Ab initio calculation of transition dipole moments for transitions between valence states in oxygen molecules

Results of ab initio calculations of potential-energy curves for 20 singlet and 20 triplet valence states of oxygen with configuration interaction taken into account in the 6-31G basis are presented. Transition dipole moments of triplet-triplet (1³Π_g ← B ³Σ _u ^? , 1³Π_g ← A ³Σ _u ⁺ , 1³Π_g ← A′ ³Δ_u, B ³Σ _u ^? ← X ³Σ _g ^? , 2³Π_u ← 1³Π _g, 2³Σ _g ^? ← B ³Σ _u ^? , 1³Π_u ← X ³Σ _g ^? , 2³Π_u ← X ³Σ _g ^? , 2³Π _g ← A′³Δ_u, 3³Π_g ← A′ ³Δ _u, 2³Δ_u ← 2³Π_g, 3³Π_g ← B ³Σ _u ^? , and 2³Π_g ← A ³Σ _u ⁺ ) and singlet-singlet (2¹Σ _g ⁺ ← 2¹Π_u, 2¹Π_u ← 1¹Π ^g, ¹Π_u ← 2¹Δ_g, 1¹Π_g ← c ¹Σ _u ^? , ¹Π_u ← b ¹Σ _g ⁺ , 1¹Δ _u ← a ¹Δ_g, 2¹Π_u ← a ¹Δ_g, 2¹Δ_g ← 1¹Δ_u, ¹Π _u ← a ¹Δ _g, 1¹Π_u ← b ¹Σ _g ⁺ , 2¹Π_g ← 1¹Π_u, 2¹Π _g ← c ¹Σ _u ^? , 1¹Δ _u ← 1¹Π _g, f′Σ _u ⁺ ← b ¹Σ _g ⁺ , 2¹Σ _g ⁺ ← f ′¹Σ _u ⁺ , 3¹Π_g ← 1¹Δ_u) radiative transitions are calculated as functions of internuclear separation. The possibility of observing these transitions under experimental conditions is discussed.     

Ab initio nonadiabatic calculation of the sensitivity coefficients for the X 1Σ g + → B 1Σ u + ; C 1Πu lines of H2 to the proton-to-electron mass ratio

Ab initio nonadiabatic calculations of the wavelengths λ_ij of the individual lines of the Lyman X ¹Σ _g ⁺ → B ¹Σ _u ⁺ and Werner X ¹Σ _g ⁺ → C ¹Π_u series of molecular hydrogen and corresponding sensitivity coefficients K _ij = dlnλ_ij/dlnγ have been performed. These quantities are necessary for testing a possible change in the proton-to-electron mass ratio γ = m _p/m _e in the process of cosmological evolution. The basic contribution to K _ij comes from the difference between the average kinetic energies of vibrations of combined states. Nonadiabatic interactions are important for a small number of locally-perturbed rovibrational levels of the B ¹Σ _u ⁺ and C ¹Π _u ⁺ states, for which change in K _ij that is caused by nonadiabatic effects reaches 14%, which can lead to a significant systematic shift in the estimate of the parameter γ.     

Calculation of molecular constants for the X 1Σ g + , A 1Σ u + , B 1Πu, and a 3Σ u + electronic states of 39K2

The molecular constants are calculated for the X ¹Σ _g ⁺ , A ¹Σ _u ⁺ , B ¹Π_u, and a ³Σ _u ⁺ and electronic states of a potassium dimer. The wave functions and vibrational energies necessary for calculating the molecular constants are determined by solving the radial wave equation with the use of potential energy curves constructed by the semiempirical method. The vibrational terms, the rotational constants, and the centrifugal distortion constants calculated from the potential curves are compared with those determined from the experimental data.     

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″).     

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)r ³Π _g ^? , (4d)s ³Δ _g ^? → (2p) c ³Π _u ^± 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 4d ³Π_g and 4d ³Δ_g states are in agreement with the experimental data. The optimal energies of rovibronic levels of the r ³Π _g ^? , s ³Δ _g ^? , c ³Π _u ^? , and c ³Π _u ⁺ states have been found and reidentification of 11 from 54 spectral lines, assigned previously to the (0-0) and (1-1) bands, was performed.     

On the non-BoltzmannA-X emission in Na2 following laser excitation of theB state

A ¹Σ _u ⁺ -X ¹Σ _g ⁺ emission in Na₂ is observed following excitation ofB ¹π _u by various lines of an argon ion laser. The excitation energy ofB ¹π _u is collisionally transferred to the (2)¹Σ _g ⁺ which then radiatively populates theA ¹Σ _u ⁺ state. The Na vapour is contained in a stainless steel crossed heat pipe with Ar buffer gas and temperature around 600°C. For all laser lines except 4579 Å, the coarse features ofA-X emission are independent of the laser wavelength. However, at high resolution the finer differences between different laser line excitation are explained. Variousv′-v″ transitions in this emission are identified. Computer simulation is presented to help explain some features of this emission.     

Interaction of Zn atoms in the 1 S and 3 P states with N2 molecules in the X 1Σ g + and A 3Σ u + states at moderate distances between the atom and molecule

An asymptotic method was used to derive analytical expressions for the matrix elements of interaction between the N₂ molecule in the X ¹Σ _g ⁺ and A ³Σ _u ⁺ electronic states and the Zn atom in the ¹ S and ³ P states. Quadrupole-quadrupole, dispersion, and exchange interactions were taken into consideration. The character of the set of diabatic vibronic potential energy surfaces of the system suggests that the energy transfer in the process N₂(A ³Σ _u ⁺ ) + Zn(¹ S) → N₂(X ¹Σ _g ⁺ ) + Zn(³ P) may prove to be rather effective.     

Chemiluminescence of bromine vapor under pulsed lamp pumping

The chemiluminescence kinetics and spectrum of gaseous Br₂ under the conditions of broadband optical pumping have been investigated. It has been found that the transition A ³Π_1u → X ¹Σ _g ⁺ is the major contributor to the luminescence spectrum.     

Optical characteristics of radiation from N<Stack><Subscript>2</Subscript><Superscript>*</Superscript></Stack> dimers in a barrier discharge

The spectral and power characteristics of radiation of the second positive system of nitrogen (C ³Π _u → B ³Π _g ) in Ar-N₂ and Ar-N₂-Cl₂ mixtures excited by barrier discharge have been studied experimentally. Addition of argon to N₂ increased the radiation power by sixfold. In the triple mixture Ar-N₂-Cl₂ = 210/0.5/0.005, minor chlorine additions increased the intensity of the C ³Π _u → _B ³Π _g transition by 26% compared to Ar-N₂ mixtures. Radiation power density of 2.7 mW/cm² has been achieved. In both binary and triple mixtures, the second positive system of nitrogen was the major contributor to radiation, while the contributions of the fourth positive system of N ₂ ^* (D ³Σ _u ⁺ → B ³Π _g ), the Vegard-Kaplan transition of N ₂ ^* (A ³Σ _u ⁺ → X ¹Σ _g ⁺ ), and the D′ → A′ band of Cl ₂ ^* were negligibly small.     

Absorption spectrum of C2 molecules near 1.06 μm

An intracavity laser spectrometer has been used to study the laser-spark absorption spectrum of C₂ radicals near 1.06 μm. The spectra recorded have been assigned, and the rotational lines of the transitions 3-0, 4-1, and 5-2 b ³Σ _g ^? -a ³Π _u and 2-1 and 1-0 A ¹Π _u -X ¹Σ _g ⁺ have been identified. The vibrational and rotational temperatures have been determined.     

Quantum mechanical calculation of rotational constants and Franck-Condon factors of diatomic molecules

In this paper, the question of reliability of the Morse potential as a potential curve for a diatomic molecule is investigated on the basis of calculating the rotational constant. It is shown that the Morse potential describes well potential curves of X¹Σ _q ⁺ and B¹Π_u electronic states of a Na₂ molecule. Calculations of Franck-Condon factors for X¹Σ _q ⁺ ? B¹Π_u band of a Na₂ molecule using wave functions of the Morse potential confirm the known correlation between the values of Franck-Condon factors and rotational constants of combined electronic states.     

Absolute population of the A 3 Σ u + metastable state of a nitrogen molecule in a glow discharge plasma

The absolute populations of seven vibrational levels of the B ³Π_g state of a nitrogen molecule in a negative glow are determined at a pressure of 0.01–5.00 Torr and a current of 100–400 mA from the absolute intensity of the lines of the nitrogen first positive system. The population of the A ³Σ _u ⁺ metastable state at different discharge parameters is found using the balance equation for this state.     

Comparative study of the semiempirical three-parameter potential energy functions for diatomic molecules

A comparative study is made of four three-parameter semiempirical potential energy functions for 32 electronic states of diatomic molecules and their ions:n ₂:X¹gS _g ⁺ ,B ³π_g,A ³ gS_u,C ³ _u,B′ ³ gS_u.a ¹ π_g, a′gS _u ^? ,Ω ¹δ_u N ₂ ⁺ :X ² gS _g ^gS +A ² π,C ² gS _u ⁺ ,B ² gS _u ⁺ CO:X¹gS⁺,a ³ π, a′³ gS_u,e ³ gS^?,d ³gD₁,A ¹π CO⁺:X²gS⁺,A ² π,B ²gS⁺ O₂:X³gS _g ^? ,B ³ gS_u,c ¹ gS _u ^? ,b ¹gS _g ^s ,a ¹ δ_g,c ³ δ_u O ₂ ⁺ :X ²π_g,A ² π_g, a¹ π_g,b ⁴ gS _g ^? A program for numerically integrating the radial Schrödinger equation by the Cooley method is worked out. Certain additional units are introduced to conserve computer time. The resulting vibrational levels are compared with the experimental levels for all the electronic states studied. It is concluded on the basis of this analysis that it is not possible to describe equally well all the electronic states of various molecules on the basis of any single three-parameter potential function. A method for choosing a potential function for describing some particular electronic state of a diatomic molecule is proposed.     

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.     

Study of the absorption characteristics of molecular oxygen in the Schumann-Runge system at high temperatures: II. Experiment and comparison with calculation

Absorption cross sections of oxygen molecules in the UV spectral range are experimentally determined in the temperature range 1600–6000 K. The absorption cross sections are measured in oxygen or in its mixtures with argon behind the shock wave front. Measurements are performed for the spectral range 190–270 nm, which pertains to the electronic transition X ³Σ _g ^? → B ³Σ _u ^? of the Schumann-Runge system. The absorption cross sections are also measured at temperatures 291 and 3300 K in the range 160–185 nm. The measured absorption cross sections are compared with the calculated spectra of the O₂ molecule.     

Atomic and molecular fluorescence with long radiative decay times from laser excited Na2

Na₂ is excited (B¹Π_u←X¹Σ _g ⁺ ) in the presence of noble gases (20–700 Torr). The Na₂ fluorescence decay shows two lifetimes: a short component which corresponds to the well known lifetime of Na₂ in the B¹Π_u state [1], and a long component with a lifetime of about 0,1 μs which depends strongly on the noble gas density [2]. The same long lived radiative decay is also seen via the Na resonance fluorescence Na(3²S)←Na(3²P).     

Electronic branching ratios of spontaneous emission for transitions between states of the 3d and 2p singlet complexes of terms of H2

The ratios of probabilities (the electronic branching ratios) for the rovibronic spontaneous transitions are for the first time measured for transitions from the rotational levels with J′≤6 of the I ¹Π _g ^? , v′=0–2 and J ¹Δ _g ^? , v′=0 states to the vibrational-rotational levels of different low-lying electronic states B ¹Σ _u ⁺ , v″, J′ and C ¹Π _u ^? , v?, J′?1 of the H₂ molecule (for the vibrational quantum numbers v″≤4 and v?≤2). Values of these quantities provide a new channel of information on the internal structure of the hydrogen molecule thus far unused and should be particularly sensitive to the adiabatic values of the electronic transition dipole moments. In studying the entire set of rovibronic radiative transitions, they may significantly add to the experimental data on rovibronic terms, radiative lifetimes, and vibrational and rotational branching ratios used before. The experimental data obtained are compared to the corresponding values derived from the results of an earlier semiempirical determination and ab initio calculation of the absolute transition probabilities. Our experimental data are in remarkable agreement with the semiempirical results and significantly differ from the ab initio results. This fact directly suggests the necessity of performing more accurate ab initio calculations of the rovibronic transition probabilities for the given systems of bands.     

Emission und Schwingungsverteilung der 1. neg. Gruppe und der 2. pos. Gruppe in einem Stickstoffplasma

The intensity of the first negative system ofN ₂ ⁺ (B ² Σ _u ⁺ -X ² Σ _g ⁺ and of the second positive system ofN ₂(C ³ Π _u -B ³ Π _g ) was observed in the discharge and in the afterglow as function of discharge current. An a. c. discharge in pure nitrogen was used at pressures of about 5 torr. The intensity of the first negative system ofN ₂ ⁺ — in the discharge and in the afterglow — rises to a maximum and decreases with further increase of the discharge current. The afterglow intensity of the second positive system ofN ₂ shows a maximum too. In the discharge, however, the intensity of the second positive system ofN ₂ increases with increasing discharge current. The relative population of the vibrational levelsN _v′ =i/N _v′ =0 (i=1,2,3,4) of theB ² Σ _u ⁺ state ofN ₂ ⁺ , in the discharge and in the afterglow, increases with increasing discharge current, while the relative population of the vibrational levelsN _v′ =i/N _v′ =0 (i=1, 2, 3, 4) of theC ³ Π _u state ofN ₂ reaches a maximum in the discharge. There seems to be evidence that the first negative system ofN ₂ ⁺ is not excited by electron impact withN ₂ molecules in ground state under the discharge conditions in question.     

Time spectroscopy in theA 1 ∑ u + state of Li2. Perturbations by thea 3Π u state

We have employed time-resolved LIF spectroscopy in order to investigate perturbations in theA ¹ ∑ _u ⁺ state of the three isotopic Li₂ molecules. After a systematic check of more than 2000 individual rotation-vibration levels, 46 levels were found whose anomalous lifetimes can be interpreted by perturbations with thea ³ Π _u state. As almost all perturbed levels possess shortened lifetimes the predissociating nature of thea ³ Π _u state, caused by interaction with thex ³ ∑ _u ⁺ continuum, is revealed. On the basis of the Kovács-Budo theory of accidental predissociation we have fitted the molecular constants of thea ³ Π _u state, thex ³ ∑ _u ⁺ potential curve and the electronic parts of the perturbation matrix elements do that the observed lifetimes of all levels in the 78 investigatedA ¹ ∑ _u ⁺ ?a³ Π _u term-crossing regions can be understood.