Rovibronic Levels Research Articles

Group theoretical treatment of Jahn–Teller versus spin-orbit effects on geometries, rovibronic levels and nuclear spin species of bismuth and antimony clusters

Clusters of very heavy group 15 elements, particularly those of Sb and Bi are intriguing due to the interplay of vibronic and relativistic effects, which quench the Jahn–Teller distortion, and thus resulting in the retention of higher symmetry in the double group. Group theoretical treatment of Bi n clusters and comparisons with Sb n clusters as a function of cluster size and coordination polyhedra has been carried out. The spin-orbit and Jahn–Teller effects have dual roles, thus resulting in interesting rovibronic and nuclear spin species arising from spin-9/2 209Bi. The rovibronic and nuclear spin species of 121Sb and 123Sb are also quite interesting due to their equal relative abundance and high nuclear spin. It has been shown by using group theoretical and combinatorial methods that these clusters exhibit interesting nuclear spin multiplets and distributions of rovibronic levels as a function of polyhedral geometry, which is influenced by the quenching of Jahn–Teller pseudorotation by spin-orbit effects in heavier Bi n clusters. The results are contrasted with Sb n clusters which undergo Jahn–Teller pseudorotations. It is also pointed out how the techniques considered here can be applied to Tl n and In n clusters.

Predissociation Mechanism and Dynamics of HCP

In the present study, we have observed absorption, fluorescence excitation, and CP radical action spectra of the HCP molecule in the vicinity of the dissociation threshold to H((2)S) + CP(X (2)Sigma(+)). In addition, we have measured the rotational distribution of the CP radical produced from certain single rovibronic levels of the parent HCP molecule. It is found that the CP radical action spectrum starts to appear at the point where the fluorescence intensity decreases suddenly. On the basis of the precise energetic consideration between the parent and the product rovibronic energies, the dissociation energy of HCP to H((2)S) + CP(X (2)Sigma(+)) is determined to be 41 662.3 +/- 0.5 cm(-1). The energy distribution in the predissociation is found to be basically statistical; however, the prominent preferences in the rotational distributions or nonstatistical distributions are observed only when the vibronic energy of the parent level is smaller than the dissociation threshold energy. This preference is qualitatively interpreted by the inefficient energy transfer from the rotational to the vibrational degrees of freedom in the exit region of the X state potential energy surface. As a result, the dissociation proceeds along the linear H-C-P configuration, and this geometrical restriction makes nonstatistical rotational distribution of the CP radical.

Renner–Teller effect in linear tetra-atomic molecules. II. Rovibronic levels analysis of the X Π2u electronic state of HCCH+

The variational approach detailed in the previous paper (Paper I) for the treatment of the Renner-Teller effect in linear tetra-atomic molecules including all degrees of freedom and couplings between angular momenta is applied for HCCH(+). The accurate six-dimensional potential energy surfaces of the X (2)Pi(u) electronic state, presented in Paper I is incorporated in the variational treatment in order to obtain all rovibronic levels including the spin-orbit coupling for 1/2 < or = J < or = 7/2 and up to 2600 cm(-1) above the global zero point energy. The "pure" stretching levels are calculated up to 11,000 cm(-1) from the stretching zero point energy. The calculated rovibronic energies are compared with previous theoretical and experimental data. The mean agreement with the zero kinetic energy photoelectron measurements of Tang et al. [J. Chem. Phys. 125, 133201 (2006)] is of 16.7 cm(-1). The Renner-Teller parameters have been determined at nu(trans) = 690.0 cm(-1), epsilon(trans) = 0.30, nu(cis) = 715.0 cm(-1), and epsilon(cis) = -0.063. A detailed analysis of the rovibronic Hund's cases is presented and the rotational structures of some vibronic bands recorded by Yang and Mo [J. Phys. Chem. A 110, 11001 (2006)] are given.

Optimal values of rovibronic energy levels for triplet electronic states of molecular deuterium

An optimal set of 1050 rovibronic energy levels for 35 triplet electronic states of D2 has been obtained by means of a statistical analysis of all available wavenumbers of triplet–triplet rovibronic transitions studied in emission, absorption, laser and anticrossing spectroscopic experiments of various authors. We used a new method of analysis (Lavrov and Ryazanov 2005 JETP Lett. 81 371–4), which does not need any a priori assumptions concerning the molecular structure, being based on only two fundamental principles: Rydberg–Ritz and maximum likelihood. The method provides the opportunity to obtain the root-mean-square estimates for uncertainties of the experimental wavenumbers independent from those presented in the original papers. A total of 234 from 3822 published wavenumber values were found to be spurious, while the remaining set of the data may be divided into 20 subsets (samples) of uniformly precise data having close to normal distributions of random errors within the samples. New experimental wavenumber values of 125 questionable lines were obtained in the present work. Optimal values of the rovibronic levels were obtained from the experimental data set consisting of 3713 wavenumber values (3588 old and 125 new). The unknown shift between levels of ortho- and para-deuterium was found by least-squares analysis of the a3Σ+g, v = 0, N = 0 ÷ 18 rovibronic levels with odd and even values of N. All the energy levels were obtained relative to the lowest vibro-rotational level (v = 0, N = 0) of the a3Σ+g electronic state, and presented in tabular form together with the standard deviations of the empirical determination. New energy-level values differ significantly from those available in the literature.

Non-adiabatic transitions from the I2(E) induced by the transition dipole moment of I2(E–D) and the electric dipole moment of collision partners

Optical–optical double resonance spectroscopy is used to obtain total rate constants, electronic branching ratios, and vibrational product state distributions for non-adiabatic transitions among the first-tier ion-pair states of the I2 molecule excited to the E0g+,vE=8,13,19;JE≈55 rovibronic levels in collisions with M=CD3I and CH3COCH3. It is shown that I2(E→MD) near-resonant transitions are caused by the interaction between the transition dipole moment of I2(E–D) and the permanent electric dipole moment of M. The I2(D) state vibrational levels populated due to polarization interaction accompanied by quasi-resonance excitation of the collision partner are also observed.

The Radiative Characteristics of the Rovibronic States of the Hydrogen Molecule: IV. Relative Probabilities of the r 3 Π−g, s 3 Δ−g → c 3 Π±u Spontaneous Transitions of the H2 Molecule

A statistical analysis of the available literature data and data obtained in this work on the wave numbers of the lines that appear in triplet-triplet rovibronic transitions of the H2 molecule was performed. This allowed us to verify and refine the controversial identification of spectral lines and find the optimum rovibronic level energy values for the c 3Π u ± , r 3Π g − , and s 3Δ g − states. The ratios between the line strengths of the P, Q, and R branches of the (4dπ)r 3Π g − , (4dδ)s 3Δ g − → (2pπ) c 3Π u ± band systems of the H2 molecule were measured systematically. The calculation results obtained in the Frank-Condon approximation differed substantially (by up to two orders of magnitude) from the experimental data. The dependences of the ratios between rovibronic line strengths of the r 3Π g − → c 3Π u ± and s 3Δ g − → c 3Π u ± transitions on the rotational quantum number N′ of the upper level were found to correlate with each other. The deviations of adiabatic theory increase as N′ grows, which is evidence of an important role played by electronic-rotational interactions in the perturbation of transition probabilities. The experimental ratios between the probabilities of rovibronic transitions satisfactorily agree with the results of calculations within the framework of the simple nonadiabatic model taking into account electronic-rotational interaction of radiating adiabatic states in the approximation of pure precession. The dependences of transition probabilities on N′ were obtained for the first time for the first four diagonal bands of the r 3Π g − , s 3Δ g − → c 3Π u ± transitions.

Non-adiabatic [formula omitted], D′, β, γ, δ transitions in the first ion-pair tier of molecular iodine induced by collisions with I 2, N 2 and CO 2

Optical–optical double resonance spectroscopy is used to obtain total rate constants, electronic branching ratios, and vibrational product state distributions for non-adiabatic transitions among the first-tier ion-pair states of the I 2 molecule excited to the E 0 g + , v E = 8, 13, 19; J E ≈ 55 rovibronic levels in collisions with M = I 2, N 2 and CO 2. It is shown that I 2 ( E → M D ) near-resonant transitions are caused by the interaction between the transition dipole moment of I 2(E–D) and the electric quadrupole moment of M. Besides, there are transitions induced by polarization interactions of the collision partners. Wide non-resonant vibrational distributions at the final states correspond to them. The I 2(D and β) state vibrational levels populated in the transitions accompanied by excitation of IR active vibrational mode, CO 2(01 10 ← 000) ν 2e 1u(667 cm −1), are observed. It is shown that rotational excitation of the collision partners can compensate energy mismatch between initial and final rovibrational levels.

Quantum State-Resolved Collision Relaxation of Highly Vibrationally Excited SO2

Collision depopulation cross sections of 13 single, highly vibrationally excited levels with 45,000 cm(-1) energy in the electronic ground state of SO(2) in collision with CO in a supersonic jet have been measured. The measurements for these single highly excited quantum states are conducted through pressure dependence of the decay of the fluorescence quantum beat resulted from their coupling with the rovibronic levels in the optically allowed transitions to the (140), (210), and (132) C(1)B(2) levels. The relaxation cross sections of these highly excited states, each with well-defined energy and symmetry, range from 27 to 187 A(2) with an average of 71 A(2). This average cross section is much larger than the hard sphere cross section of 48 A(2). The relaxation cross section is also found to be larger for the quantum states with a larger matrix element in coupling with the "bright" electronically excited level. Both observations suggest a substantial contribution from long range interactions in collision relaxation of highly excited molecules.

State-selective photodissociation dynamics of formaldehyde: Near threshold studies of the H+HCO product channel

The laser-induced photodissociation of formaldehyde in the wavelength range 309<lambda<330 nm has been investigated using H (Rydberg) atom photofragment translational spectroscopy. Photolysis wavelengths corresponding to specific rovibronic transitions in the A (1)A2<--X (1)A1 2(0)(1)4(0)(3), 2(0)(2)4(0)(1), 2(0)(2)4(0)(3), 2(0)(3)4(0)(1), and 2(0)(1)5(0)(1) bands of H(2)CO were studied. The total kinetic energy release spectra so derived can be used to determine partial rotational state population distributions of the HCO cofragment. HCO product state distributions have been derived following the population of various different N(Ka) levels in the A (1)A2 2(2)4(3) and 2(3)4(1) states. Two distinct spectral signatures are identified, suggesting competition between dissociation pathways involving the X (1)A1 and the a (3)A2 potential energy surfaces. Most rovibrational states of H(2)CO(A 1A(2)) investigated in this work produceH+HCO(X (2)A') photofragments with a broad kinetic energy distribution and significant population in high energy rotational states of HCO. Photodissociation via the A (1)A2 2(2)4(3) 1(1,1) (and 1(1,0)) rovibronic states yields predominantly HCO fragments with low internal energy, a signature that these rovibronic levels are perturbed by the a (3)A2 state. The results also suggest the need for further careful measurements of the H+HCO quantum yield from H(2)CO photolysis at energies approaching, and above, the barrier to C-H bond fission on the a (3)A2 potential energy surface.

High resolution vacuum ultraviolet emission spectrum of D2: The B′Σu+1→XΣg+1 band system

In this work, we have extended our previous high resolution study of the vacuum ultraviolet emission spectrum of the D2 molecule [M. Roudjane, et al. J. Chem. Phys. 125, 214305 (2006)] up to 124.2 nm in order to investigate the B' 1Sigmau+-->X 1Sigmag+ band system. The analysis of the spectrum has been carried out by means of a complex spectrum visual identification code IDEN [V. I. Azarov, Phys. Scr. 44, 528 (1991); 48, 656, (1993)] and supported by theoretical calculations using ab initio data [L. Wolniewicz, J. Chem. Phys. 103, 1792 (1995); 99, 1851 (1993); G. Staszewska and L. Wolniewicz, J. Mol. Spectrosc. 212, 208 (2002); L. Wolniewicz and G. Staszewska, 220, 45 (2003)] which provided level energies and transition probabilities. More than 1480 new emission lines have been observed and 109 bands belonging to the B' 1Sigmau+-->X 1Sigmag+ system have been identified between 84.1 and 121.6 nm. Except for the upsilon'-0 bands that were reported in absorption [I. Dabrowski and G. Herzberg, Can. J. Phys. 52, 1110 (1974)], all the upsilon'-upsilon" bands are reported here for the first time. The analysis led to the determination of 111 rovibronic energy levels in the B' 1Sigmau+ state, of which 31 with higher rotational numbers J are new. Observed perturbations are accounted for through a set of coupled equations involving the four excited electronic states B 1Sigmau+, B' 1Sigmau+, C 1Piu, and D 1Piu and including nonadiabatic couplings. The solution of this set provides the percent contribution of these four states to each of the observed rovibronic level.

Ab Initio Treatment of the Chemical Reaction Precursor Complex Br(2P)−HCN. 2. Bound-State Calculations and Infrared Spectra

Rovibronic energy levels and properties of the Br(2P)-HCN complex were obtained from three-dimensional calculations, with HCN kept linear and the CN bond frozen. All diabatic states that correlate to the 2P3/2 and 2P1/2 states of the Br atom were included and spin-orbit coupling was taken into account. The 3 x 3 matrix of diabatic potential surfaces was taken from the preceding paper (paper 1). In agreement with experiment, we found two linear isomers, Br-NCH and Br-HCN. The calculated binding energies are very similar: D0 = 352.4 cm(-1) and D0 = 349.1 cm(-1), respectively. We established, also in agreement with experiment, that the ground electronic state of Br-NCH has |Omega| = (1/2) and that Br-HCN has a ground state with |Omega| = (3/2), where the quantum number, Omega, is the projection of the total angular momentum, J, of the complex on the intermolecular axis R. This picture can be understood as being caused by the electrostatic interaction between the quadrupole of the Br(2P) atom and the dipole of HCN, combined with the very strong spin-orbit coupling in Br. We predicted the frequencies of the van der Waals modes of both isomers and found a direct Renner-Teller splitting of the bend mode in Br-HCN and a smaller, indirect, splitting in Br-NCH. The red shift of the CH stretch frequency in the complex, relative to free HCN, was calculated to be 1.98 cm(-1) for Br-NCH and 23.11 cm(-1) for Br-HCN, in good agreement with the values measured in helium nanodroplets. Finally, with the use of the same potential surfaces, we modeled the Cl(2P)-HCN complex and found that the experimentally observed linear Cl-NCH isomer is considerably more stable than the (not observed) Cl-HCN isomer. This was explained mainly as an effect of the substantially smaller spin-orbit coupling in Cl, relative to Br.

The radiative characteristics of the rovibronic states of the hydrogen molecule: III. The probabilities of the h 3Σ g + , g 3Σ g + , i 3Π g + , j 3Δ g + → c 3Π u ± spontaneous transitions in the H2 molecule

The absolute values of radiative transition probabilities were obtained semiempirically for the h3Σg+, g3Σg+, i3Πg+, j3Δg+ → c3Πu± band systems of the H2 molecule. The experimental data on rovibronic terms were analyzed using the nonadiabatic model taking into account the interaction of the 3s3Σg+, 3d3Σg+, 3d3Πg, and 3d3Δg states in the pure precession approximation. Published semiempirical values of the expansion coefficients of the perturbed wave functions of the rovibronic levels of upper electronic states over the Born-Oppenheimer basis set were used. The dipole moments of the 3s3Σg+, 3d3Σg+, 3d3Πg, and 3d3Δg → 2p3Πu electronic transitions were found from the measured relative probabilities of spontaneous transitions and radiative lifetimes of rovibronic levels with the use of the calculated overlap integrals between the vibrational wave functions of the combining states obtained from ab initio potential curves. The probabilities of transitions from the rovibronic levels of the 3d3Λg− and 3d3Λg+ states were found to be substantially different (by factors of up to 20 and 3.5 for transitions from the i3Πg and j3Δg states, respectively) because of qualitatively different nonadiabatic effects of the perturbation of electronic states with different Kronig symmetries (Λ+ and Λ−).

Ab initio study of the C2O+ cation

The first electronic states of C2O+ correlating to the first asymptotes of dissociation are presented. From accurate MRCI+Q/cc-pV5Z calculations it is shown that the electronic ground state is the X2Π state and the first excited state the a4Σ− state lying very close to the X2Π state, cm−1. For both states the three-dimensional PEFs are determined for displaced geometries in the range bohr and bohr about the equilibrium bond lengths and . The rovibronic levels up to 2200 cm−1 and J=P=7/2 are obtained for X2Π and the rovibrational levels of 4Σ− up to 5000 cm−1 and K = 4. The spin–orbit coupling between both states is investigated.

Rovibronic symmetry and nuclear spin analysis of octanitrocubane

Octanitrocubane is shown to possess interesting nuclear spin statistics and rovibronic level patterns in its equilibrium chiral ( D 4) symmetry both due to 17O and 14N nuclear spin species. The populations and distributions of rovibronic levels will be influenced by the chiral symmetry and the nuclear spin species and spin statistical weights due to 17O, 14N and 13C species. We have computed the nuclear spin species and spin statistics and correlations of the rovibronic levels and spin species in different symmetries. Our predicted results could aid in the interpretation of 17O dynamic NMR, vibronic and rovibronic spectra of gas-phase octanitrocubane.

Ab initio study of the spectroscopy of the X2Π electronic ground states of CNO and NCO

The X 2Π electronic ground states of NCO and CNO have been investigated by complete ab initio methods. The dependence of the Renner–Teller parameters, ϵ and ω 2 average , on the ab initio method and on the basis set have been studied. These parameters have also been compared to experimental data for NCO. The potential energy surfaces of the X 2Π state have been determined by the MRCI method and the cc-pVQZ basis set for NCO and CNO. The rovibronic levels of both isomers have been calculated variationally up to approximatively 4000 cm −1 for J ⩽ 5/2 and K ⩽ 2, with the inclusion of the geometry dependence of the spin–orbit coupling. The agreement with experimental data obtained for NCO is remarkable. A similar accuracy for the ab initio rovibronic levels of CNO is expected since no experimental data exists for this isomer.

Hyperfine coupling of the iodine E0+g, vE = 19 and γ1u, vγ = 18 ion-pair states

A considerable difference of iodine emission spectra after optical–optical double resonance excitation of the E0+g, vE = 19, JE ≈ 55 and JE ≈ 85 rovibronic levels is observed. The latter include strong transitions from the γ1u ion-pair state to valence ones. This feature is interpreted as a result of hyperfine coupling of near-resonant E0+g, vE = 19, JE = 81 and γ1u, vγ = 18, Jγ = 80 states. The hyperfine matrix element and dipole moment functions of transitions from the γ state are estimated. The hyperfine g/u mixing of the iodine ion-pair states is observed for the first time.

Observation of perturbations in the rovibronic transition probabilities for the (4d)r 3Π g − , (4d) s 3 Δ g − → (2p) c 3Π u ± band systems of the H2 molecule

The ratios of the radiative transition probabilities for the lines of the P, Q, and R branches of the (4d)r3Πg−, (4d)s3Δg− → (2p) c3Πu± band systems of the H2 molecule have been measured for the first time. Significant (to two orders of magnitudes) differences are found between the experimental values and the adiabatic theory predictions. It is established that the results of the nonadiabatic calculation performed by us in the pure-precession approximation taking into account the electronic-rotational interaction of the 4d3Πg and 4d3Δg states are in agreement with the experimental data. The optimal energies of rovibronic levels of the r3Πg−, s3Δg−, c3Πu−, and c3Πu+ states have been found and reidentification of 11 from 54 spectral lines, assigned previously to the (0-0) and (1-1) bands, was performed.

Observation of the predissociated, quasilinear B̃(A′1) state of CHF by optical-optical double resonance

We report the first observation of the predissociative B state of a halocarbene molecule. Rovibronic energy levels were measured in the B(1A') state of CHF by fluorescence dip detected optical-optical double resonance spectroscopy via the A state. The origin was found to lie 30 817.4 cm-1 above the zero point level of the X state. Rotational transitions within six purely bending states, and states involving one or two quanta of CF-stretch were observed, including the vibrational angular momentum components. Interpretation of the spectrum, with support of ab initio calculations, shows that CHF is quasilinear in the B state with a small (-200 cm-1) barrier to linearity which lies below the zero-point level. The rotational constant, B=1.04 to 1.09 cm-1, depending on vibrational state, again in good agreement with theory. All observed B state levels were predissociative, as evidenced by Lorentzian line broadening. Linewidths varied with initial state from 0.7-10.8 cm-1, corresponding to excited state lifetimes of 0.5-8 ps.

Semiempirical study of perturbations of the landé g factors of electronic-vibrational-rotational levels of hydrogen: IV. The I 1Π−g, R 1Π−g, J 1Δ−g, and S 1Δ−g states of the H2 and D2 molecules

Values of the Lande g factors are obtained for the first time for rovibronic levels of the (3d)J1Δg− state of the D2 molecule and of the (4d)S1Δg− state of the H2 and D2 molecules. Semiempirical values of these quantities are obtained for the first time for the (4d)R1Πg− state of the H2 molecule and the (3d)I1Πg− and (4d)R1Πg− states of the D2 molecule. These values are determined in terms of the nonadiabatic model, which takes into account the interaction between the ndπ1Πg and ndδ1Δg (n = 3 and 4) states in the approximation of pure precession, with the use of the semiempirical values obtained by us for the expansion coefficients of wave functions in the adiabatic basis functions and the results of our numerical calculation of overlap integrals of the vibrational wave functions of these states. The values thus obtained are in good agreement with the data available in the literature. It is found that the interference effects of coupling of the ndπ1Πg and ndδ1Δg states lead to significant perturbations of the dependences of the g factors of vibronic levels on the rotational quantum number as compared to the adiabatic results. These perturbations are regular (reaching a factor of nine) for the I1Πg− and R1Πg− states and irregular (reaching a factor of 50) for the J1Δg− and S1Δg− states. The nonadiabatic values of g factors obtained in our previous studies for the H2, HD, and D2 molecules in the i3Πg− and j3Δg− states are improved by an additional inclusion of adiabatic effects. It is established that the effect of the electron spin on the g factor values for rovibronic levels of the 3dΔg− states is significant and reaches 25% for H2 and 130% for D2.

The radiative characteristics of hydrogen rovibronic states: II. The probabilities of the i 3Π g − , j 3Δ g − → b 3Σ u + , c 3Π u ± spontaneous transitions in H2, HD, and D2

The absolute probabilities of radiative rovibronic transitions in the i 3Π − , j 3Δ − → c 3Π ± band systems of H2, HD, and D2 and the probabilities, integrated over wave numbers, of bound-free i 3Π − , i 3Π − , j 3Δ − → b 3Σ + transitions in H2 were calculated semiempirically. The experimental data were analyzed using the nonadiabatic model that included the electron-rotational interaction of the 3d 3Π g and 3d 3Δ g states in the pure precession approximation. The coefficients of the expansion of the wave functions of the rovibrational levels of radiative electronic states in Born-Oppenheimer basis functions were found from the experimental data on rovibronic terms. The dipole moments of the 3d 3Π g → 2p 3Σ + , 3d 3Π g → 2p 3Π u , and 3d 3Δ g → 2p 3Π u electronic transitions were determined from the measured relative probabilities of spontaneous transitions and radiative lifetimes of rovibronic levels by calculating vibronic matrix elements for ab initio potential curves. The semiempirical and ab initio data on the dipole moments and probabilities of spontaneous transitions are compared. The results obtained by comparing the transition probabilities between the corresponding triplet and singlet electronic states of H2 and D2 are presented.