2Σ States Research Articles

Far Infrared Spectrum of SO in the 3Σ and 1Δ Electronic States

Far Infrared Spectrum of SO in the 3Σ and 1Δ Electronic States

Separation of quadratic and linear external field effects in high J quantum beats

We discuss quantum beats in electronically excited molecular states with high rotational angular momenta J appearing in time resolved fluorescence in conditions of quadratic and linear energy shift dependence on magnetic quantum number M and external field strength. Density matrix formalism is used to obtain in explicit form the expressions for time dependent fluorescence intensity after δ-function pulsed excitation. In case of pure quadratic Stark effect, which is typical for 1Σ state diatomics, excited state quantum beats for J≫1 exhibit a regular, or ‘‘grill’’ structure, consisting of narrow equidistant ‘‘principal’’ peaks with equal relative amplitudes on the exponential decay background. At linear polarized excitation the time intervals between the adjacent peaks are 2π/ω20, ω20 being the splitting frequency between coherently excited M-sublevels with M=2 and M′=0. If an admixture of linear contribution is present in field induced level shifts, the grill structure is superimposed by a single frequency harmonic modulation. A special geometry was found in which the quadratic beats are fully absent and the modulated grill pattern is brought into existence only by the influence of linear term. Such a case takes place when the light polarization vector in fluorescence is directed at 45° angle with respect to the exciting light polarization vector and yields the most sensitive way to separate quadratic and linear contribution. We considered the examples when the first order term appears by a combined action of electric and magnetic field, as well as due to the e–f level electric field induced mixing, with the parameters typical for the NaK molecule.

An Energy Level Diagram of the Known Electronic States of NiF Determined by Radiative and Collisional Transfers

A study Of collisional and radiative energy transfers between the electronic states of NiF has made possible the determination of the relative positions of most of the electronic states involved in the already rotationally analyzed bands. The presence of three lower 2Π, 2Δ, and 2Σ states is now precisely determined. This experimental work is in good agreement with a recent theoretical study (P. Carette, C. Dufour, and B. Pinchemel, J. Mol. Spectrosc. 161, 323, 1993).

Electronic and geometric structure of the diatomics ScN, ScP and ScAs

The ground and low-lying excited states of ScN, ScP and ScAs have been studied at the MCSCF and MCSCF + 1 + 2 level. They all have a triply bonded 1Σ + ground state and several low-lying boubly bonded states of 3Σ +, 1Π and 3Π symmetry. The calculated bond energies (relative to the ground state atoms) and bond lengths of the 1Σ + states are ScN (2.72 eV, 1.768 Å) ScP (1.54 eV, 2.277 Å) and ScAs (1.36 eV, 2.389 Å). Our calculated bond length for ScN is in reasonable agreement with the experimental result (1.695 Å) of Ram and Bernath. The 3Σ + state which has two π bonds and no σ bond is 0.33 eV above the 1Σ + in ScN and 0.80 and 0.87 eV in ScP and ScAs.

Ab initio MO studies on dissociative electron attachment of vinyl chloride. The simplest chlorine-containing hydrocarbon having a CC π system

The potential energy surface of the vinyl chloride radical anion, which is the simplest chlorine-containing hydrocarbon anion having a CC π system, has been studied by ab initio molecular orbital theory. The calculated results indicate that the initial 2Π state is rapidly changed to the repulsive 2Σ state by a CCl out-of-plane deformation during CCl dissociation. While no metastable 2Π state is found on the potential energy surface, the same kind of planar metastable weak complex is found on the minimum energy path as in the case of the methyl chloride radical anion. The differences and similarities between the CCl dissociation minimum energy paths of the vinyl chloride and methyl chloride radical anions are also discussed.

Rotational Spectroscopy of the CoH Radical in Its Ground 3Φ State by Far-Infrared Laser Magnetic Resonance: Determination of Molecular Parameters

Five rotational transitions of CoH in its ground 3Φ state have been detected by far-infrared laser magnetic resonance, three in the lowest Ω = 4 component and two in the Ω = 3 component. All the Zeeman transitions show an octet hyperfine pattern due to the 59Co nucleus ( I = 7/2). The much smaller proton doubling was also resolved for most transitions. The data have been fitted to experimental accuracy by an effective Hamiltonian for a molecule in an isolated 3Φ state. The electron orbital and spin g factors determined by the data confirm conclusively that the ground state of CoH is a 3Φ state. The accurate measurement of the rotational constant allows the equilibrium bond length to be determined: r e = 0.15138435(80) nm. A small Λ-type doubling was resolved in the 3Φ 3 component, suggesting the proximity of a 3Σ state among the low-lying electronic states. The cobalt hyperfine splittings have been fitted to determine magnetic dipole and electric quadrupole parameters, which are interpreted in terms of the dominant configuration description for the 3Φ ground state.

Collision-induced dissociation of oriented CO + ions. Probing potential energy curves by ion collision spectrometry

Translational energy spectra of C + and O + fragments produced in the collision-induced dissociation of ground state CO + ions have yielded kinetic energy release distribution functions. These are compared with theoretical simulations that have been carried out by reflecting the probability distribution of the zeroth vibrational state of the 2Σ state onto various low-lying excited state potential energy curves of the CO + molecular ion which have been computed using contemporary ab initio molecular orbital techniques.

Laser spectroscopy of the A 2Π-X 2Σ system of TiN

Five bandhead positions of the A 2Π- X 2Σ system of TiN between 6146 and 6236 Å have been studied using resolved laser induced fluorescence spectroscopy. Δ V=0 and ±1 transitions have been observed. The ground-state vibrational frequency has been measured to be 1039.8 cm -1, which is in excellent agreement with values obtained by Douglas and Veillette previously. The molecular constants obtained have been used to construct the potential energy curves for the A 2Π and X 2Σ states from which the Franck-Condon factors were also calculated.

The molecular parameters of the antimony monodeuteride radical from diode laser spectroscopy

Extensive measurements of the 3Σ ground state infrared spectrum of the antimony monodeuteride radical (SbD) have been carried out using a diode laser spectrometer. Transitions of the fundamental band of all three components of two isotopomers of SbD were measured with a nominal accuracy of ±0.001 cm−1. Only transitions of the O+ component of the v=1←2 hotband were intense enough to be observed. The entire data set was fitted as a single 3Σ state and accurate molecular parameters determined. The LMR data of Stackmann et al. [Mol. Phys. (in press)] on SbH provided invaluable aid with the assignment. Measurements were also carried out on two isotopomers of SbH in order to improve the molecular parameters available for these species.

Optical excitation of the b 4Σ − -X Π transition in NO

The NO(b 4Σ −) state, in v=2−5, has been excited from the X 2Π ground state by optical pumping, and detected by b 4Σ −-a 4Π Ogawa band emission. Line positions have been measured to ±0.5 cm −1, utilizing the fact that these excitation spectra simultaneously show the b-X bands and the doublet bands that are found in the 187–205 nm tuning range used in the experiments. As a result, the relative positions of the NO quartet and doublet manifolds can be specified to a precision considerably improved over the previous estimate of ±2 cm −1. Predissociation in b( v=5) is evident in each rotational branch commencing at J=16.5, and appears to be much stronger than in the nearby B 2Π v=7 level. From the observed branch intensities, it is shown that the transition receives its oscillator strength through spin-orbit interaction between the b 4Σ − state and various 2Σ, 2Π, and 2Δ states. An estimate of the relative oscillator strengths for the forbidden b-X and allowed B-X transitions indicates that B-X is favored by about three orders of magnitude. As most of the NO (b) radiates to the NO(a) state, this study provides a means of directly populating the low- v levels, principally v=1, 2, of NO(a). There is strong collisional coupling between the doublet and the b 4Σ − states, as shown by the fact that excitation spectra of the NO A 2Σ +, B 2Π, and D 2Σ + states can be measured from detection of the Ogawa bands. A search was carried out for emission resulting from excitation of the b( v=6) level, the first lying above the dissociation limit. No such emission was seen, suggesting that rapid predissociation occurs through the a 4Π continuum; earlier reports of emission from b( v=6) are shown, based on spectral simulation, to be in error. Generation of the NO(E 2Σ +) state was observed concomitantly with NO(D) excitation, which must involve an energy pooling mechanism.

Electron propagator calculations on the adiabatic electron binding energies of C3

New techniques of electron propagator theory (EPT) are applied to C3, C3+, and C3−. Gradients of second-order EPT ionization energies and electron affinities are combined with gradients of second-order many-body perturbation theory for the neutral to produce gradients of the ion total energies. Optimized geometries of the ions, vibrational frequencies, and adiabatic electron binding energies are calculated with these methods. A renormalized self-energy is used to produce improved vertical and adiabatic ionization energies and electron affinities. For the cation, the 2B2 state with C2v symmetry and the 2Σ state with C∞v symmetry are very close in energy. The optimized 2Σu structure is a transition state with an imaginary frequency of σu symmetry that lies 2.8 kcal/mol above the 2B2 state. The adiabatic ionization energy is calculated to be 11.9 eV. The anion in the 2Πg state lies 1.8 eV below the neutral in these calculations.

Ab initio effective Hamiltonian calculations on the valence states of SH and SH +

The second-order ab initio effective valence shell Hamiltonian of quasi-degenerate many-body perturbation theory has been used to determine the valence state potential energy curves of SH and SH +. The calculated spectroscopic constants of various valence states are in good agreement with those of experiments or configuration interaction calculations. The experimentally known B 2Σ state has been closely examined. And it is confirmed that the B 2Σ state be the Rydberg 2Σ − state as suggested by Hirst and Guest. This conclusion is readily drawn from the unique nature of the effective valence shell Hamiltonian, which can simultaneously determine the valence states of a molecule and its ions.

Relativistic calculations on platinum hydride using effective core potentials and first-order perturbation theory

A b initio relativistic calculations have been performed for the two lowest electronic states of the PtH molecule, with relativistic effects accounted for by means of relativistic core potentials and first-order perturbation theory. Electron correlation has been treated at the multireference configuration interaction level. The 2Σ and 2Δ states are close in energy, with the Σ state somewhat lower, according to the core potential calculations. It is concluded that a method which gives a correct atomic description is imperative to describe the spectroscopy of the molecule.

Diatomic Molecule as a Deformable Body

On the basis of the deformable body model and harmonic potential approximation, a nonlinear Hamiltonian describing rovibrational states of diatomic molecules has been derived. The proposed approach is extended to include the Simons—Parr-Finlan potential, and the obtained equations are applied in evaluation of molecular constants and in reproduction of rovibrational spectra of the 1Σ state of 12 C 32 S, 13C160 and rotational spectra of 12C160 molecules. A comparison with the standard Dunham results is also made. PACS numbers: 33.10.Cs, 33.10.Jz

MCSCF determination of the KO molecule ground state.: CAS and basis set dependence

Ab initio calculations at the MC/CASSCF level are used to determine in an accurate way the nature and position of the ground state of the KO molecule. The characteristic 2Π and 2Σ + alkali monoxide ionic states show a theoretical energy separation of about 0.04 eV, which produces opposite results by authors in favour of one or the other symmetry. We test the basis set dependence and active space dependence of the calculated energetical ordering of both states, with an extensive study of the active orbitais selection; the results show a ground state of 2Σ + symmetry.

Resonance-enhanced multiphoton ionisation spectroscopy of the NH (ND) radical. Part 2.—Singlet members of the 3p Rydberg complex

We report new, or improved, spectroscopic data for three singlet excited electronic states, the f1Π, g1Δ and h1Σ states of the imidogen radical (NH and ND). Each of these states is observed via the two-photon resonance enhancements they provide in the multiphoton ionisation spectrum of a 1Δ state NH (ND) radicals. All three states are assigned as members of the Rydberg 3p complex, with leading configuration … 3σ21π13pλ1. The available evidence points to the h 1Σ state having + parity, but this cannot be confirmed in the present study. The separation of the f 1Π and g 1Δ origins is comparable to the energy of one quantum of N—D stretching vibration; as a result, transitions to vibrationally excited (v′>0) levels of the f 1Π state of ND are seen to gain intensity from, and to be perturbed by, the near-resonant g 1Δ levels with quantum number v′–1.

Theoretical study of HCl+ : Potential curves, radiative lifetimes, and photodissociation cross sections

Configuration interaction wave functions and potential energy curves have been calculated for the four lowest states of 2Π and 2Σ+ symmetry and the lowest state of 4Σ−, 2Σ−, 2Δ, and 4Π symmetry for the molecular ion HCl+. Dipole moment functions of the X 2Π and A 2Σ+ states are presented as well as dipole moments for transitions from the X state to dipole-allowed excited states. The electronic wave functions were constructed to give a balanced description of Rydberg–valence interactions. The computed radiative lifetime of the X 2Π(v=1) is found to be in good agreement with previous theoretical and experimental values. Oscillator strengths, transition probabilities, and radiative lifetimes are calculated for the A 2Σ+–X 2Π transition for vibrational levels v′≤6 and compared to previous theoretical and experimental results. Vibrational levels v′≥7 of the A 2Σ+ state are predissociated by the 4Π, 4Σ−, and 2Σ− states. Theoretical photodissociation cross sections are calculated showing that photodissociation occurs primarily through absorption into the (3) 2Π and (3) 2Σ+ states in the wavelength region λ<100 nm and also the 2Σ−, 2Δ, and (2) 2Π states for wavelengths λ>100 nm.

The spectrum of NiF: Identification of the three lower 2Δ, 2Σ, and 2Π states

Revisiting the experimental spectra of three transitions of NiF already analyzed ( J. Mol. Spectrosc. 77, 29 (1979); J. Phys. B 14 2569 (1981)) we show that two transition 2Π 3 2 - 2Δ 5 2 (22 125 cm −1) and 2Π 3 2 - 2Σ (21 381 cm −1) share a common upper electronic level as observed by Bai and Hilborn ( Chem. Phys. Lett. 128, 133 (1986)). The third transition lying at 21 275 cm −1 is a 2Δ 3 2 - 2Π 1 2 or a 2Π 1 2 - 2Δ 3 2 transition. Our analysis shows that the Λ-doubling responsible for the fine structure arises from the lower state. A fourth transition (21 931 cm −1) is partially analyzed as a 2Π 1 2 - 2Σ transition. Three different lower electronic states ( 2Δ, 2Σ, 2Π) can be supposed to arise from the 3 d 9 lower orbital of Ni + as expected in a strongly ionic molecule. Two of them are identified ( 2Δ and 2Σ). The 2Π state can be the lower state of the 21 275 cm −1 transition or possibly an unobserved state strongly mixed with the 2 Δ 3 2 lower level in which it induces a large fine structure under the hypothesis that the 21 275 cm −1 band is that of a 2Π 1 2 - 2Δ 3 2 transition.

A simple predictive model of chemical potentials: H2(1Σg) and Li2(1Σg)

A simple model for van der Waals potentials presented earlier [J. Chem. Phys. 80, 3726 (1984)] has been extended to describe chemical bonds by including the exchange-dispersion term of Herring and Flicker. For H2, the 1Σ ground state potential is predicted in excellent agreement with the accurately known ab initio potential, the well depth being reproduced to within 0.6%. New two configuration self-consistent-field (SCF) calculations for the 1Σ and the 3Σ states of Li2 have made it possible to test the model for this system as well. Here the discrepancy is only 3% in the well depth for the 1Σ Li2 potential.

Rotational analysis of the nonthermal NO(A 2Σ+, v′=0) distribution observed in the N2(A 3Σ+u, v′=0)+NO(X 2Π, v″=0) energy transfer reaction

A rapidly pumped discharge-flow reactor was constructed to characterize the N2(A 3Σ+u,v′)+NO(X 2Π, v″=0) energy transfer (ET) reaction. Emission spectra of the NO γ bands from the product NO A 2Σ state formed in the title reaction were collected with a 2.2 m vacuum-ultraviolet spectrograph monochromator utilizing both photographic and photoelectric techniques. The rotational structure of the γ bands resulting from the title reaction is resolved with a spectral resolution of Δλ∼0.1 Å. The product NO(A,v′) emission spectra were measured as a function of total pressure (∼0.8≤pTOTAL≤∼3.0 Torr) and initial N2(A,v′) population distribution at 298 K. The product NO(A,v′,N′) rotational distributions yield temperatures much higher than room temperature (>1600 K) and are discussed in detail. Vibrational level specific bimolecular rate constants kv′ ’s for the N2(A,4≤v′≤6)+NO reaction were measured using N2(B 3Πg–A 3Σ+u) laser-excited fluorescence detection with a fixed reaction time. The kv′ ’s are (9.5±1.0), (11.3±1.2), and (11.2±1.1)×10−11 cm3 molecule−1 s−1 for v′=4, 5, and 6, respectively. A comparison with previous measurements is presented.