Renner-Teller Coupling Research Articles

Fermi polyads and rovibronic spectrum of the X 2Πg state of BO2

Using ab initio electronic structure calculations, the three dimensional potential energy functions have been generated for the X 2Πg electronic ground state of BO2 . Spin–rovibronic energy levels have been calculated up to 4000 cm−1, Ka=3 by a variational approach accounting for full dimensionality, anharmonicity, rotation–vibration, spin, and Renner–Teller coupling. Almost all of the approximately 70 experimentally known vibronic levels up to 4000 cm−1 have been reproduced to within 10 cm−1. All vibronic energy levels (J=P) up to 4000 cm−1 are given for the 11BO2 isotope. From the composition of the rovibronic wave functions for the Fermi polyads new assignments were made. The anharmonic resonances have been investigated in the framework of a complete three dimensional Brown–Joergensen Hamiltonian for quartic force fields in dimensionless normal coordinates.

Renner–Teller and spin–orbit interactions in SiH2

Experimental data on SiH2 have been reanalyzed to show the existence of a large number of strong, but erratic rotational perturbations which are correlated with anomalous fluorescence lifetimes. These results have been interpreted using a model for the combined effects of Renner–Teller coupling between the two singlet states and spin–orbit coupling with the lowest triplet. In this model, the vibrational and K-type rotational levels of the X̃ 1A1 and the à 1B1 states of SiH2 have been fitted by least squares to give a pair of Born–Oppenheimer curves for the combining electronic states. These have been used to calculate the interaction matrix elements of the spin–orbit coupling with the ã 3B1 state. Large interactions between the 1B1 and the 3B1 states are calculated even though the direct interaction of the states is forbidden. Thus we can rationalize the existence of both the strong rotational perturbations and the unusual radiative lifetimes. Lack of knowledge of the exact location of the triplet state, and of the rovibronic structure associated with this state, precludes a detailed fit of the type recently made for CH2. We have also calculated the rotational constants for a range of vibronic states of SiH2. Analogous rotational constants and band origins of SiD2 have also been calculated using the potential curves derived from the fit to SiH2. The agreement between the calculated origins and those measured experimentally is very satisfactory.

Radiative lifetimes of CH2(b 1B1)

Radiative lifetimes are reported for CH2(b 1B1) in a wide range of rotational states in the (0,14,0), (0,15,0), (0,16,0), and (0,17,0) vibrational levels. Laser photolysis of ketene in a supersonic-jet expansion produced CH2(a 1A1) which was excited to single rovibrational levels of the (b 1B1) state by a second laser. Analysis of the temporal evolution of the fluorescence (b 1B1)–(a 1A1) yielded collision-free radiative lifetimes for the (b 1B1) state. The measured lifetimes range from about 4 to 10 μs and decrease with increasing vibrational energy. For the (0,14,0) overtone, the lifetimes increase slightly as a function of J (Ka=0). However, the lifetimes of rotational levels with Ka=0 in the (0,16,0) vibrational state are found to be independent of the rotational state. Calculations of the vibronic lifetimes show that the considerable lifetime lengthening when Ka≥1 is due to Renner–Teller coupling to the ã 1A1 state. The random lifetime fluctuation observed in some vibronic bands is probably due to spin–orbit coupling to the X̃ 3B1 state, e.g., 413 and 414 of (0,15,0). Here the radiative lifetime of the singlet component is shorter than that of the corresponding triplet component.

CO product distributions from the visible photodissociation of HCO

The final state distribution of carbon monoxide produced in the photodissociation of the formyl (HCO) radical has been studied both experimentally and theoretically. Renner–Teller coupling between the excited HCO Ã state and the ground state leads to dissociation and yields H and CO. Vibrational and rotational distributions have been measured for CO produced after excitation to specific vibrational levels on the Ã←X̃ transition of HCO cooled in a supersonic expansion. The strongest transitions are for excitation to vibrational states with six to 16 quanta in the bending mode, and dissociation from these states produces inverted CO rotational distributions with average rotational quantum numbers <J≳ in the 22–33 range. The value of <J≳ increases monotonically with the vibrational quantum number describing the bend of the excited triatomic. Experiments involving excitation of one quantum of the C–H stretching motion have revealed that this vibration results in increased rotational excitation of the product CO with values of <J≳ as high as 41. In contrast, experiments indicate that the C–O stretching mode of HCO acts nearly as a spectator during the dissociation process. Excitation of HCO states with one quantum of C–O stretch yields vibrationally excited CO as the dominant dissociation product, but with a rotational distribution similar to that for CO(ν=0) produced following the excitation of HCO states without the quantum of C–O stretch. Classical trajectory calculations on an ab initio potential energy surface have modeled many of the experimental features and trends of the CO product distributions. There are, however, some discrepancies in the positions of rotational maxima and in the efficiency of the coupling of the C–O vibration of HCO to the dissociation coordinate. It is not clear whether these are due to approximations made in the modeling or inaccuracies in the potential energy surface.

Study of Renner–Teller, spin–orbit, and Fermi-resonance interactions in X̃ 2Π (v1v20) levels of NCO by stimulated emission pumping spectroscopy

We report extensive measurements of rovibronic levels in the 020/100 and 040/120/200 Fermi-resonant polyads of NCO. The levels were accessed by the technique of stimulated emission pumping spectroscopy in a supersonic free jet expansion following excitation of bands in the à 2Σ+−X̃ 2Π spectrum of the radical. The data were analyzed in terms of an effective Hamiltonian which explicitly included reference to all the possible vibronic levels of 2Π symmetry in the polyad under consideration. The effects of levels outside these were treated by perturbation theory. The model was successful in fitting the data close to the experimental measurement precision and the resulting parameters were interpreted in terms of the harmonic and anharmonic vibrational terms. The effective Renner–Teller coupling parameter in NCO varied with vibrational level; however, parameters describing the Fermi-resonance interaction were found to be constant for all the levels investigated.

A perturbation theory guide to open-shell complexes: OH–Ar(X 2Π)

Perturbation theory is used to understand the experimentally observed stimulated emission spectra of OH–Ar(X 2Π). A useful zero-order Hamiltonian for an open-shell van der Waals complex is presented, and the most important perturbation terms are identified: rotational decoupling ( j⋅s), Renner–Teller coupling (V̂2), and a Coriolis interaction (J⋅j). This treatment reveals those parts of the Hamiltonian which are responsible for various unusual features in the spectra of open-shell complexes, such as the large parity splittings in certain vibrational bands and spin–orbit–induced predissociation of the OH–Ar(X 2Π) complex. The magnitude of the parity splitting is shown to be directly proportional to the change in the intermolecular potential when the odd electron in the free radical lies in or out of the O–H–Ar plane, the A′ and A″ surfaces. The measured splitting is used to infer the magnitude of the difference between the A′ and A″ potential-energy surfaces (∼12 cm−1) in the region sampled by the first excited bend.

Reactions of boron atoms with molecular oxygen. Infrared spectra of BO, BO2, B2O2, B2O3, and BO−2 in solid argon

Boron atoms from Nd:YAG laser ablation of the solid have been codeposited with Ar/O2 samples on a 11±1 K salt window. The product infrared spectrum was dominated by three strong 11B isotopic bands at 1299.3, 1282.8, and 1274.6 cm−1 with 10B counterparts at 1347.6, 1330.7, and 1322.2 cm−1. Oxygen isotopic substitution (16O18O and 18O2 ) confirms the assignment of these strong bands to ν3 of linear BO2. Renner–Teller coupling is evident in the ν2 bending motion. A sharp medium intensity band at 1854.7 has appropriate isotopic ratios for BO, which exhibits a 1862.1 cm−1 gas phase fundamental. A sharp 1931.0 cm−1 band shows isotopic ratios appropriate for another linear BO2 species; correlation with spectra of BO−2 in alkali halide lattices confirms this assignment. A weak 1898.9 cm−1 band grows on annealing and shows isotopic ratios for a BO stretching mode and isotopic splittings for two equivalent B and O atoms, which confirms assignment to B2O2. A weak 2062 cm−1 band grows markedly on annealing and shows isotope shifts appropriate for a terminal–BO group interacting with another oxygen atom; the 2062 cm−1 band is assigned to B2O3 in agreement with earlier work. A strong 1512.3 cm−1 band appeared on annealing; its proximity to the O2 fundamental at 1552 cm−1 and pure oxygen isotopic shift suggest that this absorption is due to a B atom–O2 complex.

Electronic states of the O 3+ radical cation

Highly correlated MRCI wavefunctions have been used to calculate the symmetry ordering of the doublet and quartet states in the Franck-Condon region of the photoelectron spectrum of ozone. In addition, parts of the potential energy functions of the four lowest doublet states of O 3 + have been mapped by ab initio valence CASSCF calculations. The results allow an unambiguous symmetry assignment of the photoelectron spectrum of ozone in the region from 12.5 to 14 eV. The almost degenerate two lowest electronic states (X 2A 1 and A 2B 2) form a conical intersection in the Franck-Condon region for the photoionization of ozone and are coupled by the antisymmetric stretching mode. Photofragmentation of O 3 + by visible light results from transitions reaching conical intersections between the 2A 2 and 2B 1 states. Regions are found where Renner-Teller and Jahn-Teller coupling exist.

Renner-Teller, spin-orbit and Fermi-resonance interactions in X 2Π NCS investigated by LIF spectroscopy

The electronic spectrum of the NCS radical is obtained following UV excimer-laser photolysis of C2H5NCS in a large excess of inert gas in a supersonic free jet expansion. The spectrum is complicated by the presence of Renner-Teller and spin-orbit coupling and a Fermi resonance between the doubly excited bending vibration and v 3, the CS stretching vibration. Bending vibronic level structure in the X 2Π ground state of the radical is determined from a variety of laser-induced-fluorescence techniques, including stimulated-emission pumping. These energy levels are used to determine vibronic-coupling parameters for the radical. Coupling between close-lying bending levels with different v 2 and K (= Λ + l) is found to be important because some of these levels are close together in NCS owing to the very large spin-orbit coupling. A parameter representing this effect is related to the dipolar contribution ε1 to the Renner-Teller coupling parameter ε by applying perturbation theory to a simple model involving the X 2Π and B 2Σ+ electronic states of NCS. This procedure results in an estimate for ε1 that agrees approximately with that determined from the vibronic-coupling parameter g K, assuming the same model for the interacting electronic states.

Dynamics and spectroscopy of PH2(Ã 2A1)

The radiative lifetimes and quenching rate constants due to parent molecules PH3 of PH2(à 2A1;0v′20; Ka=0 and K′a=1) have been selectively measured for v2=0,1,2,3, and 4 using the laser induced fluorescence technique. The data found in this work do not confirm those reported in literature. Laser induced fluorescence spectra of PH2(à 2A1;060) have been observed for the first time. These new data and observations do not support the hypothesis of a predissociation of PH2(à 2A1) starting up at v′2=4 proposed by some authors. The Renner–Teller coupling between à 2A1 and the higher vibrational levels of X̃ 2B1 seems to be the origin of the lengthening of the radiative lifetimes of PH2(à 2A1;0,v2=1 and 2,0; K′a=1) with respect to those found for the corresponding vibrational levels with Ka=0. Evidence of collision induced vibrational relaxation of PH2(à 2A1,v′2=4→v2=3) has also been observed.

Renner-Teller and spin-orbit interactions between the1A1,1B1and3B1states of CH2

The [btilde]1B1-a1A1 spectrum of the CH2 radical exhibits singlet-triplet perturbation of the a and the [btilde] states, even though the direct first-order interaction between the [btilde]1B1 and [Xtilde]3B1 states is forbidden. We have derived a model for such interactions that involves both Renner-Teller and spin-orbit coupling. The results of calculations made using this model show that the effect of the Renner-Teller coupling is to generate 1B1-3B1 interactions that are as large as those between the 1A1 and 3B1 states. These effects are much larger than those normally expected when second-order singlet-triplet coupling occurs. From these calculations, we have identified the triplet-state levels responsible for the [btilde]-[Xtilde] perturbations, and have refined the triplet-state potential.

The production of electronically-excited species from the photolysis of N2H4and N2D4at 193 nm

Emission in the spectral region 300–900 nm has been observed following 193 nm excimer laser photolysis of N2H4 and N2D4. Electronically-excited NH(A) and ND(A) are formed by a two photon process with rotational and vibrational distributions that can be characterized by a single temperature of ∼ 4000 K and ∼ 3800 K, respectively. The visible spectrum in the region 420–900 nm shows a broad and largely unstructured continuum emission upon which is superimposed a large number of well-resolved spectral features corresponding to NH2(Ã) (or ND2(Ã)). This emission is formed by a single photon process that is essentially synchronous with the laser pulse and it is suggested that NH*2 is formed directly by cleavage of the N-N bond in hydrazine. The visible emission is found to show two lifetimes; one of ∼ 25 μs and the other in excess of 100 μs, depending whether the measurement is performed on discrete spectral features or on the total emission. It is suggested that the longer component is associated with the continuum emission and possibly results from a Renner-Teller coupling of the excited NH2(Ã, 2 A 1) state with high vibrational levels of the ground state, NH2([Xtilde], 2 B 1). Experiments with various buffer gases show that for the high vibrational levels of the NH*2 populated, vibrational relaxation of the NH*2 takes place on a timescale that is comparable to electronic quenching.

Dispersed fluorescence studies of the NCO radical

Rotational transitions to excited vibrational levels of the [Xtilde] 2Π state of the NCO free radical have been studied in the gas phase by dispersion of laser induced fluorescence from the (000) level of the first excited electronic state (A 2∑+). The vibrational levels involved are the 2Π vibronic components of the (100) and (020) states which perturb each other through a Fermi resonance. Transitions from the (000) level of the A state to the (100) level of the [Xtilde] state are much stronger than those to the k 2Π(020) levels which in turn are stronger than those to the μ2Π (020) levels. Measurements have been made of the wavenumbers of 199 such transitions and the whole data set has been fitted to a model which takes the perturbing effects of Renner-Teller coupling and Fermi resonance explicitly into account. The model is more than adequate, the quality of the fit being limited by the precision of the experimental data (about ±0·15 cm-1). The positions of the k 2Π and μ 2Π components of the (020) lev...

Visible absorption and magnetic-rotation spectroscopy of 1CH2: The analysis of the b̃ 1B1 state

The b̃1B1←ã 1A1 spectrum of CH2 radical has been recorded with Doppler-limited resolution in the 15 600–18 650 cm−1 wavelength region by laser flash-kinetic absorption spectroscopy. Singlet methylene is produced by photolysis of ketene at 308 nm. Assignments for 477 transitions originating from 1A1(0,0,0) and (0,1,0) levels with J≤8 and Ka≤5 are reported from some 10 000 lines observed. Term values are given for these 1A1 levels and 1B1(0,v2,0) levels with 13≤v2≤17. Magnetic-rotation signals were observed for 60% of the 424 lines studied. This anomalous Zeeman effect is explained by singlet–triplet mixing in both ã and b̃ states. Extensive singlet–triplet mixing occurs for 1B1 levels with Ka≠0; this mixing is allowed in second order by Renner–Teller coupling of b̃ 1B1 with ã 1A1 and by spin-orbit coupling via ã 1A1 to X̃ 3B1. The consequent shifts prevent determination of accurate rovibrational structural parameters for the 1B1 state.

Inclusion and assessment of Renner–Teller coupling in transition state theory for Π states: Application to O(3P)+H2

The inclusion of the Renner–Teller effect in the treatment of linear electronically degenerate transition states in the context of transition state theory is indicated. The magnitude of the effect is shown to be significant for the O(3P)+H2→OH+H reaction at room temperature. Various approximations to the Renner–Teller effect which employ decoupled potential energy surfaces are evaluated over a range of values likely to be encountered in transition states.

The role of inter-state Renner-Teller coupling in the dissociation of triatomic molecules

An evolving wavepacket study has been made of the rate of radiationless transition from a linear excited electronic state of a triatomic molecule to a lower dissociative bent state, brought about by vibronic interaction (the Renner-Teller effect) where both states correlate with a Π state in the linear configuration. The rate is found to increase (i) with decrease in the quantum number π2 of the upper state bending vibration, (ii) with increase in the quantum number K for the axial component of the total rotational angular momentum, and (iii) with increase in the divergence between the two Born-Oppenheimer potential curves upon bending. There is a maximum crossing probability of 50 per cent during one half-period of the bending vibration. The model is validated by calculating the rate of dissociation of HCO ⪷A 2 A″ → H + CO, giving close agreement with experiment. It is then applied in a discussion of the dissociation pathways for the [Btilde] 1 A 1 state of H2O, providing an explanation for the low quantum yield of OH in its A 2Σ+ state (+ H) even though these states are adiabatically correlated.

High-resolution UV photoelectron spectrum of CO 2

The highly-resolved HeI photoelectron spectrum of CO 2 is presented and its vibrational structure studied in detail. In the X̃ 2Π g ionic state the v 3 antisymmetric mode is found to be excited in double quanta ( v 1- v 2- v 3 = 0. 0. 2) with energy hv 3 = 181 meV. In the C̃ 2Σ g + state a single quantum of the same mode is found to be excited ( hv 3 = 189 meV) in combination with a v 1 excitation. Vibronic interaction with vibrational levels in the B̄ 2Σ u + state of the ion is suggested to promote this (1, 0, 1) excitation. It is established that inelastic scattering processes contribute to the vibrational structure in the C̃ 2Σ g + band. The spin-orbit splitting in the X̃ 2Π g is determined to be 19±1 meV and 10±2 eV in the Ā 2Π u state. Vibronic structure is resolved in the X̃ 2Π g band where the Renner-Teller coupling constant is determined to be ϵ = 0.21±0.02 and the vibrational energy of the v 2 mode as 60±7 meV. In the Ā 2Π u state the v 2 energy is found to be hv 2 = 60 meV from the observed hot-band structure.

Ab initio treatment of the Renner-Teller effect for the X 2 B 1 and A 2 A 1 electronic states of NH2

A large AO basis including atom-centred f- and s- and p-type bond functions is employed to obtain potential curves for the X 2 B 1 and A 2 A 1 states of NH2 at close to the full CI level of treatment. Two different matrix methods are then applied to describe the Renner-Teller coupling between the bending vibrational states of the two electronic species; excellent agreement is found between the two sets of theoretical results. Use of a simple kinetic energy operator with a constant reduced mass leads to a term value spectrum which agrees to within 100 cm-1 for the measured locations of all low lying vibronic levels in this system and to within 300 cm-1 of the highest lying such species observed to date. Similarly good agreement is found for the ND2 and NHD isotopic species, whereby in these cases the amount of vibronic coupling is, not surprisingly, found to be markedly less than in NH2 itself. Equilibrium bond lengths and angles of this system are calculated to agree to within 0·01 Å and 1° of their observed values and computed vibrational frequencies are found to agree to within 3 per cent of their measured counterparts. The ab initio T e value for the A 2 A 1-X 2 B 1 transition is 11 350 cm-1, in very good accord with the value recently reported by Jungen, Hallin and Merer of 11 294 cm-1 based on an empirical fitting procedure to the observed results, but the calculated barrier height of 980 cm-1 in the A 2 A 1 state is 250 cm-1 greater than the corresponding value obtained from the JHM empirical fit. Furthermore such discrepancies between ab initio CI and empirically fitted potential data become much greater for small bond angles beyond ϑ = 90°, whereby it is argued that uncertainties in the form of the bending kinetic energy operator for large amplitude motion as well as failure to consider a low-energy 2 B 2 state in NH2 which undergoes a Jahn-Teller intersection with 2 A 1 in the neighbourhood of ϑ = 70° make it difficult for empirical fitting procedures to obtain high accuracy for the potential curves in the small angle bending region. Finally the computed intensity distributions for the A 2 A 1-X 2 B 1 transition in this system are found to be in almost quantitative agreement both with what has been measured and also with what is obtained in the JHM fitting procedure.

Ab initio CI calculation of the band structure in the A2B1–X2A1 electronic transition of BH2

Ab initio MRD-CI calculations have been carried out to nearly full-CI accuracy for several large AO basis sets (including f functions) for the potential curves of the BH2 molecule in its X2A1 and A2B1 electronic states. A two-dimensional vibrational treatment of the bending modes in this system has been performed employing a variational method which takes account of both Renner–Teller coupling and large-amplitude motion. The resulting structural data agree to within 0.002 Å and 2° of measured bond distance and angles and the computed bending frequencies are found to be in error by less than 30 cm−1; in addition predictions of the as yet unobserved stretching frequencies are also reported for both electronic states. In the best theoretical treatment the v2′′ = 0 → v2′ = 1 transition energy to the linear upper state is calculated to be 4145 cm−1, in excellent agreement with the corresponding value of 4190 cm−1 obtained by extrapolation of the three higher-energy band frequencies actually observed by Herzberg and Johns provided a renumbering of these levels (namely as v2′ = 9, 11, and 13) is undertaken relative to the originally preferred experimental interpretation. It is also pointed out that some of the earlier reported discrepancies between calculation and experiment regarding transition energies in this band system are actually due to a misinterpretation of the definition of the experimental fitting parameter T00 in previous theoretical work.

Effect of quadratic interactions on the resonance raman scattering of T × t 2 jahn-teller systems

Raman excitation profiles and depolarization dispersion curves are calculated for T × t 2 Jahn-Teller systems that are subject to quadratic vibronic (Renner-Teller) coupling as well as frequency changes of the active vibrational mode.