Calculation of the vertical ionization potentials of HCNO,HNCO, HOCN,and HN3 by perturbation corrections to Koopmans'Theorem

Vertical ionization potentials (VIP's) have been calculated for HCNO, HNCO, HOCN, and HN₃, using Rayleigh—Schrödinger perturbation theory (RSPT) to determine corrections to Koopmans' Theorem. The calculated VIP's are used to resolve discordances between previous assignments of the PE spectra of HCNO, HNCO, and HN₃. Very little is known about HOCN. The present work contains predicted VIP's for this molecule, which it is hoped will aid in its identification in the laboratory. A diagram is presented correlating the VIP's of the isoelectronic series N₂O, HN₃, HOCN, HNCO, HCNO, and CO₂. It is shown that the variation in the magnitudes of the VIP's associated with the ionization of π electrons, and in the splittings induced in these VIP's by deviations from a linear geometry, can be accounted for qualitatively using a simple Hückel model.     

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.     

The Raman Spectrum and Full Vibrational Assignment of Ethylenediamne Dihydrochloride

A full vibrational analysis was recently made for the H³N⁺CH₂CH₂N⁺H₃ ion, on the basis of infrared measurements, and a partial vibrational assignment proposed¹. The observed fundamentals were interpreted In terms of a C_2h, symmetry for the ion. There are thirty-six fundamentals (r - lla_g + 8A_u + 7B_g + 10B_u; A_g and B_g Raman-active only; A_u and B_u infrared-active only). In addition to the eighteen infrared-active vibrations, a number of bands was observed which were assigned as formally forbidden Raman-active modes, excited by strong hydrogen bonding causing departure from the exact site symmetry of the species.     

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.     

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.     

Intensities of the laser-induced fluorescence of 130Te2 and electronic transition strengths for the AOu+-XOg+ and BOu+-XOg+ systems

The intensities of the laser-induced fluorescence spectra of ¹³⁰Te₂, excited by Ar⁺ and He-Cd⁺ lasers, are measured for the AO_u⁺-XO_g⁺ and BO_u⁺-XO_g⁺ systems. The RKR potentials of the A, B and X states are calculated. These potentials are used for calculating Franck-Condon factors and r-centroids with due respect to rotation. The relative r-centroid dependences of the electronic transition strength were obtained first and then normalized in lifetimes.     

Ab initio MRD-CI investigation of the electronic spectrum of glyoxal (CHO)2

Multireference configuration interaction (MRD-CI) calculations are used to compute the electronic spectrum of glyoxal (CHO)₂, a key species in atmospheric chemistry. The calculations place the first dipole-allowed transition 1¹A_u←X¹A_g at 2.80?eV (442.8?nm) with an oscillator strength of 0.0002 and the dipole forbidden 1¹B_g?←?X¹A_g transition at 4.22?eV (293.8?nm), in accordance with prior experiments. In addition, a much stronger transition (3¹B_u?←?X¹A_g) at 8.51?eV (145.7?nm) is predicted, which has not yet been reported in the literature. This transition corresponds to 1b_g?→?2a_u excitation and can be characterized as π(CO)?→?π?(CO) type in accordance with the computed relatively large oscillator strength f?=?0.38. The corresponding triplet states are also computed.     

Absorption and resonance Raman spectroscopy of the 1Bu state of trans‐1,3,5‐hexatriene including vibronic coupling

The vibronic coupling between the first excited S₁ (2¹A_g) and the second excited S₂ (1¹B_u) singlet electronic states in spectroscopy of trans‐1,3,5‐hexatriene molecule is investigated on the basis of a model consisting of two electronic states coupled by two vibrational modes. Employing a perturbation theory that treats the intramolecular couplings in a perturbative manner, the absorption and resonance Raman cross sections and excitation profiles of this molecule are calculated using the time‐correlation function formalism. The non‐Condon corrections are included in evaluation of cross sections. The multidimensional time‐domain integrals that arise in these calculations have been evaluated for the case in which S₀ (1¹A_g) S₂ (1¹B_u) electronic transition takes place between displaced and distorted harmonic potential energy surfaces. The calculated spectra are in good agreement with the experimental ones. Copyright © 2011 John Wiley & Sons, Ltd.     

High-resolution Fourier spectrometry of 14N2 and 15N2 infrared emission spectrum: Extensive analysis of the W3Δu - B3Πg system

The infrared spectrum of the nitrogen molecule, excited in a microwave discharge, has been recorded in high resolution by Fourier spectrometry in the range 2500–15 000 cm^?1. The precision of the measurements is estimated to be about 0.003 cm^?1. We have analyzed 19 bands of the W³Δ_u-B³Π_g system of ¹⁴N₂, with 0 ≤ v′ ≤ 7, and three bands of ¹⁵N₂ lying between 2500 and 5900 cm^?1. The molecular constants of the ³Δ_u and B³Π_g states have been determined by direct approach using an iterative nonlinear least-squares procedure. It has proved convenient to describe the levels of W³Δ_u state in a case a basis although in fact they approximate those of Hund's case b. Derived values of equilibrium constants of W³Δ_u are, in cm^?1: T_e = 8875.3347 (with origin taken in A, ³Σ_u⁺v = 0 level); ω_e = 1506.4859; ω_eχ_e = 12.5469; B_e = 1.4702537; α_B = 0.0170389; D_e = 0.55958 × 10^?5. RKR potential energy curves for the two states are constructed, and the Franck-Condon factors calculated for the W-B system.     

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.     

The ionization energies of bent and twisted double bonds. Part II. Tricyclo[4.2.2.22,5] Dodecadiene-1 (2),5 (6)

The electronic structure of the title compound (1) has been investigated using He(Iα) PE spectroscopy and assuming the validity of Koopmans' theorem. It is found that: (a) in analogy to the situation prevailing in the cyclophanes, hyperconjugation of the out-of-phase linear combination of the π-orbitals with the ethano-bridge σ orbitals is symmetry-forbidden; (b) in agreement with the ideas developed in Part I of this series [1], the strong local B_1u-type bending of the ethylene moieties does not affect their basis energy significantly; and (c) the “through-space” coupling of the two double-bond π orbitals is of the same order as the benzene π-orbital coupling in [2ⁿ] cyclophanes, even if the net contribution to the repulsion of the two double bonds is probably small. Because of the near degeneracy of the HOMO and HOMO — 1 of 1, the ground state of the radical cation 1⁺ cannot be determined uniquely: it is either²A_g or²B_1u.     

Electron scattering from trans 1,3-butadiene molecule: cross-sections, oscillator strength and VUV photoabsorption cross-sections

Electron energy-loss spectra for the butadiene molecule were measured in the scattering angular range of 2.0° to 8.0°, in an energy-loss range from 2 to 50 eV, using 1000 eV incident electrons. The absolute generalized oscillator strength (GOS) and inelastic cross section have been determined for the \hbox{$\tilde{\rm X}^{1}$}?X1A _g  → 1¹B _u transition. The absolute elastic differential cross section was also determined spanning an angular range from 2.0° to 40.0°. From a small angle electron energy-loss spectrum, the optical oscillator distribution (photoabsorption spectrum) for the butadiene molecule was obtained in the 2 to 100 eV photon energy range. Accurate ab initio calculations have been performed, within the First Born Approximation, for generalized oscillator strength (GOS) and excitation energies for the \hbox{$\tilde{\rm X}^{1}$}?X1A _g  → 1¹B _u and \hbox{$\tilde{\rm X}^{1}$}?X1A _g  → 2¹A _g transitions. Our results emphasize the importance of using highly correlated wavefunctions and accurate methodologies in the calculation of the GOS for electron impact-induced electronic transitions in molecules.     

Dipole moment functions for electronic transitions from ion-pair states of the second tier of molecular iodine

The emission spectra caused by the transitions from the ion-pair states and f0 _g ⁺ and G1_g of the I₂ molecule are obtained by excitation of individual rovibronic levels of the molecule by the method of optical-optical double resonance. The emission spectra from the state F0 _u ⁺ populated due to collisions I₂(f) + I₂(X) are also measured. By modeling the experimental emission spectra, the dipole moment functions for the electronic transitions f _g ⁺ -B0 _u ⁺ , A0 _u ⁺ , and B″0 _u ⁺ ; G1_g-A0 _u ⁺ and B″0 _u ⁺ ; and F0 _u ⁺ -X0 _g ⁺ and a′0 _g ⁺ of the iodine molecule are reconstructed.     

Predissociation linewidths and oscillator strengths for the (2-0) to (13-0) Schumann-Runge bands of O2

Analysis of the absorption spectrum of O₂ in the Schumann-Runge bands (B³Σ_u^?-X³Σ_g^?) from the 2-0 to the 13-0 band yields oscillator strengths which are in good agreement with past theoretical calculations. Predissociation linewidths deduced from the data tend to be larger than theoretical predictions for v′ ≤ 5 and are reasonably near theory for v′ > 5. The qualitative dependence of the linewidths on vibrational level is in accord with that expected for a repulsive potential intersecting the B³Σ state near v′ = 4. For a given band the predissociation linewidth deduced from the spectra tends to increase as the total angular momentum increases. The new linewidths are smaller than some past experimental results, and this will have an impact on future calculations of the photodissociation rates of O₂, NO, and H₂O in the earth's upper atmosphere.     

用能量自洽法研究碱金属双原子分子的势能曲线

用能量自洽法(ECM)研究了碱金属双原子分子一些电子激发态的势能曲线：Na₂ 分子的2¹Π_g,4³Π_g和b³Π< sub>u电子激发态,K₂分子的a³Σ^＋_{u,2¹Πg,B¹Πu和A^{关键词： 能量自洽 双原子分子 势能 碱金属}}     

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.     

Kinetic ion-acoustic solitary waves in collisional plasmas

In this study, a bipolar high-voltage pulse with 20 ns rising time is employed to generate diffuse dielectric barrier discharge plasma using wire-plate electrode configuration in nitrogen at atmospheric pressure. The gas temperature of the plasma is determined by comparing the experimental and the best fitted optical emission spectra of the second positive bands of N₂(C³Π_u → B³ Π_g, 0-2) and the first negative bands of N₂ ⁺ (B² Σ_u ⁺ → X² Σ_g ⁺, 0-0). The effects of the concentration of argon and oxygen on the emission intensities of N₂ (C³Π_u → B³Π_g, 0-0, 337.1 nm), OH?(A ²Σ → X²Π, 0-0) and N₂ ⁺ (B² Σ_u ⁺ → X² Σ_g ⁺, 0-0, 391.4 nm) are investigated. It is shown that the plasma gas temperature keeps almost constant with the pulse repetition rate and pulse peak voltage increasing. The emission intensities of N₂ (C³Π_u → B³Π_g, 0-0, 337.1 nm), OH(A²Σ → X²Π, 0-0) and N₂ ⁺ (B² Σ_u ⁺ → X² Σ_g ⁺, 0-0, 391.4 nm) rise with increasing the concentration of argon, but decrease with increasing the concentration of oxygen, and the influences of oxygen concentration on the emission intensities of N₂(C³Π_u → B³Π_g, 0-0, 337.1 nm) and OH (A²Σ → X²Π, 0-0) are more greater than that on the emission intensity of N₂ ⁺ (B² Σ_u ⁺ → X² Σ_g ⁺, 0-0, 391.4 nm).     

Raman and infrared reflection spectroscopy in black phosphorus

The symmetry and energies of all optically active phonon modes in black phosphorous are determined by polarized Raman scattering and infrared reflection spectroscopy at room temperature. The obtained energies are; 365 and 470 cm^-1 for A_g modes, 197 for B_lg, 442 for B_2g, 223 and 440 for B_3g, 136 (TO) and 138 (LO) for B_lu, and 468 (TO) and 470 (LO) for B_2u, respectively. The small TO-LO splitting is related to the charge transfer between phosphorus atoms induced by the atomic displacement.     

High-resolution Fourier spectrometry of 15N2 infrared emission spectrum: Extensive analysis of the B3Πg-A3Σu+ system

The emission spectrum of the B³Π_g-A³Σ_u⁺ system of the ¹⁵N₂ molecule was recorded between 3500 and 12 500 cm⁻¹ with a high-resolution Fourier spectrometer. Twelve bands with 0 < v′ < 5 and 0 < v″ < 9 are analyzed. The molecular parameters of the B³Π_g and A³Σ_u⁺ states are obtained by a complete fitting procedure. Derived values of equilibrium constants are deduced; the Franck-Condon factors are calculated for the B-A system of ¹⁵N₂.