock method based on a closed-shell-type multiconfiguration self−consistent field reference state and its application to the LiH molecule

The linear response calculations in the multiconfiguration time-dependent Hartree–Fock (MCTDHF) approximation with a closed-shell-type MCSCF state as the time-independent reference state are discussed. The application to the LiH molecule with a small basis set ([4s2p1d/2s1p]) shows validity of our MCTDHF approach to the singlet ground state. Our MCSCF correlation energy is 97% of the total (=full CI) correlation energy and the MCTDHF excitation energies are in good agreements with the Δ full CI excitation energies. The Born–Oppenheimer potential energy curves for the lowest three singlet states of LiH and the corresponding vibrational level spacings, the transition moments, the oscillator strengths, and the frequency-dependent dipole polarizabilities are reported. All of these results imply the potentiality of our MCTDHF method for the future work with the larger basis set. One of such basis sets ([9s8p4d/8s7p1d]) is referentially used only at the single-configuration TDHF level, and the resultant near-Hartree–Fock polarizability and Thomas–Reiche–Kuhn sum rule is very promising.

Nonreactive collinear close-coupled transition probabilities for nitrogen + oxygen, hydrogen + chlorine, and oxygen + chlorine at 0.5-3.2 eV

Close-coupled calculations have been carried out in the collinear geometry for N{sub 2} + O{sub 2} (2.0-3.2 eV), H{sub 2} + Cl{sub 2} (0.5-2.0 eV), and O{sub 2} + Cl{sub 2} (0.5-2.0 eV). The nonreactive transition probabilities reported are converged to at least three figures, even for transitions where the change in vibrational quantum number for one or both of the molecules is large or where the initial vibrational quantum numbers are large. These results greatly extend the mass ratio (or ratio of the two molecules, vibrational energy level spacings) for the two colliding species and should prove useful in assessing the accuracy of collision theory approximations.

Vibrational level structure of highly excited SO2 in the electronic ground state as studied by stimulated emission pumping spectroscopy

The stimulated emission pumping (SEP) spectroscopy is applied to SO2 cooled rotationally in a supersonic free jet to investigate the vibrational and rotational level structure in the 17 300–17 900, 21 400–21 500, and 22 200–22 500 cm−1 regions of the electronic ground state. It is concluded that respective vibrational levels are found to couple with each other by the network of Fermi and Coriolis interactions on the basis of the following grounds: (1) there are a number of Fermi pairs of the vibrational levels, and (2) the number of vibrational levels identified as the final states of the SEP transitions increases for rotational levels with larger rotational quantum numbers J and Ka. The distribution of the nearest neighbor vibrational level spacing shows that the vibrational quantum dynamics in the observed regions is almost quasiperiodic and the onset of the quantum chaos is estimated to be above 17 900 cm−1.