A comprehensive theoretical investigation of the electronic states of Ca2 up to the Ca(4s(2) 1S) + Ca(4s5p 1P) dissociation limit

A theoretical survey of the electronic structure of Ca(2) is presented using two-electron pseudopotentials complemented by core-polarization operators on Ca atoms and multireference configuration interaction/quasidegenerate perturbation theory (MRCI/QDPT) treatment of molecular excited states. The spectroscopic constants of 70 electronic states up to 30,000?cm(-1) above the ground state are determined. This implies all Ca(2) states dissociating up to the Ca(4s(2) (1)S) + Ca(4s5p (3,1)P) dissociation limits. All spin states (singlet, triplet, and quintet) are investigated. The work emphasizes the variety of interactions implying singly valence and lowest Rydberg excited states, doubly excited states generated by atom pairs (3)P(4s4p) + (3)P(4s4p), or (3)P(4s4p) + (3)D(4s3d), 4p3d double excitations asymptotically localized on a single-atom. Zwitterionic Ca(+) + Ca(-) configurations are evidenced and shown to induce specific electronic patterns in (1)Σ(g)(+), (3)Σ(g)(+), (1)Σ(u)(+), (3)Σ(u)(+), (1)Π(g), (3)Π(g), (1)Π(u), and (3)Π(u) symmetry manifolds. They also provide insight for qualitative features (barriers) found for the lower electronic states already investigated in previous publications by other authors.     

Quantum defect theory of dipole and vibronic mixing in Rydberg states of CaF

The Rydberg spectra of CaF combine the simplicity of a single electron outside a doubly closed-shell Ca2+F- ion core with the exceptional polarity of the ion core. A global multichannel quantum defect (MQDT) fit to 612 previously assigned levels, 507 from n approximately = 12-18, N=0-14, v+=1, 97 from n approximately = 9-10, N=0-14, v+=2, and 8 from n approximately = 7, N=3-10, v+=3, produces the complete L=0-3 quantum defect matrix mu (with the exception of one element) and 19 of 20 elements of the partial differentialmu/differentialR matrix, as well as the molecular constants of the CaFX 1sigma+ state [omega(e)+=694.58(14), omega(e)x(e+)=2.559(40), B(e+)=0.373 07(16) cm(-1), and the v=0, N=0 to v(+)=0, N(+)=0 ionization energy, 46,996.40(8) cm(-1)]. This experimentally determined mu(R) matrix is unusual in the completeness of its representation of the spectrum of both core-penetrating and nonpenetrating Rydberg series, including both local perturbations and vibrational autoionization rates, as well as all dynamical processes encoded in the spectrum that result from the scattering (at negative energy) of the Rydberg electron off the Ca2+F- ion core. The MQDT theory is presented in a form that clarifies the relationships of the reaction (K) and phase (P) matrices of MQDT to effective Hamiltonian models for local interactions between accidentally near degenerate levels. In particular, a Hund's case (b) like representation of the Hamiltonian is described in which the rovibronic K matrix is diagonalized and the P matrix, which contains information about the v+, N+ eigenstates of the ion, becomes nondiagonal.     

High-resolution millimeter wave spectroscopy and multichannel quantum defect theory of the hyperfine structure in high Rydberg states of molecular hydrogen H2

Experimental and theoretical methodologies have been developed to determine the hyperfine structure of molecular ions from detailed studies of the Rydberg spectrum and have been tested on molecular hydrogen. The hyperfine structure in l=0-3 Rydberg states of H2 located below the X 2Sigmag+(v+=0,N+=1) ground state of ortho H2+ has been measured in the range of principal quantum number n=50-65 at sub-MHz resolution by millimeter wave spectroscopy following laser excitation to np and nd Rydberg states using a variety of single-photon and multiphoton excitation sequences. The np1(1), nd1(1), and the nf1(0-3) Rydberg states were found to be metastable and to have lifetimes of more than 5 micros beyond n=50. Members of other series, such as the nd1(2), nd1(3), and the np1(0) series, were found to have lifetimes of more than 1 mus. Local perturbations induced by low-n Rydberg states belonging to series converging on rovibrationally excited levels of H2+ reduce the lifetimes in narrow ranges of n values. The hyperfine structure is strongly dependent on the value of the orbital angular momentum l. In the penetrating s and p states at n approximately 50 the exchange interaction dominates over the hyperfine interaction and the levels can be labeled by the total electron spin angular momentum quantum number S (S=0 or 1). In the less penetrating d and f Rydberg states, the hyperfine interaction between the core nuclear and electron spins is larger than the exchange interaction and the Rydberg states are of mixed singlet and triplet character. A procedure based on the Stark effect and on the systematic analysis of selection rules and combination differences was developed to determine the orbital and the total angular momentum quantum numbers l and F and to construct an energy map of p and f Rydberg levels between n=54 and 64 with relative positions of an accuracy of better than 1 MHz. Multichannel quantum defect theory (MQDT) was extended to treat the hyperfine structure in molecular Rydberg states and was used to analyze the observed hyperfine structure of the p and f Rydberg states of H2. The frame transformation between the Born-Oppenheimer channels described by the angular momentum coupling scheme (abetaJ) and the asymptotic channels described by the (e[bbetaS+]) coupling scheme was derived and enables an elegant treatment of all intermediate coupling cases. Purely ab initio quantum defect theory reproduced the experimentally determined positions to within 40 MHz for the p levels and 13 MHz for the f levels. By slight adjustments of the quantum defect functions and their energy dependences and by consideration of the p-f interaction, of the singlet-triplet splittings of the f levels, and of the departure of the ionic levels from pure coupling case (bbetaS+), the agreement between theory and experiment could be improved to 600 kHz. By comparing the results of MQDT calculations of the hyperfine structure of f Rydberg levels with those of coupled equations calculations, the frame transformation approximation of MQDT was shown to be accurate to within 300 kHz. The extrapolated ionic hyperfine structure of the X 2Sigmag+(v+=0,N+=1) ionic level corresponds to the ab initio prediciton of Babb and Dalgarno [Phys. Rev. A 46, R5317 (1992)] within the experimental error.     

Theoretical spectroscopy and metastability of BeS and its cation

Multiconfiguration self-consistent field and multiconfiguration reference interaction including the Davidson’s correction techniques were employed to calculate the potential energy curves (PECs) of the BeS/BeS⁺ electronic states correlating to the 4/5 lowest dissociation limits. After nuclear motion treatment, we deduced reliable spectroscopic data for the neutral and cationic bound states. For BeS, the transition moments and spin-orbit couplings were also evaluated and used later with the PECs to deduce the rovibronic transition probabilities and the radiative lifetimes in the low-lying states, and to investigate the unimolecular decomposition processes of BeS (X¹Σ⁺, A¹Π, ³Σ⁺ and B¹Σ⁺) leading to Be(¹S_g) + S(³P_g). The prominent mechanism is a spin-orbit induced predissociation via the repulsive BeS(1³Σ⁻) state. Finally, we give the single ionization spectrum of BeS (X¹Σ⁺) populating the BeS⁺ (X²Π, 1²Σ⁻, 1²Σ⁺, 1²Δ, 2²Σ⁺, 2²Π and 3²Π) electronic states. The adiabatic ionisation energy of BeS is estimated to be ∼9.15 eV.     

Shedding light on a dark state: the energetically lowest quintet state of C2

In this work we present a deperturbation study of the d?(3)Π(g), v=6 state of C(2) by double-resonant four-wave mixing spectroscopy. Accurate line positions of perturbed transitions are unambiguously assigned by intermediate level labeling. In addition, extra lines are accessible by taking advantage of the sensitivity and high dynamic range of the technique. These weak spectral features originate from nearby-lying dark states that gain transition strength through the perturbation process. The deperturbation analysis of the complex spectral region in the (6,5) and (6,4) bands of the Swan system (d(3)Π(g)-a?(3)Π(u)) unveils the presence of the energetically lowest high-spin state of C(2) in the vicinity of the d?(3)Π(g), v=6 state. The term energy curves of the three spin components of the d state cross the five terms of the 1?(5)Π(g) state at rotational quantum numbers N ≤ 11. The spectral complexity for transitions to the v = 6 level of d?(3)Π(g) state is further enhanced by an additional perturbation at N = 19 and 21 owing to the b?(3)Σ(g)(-), v=19 state. The spectroscopic characterization of both dark states is accessible by the measurement of 122 "window" levels. A global fit of the positions to a conventional Hamiltonian for a linear diatomic molecule yields accurate molecular constants for the quintet and triplet perturber states for the first time. In addition, parameters for the spin-orbit and L-uncoupling interaction between the electronic levels are determined. The detailed deperturbation study unravels major issues of the so-called high-pressure bands of C(2). The anomalous nonthermal emission initially observed by Fowler in 1910 [Mon. Not. R. Astron. Soc. 70, 484 (1910)] and later observed in numerous experimental environments are rationalized by taking into account "gateway" states, i.e., rotational levels of the d?(3)Π(g), v=6 state that exhibit significant (5)Π(g) character through which all population flows from one electronic state to the other.     

Accurate theoretical study of PS(q) (q = 0,+1,-1) in the gas phase

Highly correlated ab initio methods were used in order to generate the potential energy curves and spin-orbit couplings of electronic ground and excited states of PS and PS(+). We also computed those of the bound parts of the electronic states of the PS(-) anion. We used standard coupled cluster CCSD(T) level with augmented correlation-consistent basis sets, internally contacted multi-reference configuration interaction, and the newly developed CCSD(T)-F12 methods in connection with the explicitly correlated basis sets. Core-valence correction and scalar relativistic effects were examined. Our data consist of a set of spectroscopic parameters (equilibrium geometries, harmonic vibrational frequencies, rotational constants, spin-orbit, and spin-spin constants), adiabatic ionization energies, and electron affinities. For the low laying electronic states, our calculations are consistent with previous works whereas the high excited states present rather different shapes. Based on these new computations, the earlier ultraviolet bands of PS and PS(+) were reassigned. For PS(-) and in addition to the already known anionic three bound electronic states (i.e., X(3)Σ(-), (1)Δ, and 1(1)Σ(+)), our calculations show that the (1)Σ(-), (3)Σ(+), and the (3)Δ states are energetically below their quartet parent neutral state (a(4)Π). The depletion of the J = 3 component of PS(-)((3)Δ) will mainly occur via weak interactions with the electron continuum wave.     

Broad shape resonance effects in CaF Rydberg states

Results of ab initio R-matrix calculations [S. N. Altunata et al., J. Chem. Phys. 123, 084319 (2005)] indicate the presence of a broad shape resonance in electron-CaF(+) scattering for the (2)Sigma(+) electronic symmetry near the ionization threshold. The properties of this shape resonance are analyzed using the adiabatic partial-wave expansion of the scattered electron wave function introduced by Le Dourneuf et al. [J. Phys. B 15, L685 (1982)]. The qualitative aspects of the shape resonance are explained by an adiabatic approximation on the electronic motion. Mulliken's rule for the structure of the Rydberg state wave functions [R. S. Mulliken, J. Am. Chem. Soc. 86, 3183 (1964)] specifies that, except for an (n*)(-32) amplitude scale factor, every excited state wave function within one Rydberg series is built on an innermost lobe that remains invariant in shape and nodal position as a function of the excitation energy. Mulliken's rule implies a weak energy dependence of the quantum defects for an unperturbed molecular Rydberg series, which is given by the Rydberg-Ritz formula. This zero-order picture is violated by a single (2)Sigma(+) CaF Rydberg series at all Rydberg state energies (n*=5-->infinity, more so with increasing n*) below the ionization threshold, under the broad width of the shape resonance. Such a violation is diagnostic of a global "scarring" of the Rydberg spectrum, which is distinct from the more familiar local level perturbations.     

Photofragmentations, state interactions, and energetics of Rydberg and ion-pair states: two-dimensional resonance enhanced multiphoton ionization of HBr via singlet-, triplet-, Ω = 0 and 2 states

Mass spectra were recorded for one-colour resonance enhanced multiphoton ionization (REMPI) of H(i)Br (i = 79, 81) for the two-photon resonance excitation region 79,040-80,300 cm(-1) to obtain two-dimensional REMPI data. The data were analysed in terms of rotational line positions, intensities, and line-widths. Quantitative analysis of the data relevant to near-resonance interactions between the F(1)Δ(2)(v' = 1) and V(1)Σ(+)(v' = m + 7) states gives interaction strengths, fractional state mixing, and parameters relevant to dissociation of the F state. Qualitative analysis further reveals the nature of state interactions between ion-pair states and the E(1)Σ(+) (v' = 1) and H(1)Σ(+)(v' = 0) Rydberg states in terms of relative strengths and J' dependences. Large variety in line-widths, depending on electronic states and J' quantum numbers, is indicative of number of different predissociation channels. The relationship between line-widths, line-shifts, and signal intensities reveals dissociation mechanisms involving ion-pair to Rydberg state interactions prior to direct or indirect predissociations of Rydberg states. Quantum interference effects are found to be important. Moreover, observed bromine atom (2 + 1) REMPI signals support the importance of Rydberg state predissociation channels. A band system, not previously observed in REMPI, was observed and assigned to the k(3)Π(0)(v' = 0) ←← X transition with band origin 80,038 cm(-1) and rotational parameter B(v('))=7.238 cm(-1).     

Molecular spectroscopy for ground-state transfer of ultracold RbCs molecules

We perform one- and two-photon high resolution spectroscopy on ultracold samples of RbCs Feshbach molecules with the aim to identify a suitable route for efficient ground-state transfer in the quantum-gas regime to produce quantum gases of dipolar RbCs ground-state molecules. One-photon loss spectroscopy allows us to probe deeply bound rovibrational levels of the mixed excited (A(1)Σ(+)-b(3)Π)0(+) molecular states. Two-photon dark state spectroscopy connects the initial Feshbach state to the rovibronic ground state. We determine the binding energy of the lowest rovibrational level |v' = 0, J' = 0> of the X(1)Σ(+) ground state to be D = 3811.5755(16) cm(-1), a 300-fold improvement in accuracy with respect to previous data. We are now in the position to perform stimulated two-photon Raman transfer to the rovibronic ground state.     

Theoretical spectroscopic studies of InI and InI+

Relativistic configuration interaction calculations are carried out to study the electronic structure and spectroscopic properties of InI and InI⁺. Potential energy curves of the ground and a number of low‐lying states are constructed. Spectroscopic parameters of the bound states of both species are computed and compared with the experimental and other theoretical data. Effects of spin‐orbit coupling on the spectroscopic properties are studied. Because of the presence of the heavy atoms the effect is large. The spin‐orbit splitting of the ground state (X²Π) of InI⁺ is more than 8350 cm^?1. As a result of the strong spin‐orbit interaction between X²Π and A²Σ⁺ of InI⁺, the potential energy curve of A²Σ becomes repulsive. Radiative lifetimes for the spin‐forbidden transitions such as A³Π?X¹Σ and B³Π₁ ?X¹Σ of InI and spin‐allowed transitions such as B²Σ⁺?A²Σ⁺, C²Π?A²Σ⁺, and B²Σ⁺?X²Π are calculated. Vertical and adiabatic ionization energies of InI and the electric dipole moments of both the neutral and ionic species are estimated. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Sigma,pi, and delta wavefunction forms for the hydrogen molecule

Using variational Monte Carlo methods, we examine simple, explicitly‐correlated trial wavefunction forms for the X¹Σ, B¹Σ, a³Σ, b³Σ, I¹Π_g, C¹Π_u, i³Π_g, c³Π_u, J¹Δ_g, and j³Δ_g states of the hydrogen molecule. The energies produced by our best wavefunctions are slightly above the best values in the literature. When we combine our trial wavefunction forms with the generalized Feynman‐Kac path integral method, our results are in excellent agreement with the best nonrelativistic values for these systems except for the I¹Π_g state. Our best energy for this state, ?0.65951554(6), is lower by several microhartrees than that obtained by Wolniewicz [J Mol Spectrosc 1995, 169, 329]. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Electronically excited-state properties and predissociation mechanisms of phosphorus monofluoride: a theoretical study including spin-orbit coupling

The 51 Ω states generated from the 22 Λ - S states of phosphors monofluoride have been investigated using the valence internally contracted multireference configuration interaction method with the Davidson correction and the entirely uncontracted aug-cc-pV5Z basis set. The spin-orbit coupling is computed using the state interaction approach with the Breit-Pauli Hamiltonian. Based on the calculated potential energy curves, the spectroscopic constants of the bound and quasibound Λ - S and Ω states are obtained, and very good agreement with experiment is achieved. Several quasibound states caused by avoided crossings are found. Various curve crossings and avoided crossings are revealed, and with the help of our computed spin-orbit coupling matrix elements, the predissociation mechanisms of the a(1)Δ, b(1)Σ(+), e(3)Π, g(1)Π, and (3)(3)Π states are analyzed. The intricate couplings among different electronic states are investigated. We propose that the avoided crossing between the A(3)Π(0 +) and b(1)Σ(0+) (+) states may be responsible for the fact that the A(3)Π ν' ≥ 12 vibrational levels can not be observed in experiment. The transition properties of the A(3)Π - X(3)Σ(-) transition are studied, and our computed Franck-Condon factors and radiative lifetimes match the experimental results very well.     

The VUV electronic spectroscopy of acetone studied by synchrotron radiation

The electronic state spectroscopy of acetone (CH3)2CO has been investigated using high-resolution VUV photoabsorption spectroscopy in the energy range 3.7-10.8 eV. New vibronic structure has been observed, notably in the low energy absorption band assigned to the 1(1)A(1) --> 1(1)A2 (ny --> pi*) transition. The local absorption maximum at 7.85 eV has been tentatively attributed to the 4(1)A1 (pi --> pi*) transition. Six Rydberg series converging to the lowest ionisation energy (9.708 eV) have been assigned as well as a newly-resolved ns Rydberg series converging to the first ionic excited state (12.590 eV). Rydberg orbitals of each series have been classified according to the magnitude of the quantum defect (delta) and are extended to higher quantum numbers than in the previous analyses.     

Experimental and theoretical studies of the valence-shell dipole excitation spectrum and absolute photoabsorption cross section of hydrogen fluoride

Absolute cross sectional measurements are reported of the valence-shell dipole excitation spectrum of HF obtained from suitably calibrated high impact energy, small momentum transfer, electron energy-loss scattering intensities. Detailed assignments are provided of all prominent features observed on the basis of concomitant single- and coupled-channel RPAE calculations. The measured spectrum, obtained at an energy resolution of = 0.06 eV (fwhm) in the = 9 to 21 eV interval, includes a dissociative feature centered at = 10.35 eV assigned as X¹Σ⁺ → (1π^?14σ)A¹Π, as well as numerous strong, sharp bands in the = 13 to 16 eV excitation energy region. These bands are attributed on basis of the present calculations to Rydberg (1π^?1npπ)-valence (3σ^?14σ) mixing in X¹Σ⁺ → ¹Σ⁺ excitation symmetry, which gives rise to a long conventional progression, and to strong 1π → nsσ, moderate 1π → ndσ, and weak 1π → npσ Rydberg series in X¹Σ⁺ → ¹Π excitation symmetry. A weaker 1π → ndπ Rydberg series also contributes to the spectrum in X¹Σ⁺ → ¹Σ⁺ symmetry. The calculated and measured excitation energies and f numbers, particularly for the X¹Σ → (1π^?14σ)A¹Π, → (1π^?13pπ)B¹Σ⁺, → (1π^?13sσ)C¹Π, and → (3σ^?14σ)D¹Σ⁺ transitions, are in good quantitative accord, suggesting that the overall nature of the HF spectrum is generally clarified on basis of the present studies. Finally, tentative assignments are provided of weak features observed above the 1π^?1 ionization threshold. As in previously reported joint experimental and theoretical studies of the valence-shell spectrum of F₂, high-resolution optical VUV measurements and calculated potential energy curves aid in the assignment and clarification of the HF spectrum.     

Rydberg states of the K2 molecule studied by laser spectroscopy in a supersonic beam

Rydberg states of potassium dimer have been studied in a crossed laser-molecular beam experiment. The K₂ molecules were formed in a supersonic expansion and excited by low-power cw dye laser. Two different excitation schemes have been used: The first scheme uses a single mode ring dye laser to induce near resonant two-photon transitions while in the second scheme stepwise excitation with two dye lasers is used. In each case excitation of Rydberg levels was detected by monitoring the ionization signal resulting from three-photon absorption. We report a detailed study of 700 two-photon resonances between 625 nm and 650 nm. Most of these signals can be assigned to transitions from the X¹σ _g ⁺ to¹σ _g ⁺ ,¹Π _g , and^1Δ _g states, which are all enhanced by the B¹Π _u intermediate state. Accurate rotational constants are given for the populated vibrational levels of these states. By stepwise excitation of Rydberg levels via theB ¹Π _u state we identify 3 series of Rydberg states as¹Δ _g (4S+nD),¹Σ _g ⁺ (4S+nD), and¹Σ _g ⁺ (4S+nS) with principal quantum numbers 7≦n≦20. Molecular constants of these and other observed but as yet unidentified states are given; quantum defects and dissociation energies are discussed.     

Structural and spectroscopic study of the LiRb molecule beyond the Born-Oppenheimer approximation

Adiabatic and diabatic potential energy curves and the permanent and transition dipole moments of the low-lying electronic states of the LiRb molecule dissociating into Rb(5s, 5p, 4d, 6s, 6p, 5d, 7s, 6d) + Li(2s, 2p) have been investigated. The molecular calculations are performed with an ab initio approach based on nonempirical pseudopotentials for Rb(+) and Li(+) cores, parametrized l-dependent core polarization potentials and full configuration interaction calculations. The derived spectroscopic constants (R(e), D(e), T(e), ω(e), ω(e)x(e), and B(e)) of the ground state and lower excited states are in good agreement with the available theoretical works. However, the 8-10(1)Σ(+), 8-10(3)Σ(+), 6(1,3)Π, and 3(1,3)Δ excited states are studied for the first time. In addition, to the potential energy, accurate permanent and transition dipole moments have been determined for a wide interval of internuclear distances. The permanent dipole moment of LiRb has revealed ionic characters both relating to electron transfer and yielding Li(-)Rb(+) and Li(+)Rb(-) arrangements. The diabatic potential energy for the (1,3)Σ(+), (1,3)Π, and (1,3)Δ symmetries has been performed for this molecule for the first time. The diabatization method is based on variational effective Hamiltonian theory and effective metric, where the adiabatic and diabatic states are connected by an appropriate unitary transformation.     

Observation of new Rydberg series in the many-electron transition region of N(2)

Fluorescence excitation spectra produced through photoexcitation of N(2) using synchrotron radiation in the spectral region between 50 and 62.5 nm have been obtained with a resolution of 0.004?nm. A broadband detector (in the 115-180 nm region) was employed to monitor fluorescence originated from neutral excited atomic nitrogen fragments which are produced through direct dissociation processes and predissociation from the well-known many-electron excited Rydberg states. We have identified a new Rydberg series (2 (2)Π(g)) 4sσ, a better resolved Rydberg (D (2)Π(g)) npσ series, and also the prominent Codling series converging to the D (2)Π(g), and C (2)Σ(u) (+) states of N(2) (+), respectively. By normalizing our relative fluorescence intensities to previously measured absolute fluorescence cross-section data we obtain the cross-section data of undispersed fluorescence in the 115-180?nm region. The fluorescence quantum yields for the present photodissociative excitation processes are found to be less than 0.05. The present results may provide important data for our understanding of competitions among the various decay channels of the many-electron transition states of N(2).     

Nonadiabatic quantum reactive scattering of the OH(A 2Σ+) + D2

The seams of conical intersection exist between the ground (1 (2)A(')) and the first-excited (2 (2)A(')) electronic potential energy surfaces (PESs) of OH(A (2)Σ(+),X (2)Π) + H(2) system. This intersection induces the nonadiabatic quenching of OH(A (2)Σ(+)) by D(2). We present nonadiabatic quantum dynamics study for OH(A (2)Σ(+)) + D(2) on new five-dimensional coplanar PESs. The ab initio calculations of PESs are based on multireference configuration interaction (MRCI)/aug-cc-pVQZ level. A back-propagation neural network is utilized to fit the PESs and nonadiabatic coupling. High degrees of rotational excitation of quenched OH(X (2)Π) products are found in nonreactive quenching channel, and the quenched D(2) products are vibrationally excited up to quantum number v(2) (')=8. The theoretical results of nonadiabatic time-dependent wave-packet calculation are in good agreement with the existing experimental data.