Lowest 2Π Research Articles

On the Energy-specific Photodissociation Pathways of 14N2 and 14N15N Isotopomers to N Atoms of Different Reactivity: A Quantum Dynamical Perspective

Photodissociation of the nitrogen molecule in the vacuum ultraviolet (VUV) is a major source of reactive nitrogen atoms in the upper atmosphere of Earth and throughout the solar system. Recent experimental studies have revealed strong energy dependence of the VUV photodissociation branching ratios to the N(4S3/2)+N(2D J ) and N(4S3/2)+N(2P J ) product channels, the primary dissociation pathways in the 108,000–116,000 cm−1 energy region. This produces N(2D J ) and N(2P J ) excited atoms that differ significantly in their chemical reactivity. The branching ratios oscillate with increase in the VUV excitation energy. We use high-level ab initio quantum chemistry to compute the potential curves of 17 electronic excited states and their nonadiabatic and spin–orbit couplings. The dynamics follow the sequential evolution from the optically excited but bound singlets. Spin–orbit coupling enables transfer to the dissociative triplet and quintet states. We compute the photodissociation yields through the dense manifold of electronic states leading to both exit channels. The dynamical simulations accurately capture the branching oscillations and enable a detailed look into the photodissociation mechanism. The major contribution to the dissociation is through the two lowest 3Π u states. However, for both isotopomers, at about 110,000 cm−1 there is an abnormally low dissociation rate into the N(4S3/2)+N(2P J ) channel that enables comparable participation of triplet and quintet 5Π u electronic states. This leads to the first peak in the branching ratio. At higher energies, trapping of the population in the 33Π u bound triplet state occurs. This favors dissociation to the lower-energy N(4S3/2)+N(2D J ) channel and results in the observed second switch in branching ratios.

The complex-scaled multiconfigurational spin-tensor electron propagator method for low-lying shape resonances in Be−, Mg− and Ca−

We further apply the complex scaled multiconfigurational spin-tensor electron propagator method (CMCSTEP) for the theoretical determination of resonance parameters with electron-atom systems including open-shell and highly correlated (non-dynamical correlation) atoms and molecules. The multiconfigurational spin-tensor electron propagator method (MCSTEP) developed and implemented by Yeager and his coworkers for real space gives very accurate and reliable ionization potentials and electron affinities. CMCSTEP uses a complex scaled multiconfigurational self-consistent field (CMCSCF) state as an initial state along with a dilated Hamiltonian where all of the electronic coordinates are scaled by a complex factor. CMCSTEP is designed for determining resonances. We apply CMCSTEP to get the lowest 2P (Be−, Mg−) and 2D (Mg−, Ca−) shape resonances using several different basis sets each with several complete active spaces. Many of these basis sets we employ have been used by others with different methods. Hence, we can directly compare results with different methods but using the same basis sets.

Rydberg–Ritz analysis and quantum defects for Rb and Cs atoms on helium nanodroplets

A Rydberg–Ritz approach is used for the interpretation of Rb–He and Cs–He Rydberg states and Rydberg series. Variations of the quantum defects within a Rydberg series give insight into the interaction between the alkali atom’s valence electron and the superfluid helium droplet. A screening of the valence electron from the alkali atom core by the helium droplet is observed for high Rydberg states. For states with lower principal quantum number, the effect decreases and the quantum defects are found to lie closer to free atom values, indicating an increased probability for the electron to be found inside the alkali atom core. An investigation of the spin–orbit splitting of the Cs–He nP(2Π) components reveals that the splitting of the lowest 2Π states is more atom-like [Hund’s case (c) coupling] than at higher n states [Hund’s case (a) coupling]. In addition, we report a detailed study of the droplet size dependence of Ak–He Rydberg series on the example of the Rb–He D(Δ) series. Higher Rydberg states of this series are strongly redshifted, which is also related to the screening effect.

Relativistic multireference configuration interaction calculations of lifetime of 2s22p 2P3/2 level along boron isoelectronic sequence

Lifetime of 2s22p 2P3/2 level along with fine structure separations for the lowest 2P doublet of boron-like ions, from Z=14 to Z=30 have been calculated using multireference relativistic configuration interaction (MR RCI) method based on the no-pair Dirac-Coulomb-Breit (DCB) Hamiltonian. Analytic basis sets of Gaussian-type functions are employed to expand the upper and lower components of the Dirac four-spinors in the matrix Dirac-Fock self-consistent field (DF SCF) and relativistic MR CI procedures. Error with respect to variation of basis set parameters was estimated. QED corrections were estimated by evaluation of electron self-energy and vacuum polarisation.

Ab Initio Prediction of Spectroscopic Constants of CaN in the Lowest 2 Π, 4 Σ - , 2 Σ - , and 4 Π Electronic States: A Potential Candidate for the First Calcium-bearing Interstellar Molecule

Spectroscopic constants for the lowest 2Π, 4Σ-, 2Σ-, and 4Π states of the CaN radical have been calculated by the multireference singles and doubles configuration interaction method, including Davidson's correction for quadruple excitations [MR-SDCI(+Q)], to aid in detection of the first Ca-bearing molecule in interstellar space. It is shown that the 2Π state is the ground state of CaN and that the 4Σ- state is the first excited state, although their energy difference is very small (~493.4 cm-1). This result is contrary to that for the isovalent species MgN. The calculated rotational constants for the 2Π state are Be = 10.767 GHz and B0 = 10.731 GHz, while those for the 4Σ- state are Be = 9.3807 GHz and B0 = 9.3373 GHz.

Electron detachment energies of AlAs − and AlAs 2−

The ground and low-lying excited states of AlAs −, AlAs, AlAs 2 −, and AlAs 2 are studied using DFT and CCSD(T) approximation. AlAs − has a 2Σ + ground state with a 2Π state 1.08 kcal/mol above. AlAs has a 3Σ − ground state with the lowest 3Π and 1Σ + states at 2.32 and 15.14 kcal/mol, respectively. Adiabatic electron affinity (AEA) of AlAs is 1.91 eV at the CCSD(T) level. AlAs 2 − and AlAs 2 have 1 A 1 and 2 B 2 ground states, respectively. CCSD(T) predicts the AEA of AlAs 2 to be 2.07 eV. Electron detachment processes from AlAs − and AlAs 2 − ground states are presented and discussed.

The I2(B) predissociation by solving an inverse atoms-in-molecule problem

The valence electronic states of the iodine molecule are analysed by means of a simple atoms-in-molecule model which accounts for the lowest 2P states of iodine atoms and approximates the spin-orbit interaction by its atomic part. For this model, an inverse problem is solved, i.e. non-relativistic potential energy curves and diabatic couplings are determined by a least-squares fit to known relativistic potential energy curves. The resulting adiabatic wave functions are used to calculate the electronic matrix elements responsible for natural, hyperfine and magnetic predissociation of the iodine molecule in the B0+ u: state. The results are in reasonable agreement with experimental data, being stable enough with respect to the variation of input relativistic potentials. They also indicate the importance of diabatic couplings between the non-relativistic states of the same symmetry.

MRCI Calculation, Scaling of the External Correlation, and Modeling of Potential Energy Curves for HCl and OCl

The first lowest 2Π and 2Σ+ states of OCl, as well as the 1Σ+ and 3Σ+ states of HCl, have been calculated at the ab initio MRCI level, and modeled semiempirically using the extended Hartree−Fock approximate correlation energy method. Spectroscopic RKR data and accurate ab initio energies have been used to obtain the model parameters. The vibrational levels of those states have also been calculated, and found to be in good agreement with existing spectroscopic data for the ground electronic states of the title diatomic molecules.

MRSD-CI and LDF studies of the VN X 3Δ and D 3Π states

The X 3Δ and D 3Π states of VN are investigated using ab initio multireference single and double excitation configuration interaction (MRSD-CI) and local-density-functional (LDF) techniques. The lowest 3Π→ 3Δ transition occurs around 15800 cm −1, where the dominant electronic configurations for the 3Δ and 3Π states are 9σ↑3π 41δ↑ and 8σ 23π 44π↑ 1δ↑, respectively. The spectroscopic parameters, R e, ω e, ω e x e, B e and μ, are also computed for the ground X 3Δ state. The electronic structure o this state reveals that its short internuclear distance is due to three strong bonds that involve the 3d vanadium and 2p nitrogen atomic orbitals. Extensive MRSD-CI calculations yield 51V hyperfine coupling constants that are in reasonable agreement with experiment.

A b i n i t i o calculations on the four lowest electronic states of AlF+ and AlCl+

The potential energy curves of the two lowest 2Σ+ (X,B) and the two lowest 2Π (A,C) electronic states of the AlF+ and AlCl+ molecular ions have been calculated using highly correlated multireference configuration interaction (MR-CI) wave functions. It is found that both 2Σ+ states and the C 2Πr state are bound, whereas the A 2Πi state is repulsive. Electronic transition moment functions for all six pairs of states of both ions have also been calculated and used for evaluation of the radiative transition probabilities between bound vibrational states. The calculated charge distributions show that the X and C states are dominated by Coulombic attraction between a doubly charged positive aluminum and the singly charged negative halogen ion. The results provide a new assignment of the photoelectron spectra of the neutral AlF. They are also in good agreement with the recently observed optical B–X emission spectra of both molecular ions and C–X bands of AlCl+. The absence of C–X emission of AlF+ is most likely due to predissociation of the C 2Πr state by the repulsive A 2Πi state.

Laser spectroscopy of molecular LiHe: The 3d 2 Delta p 2 Pi transition.

The rotationally resolved absorption spectrum of the 3d $^{2}\mathit{p}$ $^{2}\mathrm{\ensuremath{\Pi}}$ transition in molecular LiHe has been measured. For each of three isotropic variants $^{6}\mathrm{Li}^{3}$He, $^{6}\mathrm{Li}^{4}$He, and $^{7}\mathrm{Li}^{4}$He, six vibrational transitions have been observed from the lower 2p $^{2}\mathrm{\ensuremath{\Pi}}$(v''=0,1) electronic state to the upper 3d $^{2}\mathrm{\ensuremath{\Delta}}$(v'=0,1,2,3) electronic state. Analysis of the observed spectra has yielded values for the well depth and equilibrium separation of 1020(20) ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ at 3.37(3)${\mathit{a}}_{0}$ for the 2p $^{2}\mathrm{\ensuremath{\Pi}}$ state and 610(20) at 3.52(2)${\mathit{a}}_{0}$ for the 3d $^{2}\mathrm{\ensuremath{\Delta}}$ state. Details of our analysis and our experimental technique are presented.

Collisional quenching of O( 1D) by O( 3P)

Metastable O( 1D) atoms may be quenched in collisions with ground state O( 3P) atoms by transitions in the avoided crossing regions of the three lowest 3Π g states of O 2 of which the lowest separates to O( 3P) + O( 3P) and the two upper to O( 3P) + O( 1D). Quantal calculations of the adiabatic potential energy curves of the 3Π g , states are carried out with particular attention to an avoided crossing region in the lowest two states around a nuclear separation of 3.2 a 0. Diabatic potential matrix elements are constructed from the adiabatic curves by imposing the requirement that they be smooth everywhere. A multistate diabatic formulation is used to describe the scattering and the cross-sections for the collision-induced quenching of O( 1D) atoms are calculated. The rate coefficient for the quenching of O( 1D) atoms by O( 3P) atoms is obtained as a function of temperature. At 1000 K, the value is 1.0 × 10 −11 cm 3 s −1, accurate probably to a factor of two. The theoretical rate coefficient is consistent with the empirical value inferred from upper atmosphere data.

Threshold photoelectron spectrum of the argon 3S satellites

Lately a variety of techniques have studied the electron correlation satellites with binding energies between the Ar 3s ionization potential (29.24 eV) and the lowest 2p −2 ionization potential (43.38 eV). One of these techniques, threshold photoelectron spectroscopy, with ≈90 meV electron resolution, revealed at least 25 Individual electronic states. All of these could contribute to any other satellite spectrum, and this observation helped explain some discrepancies between previous measurements. This technique has been applied here to the same region (30 eV ⩽ Hv ⩽ 45 eV) with higher resolution (<60 meV at the Ar 3s −1 peak). In this higher resolution spectrum at least 29 Individual electronic states are present. In some cases multiplet splitting Is observed.

Quantum-Mechanical Studies of Several Helium—Lithium Interaction Potentials

The total energies for a number of states of HeLi were computed using a method of molecular orbital calculation in which the total wavefunction is taken as a linear combination of spatial configurations, each a properly antisymmetrized product of flexible one-electron functions in an elliptic coordinate system. Calculations were performed for the 2Σ ground state and a number of excited 2Σ, 2Π, 4Σ, and 4Π states of HeLi. The 1Σ ground state of the molecular ion HeLi+ was also examined to facilitate an evaluation of the neutral excited states. The lowest 2Π and 4Π states as well as two highly excited 2Σ states were found to be weakly bonding with dissociation energies of less than 1 eV. The importance of configuration interaction upon the accuracy of the calculations was examined and a method of obtaining approximate energies for highly excited states was developed. On the basis of these calculations, it is concluded that the weak bonding evidenced by some of the states of this system is due largely to the effects of orbital geometry and nuclear screening at large internuclear distances.

Societies and Academies

LONDON. Royal Society, June 27.—Lord Rayleigh: A photo-electric method of measuring the light of the night sky: with studies of the course of variation through the night.—J. C. McLennan, M. W Perrin, and H. J. C. Ireton: The action of high-speed cathode rays on acetylene.—Lord Rayleigh: Fluorescent and phosphorescent excitation of mercury vapour by the resonance frequency and lower frequencies.—T. E. Stern, B. S. Gosling, and R. H. Fowler: Further studies in the emission of electrons from cold metals. An extension of Nordheim and Fowler's work on electronic emission from clean cold metals. It explains a wide range of experimental results obtained with films of sodium (or tungsten). The normal stable sodium film formed is mono-molecular and reduces the work function from 4.5 volts to somewhat less than volts. The currents concerned are of high density; the space charge correction is negligible for the conditions of the experiments discussed.—A. E. H. Love: The stress produced in a semi-infinite solid by pressure part of the boundary. The method of potentials, invented by Boussinesq, is developed and applied to the case of uniform pressure over a circular area, among others. The solution is also discussed arithmetically with the object of throwing light on the technical question of the safety of foundations. Beneath a round pillar, there is a basin-shaped surface possessing a roughly similar property. The form of this surface is determined. In these cases failure arises through excessive stress-difference. Tensile stress is greatest near the base of a pillar, or a corner the base of a wall, and just outside it. It would not endanger a round pillar, but may be a cause of decided weakness if the boundary of the base of a wall or pillar presents a sharp corner.—A. N. Shaw and H. E. Reilley and R. J. Clark: The ageing of standard cells: increased accuracy in their use: and international comparisons.—H. Quinney: A comparison between behaviour at the Ac3 point of single crystal iron and polycrystal iron, both in the strained and unstrained states.—J. N. Pring and G. M. Westrip: An electrometric method for the determination of ozone high dilutions.—C. F. Jenkin and G. D. Lehmann: High-frequency fatigue.—J. S. Townsend and S. P. MacCallum: Ionisation by collision in monatomic gases. A discussion of some recent theories of conductivity.—?R. C. Johnson and R. K. Asundi: The structure of the high-pressure carbon bands and the Swan system. Both systems are due to a C2 molecule. Four new high-pressure bands have been found in the near ultra-violet, and two more in the near infra-red. These, with the known bands, form a single vibrational progression (n′ = 0), and both systems represent transitions to a common final state. The initial state of the high-pressure system is believed to be a normal 3P level and different in this respect from the two lower 2P levels, which are believed to be inverted.—D. M. Newitt: Gaseous combustion at high pressures (13). The experimental data from explosions of various 2CO +O2 4C0, 2H2 +O2 + xN2 and 2H2 + O2 + xA mixtures at high initial pressures have been analysed, and mean molecular heats of nitrogen and steam have been calculated for the temperature range 289°—2600° to 3000° K and for carbon dioxide for the range 289°—173° K. The results for nitrogen are in agreement with the generally accepted values, but those for steam and carbon dioxide are higher.—R. J. Clark: the direct determination of the electrostatic moments of molecules. Direct deflection in a rapidly varying field is used. Sodium and potassium atoms have either rio permanent electric moment, or one that is too small to measure. So far no polarisation by the field on these molecules has been found.—A. R. Low: On the criterion for stability of a layer of viscous fluid heated from below. Rayleigh gave a mathematical account of the modes of instability of a viscous fluid heated from below with the special assumption of zero tangential forces at the boundaries, and found unexpectedly that the top-heavy layer of fluid was stable until a certain temperature gradient, negative upwards, was exceeded. Jeffreys has reduced the problem to the solution of a linear differential equation of the sixth order with constant coefficients, the complete solution of which is now given.?R. B. Brode: The absorption coefficient for slow electrons in mercury vapour.—F. L. Usher: A mechanism of gelatinisation.—H. R. Hass and W. R. Cook: The determination of molecular forces from the viscosity of a gas.—J. C. McLennan, A. B. McLay, and M. F. Crawford: The spark spectrum of thallium (Tl III).—