3Πg State Research Articles

High resolution absorption spectrum of jet-cooled CS2 between 65 000 and 71 000 cm−1: Assignment of bent …5σu3πu and linear …2πg3 3d and 5s gerade states

The absorption spectrum of jet-cooled CS2 was photographed between 65 000 and 71 000 cm−1 at a resolution limit of 0.0008 nm. In the first half of the energy interval considered, a bending vibrational progression is assigned corresponding to the transition between the linear ground state and a bent excited state …6b29a11B2 correlating with the …5σu3πu1Πg state of the linear molecule. The same progression is observed in the (3+1) resonance enhanced ionization (REMPI) spectrum of Baker and Couris [J. Chem. Phys. 103, 4847 (1995); 104, 6130 (1996); 105, 62 (1996)]. Another observed bending progression in the [(1+1)+1] REMPI spectrum for the same region is here assigned to the other, less bent state …6b23b11A2 issuing from the …5σu3πu1Πg linear state. In both progressions, Δv1=1 transitions are also observed. In the upper half of the energy range considered, the absorption spectrum consists essentially of 210, 201, and 203 bands associated with excitation of …2πg3 3d and 5s Πg1 states. The corresponding origin bands, as well as those of all the other two-photon allowed transitions related to the same configurations, are assigned to bands observed in the [(1+1)+1] REMPI spectra. The rotational band profile associated with two-photon one-color excitation of the 3d, 5s supercomplex of CS2, is calculated using a program based on Hund’s case (e) representation. The band positions and relative intensities in the simulated contour are in excellent agreement with those assigned to origin transitions in the two-color parallel polarized REMPI spectrum. All other bands of the experimental two-photon spectrum can be assigned as the 101 bands associated with the observed 3d electronic origins. The quantum defect values used in the final band contour calculation are consistent with those obtained in an ab initio calculation. A calculation of the same type is performed for the excitation energy from 2πu and 5σu orbitals to 7σg (4sσg) and from 6σg to the valence 3πu orbital. These transitions were suggested by several authors as possible assignments in this spectral region but are indeed at much higher energy. The 4p 3Σu− and 5p 1Σu+←X̃ 1Σg+ transition bands near, respectively, the lower and higher limits of the interval studied here, are also assigned.

Erratum: Hyperfine structures of the Li27, b 3Πu, 2 3Πg, and 3 3Πg states: Continuous wave perturbation facilitated optical–optical double resonance spectroscopy [J. Chem. Phys. 105, 6192 (1996)

Erratum: Hyperfine structures of the Li27, b 3Πu, 2 3Πg, and 3 3Πg states: Continuous wave perturbation facilitated optical–optical double resonance spectroscopy [J. Chem. Phys. <b>105</b>, 6192 (1996)

Long-range interaction of the 39K(4s)+39K(4p) asymptote by photoassociative spectroscopy. I. The g− pure long-range state and the long-range potential constants

This paper reports on a comprehensive study of the long-range interaction of the K39(4s)+39K(4p) asymptotic system. We present a detailed discussion of the R-dependent angular momentum couplings and correlation between the Hund’s case (a) and case (c) molecular states. Analytical expressions for the 16 adiabatic Hund’s case (c) long-range potential curves are derived including the higher order dispersion forces and the effects of retardation. Experimentally, six Hund’s case (c) long-range molecular states (0u+, 1g, and 0g− dissociating to the 4 2S1/2+4 2P3/2 asymptote and 0u+, 1g, and 0g− to the 4 2S1/2+4 2P1/2 limit) are observed with rovibrational resolution by photoassociative spectroscopy of ultracold K39 atoms in a high density magneto-optical trap (MOT). Among the six observed long-range states, the upper 0g− “pure long-range” state has negligible short-range chemical exchange contributions and the measured molecular binding energies (v=0–26) are used to precisely determine the long-range potential constants of the 4s+4p interaction. We determine: C3Π=8.436(14) a.u., C3Σ=16.872(28) a.u., C6Π=6272(94) a.u., and C6Σ=9365(141) a.u.. Molecular constants for the three special pure long-range states, the 0g− and 1u (dissociating to the 4 2P3/2 limit and with potential minimum) and the 1u (dissociating to the 4 2P1/2 and with potential maximum), are reported. The internal consistency of the theoretical model used in this work is confirmed by the excellent agreement between the long-range potential curve of the 1g state obtained in present work (from the 0g− state) and the long-range portion of the RKR potential curve of the 1 1Πg state previously determined by conventional molecular spectroscopy. The radiative lifetime of the K 4p state derived from the dipole–dipole interaction constant C3Π is also in excellent agreement with a recent fast-beam measurement.

Dissociation dynamics of quasibound levels in the g 3Σg+ state of H2: Characterization of the continuum

Decay pathways and photofragment anisotropy parameters have been determined for a series of rovibrational levels of the g 3Σg+ state in molecular hydrogen using fast-beam photofragment spectroscopy. The g 3Σg+(v=4) levels are found to be weakly predissociated by homogeneous interaction with the lower lying n=2 a 3Σg+ state and by rotational coupling with the i 3Πg state. The observed photofragment anisotropy reveals fine and hyperfine structure depolarization. The decay of g 3Σg+(v=5) levels is dominated by barrier tunneling. The anisotropy parameters identify the symmetry of the continuum to be of mixed Σg and Πg character, which implies that hydrogen molecules can tunnel through two different barriers. The determination of the kinetic energy and the anisotropy parameter of the photofragments have resulted in a number of spectral reassignments.

Orange Flame from Active Nitrogen and Oxygen in the Absence of a Metal Catalyst Resulting from Collisional Intersystem Crossing into N2(B 3Πg)

The discovery of an orange flame is reported that appears also at higher pressures of active nitrogen and oxygen without the presence of a metal catalyst unlike previous research in over 30 years. Enhancement of emissions of the first positive band system of nitrogen was observed from various vibrational levels of the N2(B 3Πg) state. Arguments to identify the species responsible and implications to previous research of this phenomenon of homogeneous excitation and collisional intersystem crossing into N2(B 3Πg) induced by excited O2 are presented. Its probing for lasing is suggested.

Ab initio configuration interaction calculations of the predissociation of rovibrational levels of the C 3Πg and d 1Πg 3sσ Rydberg states of the oxygen molecule

Ab initio configuration interaction calculations have been carried out for seven low-lying 3,1Πg states of the oxygen molecule. Three different types of nonadiabatic couplings have been considered: spin-orbit, radial, and rotational. The complex scaling method has been employed to compute rovibrational level locations and predissociation linewidths with a basis of 200 Hermite polynomials for each of 13 different Ω electronic states. The calculations correctly predict that the v=2 level has the narrowest linewidth for the O216CΠg3 state, while v=4 is narrowest for O218. Marked variations in the linewidths of the different Ω components of the C state are explained by the fact that the π*→3sσ Rydberg and σ→π* valence Πg3 states have different occupations of the π* orbital, causing opposite orderings of their respective Ω levels. Rotational coupling is found to be important for high J values of the C state. The d 1Πg 3sσ state shows even more unusual effects by virtue of the fact that there is a sharply avoided crossing between the corresponding Rydberg diabatic state with a bound σ→π* 1Πg valence state. The calculations find irregular spacings in the d-state vibrational manifold, wide variations in linewidth for different v,J levels, and a large change in the rotational constant in successive vibrational levels, all of which effects have been earlier demonstrated in experimental work. Satellite lines are indicated for both the v=2 and 3 levels as a result of the interaction with the bound Πg1 valence state, whereby experimental verification exists only for v=2. The v=3 state has not yet been successfully identified due to the broadness of the d-X spectrum in the energy range of interest. The observed temperature dependence of the linewidths of the two features near the expected location of the v=2 level can also be understood on the basis of these calculations. Finally, the change in the predissociation mechanism for the d state from spin-orbit to radial as v changes from 0 to 2 which has been deduced experimentally is also verified in the present theoretical treatment.

Theoretical study on Pd dimer and trimer interaction with the hydrogen molecule

The H2 interaction with the Pd dimer and trimer were studied using multiconfigurational self-consistent field (MC-SCF) calculations with the relativistic effective core potential (RECP); the correlation energy correction was included in the extended multireference configuration interaction (MRCI), variational and perturbative to second order. Here, we considered the Pd2 first six states: 3Σ+u, 1Σ+g, 3Πg, 3Δxy, 1Σ+u, and 3Σ+g. For them, the four geometrical approaches included were the side-on H2 toward Pd2, for the hydrogen molecule in and out the Pd dimer plane; the perpendicular end-on H2 toward Pd2; and the perpendicular end-on Pd2 to H2. The Pd2 ground state is 3Σ+u, which only captures H2 in the C2v end-on approach, softly relaxing the H(SINGLE BOND)H bond. The closed-shell 1Σ+g captures the H2 molecule in all the approaches considered: The side-on approach of this state presents deep wells and relaxes the H(SINGLE BOND)H bond, and the end-on approach captures H2 with a relatively longer H(SINGLE BOND)H distance and also a deep well. The 3Πg state was the only one which did not capture H2. For the triangular Pd3 clusters, H2 was approached in the C2v symmetry in and out of the Pd3 plane. In the triangular case, H2 was absorbed in both spin states, with deep wells and relaxing the H(SINGLE BOND)H distance. The linear Pd3 singlet and triplet states capture outside of the Pd3 and break the H(SINGLE BOND)H bond. © 1997 John Wiley & Sons, Inc.

State-to-state collision energy transfer of 7Li2 within high-lying triplet states: Gateway effect of mixed levels in energy transfer between singlet and triplet states

State-to-state collision energy transfer in the 2 3Πg, 3 3Πg, 3 3Σ+g, 1 3Σ−g, and 1 3Δg states and from singlet to triplet states of 7Li2 has been studied experimentally by continuous wave optical–optical double resonance (OODR) resolved fluorescence spectroscopy. Propensity rules of collision-induced transitions within a triplet state have been observed. When a rovibrational (v,J) level of the F 1Σ+g or G 1Πg state was excited by OODR transition, fluorescence from high-lying triplet gerade states to the a 3Σ+u and/or b 3Πu states was always observed. This indicates that population can transfer from F 1Σ+g and G 1Πg states to triplet states by collision. Irrespective of the J of the initially excited singlet level, the most intense fluorescence from the triplet state will occur at the N or J corresponding to that of the F 1Σ+g (and/or G 1Πg)∼3Λg mixed levels. Molecular population moves to the mixed levels and then transfers to the triplet state. This clearly indicates that singlet–triplet mixed levels played the role of a gateway, through which the population moves from singlet to triplet states. The gateway levels can be perturbed levels in the same vibrational level of the F 1Σ+g or G 1Πg state, or the perturbed levels in different vibrational levels.

Collision‐induced transitions between the a1Πg, a′ 1Σu−, and w1Δu states of N2: Can they affect auroral N2 Lyman‐Birge‐Hopfield band emissions?

In the Earth's atmosphere bright ultraviolet (UV) emissions from the N2 a 1Πg state (Lyman‐Birge‐Hopfield bands) are seen, but the w 1Δu and a′ 1Σu− states, which have similar excitation cross sections, emit weakly if at all at UV wavelengths. Models of the singlet system (a, a′, and w states) have used radiative cascade, which produces transitions between excited states, and quenching, which removes molecules from them, to explain the lack of emission from the a′ and w states. Another process, which has never been properly included in such calculations, is collision‐induced electronic transitions (CIET) between the singlet states. Recent laboratory measurements of CIET involving N2 indicate that the rate constants are comparable to those for radiation, and recent measurements have yielded enough information to allow a preliminary calculation of CIET between the N2 a 1Πg, a′ 1Σu− and w 1Δu states. These calculations show that CIET can be more important than radiation for transitions between the a, a′, and w states in typical aurorae or up to the peak of typical dayglow emission profiles (∼130 km). The inclusion of CIET may allow self‐consistent modeling of observations of the Lyman‐Birge‐Hopfield (LBH) bands, one of the most prominent ultraviolet molecular emissions from the Earth's atmosphere.

Laser excitation spectroscopy of the B 1Σ+u(O+u)←a 3Πg(O+g) transition of Cd2: Vibrational analysis and rotational structure

The B 1Σ+u←a 3Πg transition of Cd2 (natural abundance) and 114Cd2 has been observed by laser excitation spectroscopy and analyzed. By exciting the Cd2 B←a transition in the visible (560≤λ≤730 nm) while monitoring B 1Σ+u→X 1Σ+g (bound→free) emission in the ultraviolet (∼270–310 nm), more than 40 red-degraded vibrational bands were recorded. Analysis of the spectrum has yielded vibrational constants for both the a 3Πg and B 1Σ+u states: ωe″=153.6±4.0 cm−1, ωe″xe″=0.52±0.06 cm−1, ωe′=105.3±1.0 cm−1, and ωe′xe′=0.44±0.03 cm−1. In addition, ΔRe≡ReB−Rea was determined to be 0.31±0.03 Å. Rotational structure has been partially resolved for 114Cd2 bands in the 620–655 nm and 719–723 nm regions, and the spontaneous emission lifetime of the a 3Πg state and the rate constant for quenching of Cd2 (a 3Πg) by collisions with background Cd atoms have been determined to be 8.6±2.5 μs and (2.2±0.3)×10−13 cm3 s−1, respectively. Also, analysis of the B→X emission (Condon internal diffraction) spectra produced when specific B 1Σ+u vibrational levels are populated has yielded ReX−ReB=0.95±0.02 Å.

Hyperfine structures of the 7Li2 b3Πu, 23Πg, and 33Πg states: Continuous wave perturbation facilitated optical–optical double resonance spectroscopy

The hyperfine structure of the b 3Πu, 2 3Πg, and 3 3Πg states of 7Li2 has been studied by continuous wave perturbation facilitated optical–optical double resonance fluorescence excitation spectroscopy. The b 3Πu state has case bβJ coupling scheme. The hyperfine splittings of the two perturbed b 3Πu v=19, N=10, J=11e, s, F1 and v=19, N=5, J=4e, a, F3 levels were resolved and hyperfine constants determined to be +9.90 MHz and −20.94 MHz, respectively. Fermi contact is the main source of the hyperfine interaction and bF(b 3Πu)=+107 MHz has been obtained. The coupling schemes of different 2 3Πg levels are different: N=4, 6 levels observed from the b 3Πu v′=19, N′=5, J′=4e, a, F3 intermediate level and the N=10 levels observed via the b 3Πu v′=19, N′=10, J′=11e, s, F1 intermediate level have case bβJ coupling; the N=5 levels observed via the b 3Πu v′=19, N′=5, J′=4e, a, F3 intermediate level and the N=9, 11 levels observed from the b 3Πu v′=19, N′=10, J′=11e, s, F1 intermediate level are closer to case bβS coupling. Hyperfine constants have been calculated and the Fermi contact constant, bF(2 3Πg)=60 MHz is obtained. The 3 3Πg state is a Rydberg state and has case bβS coupling with bF(3 3Πg)≊100 MHz.

A study of the vibronic structure in the HeI excited photoelectron spectrum of CO2 involving the X 2Πg and A 2Πu ionic states

The HeI excited photoelectron spectrum of the CO2 molecule covering the X 2Πg and A 2Πu ionic states has been recorded at a resolution of better than 5 meV. Complex vibrational structures are resolved in both photoelectron bands. In the X 2Πg state, the ν2 and ν3 modes are observed to be excited in both an odd and even numbers of quanta in addition to the ν1 mode, whereas for the A 2Πu state the spectrum is dominated by excitations of the ν1 mode alone and in combinations with excitations of the ν2 mode in two quanta involving strong Fermi resonance. The observed spectrum has been assigned by comparison with optical spectra and with calculations of the vibrational fine structure including vibronic and spin–orbit coupling.

Gd4(C2)](Cl, I)6, an Interstitially Stabilized Heteroleptic Gadolinium Sesquihalide

Abstract[Gd4(C2)](Cl, I)6 is obtained from CsI, Gd, GdCl3 and C2I4 in sealed niobium containers at 1000/800°C as black, shiny needles. The crystal structure (tetragonal, P4/mbm, Z = 2, a = 1347.5(1), c = 1212.5(1) pm) is similar to that of Na[Mo4]O6 and [Sc4B]Cl6. It may be regarded as being built from octahedra sharing common trans edges running in the [001] direction. The octahedra contain C2 units as interstitials. Every third octahedron contains a disordered C2 unit perpendicular to those in the two neighboring [Gd6(C2)] octahedra and is therefore compressed in the direction of the (pseudo) C4 axis. Calculations of the electronic structure of an “empty” [Gd4]Cl6 structure reveals a total of 13 electrons necessary to occupy all metal‐metal bonding states. The incorporation of a carbon dimer substantially alters the bonding conditions for [Gd4(C2)]X6 (X = Cl, I). The formal charge of −6 of the C2 unit is significantly reduced as πg states split up, GdGd and GdC bonding states are occupied and bonding d orbitals combine to form the lowest unoccupied energy states.

Resonance-enhanced multiphoton electron detachment spectrum of C5−

The resonance-enhanced multiphoton electron detachment spectrum of C5− was measured. The peaks observed at 470–500 nm were assigned to be 1 photon excitation of 2Πu to the 2Πg state. The vibrational structure gives the symmetric stretching frequency of ν2=718±43 cm−1 for the excited state of C5−.

Radiative and radiationless decay of resonances resulting from electronically nonadiabatic interactions: A computational approach valid for both narrow and broad linewidths and large energy shifts

The description of resonances originating from several coupled electronic states in a diabatic or approximate diabatic basis can offer both conceptual insights and computational challenges. In a three-state problem, two bound electronic states strongly coupled to a single dissociative continuum, large resonance energy shifts (thousands of cm−1), and linewidths varying over 4 orders of magnitude can be encountered. In this work a nonperturbative computational approach is developed to treat this class of resonances. Expressions for both the radiative and radiationless decay rates are developed. Although the approach is nonperturbative, the linewidth is expressed in a Golden-Rule-type formula. The resonance energy is obtained from the iterative solution of an eigenvalue problem in the bound state space. These attributes enable efficient determination both narrow and broad linewidths and large resonance energy shifts. The approach is used to characterize both radiative and radiationless decay of the 2,3 3Πg states of Al2 using a rigorous three-state diabatic basis. Lifetimes ranging from tenths of picoseconds to nanoseconds are determined. The corresponding resonance energy shifts are on the order of 4000 cm−1.

The 2 3Πg and 3 3Πg states of 7Li2: Optical–optical double resonance spectroscopy and ab initio calculations

The (2p+2p) 2 3Πg and (2s+3p) 3 3Πg states of 7Li2 have been studied both experimentally and theoretically. Vibrational levels v=0–41 of the 2 3Πg state and v=6–10 of the 3 3Πg state have been observed by perturbation facilitated optical–optical double resonance (PFOODR) spectroscopy. Our ab initio calculations show that the 2 3Πg state, although dissociating into 2p+2p atomic limit, is a Rydberg state and strongly mixed with the (2s+3p) 3 3Πg and (2s+3d) 4 3Πg Rydberg states. Our theoretical calculations show good agreement with our experimental results.

Radiationless decay of the 1,2,3 3Πg states of Al2: A fully first principles treatment using adiabatic and rigorous diabatic states

The decay mechanisms of the metastable 2,3 3Πg states of Al2 are investigated. Both nonadiabatic radiationless decay to the dissociative 1 3Πg state and radiative decay to the ground X 3Πu state are considered. The 1,2,3 3Πg states are described using state averaged multiconfiguration self consistent field/configuration interaction wave functions [ψam(r,Q)]. The derivative couplings famn(Q)≡〈ψam(r, Q)‖(d/dQ)ψan(r,Q)〉r are determined and used to construct a rigorous diabatic basis for this strongly interacting three state problem. The 2 3Πg state and somewhat surprisingly the 3 3Πg state are rapidly predissociated by the dissociative 1 3Πg state. The lifetimes for nonradiative decay of the vibrational levels of the 2 3Πg state are on the order of picoseconds while those of the 3 3Πg state are on the order of nanoseconds being reduced from the direct coupling (3 3Πg∼1 3Πg) rate of milliseconds by indirect coupling through the 2 3Πg state, (3 3Πg∼2 3Πg∼1 3Πg). Radiative decay is found to be on the order of 102 and 30 ns for the 2 3Πg and 3 3Πg states, respectively, so that radiationless decay is principal decay mechanism. Significant variation in the lifetimes of the individual vibrational levels of the 2,3 3Πg states is expected. This is attributed to the mechanism of the predissociation which involves nonadiabatic interactions near the ‘‘inner walls’’ of the 1,2 3Πg states. Although avoided crossings strongly affect the properties of the 1,2,3 3Πg states the adiabatic basis is preferred over the diabatic basis both conceptually and computationally.

High-resolution study of the luminescent electronic energy transfer reaction of Xe(3P0,2) with 14N2 and 15N2

Abstract The excitation of nitrogen molecules into the B 3Πg state by collisional energy transfer from Xe∗(3P0 and 3P2) was studied in a Xe∗ beam/N2 gas cell arrangement for the isotopic targets 15N2 and 14N2 under single collision conditions. Using a sophisticated CCD detector, high-resolution spectra of the N2(B-A) emission bands were recorded. Earlier results on 14N2 could be considerably extended and improved in accuracy. They were also revised in certain details. The 15N2 spectra exhibit dramatic isotope effects, both as regards the vibrational distribution and the rotational population of the products. These results are rationalized in terms of isotopic shifts of the vibronic semi-empirical interaction potentials [V. Aquilanti, R. Candori, F. Pirani, T. Krumpelmann and Ch. Ottinger, Chem. Phys. 142 (1990) 47].

Evidence for predissociation of N2 a 1Πg(v≥7) by direct coupling to the A′ 5Σ+g state

Predissociation of the (v=7–10) levels of the a 1Πg state in N2 is studied with translational spectroscopy. These levels are produced by the charge-transfer neutralization of a 4 keV energy N+2 beam in sodium vapor and the dissociation fragments are monitored by a time- and position-sensitive detector. Lifetimes of 300, 300, 100, and 230 (±20) ns are measured for a 1Πg(v=7, 8, 9, and 10), respectively. Quantum mechanical calculations based on Fermi’s golden rule give evidence that the predissociation is caused by direct coupling to the continuum of the A′ 5Σ+g state rather than by an indirect mechanism. The a 1Πg–A′ 5Σ+g electronic coupling matrix element is estimated to be 0.44 (±0.03) cm−1. The required change in spin multiplicity suggests that this coupling arises from a spin–spin interaction.

(3+1) resonance enhanced multiphoton ionization photoelectron spectroscopy on nf Rydberg states of carbon dioxide

The (3+1) resonance enhanced multiphoton ionization spectrum of carbon dioxide has been investigated for the (2Πg3/2,1/2)nf Rydberg states. The excitation spectrum has been obtained for the n=4–13 members, while photoelectron spectra with a resolution of 15 meV have been measured for the n=4–7 members. The photoelectron spectra demonstrate that a delicate balance exists between direct and indirect ionization processes as evidenced by the large differences in vibrational activity observed in the spectra obtained via various members of the (2Πg3/2,1/2)nf Rydberg series. Strong vibrational activity, which would be forbidden by simple selection rules, is found and interpreted to arise in part from vibronic coupling between various ionic states. Long vibrational progressions, mainly involving the symmetric stretch vibration of the X 2Πg state of the ion, indicate further severe deviations from Franck–Condon behavior. Two-color excitation of the (2Πg3/2,1/2)nf Rydberg states provides strong evidence that the superexcited states accessible at the four-photon level have a profound influence on the vibrational progressions and distributions in the photoelectron spectra. Finally, resonances associated with multiphoton excitation of atomic carbon and oxygen have been observed. The processes which might be responsible for the occurrence of these atoms are discussed.