Franck-Condon Factors and r-Centroids for the (B [sbnd] X) and (C [sbnd] X) Bands of the 107Ag 109Ag Molecule

Arrays of Franck-Condon factors q(v′, v″) and r-centroids r(v′, v″) were computed using Morse potentials for C¹Π [sbnd] X¹Σ⁺ _g and B O⁺ _u [sbnd] X¹Σ⁺ _g bands of the ¹⁰⁷Ag ¹⁰⁹Ag molecule.     

The analysis of nitrogen rotational and vibrational bands in a helium microhollow gas discharge

Emission spectroscopy is applied to measure the gas temperature T _g and the vibrational distribution of N₂ (C ³Π_u) and N₂ ⁺(B ²Σ_u ⁺) excited states from a helium microhollow gas discharge (MHGD) at atmospheric pressure. The rotational temperature T _rot of N₂ ⁺ is determined from relative intensity of the R‐branch lines of the N₂ ⁺(B ²Σ_u ⁺–X ²Σ_g ⁺) bands at 427.81 and 419.91 nm and the well‐known Boltzmann plot (BP). Using the same diagnostic technique, the rotationally resolved N₂(C ³Π_u–B ³Π_g) band at 380.49 nm is used to measure T _rot. Under our experimental conditions, T _g is equal to T _rot = 550–650 K for nitrogen molecules and shows a slight increase with the discharge current in the current range 3–10 mA. From the intensity ratio of two consecutive vibrational bands of the same sequence, the N₂(C ³Π_u) and N₂ ⁺(B ²Σ_u ⁺) vibrational temperature T _vib = 3,700–4,000 K is determined. It has been found that N₂ ⁺(B ²Σ_u ⁺) ions have non‐Boltzmann distribution in the helium MHGD, while N₂(C ³Π_u) molecules are populated according to the Boltzmann distribution. Following the Franck–Condon principle, the vibrational distribution of the ground state of N₂(X ¹Σ_g ⁺) molecules has been determined from the N₂(C ³Π_u) distribution using the inversion matrix of elements q _XC(ν ,ν ′).     

Absolute Line Intensities in Acetylene: The 1.5-μm Region

We measured 305 absolute line intensities in the ν₁+ν₃(Σ⁺_u)-0(Σ⁺_g) band of ¹²C₂H₂ and ¹³C¹²CH₂ and the ν₁+ν₂+(ν¹₄+ν⁻¹₅)⁰(Σ⁺_u)-0(Σ⁺_g), ν₁+ν₃+ν¹₄(Π_g)-ν¹₄(Π_g), and ν₁+ν₃+ν₅¹(Π_u)-ν₅¹(Π_u) bands of the main isotopomer, all observed near 1.5 μm. The absolute intensity of these bands are respectively 6.4882 (34), 0.12337 (10), 0.083746 (71), 0.58771 (28), and 0.32126 (11) cm⁻² atm⁻¹ at 296 K. In addition, we also determined Herman-Wallis factors for the first time in this spectral region.     

Selective effects of homogeneous and heterogeneous reactions in the system N21-CO

In the system N₂¹-CO, effects arising only from the reactions in the homogeneous phase have been isolated in a reactor with inert walls. After an induction period of 0.13 s, they involve a stationary rate of enhancement of N₂(B³Π_g) and N(⁴S) concentrations according to the reactions N₂(X¹Σ_g⁺)_v¹+CO→ CO(X¹Σ⁺)_v1 + N₂(X¹Σ_g⁺ and CO(X¹Σ⁺)_v1 + N₂(A³Σ_u⁺) → N (⁴S) + N(⁴S) + CO(X¹Σ⁺).In a reactor with active walls, both the above reactions in the homogeneous phase and heterogeneous reactions due to CO adsorbed on the walls are involved according to CO_ads + N₂(X¹Σ_g⁺)_{v1 ads or not} → CO(X¹Σ⁺)_v1 + N₂(X¹Σ_g⁺ and N(⁴S) + N(⁴S) + CO_ads → N₂(X¹Σ_g⁺) + CO(X¹Σ⁺)N(⁴S) + CO_ads → N₂(X¹Σ_g⁺) + CO(X¹Σ⁺). In this case, the rate of enhancement is not stationary. Furthermore, for cylindrical reactors with large diameters, the two types of reaction do not interact and their effects are additive.     

Comparison of photoelectron intensities and Franck-Condon factors in the photoionization of H2, HD and D2

The relative intensities of vibrational bands corresponding to the photoionization reactionX¹Σ_g⁺(υ″ = 0) + hv → X²Σ_g⁺(υ′ = 0, 1, 2 …) + e^? have been measured for H₂, HD and D₂, using He I radiation and a cylindrical mirror analyzer. These relative intensities differ significantly from squared overlap integrals (Franck-Condon factors) based on accurate potential curves for X¹Σ_g⁺ and X²Σ_g⁺, but are in good agreement with calculations performed by Itikawa which include the variation of transition moment with internuclear distance and the kinetic energy of the departing electron.     

The stretching fundamental bands of 13C2D2

The stretching fundamental bands of the isotopically substituted acetylene ¹³C₂D₂ have been recorded and analysed. The Raman spectra of the Q branch of v ₁ and v ₂, Σ⁺ _g -Σ⁺ _g bands, have been recorded with an instrumental resolution of about 3.0 x 10^?3 cm^?1 using inverse Raman spectroscopy. The infrared spectrum has been recorded in the region between 2350 cm^?1 and 2500 cm^?1 with an instrumental resolution of 4.0 x 10^?3 cm^?1. Transitions belonging to the v ₃, Σ⁺ _u -Σ⁺ _g , fundamental band have been identified and assigned. The vibrational energies and the rotational and centrifugal distortion constants of the excited states of all the observed transitions have been determined. The molecular parameters obtained reproduce the assigned wave-numbers with a standard deviation of the same order of magnitude as the experimental uncertainty.     

Accurate spectroscopic calculations of the 19 Λ-S states and 36 Ω states of the BC+ cation

This work computed the potential energy curves of 19 Λ-S states, which arose from the first five dissociation limits of BC⁺ cation, B⁺(¹S_g) + C(³P_g), B⁺(¹S_g) + C(¹D_g), B⁺(¹S_g) + C(¹S_g), C⁺(²P_u) + B(²P_u), and B⁺(¹S_g) + C(⁵S_u). The calculations were done for internuclear separations from 0.08 to 1.07 nm. The potential energy curves of 36 Ω states yielded from these Λ-S states were also calculated. Core-valence correlation and scalar relativistic correction, basis set extrapolation as well as Davidson correction were accounted for. Of these Λ-S states, the c¹Σ⁺, D³Π, 2¹Π, 2³Σ⁺, 2¹Δ, 3¹Σ⁺, and 4¹Σ⁺ had double wells; the 3³Π and 3¹Π states had three wells; the C³Σ^? and D³Π states were inverted with the spin-orbit coupling effect included; and the second wells of c¹Σ⁺, D³Π and 3¹Σ⁺ states, the second and the third wells of 3³Π state as well as the third well of 3¹Π state were very weakly bound, which well depths were smaller than 400 cm^?1. The spectroscopic parameters were determined for all the states. The vibrational properties were predicted only for some weakly bound states. The spin-orbit coupling effect on the spectroscopic parameters was evaluated.     

Momentum transfer dependence behaviors of ionization and dissociation of oxygen

The decay pathways of the structured ionization region of oxygen at different momentum transfers,i.e.,0,0.23 a.u.(atomic unit),and 0.91 a.u.,are studied by measuring the ion and the scattered electron coincidently.It is found that the dipole-forbidden superexcited states of(2σu)-1(c4Σu-)npσu 3Σg-← X3Σg-decay into different channels according to the principal quantum number n.The broad ridge above 35 eV,which may be due to inner-valence excited states of(2σg)-1nλ or multiply excited states,is observed both at small and large momentum transfers,and its decay channel of O++ O is dominant.     

Laser absorption spectroscopy of the A1Σu+-X1Σg+(v′, v″) bands of Na2

Laser absorption spectra of the band system A¹Σ_u⁺-X¹Σ_g⁺(v′,v″) of Na₂ in the range between 16835 and 16960 cm^?1 are analyzed. The spectra are free of first-order-Doppler broadening at low internal temperature. Rotational and vibrational assignments of 10 bands are reported. Rotational and vibrational levels, especially the (22, 1) band, are found to be perturbed by the b³Π_u state. The band origins and line frequencies calculated from previously reported constants do not reproduce the observed values. The disagreement between the calculated and observed values is discussed. More accurate constants are needed to predict the line locations.     

Deperturbation of the N2+ first negative group B2Σu+-X2Σg+

Twelve bands of the N₂⁺B²Σ_u⁺-X²Σ_g⁺ system, including v_B = 0–6 and v_X = 0–8, are reanalyzed. All effects of B²Σ_u⁺ ～ A²Π_u perturbations are explicitly considered. Despite the use of high precision (0.01 cm^?1) line measurements, no evidence for a perturber other than A²Π_u is obtained. Deperturbed constants for the B²Σ_u⁺ and X²Σ_g⁺ states are derived. The deperturbation is shown to be self-consistent and complete (excluding effects of the C²Σ_u⁺ state) by examining semiempirical relationships of the perturbation matrix elements with the spin-rotation constants of the B and X states and atomic spin-orbit parameters. A number of previous analyses of transitions involving the v_B = 3 and 5 levels are found to be incorrect.     

Investigation of N 2 + (C 2Σ u + → X 2Σ g + fluorescence excited through auger decay of the 1s −1π* resonance

A theoretical investigation of N ₂ ⁺ (C ²Σ _u ⁺ → X ²Σ _g ⁺ molecular fluorescence excited through the Auger decay of the 1s ^?1π* resonance is carried out. The fluorescence cross sections are calculated with due regard for the dependence of the matrix element of the C → X dipole transition on the internuclear distance, the interference between channels of excitation via different vibrational levels v _r of the 1s ^?1π* resonance, the rotational structure of the fluorescence band, and the predissociation of the N ₂ ⁺ C ²Σ _u ⁺ v′ ≥3) states. The calculated cross sections are in good agreement with the experimental results of recent measurements. The results of the calculations have demonstrated that the observed dependence of the cross section of the (C ²Σ _u ⁺ (v′) → X ²Σ _g ⁺ (v″) fluorescence on the excitation energy and the fluorescence wavelength for a group of bands with equal values of the difference Δv = v′ ? v″ is associated with transitions between the vibrational levels of the electronic states involved in the excitation and subsequent cascade decay of the 1s ^?1π* resonance: N₂ (v ₀ = 0) → N*₂(1s ^?1π*(v _r)) ? N ₂ ⁺ : (C ²Σ _u ⁺ (v′) → X ²Σ _g ⁺ (v″).     

Relative intensities of the rotational lines of the (0, 0) and (0, 1) bands of the B2Σ+u-X2Σ+g systems of N+2

A high resolution grating spectrometer and a hollow-cathode lamp were used to study the relative intensities for lines of the transition B²Σ⁺_u→X²Σ⁺_g of the ion N⁺₂. Mulliken's formulae are obeyed with a precision of better than 2% for N^′?30, except for the first two lines, for which the relative intensities of the P lines are 2.5% greater than Mulliken's values and the relative intensities of the R lines 2.5% lower. The differences in the positions of the doublets for the first lines increase linearly (γ′?γ″=0.015±0.002cm^-1 with γ″≈0.010cm^-1) for N′?10. An interpretation of this difference gives an order of magnitude for the perturbation parameters of the state A²Π_u(v′=10)(ξ≈9cm^-1, η≈0.06cm^-1). The effect of this perturbation on the line intensities is negligible for N′?30.     

Rotational and vibrational temperatures of electronically excited BiN radicals in a chemiluminescent flame

Rotational and vibrational temperatures of electronically excited BiN radicals in a low-pressure Bi_x+N/N₂*/N₂+Ar chemiluminescent flame have been deduced from high-resolution Fourier-transform emission spectra. Bands of three electronic transitions, a³Σ⁺(a₁1)→X¹Σ⁺(X0⁺), b⁵Σ⁺(b₁0⁺)→X¹Σ⁺(X0⁺), and b⁵Σ⁺(b₁0⁺)→a ³Σ⁺(a₁1), were analysed to determine the optical temperatures in the a³Σ⁺(a₁1) and b⁵Σ⁺(b₁0⁺) states. The rotational temperatures characterising the rotational populations in the a₁1, v=0 and 1 states were determined from the a₁→X, 0-2, 0-3, 0-4, 1-1, and 1-2 bands. The b₁→X, 0-8 and 0-11 bands, and the b₁→a₁, 0-0 bands served to determine the rotational temperature of the radicals in the b₁0⁺, v=0 state. The temperatures derived from the various bands and transitions were well consistent and the mean rotational temperature was determined to be 353±18 K, which is close to the translational temperature of the gas.Vibrational temperatures of the radicals in the a₁1 and b₁0⁺ states were derived from band intensities of the a₁→X and from the b₁→X as well as b₁→a₁ systems, respectively. The Franck-Condon factors needed were calculated with RKR potentials deduced from literature values of the rotational and vibrational constants in the three states involved. The a₁1 vibrational temperature (336±21 K) was close to the rotational temperature, while the b₁0⁺ vibrational temperature (438±36 K) differed, likely due to the previously observed perturbation of the b₁0⁺ state.     

Accurate theoretical spectroscopic investigations of the 20 Λ-S and 58 Ω states of O2+ cation including the spin–orbit coupling effect

The potential energy curves (PECs) are calculated for the 20 Λ-S states (X²Π_g, A²Π_u, B²Σ^?_g, a⁴Π_u, b⁴Σ^?_g, b′⁴Π_g, c⁴Σ^?_u, 1²Σ⁺_g, 1²Σ⁺_u, 1²Σ^?_u, 1⁴Σ⁺_g, 1⁴Σ⁺_u, 1⁴Δ_g, 1⁴Δ_u, 1⁶Σ⁺_g, 1⁶Σ⁺_u, 1⁶Π_g, 1⁶Π_u, 2⁴Π_g and 2⁴Π_u) of O₂⁺ cation and their corresponding 58 Ω states. Of these 20 Λ-S states, the 1⁶Π_u state is found to be repulsive. The 1²Σ⁺_g, 1⁴Σ⁺_u, c⁴Σ^?_u and 1⁴Δ_u states are found to possess the double well. The b⁴Σ^?_g, 1⁶Σ⁺_g, 1⁴Σ⁺_u, a⁴Π_u, A²Π_u, 1⁶Π_g and 2⁴Π_g states are found to be inverted with the spin–orbit coupling effect included. The b′⁴Π_g, 1⁶Π_g, 1⁶Σ⁺_g, 1⁴Σ⁺_u and 1⁴Δ_u states, and the second well of the 1²Σ⁺_g state are found to be the weakly bound states. The b′⁴Π_g state is found to possess one well with one barrier. The PECs are calculated by the complete active space self-consistent field method, which is followed by the internally contracted multireference configuration interaction approach with the Davidson correction in combination with the aug-cc-pV6Z basis set. The core–valence correlation and scalar relativistic corrections are included. The convergent behaviour of present calculations is discussed with respect to the basis set and theoretical level. The spin–orbit coupling effect is accounted for. The PECs are extrapolated to the complete basis set limit. The spectroscopic parameters are evaluated, and compared with available measurements. It demonstrates that the spectroscopic parameters reported here can be expected to be reliably predicted ones.     

Polarization labelling spectroscopy of the A 1Σ+u band of Na2

A result of the polarization labelling spectroscopy of the A ¹Σ⁺_u band of sodium dimer for the high vibrational quantum number υ'>20 is reported. The frequency difference δv=v_obs-v_cal is found to decrease from 2 to -3 cm^-1 as the rotational levels (υ'=27?30), where v_cal is the calculated transition frequency using the Dunham coefficients of Demtröder and Stock for the X ¹Σ⁺_g band and of Kusch and Hessel for the A ¹Σ⁺_u band.     

Electronic structure of lanthanide dimers

Relativistic energy-consistent small-core lanthanide pseudopotentials of the Stuttgart-Bonn variety and extended valence basis sets have been used for the investigation of some selected lanthanide dimers with open 4f shell, that is Ce₂, Pr₂ and Gd₂. Comparison is made with results of corresponding previous studies of La₂ and Lu₂ as well as to available experimental data. The trends in the molecular constants of the dimers of the lanthanide series are discussed. The ground state candidates of Ce₂(4f¹4f¹σ² _gπ⁴ _u ¹Σ⁺ _g, ¹Σ^? _u, ³Σ^? _g, ³Σ⁺ _u, ¹6_g, ³6_u) and Pr₂(4f²4f²σ² _gπ⁴ _u ⁵Σ⁺ _g, ⁵Σ^? _u, ⁵10_g) are degenerate within 20cm^?1 and have the same valence subconfiguration σ² _g π⁴ _u, which was previously found to give rise to the La₂(4f⁰4f⁰σ² _gπ⁴ _u ¹Σ⁺ _g) ground state. In the case of Gd₂ the 4f⁷4f⁷σ² _gσ¹ _uσ² _u; ¹⁹Σ^? _g ground state found previously is confirmed. The derived molecular constants are the best theoretical estimates available at present and show a satisfactory agreement with experimental data. Discrepancies in the vibrational constants of La², Ce² and Pr² are shown to be probably related to quite large Ar-matrix shifts.     

4 Ag ↔2 Eg Transition of Mn4+ in Cs2TiF6: MnF6 2-

We report and interpret the ⁴ A_2g ?² E_g absorption, emission, linear dichroism, MCD and MCE of the MnF₆ ^2- octahedra at sites of D_3d symmetry in single crystals of Cs₂TiF₆. The spectra show many sharp features but a simplified calculation using cubic basis functions successfully accounts for all of the major features and much of the detailed structure. The electronic levels are not split by the trigonal field in first order but trigonal distortion splits the three-fold degenerate v ₆(t_2u ) vibration of the octahedron into a two-fold degenerate v ₆(e_u ) and a non-degenerate v ₆(a_1u ) vibration and these two vibrational modes give rise to the features 213 cm^-1 and 246 cm^-1 from the zero-phonon line respectively. Similarly the v ₄(t_1u ) vibration is split into a v ₄(a_2u ) and v ₄(e_u ) vibration and give the features at 313 cm^-1 and 340 cm^-1 respectively.

Several transitions involving two or more quanta of vibration are clearly seen in the emission and MCE spectrum. At an energy shift of greater than 700 cm^-1 from the zero-phonon transition these features are found to consist of progressions in the v ₁(a_1g ) breathing mode and the v ₂(e_g ) two-fold degenerate Jahn-Teller active mode. This structure can again be explained, with one exception, in terms of a calculation which assumes cubic basis functions. The exception is the reversal in sign of the MCE at a frequency v ₆(e_u ) + v ₂(e_g ) compared with that at v ₆(e_u ) which is not fully understood.     

Electron-vibrational energy exchange in collisions of electronically excited N2(A 3Σ u + ) molecules with Zn(X 1 S) atoms

The interaction matrix between the N₂ molecule in the X ¹Σ _g ⁺ and A ³Σ _u ⁺ states and the Zn atom in the ¹ S and ³ P states calculated earlier by the asymptotic method was used to find the rate constants for the electron-vibrational energy exchange N₂(A ³Σ _u ⁺ , v) + Zn(¹ S) → N₂(X ¹Σ ₈ ⁺ , v′) + Zn(³ P). The calculations were performed by the transition state method, and the probabilities of transitions between intersecting electron-vibrational terms of the system in motion along the reaction coordinate were determined by the Landau-Zener equation. The calculated electron excitation transfer constants between N₂(A ³Σ _u ⁺ , v = 1, 0) and Zn(¹ S) over the temperature range 300–900 K were on the order of 10^?11?10^?12 cm³/s.     

Observation of the c3Πu-X1Σg+ intersystem transition in the absorption spectrum of P2

The observation of the c³Π_u-X¹Σ_g⁺ intersystem transition of P₂ is reported. The 6-0 band of the system was identified on high resolution absorption plates teken on the NRC 10-m vacuum spectrograph at Ottawa. A rotational analysis of the band is given together with that of the adjacent 5-0 band of the C¹Σ_u⁺-X¹Σ_g⁺ system, the upper level of which is involved in a mutual perturbation with the c³Π_u, v = 6 level. The interaction parameters for the perturbation are derived. It is proposed that the appearance of the 6-0 band of the c³Π_u-X¹Σ_g⁺ transition is due to intensity borrowing from the strong, allowed C¹Σ_u⁺-X¹Σ_g⁺ system. Accurate values for the energies of the c³Π_u, b³Π_g, and a³Σ_u⁺ states relative to the ground state are given. The analysis of two other bands, 2-0 and 7-0, of the C¹Σ_u⁺-X¹Σ_g⁺ system whose upper levels likewise interact strongly with the c³Π_u state are also given.     

Electronic absorption spectrum of CO+ in an ion beam

The He+He⁺¹ interactions have been studied, as a function of the internuclear separation R, in terms of the electronic forces acting on the nuclei and the change in the charge distribution. The analysis reveals that at large R the atomic densities are polarized inwards, causing an attractive force on each nucleus, while at small R the difference in the nature of the interactions in the ²Σ_u and ²Σ_g systems is noted. It is seen that the He+He⁺¹ (²Σ_u) interaction is less attractive than the He⁺¹+He⁺¹ interaction at lower values of R.