Radial dependence of spin-orbit and Λ-doubling parameters in the X2Π ground state of hydroxyl

Experimental spin-orbit and Λ-doubling constants of OH X²Π in the vibrational range v ≤ 10 were inverted to their operator forms. The A(r) radial form derived from the spin-orbit coupling constants has been used to calculate the spin-orbit distortion parameters, A_Dv, in the range v ≤ 4. These A_Dv values have been used to separate the totally correlated γ_v and A_Dv values obtained experimentally. Radial forms of the composite lambda-doubling operators p(r) and q(r) were generated using, for the first time, the generalized inversion procedure proposed by Watson.     

Theoretical study of the spin-orbit coupling in the X2Π state of OH

The spin-orbit coupling constant, A(r), as a function of internuclear distance (r) was computed for the X²Π state of OH, using the microscopic spin-orbit Hamiltonian, extended basis sets, and extensive configuration-interaction wavefunctions. Our best theoretical results are in excellent agreement with the “experimental” A(r) functions deduced from an inversion of the observed A_v. Our calculated first-order contributions to A_v, v ≤ 10, obtained by vibrationally averaging our theoretical A(r) function using the X²Π RKR potential, differ from experiment by less than 0.12%. A minimum occurs in the A_v at v = 7 in agreement with experiment, reflecting the local minimum in A(r) near 2.8 bohr. The second-order contributions to A_v are only about 0.1% for v ≤ 10. They arise mainly from the A²Σ⁺ state for the lower vibrational levels, but each of the A²Σ⁺, B²Σ⁺, (1)²Σ^?, (1)⁴Σ^?, and (1)²Δ states contributes significantly for higher vibrational levels. Spin-orbit centrifugal distortion parameters, A_Dv and a_Dv, are reported for v ≤ 6. The theoretical A_Dv are also in excellent agreement with experiment when the “experimental” A(r) function has the same slope at the equilibrium separation as that obtained from the effective spin-rotation constants of OH, OD, and OT.     

The uv spectrum of 18OD

The combined high-resolution ultraviolet (uv) absorption spectrum of ¹⁶OD and ¹⁸OD was obtained. State selective measurements of the transitions from the electronic ground state to the first excited electronic state, $\text{A}\text{?}{}^2\text{Σ}{}^{\mathrm{+}}\text{←}\text{X}\text{?}{}^2\text{Π}$, in the 0-0 vibronic band were performed by means of a narrow bandwidth dye laser system. Evaluation of these transition frequencies in wave-numbers yielded molecular constants as well as rotational term values for each of the isotopic species. A computer program based on a linearized least-squares procedure was used to determine the molecular constants and term values. The term value formulas which were employed for this purpose, take into account the Λ splitting and the centrifugal distortion of the diatomic species. The transitions, recalculated from the semiempirically determined term values agree with the measured absorption lines to better than 0.1 cm^?1. The following molecular constants are reported: B, D, H, the rotational constants of the ²Π and ²Σ⁺ states; O₀, P₀, Q₀, the constants of the Λ splitting of the ²Π state; A and A₁; the constants of the spin-orbit coupling of the ²Π state; and γ₀, the constant of the p doubling of the ²Σ⁺ state. Futhermore, term values up to J″ and J′ of 25.5 and the corresponding uv transitions are given.     

Doppler-limited dye laser excitation spectrum of the C2 Swan band (v′ − v″ = 1 − 0)

The dye laser excitation spectrum of the Swan band (v′ ? v″ = 1 ? 0) has been observed with Doppler-limited resolution. The C₂ molecule was generated by the reaction of microwave discharge products of CF₄ with CH₄. The high sensitivity of laser excitation spectroscopy has enabled us to observe not only $\text{ΔΩ}\text{= 0}$ transitions, but also $\text{ΔΩ}\text{= ± 1}$ transitions and to determine molecular constants including the spin-orbit coupling constant for both the d³Π_g and a³Π_u states. The parameters thus obtained for a³Π_u were favorably compared with those previously obtained from the Ballik-Ramsay band. The present results on the d³Π_gv = 1 state were combined with those of an earlier Fourier spectroscopic study on the Swan band (v′ ? v″ = 0 ? 0) to derive equilibrium molecular constants for the d³Π_g state. The contributions of the spin-rotation interaction and the centrifugal correction for the spin-orbit coupling to the energy levels in a ³Π state have been discussed in detail.     

Spin-orbit and spin-rotation coupling in doublet states of diatomic molecules

The spin-rotation interaction and the centrifugal correction to the spin-orbit coupling make indistinguishable contributions to the energy levels of a diatomic molecule in a multiplet state with Λ ≠ 0. A previous method of separating these two contributions, based on the use of the vibrational dependence of the spin-orbit coupling constant, is unreliable. It is suggested here that a better procedure is one based on the isotope dependences of the spin-rotation coupling constant γ and the centrifugal correction to the spin-orbit coupling constant A_D. Both γ_e and A_De are shown to be inversely proportional to μ, the reduced mass of the molecule, but their contributions to the energy have different isotope effects. The method is used to determine values of γ_e and A_De for the X²Π state of HCl⁺, and the form of the spin-orbit coupling function A(r) in the vicinity of the equilibrium bond length is derived. The implications for RKR calculations are considered briefly.     

The far-infrared laser magnetic resonance spectra of the OD radical in ground and vibrationally excited states

Laser magnetic resonance spectra of the OD radical in low-lying vibrational levels of the X²Π state have been recorded at a variety of wavelengths in the far-infrared. The spectra have been assigned to rotational and fine-structure transitions and fitted to a model Hamiltonian to determine the appropriate molecular parameters for the levels v = 0 to 3. The results are compared with those from previous studies of OD in these vibrational levels.     

On the cΠ (v = 0) state of carbon monoxide

A full analysis of the near infrared c³Π-b³Σ⁺ (0-0) band is given and term values for both states determined. The c³Π (v = 0) state was jointly analysed with the perturbing k³Π (v = 2) state and data from the c³Π-X¹Σ⁺ (0-0) transition and 3A band system were included. It is shown that the available data are consistent with the c³Π (v = 0) state having near Hund’s case b coupling with a spin-orbit constant of A = 0.45 ± 0.02 cm⁻¹, a homogeneous perturbation with the k³Π (v = 2) state, and Λ-type doubling arising predominantly from its interaction with the j³Σ⁺ state. A discrepancy with a more recent report of the 3A band system is identified and discussed. The perturbed b³Σ⁺ state term values are consistent with a previously reported five state interaction model.     

Deperturbation of DΠ v = 4 level of ScF molecule: Characterization of the Π perturber from analyses of DΠ-XΣ 4-2 and DΠ-AΔ 4-4 LIF transitions

High resolution emission spectra of ScF molecule have been observed in the region of 21 120-21 300 cm⁻¹ and of 15 640-15 710 cm⁻¹. The rotational structures in 4-2 band of D¹Π-X¹Σ⁺ and in 4-4 band of D¹Π-A¹Δ were assigned. Rotational analysis reveals the presence of localized perturbations in the upper state D¹Π v = 4 level at different values of J for the two parity sublevels, e and f. These perturbations are interpreted as the consequence of a spin-orbit interaction between D¹Π state and a triplet state of ³Π symmetry. A matrix model describing the energies within the two interacting levels, has been used to fit term-values. Spectroscopic constants are obtained for A¹Δ v = 4, D¹Π v = 4 and for the ³Π perturbing level. The magnitude of the spin-orbit interaction is estimated.     

The lower excited states of CS: A study of extensive spin-orbit perturbations

We present previously unpublished data on the A¹Π, e³Σ^?, d³Δ_i, $\text{a′}{}^3\text{Σ}{}^{\mathrm{+}}$, and a³Π states of CS from uv emission and absorption transitions to the X¹Σ⁺ ground state. Term values obtained from d³Δ_i ← a³Π ir emission bands are also included. Rotational analyses are presented for about 50 new fine-structure components in some 30 new vibrational levels, together with extended data and analyses for many of the previously observed levels. The data now availabe for these five electronic states more than triples that previously published. Vibrational numbering for the e, d, and a′ states is established by data for minor isotopes. In a Hund's case a-b basis, off-diagonal spin-orbit elements (incipient case c effects) produce extensive coupling among these levels, not only for perturbation crossings but also between levels widely separated in energy. A systematic deperturbation requires two stages, which are iterated. Term values computed from the spectral lines are used to fit parameters of Hamiltonian matrices for groups of nearby, coupled levels. Additional shifts are computed by second-order perturbation theory from the electronic interactions deduced from vibronic coupling elements. The resultant parameters satisfy certain tests for self-consistency; they conform to low-order polynomials in $\text{v +}\text{1}\text{2}$, and vibrational overlap factors from wave-functions computed with RKR potential curves are proportional to the vibronic coupling elements, to within experimental error in most cases. To obtain this self-consistency, we have computed and applied normally neglected centrifugal distortion effects in the off-diagonal coupling elements and in the second-order perturbation sums. We also present and interpret the diagonal spin-orbit fine structure in the a and d states, including the centrifugal distortion parameters, A_D, for the latter, and values for several fitted second-order elements. Possible assignments for three additional perturbations of the A¹Π state and one faint band are discussed in view of ¹Δ, ¹Σ^?, and ⁵Π states that are also expected to occur in the region studied. Tentative parameters for the D¹Δ state are obtained from one possible set of assignments.     

Fine structure of the close-lying A 2Π and B 2Σ+ states of BaH and BaD

Molecular parameters for the close-lying and strongly interacting A ²Π and B ²Σ states of BaH and BaD have been re-evaluated by means of a numerical matrix diagonalization procedure. The results obtained according to this exact method deviate considerably from the effective ones of previous investigations, particularly with respect to the A ²Π-B ²Σ⁺ interaction matrix elements which describe the large Λ-doubling and spin-splitting. The new values of the Λ-doubling and spin-splitting parameters are in excellent agreement with pure precession values for L = 2, and thus the present results form an interesting extension of the pure precession model which so far has been found applicable in a number of cases for which L equals one. The pure precession result L = 2 indicates that the outermost electron of the A ²Π and B ²Σ⁺ states must be a d-electron, and this requires a re-assignment of the configuration quantum numbers of these states. Strong local perturbations are observed in the rotational levels of the A ²Π state of both BaH and BaD, and the result L = 2 now yields a further confirmation of the previous assumption that a ²Δ state causes these perturbations. In the case of BaD the electronic + vibrational energy and the rotational constants (B_v , D_v ) of the perturbing level could be determined from the perturbed A ²Π term values, and in particular the value of the interaction matrix element leads to the conclusion that there is a A ²Π, v = 0 - ²Δ, v = 2 interaction. Finally the influence of the A ²Π - ²Δ, Δv = 0 interaction on the A ²Π and B ²Σ⁺ molecular parameters was investigated.     

Part of the far-infrared laser magnetic resonance spectrum of the HF free radical

Transitions between the spin-rotational levels of the HF⁺ radical in the v=0 level of the X²Π ground state have been observed by the technique of laser magnetic resonance at far-infrared wavelengths. Because of the large spin-orbit coupling in this ²Π state, the detection of the fine-structure transitions required the use of very short-wavelength laser lines (down to 40 μm). These observations have provided accurate information on the ¹⁹F hyperfine splittings in rotational levels of the upper spin component for the first time which has enabled the complete determination of the hyperfine structure for this molecule. An effective Hamiltonian was used to model the experimental measurements; this provided considerably more accurate values for the various molecular parameters than previously available. Using these parameters, predictions of the transition frequencies between the low-lying spin-rotational levels of the radical at zero magnetic field have been made.     

Difference frequency laser spectroscopy of OH and OD: Simultaneous fit of the infrared and microwave lines

The fundamental vibration rotation bands of OH and OD have been observed with an estimated accuracy of 0.001 cm^?1. Simultaneous fits of the infrared and microwave data are performed to improve the molecular constants in the v = 0 and v = 1 states. The correlated parameters γ_v and A_D are determined by combining the data for OH and OD. Some discussion is presented on the correlated molecular parameters.     

Rotational analysis of the A2Πu-X2Πg Second Negative band system of O2+

Existing high-resolution data for the $\text{O}{}_2{}^{\mathrm{+}}\text{A}{}^2\text{Π}{}_{\mathrm{u}}\text{- X}{}^2\text{Π}{}_{\mathrm{g}}$ Second Negative band system have been analyzed using a nonlinear least-squares fit that employs numerically diagonalized Hamiltonians. Values for the full set of molecular constants of the A²Π_u and X²Π_g states are obtained for the first time. In addition to values for ν₀(v′, v″), B_v, and D_v, the values for the spin-orbit coupling constants A_v are determined for both states. For the X²Π_g state, which is near Hund's case (a), the agreement between these A_v″ values and those predicted by theory is good. However, for the A²Π_u state, which is much nearer to case (b), these A_v′ values and theory disagree both in magnitude and in variation with vibrational level. The A²Π_u state is an inverted state for vibrational levels v′ ≤ 5 and is a regular state for levels v′ = 6–8 (the upper limit of present high-resolution data). Λ-doubling parameters are determined for the X²Π_g state, the only state where Λ-doubling is statistically significant. Spin-rotation interaction is not statistically significant for either state. Dunham Y_i0 and Y_i1 expansion coefficients are determined for each state. Theoretical D_v values calculated from RKR potentials are used to improve the B_v values in the reduction of the data.     

Fourier spectroscopy of the OD infrared spectrum. Merge of electronic,vibration-rotation,and microwave spectroscopic data

The OD infrared spectrum, emitted in a flame of deuterium and oxygen, has been recorded for the first time in the 2-μm spectral range with a Fourier Transform spectrometer. A simultaneous fit of the ir 2-0, 3-1, 4-2, 5-3, 3-0, 4-1 vibration-rotation bands, of the uv data (0-0, 1-1, 2-2, 0–1 bands of the A²Σ⁺ → X²Π transition) and of the microwave data, gives accurate molecular constants for the ground-state vibrational levels up to v = 5. The classical “unique perturber approach” and the effective Hamiltonian of Brown for ²Π states, have been successively used for the reduction of the spectroscopic data.     

The valence states of NO+

Spectroscopic constants for the eight lowest electronic states of the NO⁺ ion are tabulated. These constants result from reanalysis of previously reported optical and photoelectron spectra and interpolation from corresponding states of the isoelectronic molecules CO and N₂. Similar spin-orbit perturbations of the A¹Π states of NO⁺ and CO are compared. An interpretation is given of previously reported emission from a beam of long-lived states of NO⁺. The intensities of ionizing transitions from NO X²Π (v = 0) observed in photoelectron spectra are compared with calculated Franck-Condon factors.     

A Reanalysis of theA1Π–X1Σ+Transition of AlBr

TheA¹Π–X¹Σ⁺transition of aluminum monobromide (AlBr) near 2800 Å was recorded using a Bruker IFS 120 HR Fourier transform spectrometer at nominal resolutions of 4 and 0.03 cm⁻¹. All bands showP,Q, andRbranches and all are degraded to longer wavelengths. The 0–0 band is the most intense and the Δv= 0 sequence dominates the observed spectrum. Each band appears doubled due to the natural isotopic abundances of⁷⁹Br (50.69%) and⁸¹Br (49.31%). Band origin shifts due to isotopic substitution of bromine were examined to confirm the assignments of isotopic species. The rotational structure of the 0–1, 1–2, 0–0, 1–1, and 2–2 bands was assigned and fitted. These data were merged with previously reported photographic data for the 1–0, 2–1, 3–2, 2–0, and 3–1 bands and also infrared and microwave measurements to provide an improved set of constants for both electronic states. The rotational constants for each vibrational level in theX¹Σ⁺state vary smoothly with increasing vibrational quantum number and thus an expansion of the constants in terms of equilibrium values is recommended. An expansion of theA¹Π rotational constants in terms of equilibrium values is not recommended as the distortion constants do not change smoothly with increasing vibrational quantum number. Therefore, the rotational constants for theA¹Π state were determined for each individual vibrational level. This approach leads to vastly improved vibrational constants for theA¹Π state by reducing correlations between rotational and vibrational constants. This problem is serious for theA¹Π state owing to severe departures from harmonic behavior in thev= 2 andv= 3 levels.     

Analysis of perturbations in the A2Π-X2Σ+ “Red” system of CN

Deperturbed vibration-rotation constants of the A²Π(v′ = 0 to 12) and X²Σ⁺(v″ = 0 to 8) states of CN are obtained. Specroscopic data from several sources are combined using a weighted, nonlinear least-squares fitting routine. The diagonalized effective Hamiltonian matrix contains as many as two ²Π and four ²Σ⁺ mutually interacting vibronic levels. Perturbations of A²Π by both X²Σ⁺ and B²Σ⁺ are treated simultaneously. The deperturbed constants and interaction matrix elements obtained provide a significantly more accurate representation of all perturbed and unperturbed observed lines than the previously reported values. The electronic factors of the spin-orbit and rotation-electronic perturbation matrix elements for the A ～ X and A ～ B interactions are determined and several previously unreported perturbations are detected and analyzed. Merged constants and Dunham coefficients are calculated; a detailed statistical treatment of the parameters and error estimates has also been carried out.     

Sub-Doppler laser absorption spectroscopy of the AΠi − XΣ (1, 0) band of CN: Measurement of the N hyperfine parameters in AΠ CN

Measurements of multiple rotational lines in the (1, 0) band of the A²Π_i − X²Σ⁺ “red” system of the cyanogen radical (CN) at sub-Doppler resolution are reported. The CN radical was produced by 193 nm photodissociation of NCCN (ethane dinitrile) and detected with a Ti:sapphire ring laser operating near 10 900 cm⁻¹. The sample was exposed to a weak, frequency-modulated probe beam and a strong, counterpropagating bleach laser beam. Demodulated probe laser signals display absorption and dispersion features derived from Doppler-free saturation of the hyperfine components as the laser scans across the central region of a Doppler-broadened rotational line spectrum. Hyperfine-resolved transition frequencies were combined with known ground-state X²Σ hyperfine term values to determine A²Π state hyperfine term values, which were analyzed in terms of an effective Hamiltonian for the A²Π state. All the expected hyperfine and ¹⁴N quadrupolar parameters were determined and their values analyzed in terms of a simple molecular orbital picture of the bonding in the radical. Higher sensitivity obtained with 400 kHz amplitude modulation of the bleach laser and additional phase-sensitive detection allowed hyperfine splittings in some rotational lines of ¹³C¹⁴N to be observed in natural abundance. Excited state hyperfine splittings were determined for a selection of rotational states, but not enough to determine the ¹³C hyperfine parameters.     

Optical-Optical Double Resonance Spectroscopy of the 1g(P1)-AΠ (1u)-XΣg Transition of I2

Optical-optical double resonance spectroscopy was used to study the 1_g(³P₁) ion-pair state of I₂ correlating to I⁻(¹S)+I⁺³P₁) at the dissociation limit. We gained access to the 1_g(³P₁) state though the A³Π (1_u) state in the (1+1) photon-excitation scheme. The pump laser excited the A³Π (1_u)-X¹Σ_g⁺ transition at a fixed frequency for state selection. The probe laser was scanned to detect the 1_g(³P₁)-A³Π (1_u) resonance by monitoring the ultraviolet emission from the 1_g(³P₁) state at 278 nm. The 1_g(³P₁) state was observed in a vibrational progression consisting of P and R doublets. An energy level analysis was carried out for the 1_g(³P₁) state in the 0≤ v ≤ 14 and 12≤J≤135 range, which led to a set of molecular parameters including the Ω-doubling constant. The Ω-doubling of the 1_g(³P₁) state was discussed by the pure precession model and interpreted to occur through the heterogeneous coupling with the 0_g⁻(³P₁) state correlating to the same ionic asymptote.     

Faraday Laser Magnetic Resonance Spectroscopy of Vibrationally Excited C2H

The gas phase spectrum of the C₂H radical in the region between 3191 and 3342 cm⁻¹has been studied using a Faraday LMR spectrometer with a CO overtone laser. The C₂H molecules were produced in an electric dc glow discharge of normal type containing a mixture of helium, acetylene, and hydrogen. We observed two bands of theX²Σ⁺→A²Π electronic transition with origins at 3321 and 3229 cm⁻¹. The lower level of both bands was the first excited bending level of the electronic ground stateX. The upper levels were assigned to two²Π vibronic levels with term values of 3693 and 3600 cm⁻¹, respectively. They correspond to mixtures of vibrationally excited levels of theXelectronic state with the lowest vibronic level of the first excited electronic stateA. From the analysis of the spectra we could determine the orbitalgfactors of the upper levels. These parameters are a very sensitive measure for the mixing between theXandAelectronic states. The experimentally derived values were compared with theoretical values, obtained byab initiocalculations, and could be explained by the theoretical model using an improved energy distance between theXandAstates.