3Πg State Research Articles

Photodissociation of CO2 via the 1Πg state: Wavelength-dependent imaging studies of O(1D2) photoproducts.

Photodissociation of CO2 via the 1Πg state is investigated using a time-sliced velocity-mapped ion imaging apparatus combined with a tunable vacuum ultraviolet photolysis source. The main O(1D2) + CO(X1Σ+) channel is directly observed from the measured images of O(1D2) photoproducts at 129.08-134.76nm. The total kinetic energy release spectra determined based on these images show that the energetic thresholds for the O(1D2) + CO(X1Σ+) photoproducts correspond to the thermochemical thresholds for the photodissociation of CO2(v2 = 0) and CO2(v2 = 1). One significant difference among the CO(X1Σ+, v) vibrational distributions for the predominant CO2(v2 = 0) dissociation is that the population of CO(v = 0) becomes favorable at 130.23-133.45nm compared to the Boltzmann-like component (v > 0) that always exists at 129.08-134.76nm. The wavelength dependences of the overall β are found to follow the variation trend of the CO(v = 0) abnormal intensity. The vibrational state-specific β values present a roughly decreasing trend with an increase in v, whereas β(v = 0) appears to be significantly larger than β(v = 1) at 130.23-133.45nm compared to 134.76 and 129.08nm. The non-statistical CO(v = 0) with larger β values at 130.23-133.45nm implies that an additional pathway may open through the conical intersection coupling to the dissociative 21A' state, except for the ever-existing pathway that yields the Boltzmann-like component. In contrast, at 129.08nm, the restoration of the statistical equilibrium in the CO(X1Σ+, v) vibrational distribution may be caused by the emergence of novel dissociation pathways arising from the participation of the 31A″ state.

An ab initio spectroscopic model of the molecular oxygen atmospheric and infrared bands.

We present a unified variational treatment of the magnetic dipole matrix elements, Einstein coefficients and line strength for general open-shell diatomic molecules in the general purpose diatomic code Duo. Building on previous work in which similar expressions for the electric quadrupole transitions were developed, we also present a complete ab initio spectroscopic model for the infrared, electric dipole-forbidden, spectrum of the 16O2 molecule. The model covers seven states, namely the X 3Σ-g, a 1Δg, b 1Σ+g, I 1Πg, II 1Πg, I 3Πg and II 3Πg states, for which 7 potential energy, 6 electronic angular momentum, 7 spin-orbit, and 14 quadrupole moment curves are calculated using ic-MRCI theory and an aug-cc-pV5Z basis set. These curves are diabatised to remove avoided crossings between the excited Π states, and the resultant properties are used to produce a line list for higher-order transitions of astrophysical interest.

Ozone Photodissociation in the Singlet Channel at 226 nm.

We report the rotational state distribution and vector correlations of the O2(a 1Δg, v = 0) fragments arising from the 226 nm photodissociation of jet-cooled O3. Consistent with previously reported trends, the rotational distribution is shifted to higher rotational states with decreasing wavelength. We observe highly suppressed odd rotational state populations due to a strong Λ-doublet propensity. The measured rotational distribution is in agreement with classical trajectory calculations for the v = 0 products, although the distribution is slightly narrower than predicted. The spatial anisotropy follows the previously observed trend of decreasing β with increasing photon energy with β = 0.72 ± 0.14 for v = 0, j = 38. As expected for a triatomic molecule, the v-j correlation is consistent with v perpendicular to j, but the measured correlation is nonlimiting due, in part, to rotational and translational depolarization. The j-dependent line width of the O2(a 1Δg) REMPI spectrum is also discussed in connection with the lifetime of the resonant O2(d 1Πg) state due to predissociation via the II 1Πg valence state.

Diabatic Valence-Hole States in the C2 Molecule: “Putting Humpty Dumpty Together Again”

Despite the long history of spectroscopic studies of the C$_2$ molecule, fundamental questions about its chemical bonding are still being hotly debated. The complex electronic structure of C$_2$ is a consequence of its dense manifold of near-degenerate, low-lying electronic states. A global multi-state diabatic model is proposed here to disentangle the numerous configuration interactions within four symmetry manifolds of C$_2$ ($^{1}\Pi_g$, $^{3}\Pi_g$, $^{1}\Sigma_u^+$, and $^{3}\Sigma_u^+$). The key concept of our model is the existence of two "valence-hole" configurations, $2\sigma_g^22\sigma_u^11\pi_{u}^33\sigma_g^2$ for $^{1,3}\Pi_g$ states and $2\sigma_g^22\sigma_u^11\pi_{u}^43\sigma_g^1$ for $^{1,3}\Sigma_u^+$ states that derive from $3\sigma_g\leftarrow2\sigma_u$ electron promotion. The lowest-energy state from each of the four C$_2$ symmetry species is dominated by this type of valence-hole configuration at its equilibrium internuclear separation. As a result of their large binding energy (nominal bond order of 3) and correlation with the 2s$^2$2p$^2$+2s2p$^3$ separated-atom configurations, the presence of these valence-hole configurations has a profound impact on the $global$ electronic structure and unimolecular dynamics of C$_2$.

Multi-path effect in population transfer dynamics of the photoassociation of hot Mg atoms by a femtosecond laser pulse

We investigate the thermal photoassociation dynamics of the Mg atoms, from the X1Σg+ state to the (1)1Πg state, or to the other three higher excited states |i〉=(1)1Πu,(2)1Πu,(2)1Σu+. The weak two-photon coupling between X1Σg+ and (1)1Πg, the strong three-photon couplings between X1Σg+ and |i〉, and the one-photon couplings between (1)1Πg and |i〉 can form several different transition paths. We find that X1Σg+⟶+3ℏω|i〉⟶-ℏω(1)1Πg is the major path and the “V”-type Raman transition path from |i〉 to (1)1Πg takes the second place.

Radiation Measurements of N<sub>2</sub> 1+ Band in Low-pressure Microwave-discharged Nitrogen Plasma

Spectroscopic measurements of low-pressure microwave-discharged nitrogen plasma in the wavelength region of 410 to 790 nm were conducted by changing the flow rate and the net incident power of microwave. The N2 2+ and N2+ 1－ bands in shorter wavelength region and the N2 1+ band in longer wavelength region were observed. In this study, radiation from N2 B 3Πg state on v′> 12 in the N2 1+ band, which normally observed in such as Lewis-Rayleigh afterglow, was investigated in detail. As a result, it was found that the intensity tends to relatively increase as the flow rate increases.

Investigation of photoassociation with full-dimensional thermal-random-phase wavefunctions

By taking the femtosecond two-photon photoassociation (PA) of magnesium atoms as an example, we propose a method to calculate the thermally averaged population, which is transferred from the ground X1Σg + state to the target (1)1Πg state, based on the solution of full-dimensional time-dependent Schrödinger equation. In this method, named as method A, we use thermal-random-phase wavefunctions with the random phases expanded in both the vibrational and rotational degrees of freedom to model the thermal ensemble of the initial eigenstates. This method is compared with the other two methods (B and C) at different temperatures. Method B is also based on thermal-random-phase wavefunctions, except that the random-phase expansion is merely used for the vibrational degree of freedom. Method C is based on the independent propagation of every initial eigenstate, instead of the thermal-random-phase wavefunctions. Taking the (1)1Πg state as the target state, it is found that although these three methods can present the same population on the (1)1Πg state, the computation efficiency of method A increases dramatically with the increase in temperature. With this efficient method A, we find that the PA process at 1000K can also induce rotational coherence, i.e., the molecular field-free alignment in the excited electronic states.

Electron collisions with molecular nitrogen in its ground and electronically excited states using the R-matrix method

A comprehensive study of electron collisions with the X 1Σg + ground state as well as the metastable A 3Σu + and a 1Πg excited states of the N2 molecule is reported using the fixed-nucleus R-matrix method. Integral elastic scattering and electronic excitation cross sections from the X 1Σg + ground state to the eight lowest electronic states, A 3Σu +, B 3Πg, W 3Δu, B′ 3Σu −, a 1Πg, a′ 1Σu −, w 1Δu and C 3Πu, overall agree well with the available experimental and theoretical results although updates of some recommended values are suggested. Accurate electron impact electronic transition cross sections starting from the A 3Σu + and a 1Πg metastable excited states are reported. The total summed electronic transition cross sections from the a 1Πg state is dominant: an order of magnitude higher than those of the X 1Σg + ground state. The de-excitation cross sections generally show a downward trend with increasing incident electron energy, which is different from the elastic and electronic excitation cross sections which generally increase with collision energy. There is a prominent 2Πu symmetry resonance peak at 2.8 eV for electronic de-excitation scattering of a 1Πg → B 3Πg, which significantly contributes to the total summed cross sections from the a 1Πg excited state. The present results provide a new insight which will aid understanding of electron spectra in the atmosphere of the Earth and Titan.

An update to the MARVEL data set and ExoMol line list for 12C2

ABSTRACT The spectrum of dicarbon (C2) is important in astrophysics and for spectroscopic studies of plasmas and flames. The C2 spectrum is characterized by many band systems with new ones still being actively identified; astronomical observations involve eight of these bands. Recently, Furtenbacher et al. presented a set of 5699 empirical energy levels for 12C2, distributed among 11 electronic states and 98 vibronic bands, derived from 42 experimental studies and obtained using the MARVEL (Measured Active Rotational-Vibrational Energy Levels) procedure. Here, we add data from 13 new sources and update data from 5 sources. Many of these data sources characterize high-lying electronic states, including the newly detected 3 3Πg state. Older studies have been included following improvements in the MARVEL procedure that allow their uncertainties to be estimated. These older works in particular determine levels in the C 1Πg state, the upper state of the insufficiently characterized Deslandres–d’Azambuja (C 1Πg–A 1Πu) band. The new compilation considers a total of 31 323 transitions and derives 7047 empirical (marvel) energy levels spanning 20 electronic and 142 vibronic states. These new empirical energy levels are used here to update the 8states C2 ExoMol line list. This updated line list is highly suitable for high-resolution cross-correlation studies in astronomical spectroscopy of, for example, exoplanets, as 99.4 per cent of the transitions with intensities over 10−18 cm molecule−1 at 1000 K have frequencies determined by empirical energy levels.

Molecular Rydberg-state excitation in laser pulses: bandwidth and orbital symmetry.

We have performed a comparison study of the Rydberg-state excitation of model molecules (1πg and 1πu states) in different laser fields by the approaches of time-dependent Schrödinger equation and a fully quantum-mechanical model, and both simulations show good accordance. It is found that the peak structure of the Rydberg-state population vs laser intensity becomes pronounced for longer laser pulses due to the stronger interference effect between the subwave packets released in different optical cycles, and the locations of the intensity-dependent peaks closely satisfy the multi-photon resonant transition condition. In addition, it is demonstrated that the populations of the Rydberg states possessing the identical parity oscillate in an inverse manner with increasing laser intensity for different initial states (1πg and 1πu), and the aforementioned distinct phenomenon is attributed to the additional phase introduced by the symmetry of 1πg state with respect to that of 1πu state.

The UV Spectrum of the Lyman‐Birge‐Hopfield Band System of N2 Induced by Cascading from Electron Impact

AbstractWe have measured in the laboratory the far ultraviolet (FUV: 125.0–170.0 nm) cascade‐induced spectrum of the Lyman‐Birge‐Hopfield (LBH) band system ( ) of N2 excited by 30–200 eV electrons. The cascading transition begins with two processes: radiative and collision‐induced electronic transitions (CIETs) involving two states ( and w1Δu → a1Πg), which are followed by a cascade induced transition at the single‐scattering pressures employed here. Direct excitation to the a‐state produces a confined LBH spectral glow pattern around an electron beam. We have spatially resolved the electron‐induced glow pattern from an electron beam colliding with N2 at radial distances of 0–400 mm at three gas pressures. This imaging measurement is the first to isolate spectral measurements in the laboratory of single‐scattering electron‐impact‐induced fluorescence from two LBH emission processes: direct excitation, which is strongest in emission near the electron beam axis; and cascading‐induced, which is dominant far from the electron beam axis. The vibrational populations for vibrational levels from v′ = 0–2 of the a 1Πg state are enhanced by radiative cascade and CIETs, and the emission cross sections of the LBH band system for direct and cascading‐induced excitation are provided at 40, 50, 100, and 200 eV.

Transition properties of the X3Σ–g, A′3Δu, A3Σ+u, B′′3Πu, B3Σ–u, and B′3Πg states of sulphur dimer

In this study, we calculated the properties of the transition between six lowest-lying triplet states (X3Σ–g, A′3Δu, A3Σ+u, B′′3Πu, B3Σ–u, and B′3Πg) of sulphur dimer. The calculations were made with the CASSCF method, followed by the valence icMRCI approach. It was found that the radiative lifetime of the B3Σ–u state is in the order of 10 ns. The Einstein A coefficients of certain vibronic emissions from the B3Σ–u – X3Σ–g system were large, and the radiative lifetimes of the B′Πg and B′′Πu states were found to be in the order of 1 and 10 µs, respectively. The B′3Πg – A′3Δu, B′3Πg – A3Σ+u, and B′′3Πu – X3Σ–g transitions were strong and could be measured by spectroscopy. In contrast, the B′3Πg – B′′3Πu and B′3Πg – B3Σ–u transitions were weak and therefore, difficult to be detected via spectroscopy. The distributions of the radiative lifetimes with varying rotational angular momentum quantum number were evaluated for some lower vibrational states of the B′′3Πu, B3Σ–u, and B′3Πg states. The spin–orbit coupling effect on the transition properties of the B′′Πu – X3Σ–g system was also studied. The radiative lifetimes of the B′′3Πu, 0+, B′′3Πu, 1, and B′′3Πu, 2 states were in the order of 10−6 – 10−7, 10−6 – 10−7, and 10−5 s, respectively. The transition properties reported in this study can be used to guide the detection of sulphur dimers in both laboratory experiments and astrophysical environments.

Imaging the dissociation dynamics of Si2+ via two-photon excitation at 193 nm

In the one-color experiment at 193 nm, we studied the photodissociation of Si2+ ions prepared by two-photon ionization using the time-sliced ion velocity map imaging method. The Si+ imaging study shows that Si2+ dissociation results in two distinct channels: Si(3Pg)+Si+(2Pu) and Si(1D2)+Si+(2Pu). The main channel Si(3Pg)+Si+(2Pu) is produced by the dissociation of the Si2+ ions in more than one energetically available excited electronic state, which are from the ionization of Si2(v=0−5). Particularly, the dissociation from the vibrationally excited Si2(v=1) shows the strongest signal. In contrast, the minor Si(1D2)+Si+(2Pu) channel is due to an avoided crossing between the two 2Πg states in the same symmetry. It has also been observed the one-photon dissociation of Si2+(X4Σg−) into Si(1D2)+Si+(2Pu) products with a large kinetic energy release.

Ultrafast F2− photodissociation by intense laser pulses: a time-resolved fragment imaging study

We present time-resolved coincidence imaging of F2− photodissociation by 400nm and intense 800nm ultrafast pulses. Coincidence fragment imaging reveals parallel and perpendicular single photon dissociation on 2Σg+ and 2πg states, and additional intense-field dissociation features.

Nonadiabatic effects on the positions and lifetimes of the low-lying rovibrational levels of the GK 1Σ and H 1Σ states of H2.

The term values of rovibrational levels of the GK 1Σ+g and H 1Σ+g states of H2 have been measured with absolute and relative accuracies down to 10-4 cm-1 (≈3 MHz) and 10-6 cm-1 (≈30 kHz), respectively, by measuring transitions to long-lived high-n Rydberg states using single-mode cw laser radiation and a collimated supersonic beam of cold H2 molecules. The term values are compared with those determined in earlier experimental and theoretical investigations and the comparison points at discrepancies and a need for improved theoretical treatments of nonadiabatic, relativistic and radiative corrections for these states. The lifetimes of several low-lying rovibrational levels of the GK, H and I+ 1Πg states have been determined in pump-probe experiments. These lifetimes reveal a significant dependence on the electronic, vibrational and rotational excitation and also deviate from results obtained in earlier experimental and theoretical investigations.

Insight from first principles into the stability and magnetism of alkali-metal superoxide nanoclusters

Alkali-metal superoxides are gaining increasing interest as 2p magnetic materials for information and energy storage. Despite significant research efforts on bulk materials, gaps in our knowledge of the electronic and magnetic properties at the nanoscale still remain. Here, we focused on the role that structural details play in determining stability, electronic structure, and magnetic couplings of (MO2)n (M = Li, Na, and K, with n = 2–8) clusters. Using first-principles density functional theory based on the Perdew-Burke-Ernzerhof and Heyd-Scuseria-Ernzerhof functionals, we examined the effect of atomic structure on the relative stability of different polymorphs within each investigated cluster size. We found that small clusters prefer to form planar-ring structures, whereas non-planar geometries become more stable when increasing the cluster size. However, the crossover point depends on the nature of the alkali metal. Our analysis revealed that electrostatic interactions govern the highly ionic M–O2 bonding and ultimately control the relative stability between 2-D and 3-D geometries. In addition, we analyzed the weak magnetic couplings between superoxide molecules in (NaO2)4 clusters comparing model Hamiltonian methods based on Wannier function projections onto πg states with wave function-based multi-reference calculations.

Factorisation of zero-width resonance wave functions

ABSTRACTA zero-width resonance (ZWR) is also called a bound state in a continuum. Such resonances occur when the Floquet method is applied to a diatomic molecule submitted to a continuous wave field. This circumstance requires particular choices of wavelength and electric field amplitude. The corresponding wave function can be factorised with a method devised for bound states. The result is a product of an electronic factor depending parametrically on the nuclear coordinate by a nuclear factor. The factorisation of the wave function is done through the introduction of a fictitious time-independent Hamiltonian yielding the same coupled equations as the Floquet algorithm applied to the time-dependent Hamiltonian. The potential which determines the nuclear factor is calculated and used to recover the real ZWR quasi-energy. Application is made to the molecule Na2 prepared by photoassociation in the metastable 3Σ+u state. Photodissociation of this state by laser-coupling to the (1)3Πg state requires an intensity low enough to require the consideration of only two channels (one photon interaction) in the application of the Floquet method.

Cross sections for electron collision with difluoroacetylene

We report a detailed calculation of total elastic, differential elastic, momentum transfer and electronic excitation for electron impact on difluoroacetylene (C2F2) molecules using the R-matrix method at low energies. After testing many target models, the final results are reported for the target model that gave the best target properties and predicted the lowest value of the shape resonance. The shape resonance is detected at 5.86 eV and 6.49 eV with the close-coupling and static exchange models due to 2Πg (2B2g, 2B3g) states. We observed that the effect of polarization becomes prominent at low energies below 4 eV, decreasing the magnitude of the elastic cross section systematically as it increases for C2F2. We have also computed elastic cross sections for C2H2, C2F4 and C2H4 with a similar model and compared with the experimental data for these molecules along with C2F2. General agreement is found in terms of the shape and nature of the cross section. Such a comparison shows the reliability of the present method for obtaining the cross section for C2F2. The calculation of elastic scattering cross section is extended to higher energies up to 5 keV using the spherical complex optical potential method. The two methods are found to be consistent, merging at around 12 eV for the elastic scattering cross section. Finally we report the total ionization cross section using the binary encounter Bethe method for C2F2. The perfluorination effect in the shape and magnitude of the elastic, momentum transfer and ionization cross sections when compared with C2H2 showed a similar trend to that in the C2H4–C2F4 and C6H6–C6F6 systems. The cross-section data reported in this article could be an important input for the development of a C2F2 plasma model for selective etching of Si/SiO2 in the semiconductor industry.

Study of infrared emission spectroscopy for the B(1)Δg-A(1)Πu and B'(1)Σg(+)-A(1)Πu systems of C2.

Thirteen bands for the B(1)Δg-A(1)Πu system and eleven bands for the B'(1)Σg(+)-A(1)Πu system of C2 were identified in the Fourier transform infrared emission spectra of hydrocarbon discharges. The B'(1)Σg(+)v = 4 and the B(1)Δg v = 6, 7, and 8 vibrational levels involved in nine bands were studied for the first time. A direct global analysis with Dunham parameters was carried out satisfactorily for the B(1)Δg-A(1)Πu system except for a small perturbation in the B(1)Δg v = 6 level. The calculated rovibrational term energies up to B(1)Δg v = 12 showed that the level crossing between the B(1)Δg and d(3)Πg states is responsible for many of the prominent perturbations in the Swan system observed previously. Nineteen forbidden transitions of the B(1)Δg-a(3)Πu transition were identified and the off-diagonal spin-orbit interaction constant AdB between d(3)Πg and B(1)Δg was derived as 8.3(1) cm(-1). For the B'(1)Σg(+)-A(1)Πu system, only individual band analyses for each vibrational level in the B'(1)Σg(+) state could be done satisfactorily and Dunham parameters obtained from these effective parameters showed that the anharmonic vibrational constant ωexe is anomalously small (nearly zero). Inspection of the RKR (Rydberg-Klein-Rees) potential curves for the B'(1)Σg(+) and X(1)Σg(+) states revealed that an avoided crossing or nearly avoided crossing may occur around 30,000 cm(-1), which is responsible for the anomalous molecular constants in these two states.

Influence of a strong magnetic field on the hydrogen molecular ion using B-spline-type basis-sets**Project supported by the National Natural Science Foundation of China (Grant No. 11204389) and the Natural Science Foundation Project of Chongqing (Grant Nos. CSTC2012jjA50015 and CSTC2012jjA00012).

As an improvement on our previous work [J. Phys. B: At. Mol. Opt. Phys. 45 085101 (2012)], an accurate method combining the spheroidal coordinates and B-spline basis is applied to study the ground state 1σg and low excited states 1σu, 1πg,u,1δg,u,2σg of the in magnetic fields ranging from 109 Gs (1 Gs = 10−4 T) to 4.414 × 1013 Gs. Comparing the one-center method used in our previous work, the present method has a higher precision with a shorter computing time. Equilibrium distances of the states of the in strong magnetic fields were found to be accurate to 3∼5 significant digits (s.d.) and the total energies 6∼11 s.d., even for some antibonding state, such as 1πg, which is difficult for the one-center method to give reliable results while the field strength is B ≥ 1013 Gs. For the large disagreement in previous works, such as the equilibrium distances of the 1πg state at B = 109 Gs, the present data may be used as a reference. Further, the potential energy curves (PECs) and the electronic probability density distributions (EPDDs) of the bound states 1σg, 1πu, 1δg and antibonding states 1σu, 1πg, 1δu for B = 1, 10, 100, 1000 a.u. (atomic unit) are compared, so that the different influences of the magnetic fields on the chemical bonds of the bound states and antibonding states are discussed in detail.