Nonadiabatic effects in the B, C, B′, and D states of H2

The Kolos-Wolniewicz potentials for the H₂$\text{B}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ and C¹Π_u states were used together with the hypothesis of pure precession for the rotation-electronic interaction, to calculate the nonadiabatic energy levels of these states for J = 1 to 5. The complete coupling matrix was computed using accurate numerical vibrational wavefunctions. The calculated Λ-doubling of the v = 0 to 12 C vibrational levels generally agrees well with experimental values, and the nonadiabatic shifts in the B rotational constants qualitatively explain the difference between the theoretical and RKR potentials for this state.The interaction of the B′${}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ and D¹Π_u states was also investigated, but only qualitatively since adiabatic potentials of sufficient accuracy do not exist for these states. The Λ-doubling of the Dv = 0 rotational levels agrees well with the experimental values. An appreciable “background” nonadiabatic shift in the B′ rotational constants was found. This shift, which is nearly 5 percent of B_v, is in addition to that of strong local two-level interactions and was not “deperturbed” in constructing the B′ RKR potential. The result is that the RKR turning points differ by about 0.04 au from the “true” adiabatic turning points. This conclusion is supported by a Hartree-Fock calculation of the B′ potential to the left of R_e.     

Rotational Analysis of the A2Π → X2Σ+ visible band system of boron monoxide,BO

Seventeen bands of the A²Π → X²Σ⁺ system of ¹¹BO with v′ ≤ 8 and v″ ≤ 5, and 13 bands of the same system of ¹⁰BO with v′ ≤ 6 and v″ ≤ 4 have been photographed at high resolution and rotationally analyzed. No local perturbations, except for the already known perturbation of A²Π, v = 4 with X²Σ⁺, v = 17 in ¹¹BO have been found for either isotope. The constants obtained from least-squares fits of the line positions of individual bands have been merged for each isotope to obtain single-valued estimates. RKR turning points for the two electronic states are reported.     

Revised molecular constants,RKR potential,and long-range analysis for the B3Π(0u+) state of Cl2, and rotationally dependent Franck-Condon factors for Cl2 (BX1Σg+)

Literature data for the line frequencies of the B³Π(0_u⁺) ← X¹Σ_g⁺ transition of Cl₂ are fitted directly by least squares to obtain new molecular constants. The constants from individual bands are merged to obtain single-valued estimates of the rotational constants for each vibrational level of the B state. The results are combined with recent data from the B → X system in emission to obtain new RKR turning points for the B and X states, and Franck-Condon factors for the B-X system. The new constants are also used to provide revised long-range parameters for Cl₂(B) which differ from those of earlier work. In particular, the coefficient C₅ of the leading term in the inverse-power long-range potential is now found to be $\text{C}{}_5\text{= 1.16(2) × 10}{}^5\text{A}\text{?}{}^5\text{cm}{}^{\mathrm{?1}}$. Theoretical results for the variation of centrifugal distortion parameters for levels near dissociation are tested for D_v and H_v, and an extrapolation based on this behavior is used to facilitate determination of reliable B_v and G(v) values for the highest observed B-state levels.     

Improved molecular constants for the and states of NaH

Improved molecular constants for the and states of the NaH molecule are presented. NaH molecules are produced by reactive scattering of H and Na₂ in a crossed beam experiment. High vibrational levels (6 9) of the NaH molecules are predominantly populated. Their excitation spectrum in the range has been measured using a new variant of Doppler spectroscopy. The transition frequencies involving the vibrational levels 2 8 in the and 6 9 in the state have been determined with an accuracy of better than . Using also previously published data a new set of molecular constants for the and state is derived. In particular, the vibrational dependence of the rotational constants B, D and H as well as some of v”-v' band origins for and is determined. The transition frequencies measured here or published previously are reproduced by these new coefficients with an accuracy of 0.1 cm^-1 [rms value] with a maximum deviation of 0.4 cm^-1. New RKR potential energy curves have been calculated up to the turning points of the levels v” = 9 in the state and v' = 25 in the state. Received 21 August 1999     

Rotational analysis of the B2Σ+ → X2Σ+ system of the aluminum monoxide radical,AlO

Twenty-five bands of the B²Σ → X²Σ system of AlO with 0 ≤ v′ ≤ 9 and 0 ≤ v″ ≤ 6 have been photographed at high resolution. The measured positions of the assigned lines of each band have been fitted by least-squares to obtain estimates of the constants (B′, D′, B″, D″), the band origin, and Δγ_v′,v″, which is the difference of the upper and lower state spin-doubling constants (γ′_v and γ″_v). The parameters from individual bands have been merged to single-valued estimates, as well as to polynomial representations in ($\text{v +}\text{1}\text{2}$). Although the spin-doubling constants are not found absolutely for either state, their vibrational dependences are well determined. The data are employed in the computation of RKR potential energy curves and an array of Franck-Condon factors and r-centroids.     

Use of calculated centrifugal distortion constants (Dν, Hν, Lν and Mν) in the analysis of the B ← X system of I2

Fourier spectroscopy measurements of 14 703 lines from the B-X band system of I₂ are analyzed using centrifugal distortion constants calculated from RKR curves by the perturbation theory method of Hutson [J. Phys. B14, 851–857 (1981)]. Only vibrational and rotational constants are varied in the least-squares fits, with the centrifugal distortion constants fixed at the calculated values. The fit obtained in the present work is as good as when the centrifugal distortion constants are treated as independent parameters, but the molecular constants obtained are physically more meaningful because the statistical correlation between parameters is reduced. The analysis includes B-state vibrational levels up to v′ = 72, which is bound by only 0.5% of the well depth; the method used for calculating centrifugal distortion constants remains reliable even this close to dissociation. It is found that centrifugal distortion constants up to fifth order make significant contributions to the observed line positions.     

New observations and analyses of the laser excited fluorescence of the A1Σu+-X1Σg+ bands of the Na2 molecule

A medium power (～50 mW, 6328 Å) HeNe laser is used to excite the A¹Σ_u⁺-X¹Σ_g⁺ fluorescence of the Na₂ molecule in a crossed heat pipe oven. The spectrum in the region 5800–8500 Å is recorded both photographically (3.4 M Ebert) and photoelectrically (GaAs detector) with an emphasis on accurate relative intensities and on the observation of higher vibrational levels in the ground state close to the dissociation limit. P and R doublets in four series originating from (v′ = 14, J′ = 45), (v′ = 16, J′ = 17), (v′ = 22, J′ = 86), and (v′ = 25, J′ = 87) levels are observed and identified. The first two series, known from earlier work, are extended further to longer wavelengths to include 13 to 17 additional ground-state vibrational levels. The latter two series are observed for the first time. They originate from higher J′ levels and span a wide range of v″ levels (0 ≤ v″ ≤ 48). Effective RKR potentials for specific J″ (= 17, 45, 86, and 87) quantum numbers of the ground state are constructed and from them the true (rotationless) potential energy curve (for X¹Σ_g⁺) is derived which (a) reproduces the RKR curve previously given by Kusch and Hessel and (b) extends the curve from 5.77 to 7.26 Å (outer turning point). The dissociation energy D_e is estimated from these data to be 6022 ± 21 cm^?1.     

Transition Probabilities in the BΣ-XΣ and the BΣ-AΠ Electronic Systems of MgO

Transition probabilities for the B¹Σ⁺-X¹Σ⁺ and the B¹Σ⁺-A¹Π electronic systems are presented for v=0-4 and J=0-150 in each electronic state. The functional form of the electronic transition moment for the B-X transition is taken from published ab initio results. The B-A moment is assumed to have the same form and is scaled using empirical branching ratio data. The R_e(r) are used with Rydberg-Klein-Rees (RKR) wavefunctions to calculate transition probabilities for v=0-4 and J=0-150. The RKR potentials were calculated based on empirical spectroscopic constants.     

Laser-induced fluorescence of Pb2

Pb₂, which occurs in lead vapor, was studied by the technique of laser-induced fluorescence using single-mode Ar-laser excitation. The fluorescence observed could be classified into the F-X system. Ten progressions involving vibrational quantum numbers v′ = 0?9 and v″ = 0?22 were analyzed. Including collision-induced lines, rotational quantum numbers from J = 25 to J = 300 were observed. The vibrational constants and the numbering of the states had to be reassigned. For the first time rotational constants were determined for the Pb₂ molecule. The internuclear distances of ²⁰⁸Pb₂ in the F and X state are $\text{r = 3.079}\text{A}\text{?}$ and $\text{r}{}_{\mathrm{<mtext>e</mtext>}}\text{= 2.930}\text{A}\text{?}$, respectively. Using the constants derived RKR potentials and Franck-Condon factors were calculated, which confirmed the vibrational assignments and constants.     

The A3Π(1) → X1Σ+ emission spectrum of ICl in the near infrared: Rotational analysis of bands in the v′ = 0, 1, 2, 3, 4, progressions and molecular constants for the X1Σ+ and A3Π(1) states by merging with absorption data

Ten bands of the A³Π(1) → X¹Σ⁺ emission system of I³⁵Cl, lying at wavelengths of 8180 – 10000 Å, have been analyzed rotationally in the ranges 0 ≤ v′ ≤ 4 and 6 ≤ v″ ≤ 9. Constants determined from least-squares fits of frequencies of individual bands are merged with constants derived from absorption data. RKR potentials for both states are reported, and the Franck-Condon factors for ICl (A-X) have been computed for 0 ≤ v′ ≤ 35 and 0 ≤ v″ ≤ 9.     

Franck-Condon factors and absolute transition probabilities for the if (B3Π0+-X1Σ+) transition

Improved spectroscopic constants have been used to calculate Rydberg-Klein-Rees (RKR) potentials and Franck-Condon factors for the IF(B³Π₀₊-X¹Σ⁺) transition. The Franck-Condon factors are generally in good agreement with previously calculated values, but differ by as much as 30% for transitions from higher levels of the B-state. Several experimentally measured relative transition moment functions have been evaluated and the best scaled, so that the total transition probability calculated for each B-state vibrational level, A(v'), matched measured values. The scaled function was then used to calculate individual transition probabilities, A(v',v), for the vibronic transitions.     

The B3Π(0+) → X1Σ+ emission spectrum of 79BrF and 81BrF in the range 6250–8700 Å: Rotational analysis of bands in the v′ = 0, 1, 2, 3, 4 progressions,and merged molecular constants for the X1Σ+ and B3Π(0+) states

Sixteen emission bands of the B³Π(0⁺) → X¹Σ⁺ systems of ⁷⁹BrF and ⁸¹BrF have been analyzed rotationally. Measured line frequencies are fitted by least-squares to determine the rotational constants and origin for each band. The least-squares results for 0 ≤ v′ ≤ 4 and 4 ≤ v″ ≤ 12 are merged with constants from previously reported B ← X absorption and X-state microwave data. RKR potentials for the two states and Franck-Condon factors and r-centroids for the BrF (B-X) system are reported.     

High-resolution Fourier spectrometry of 14N2 infrared emission spectrum: Extensive analysis of the B3Πg-A3Σu+ system

The B³Π_g-A³Σ_u⁺ system of N₂ excited in a microwave discharge was recorded between 3 000 and 18 000 cm^?1 with a high-resolution Fourier spectrometer. There are no observed irregularities in the levels of the A³Σ_u⁺ and B³Π_g states at least for the values of v and J considered here, except the predissociation in the B³Π_g state for v = 12 and J higher than 33. This predissociation will be checked with more complete data in another article. Thirty three bands of the first positive system with 0 ≤ v′ ≤ 12 and 0 ≤ v″ ≤ 8 are analyzed. The molecular parameters of the B³Π_g and A³Σ_u⁺ are obtained by a complete fitting procedure. Derived values of equilibrium constants are deduced; RKR potential energy curves for the two states are constructed, and the Franck-Condon factors calculated for the A-B system.     

The 5Σg and 6Σg Rydberg States of Li2: Observation and Calculation

The ⁷Li₂ 5¹Σ_g⁺ and 6¹Σ_g⁺ states have been studied both experimentally and theoretically. Vibrational levels v=1-26 of the 5¹Σ_g⁺ state and v=2-14 of the 6¹Σ_g⁺ state were observed using pulsed optical-optical double resonance technique. The 5¹Σ_g⁺ state has an unusual potential energy curve with a shelf near v=11. Dunham coefficients for the v=0-9 levels of the 5¹Σ_g⁺ state have been obtained. RKR potential energy curves of these two were generated. Ab initio potentials are in good agreement with the RKR potentials.     

Photoassociative spectroscopy of the long-range state

The photoassociative spectroscopy of the Cs₂ 0 g ^- long-range molecular state dissociating into the asymptote is performed, using cold cesium atoms in a vapor-cell magneto-optical trap (MOT). Vibrational levels from v =0 to v =132 are identified, and their rotational structure is well resolved up J =8 for levels below v =74. These data are analyzed in terms of the Rydberg-Klein-Rees (RKR) procedure, and correspond to 99.6% of an effective potential curve with a minimum at ? and a cm^-1 depth. Both ab initio calculations and simple model estimations predict a double-well structure for this potential curve, which cannot be reproduced presently by the RKR approach but which is confirmed by the presence of giant structures in the spectrum. The 1_u()long-range state is also observed for the first time in Cs₂.     

Microwave spectrum of γ-valerolactone

An Ar⁺ laser at 4579 Å is used to excite the B¹Π_u-X¹Σ_g⁺ fluorescence of the ⁶Li⁷Li molecule in a crossed heat pipe oven. The spectrum in the region 4400–6300 Å is recorded photoelectrically with an emphasis on the observation of higher vibrational levels in the ground state close to the dissociation limit. P and R doublets corresponding to v″ ≤ 26 originating from the (v′ = 13, J′ = 19) level are observed and identified using mass-reduced quantum numbers. Two additional ⁶Li⁷Li series, known from earlier work of Velasco, Ottinger, and Zare, are also analyzed. These data are used to construct effective Rydberg-Klein-Rees (RKR) potentials for specific J″ (=9, 19) quantum numbers of the ground state and from them the true (rotationless) potential energy curve (for X¹Σ_g⁺) is derived. This extends the previously known curve of Li₂ from 4.28 to 5.18 Å (outer turning point); this turning point corresponds to an energy which is approximately 88% of the dissociation energy, which is estimated here to be 8516 ± 18 cm^?1.     

Rotational vibrational analysis of the BΠ (0) - XΣ band system of BrCl and BrCl

24 bands of the B³Π(0⁺) ← X¹Σ⁺ system of ⁷⁹Br³⁵Cl and ⁸¹Br³⁵Cl have been photographed at high resolution. Direct least-mean square fits of the measured line frequencies were made to determine band origins and rotational constants in the ranges 1 ≤ v″ ≤ 7, 2 ≤ v′ ≤ 8. A reiterative procedure was adopted in which the higher order centrifugal distortion constants (D_v, H_v) were constrained to theoretical values calculated from RKR potential curves. The results of the analysis are used to obtain a set of Franck-Condon factors and r-centroids for the B-X system of BrCl.     

High vibrational levels of the X state of ICl,and the electronic-coriolis coupling of the X and A states

Ro-vibrational levels of the ground state of ICl have been measured in the range v_x = 35–73 and J_x < 55 using three-stage polarization-labeling spectroscopy. When merged with established microwave and fluorescence data for the lower levels, these results lead to a self-consistent set of spectroscopic constants G_v, B_v, D_v and H_v for all levels v_x ≤ 73. The highest G_v and G_v + F_J term values recorded are, respectively, 52.7 and 1.37 cm^?1 below the dissociation limit. Coefficients of the long-range interaction I + Cl are determined by analysis of the outer wings of the RKR potentials for the X(0⁺) and A′(2) states. Electronic rotational interaction between X and the well-known A(1) state of ICl is shown to account for at least a major part of the $\text{Ω-doubling}$ splitting observed in A: the electronic matrix element characterizing this interaction is shown to be strongly r-dependent, and reasons for this are reviewed.     

Studies of labile molecules with a tunable dye laser: Laser excitation spectrum of BrF (B3Π(0+)-X1Σ+)

The B³Π(0⁺) ← X¹Σ⁺ absorption spectrum of BrF (4850–5200 Å) has been observed by the technique of laser emission spectroscopy. Fluorescence was excited by a pulsed, scannable dye laser with a 0.1 Å bandwidth. Rotational analysis has been carried out for six bands of the v″ = 0 progression (8 ≥ v′ ≥ 3) of ⁷⁹BrF and ⁸¹BrF. Rotational constants for the B³Π(0⁺) state are reported for the first time. RKR potential energy curves for both states, and an array of Franck-Condon factors and r-centroids for the transition, have been calculated. Bands with v′ > 8 were not observed in fluorescence owing to the onset of predissociation near J′ = 28 of the v′ = 8 level. An upper limit for the ground state dissociation energy is D₀″ (BrF, X¹Σ⁺) ≤ 20 880 cm^?1.     

The RKR potential energy curves for the X1Σ+ and A1Σ+ states of KH

New isotopically combined spectroscopic constants were obtained for the X¹Σ⁺ and A¹Σ⁺ states of $\text{KH}\text{KD}$. These constants were used to construct new isotopically combined Rydberg-Klein-Rees (RKR) potential energy curves up to v″ = 4 of the X¹Σ⁺ state and up to v′ = 26 of the A¹Σ⁺ state.