Quasi-relativistic treatment of the low-lying KCs states

The potential energy curves, permanent and transition dipole moments as well as spin-orbit and angular coupling matrix elements between the KCs electronic states converging to the lowest three dissociation limits were evaluated in the basis of the spin-averaged wavefunctions corresponding to pure Hund’s coupling case (a). The quasi-relativistic matrix elements have been obtained for a wide range of internuclear distance by using of small (9-electrons) effective core pseudopotentials of both atoms. The core-valence correlation has been accounted for a large scale multi-reference configuration interaction method combined with semi-empirical core polarization potentials. The static dipole polarizabilities of the ground X¹Σ⁺ and a³Σ⁺ states were extracted from the closed-shell coupled-cluster energies by the finite-field method. Among the singlet and triplet Σ⁺ states manifold the pronounced avoided crossing effect between repulsive walls of the (2,3)³Σ⁺ states has been discovered and analyzed by finite-difference calculation of radial coupling matrix elements. The resulting transition dipole moments and potentials were used to predict radiative lifetimes and emission branching ratios of excited vibronic states while the calculated angular coupling matrix elements were transformed to Λ-doubling constants of the (1,2)¹Π states and magnetic g-factor of the ground state. The accuracies of the present results are discussed by comparing with experimental data and preceding calculations.     

Low-lying electronic states of LiF molecule with inner electrons correlation

The potential energy curves and dipole moments of the low-lying electronic states of LiF molecule are performed by using highly accurate multi-reference configuration interaction with Awcv5z basis sets. 1s, the inner shell of Li is considered as the closed orbit, which is used to characterise the spectroscopic properties of a manifold of singlet and triplet states. 16 electronic states correlate with two lowest dissociation channels Li(²S)+F(²P) and Li(²P)+F(²P) are investigated. Spectroscopic parameters of the ground state X¹Σ⁺ have been evaluated and critically compared with the available experimental values and the other theoretical data. However, spectroscopic parameters of 1³Π, 1¹Δ, 1¹Σ^?, 1¹Π, 1³Σ⁺, 2³Σ⁺, 1³Δ, 1³Σ^?, 2³Π, 2¹Π, 3³Π, 3¹Π and 3³Σ⁺ states are studied for the first time. These 13 excited states have shallow potential wells, and the dispersion coefficients of these excited states are predicted. In additional, oscillator strengths of excited states at equilibrium distances are also predicted.     

Multireference configuration interaction study of ground and low-lying excited states of the AlC radical

This work explored the spectroscopic parameters and vibrational properties of the 21 Λ–S and 42 Ω states of the AlC radical. The PECs were calculated with the CASSCF method, which was followed by the icMRCI+Q approach. The A⁴Π, a²Π, 5²Π, 2²Δ, and 1²Φ states as well as the first well of B⁴Σ^? state were inverted with the spin–orbit coupling (SOC) effect included; the 1⁴Δ, 1⁴Σ⁺, and 2²Σ^? states as well as the second wells of the B⁴Σ^?, 2²Σ⁺, 3²Σ⁺, 4²Π and 5²Π states were weakly bound, which well depths were less than 650 cm^?1; the B⁴Σ^?, 2²Σ⁺, 3²Σ⁺, 4²Π, 5²Π, and 2²Δ states had double wells and the second wells of these states except for B⁴Σ^? had only several vibrational states; the avoided crossings existed between the 2²Σ⁺ and 3²Σ⁺ states, the 3²Σ⁺ and 4²Σ⁺ states, the B⁴Σ^? and 3⁴Σ^? states, the 2²Δ and 3²Δ states, the 4²Π and 5²Π states, the 5²Π and 6²Π states, as well as the 2⁴Π and 3⁴Π states. The extrapolation scheme, core–valence correlation and scalar relativistic corrections were included. The spectroscopic parameters and vibrational properties were determined. The TDM curves between two different Λ–S states were calculated and Franck–Condon factors of some transitions were evaluated. The SOC effect on the spectroscopic and vibrational properties was evaluated.     

Theoretical studies on 14 Λ-S and 30 Ω states of BeBr molecule: potential energy curves,spectroscopic parameters and spin–orbit couplings

Using the complete active space self-consistent field (CASSCF) method followed by the internally contracted multi-reference configuration interaction (MRCI) approach in combination with the correlation-consistent basis sets, this paper studies the potential energy curves of X²Σ⁺, 2²Σ⁺, 3²Σ⁺, 1²Σ^?, A²Π, 2²Π, 3²Π, 1²Δ, 1⁴Σ⁺, 2⁴Σ⁺, 1⁴Σ^?, 1⁴Π, 2⁴Π and 1⁴Δ Λ-S states of BeBr molecule and the corresponding 30 Ω states for the first time. All the Λ-S states correlate to the first two dissociation channels, Be(¹S_g) + Br(²P_u) and Be(³P_u) + Br(²P_u), of BeBr molecule. Of these Λ-S states, the 3²Π and 2⁴Π are found to be repulsive without the spin–orbit coupling, whereas 1⁴Π, 2⁴Π, 3²Π and 2⁴Σ⁺ are found to be repulsive with the spin–orbit coupling included. A²Π and 2²Σ⁺ possess the double well whether the spin–orbit coupling effect is included or not. Only 1⁴Σ⁺, 1⁴Σ^?, 1²Π and 2²Π are found to be the inverted Λ-S states. The spin–orbit coupling is accounted for by the state interaction approach with Breit–Pauli Hamiltonian using the all-electron cc-pCVTZ basis set. The potential energy curves determined by the internally contracted MRCI method are corrected for size-extensivity errors by means of the Davidson correction. Core–valence correlation correction is calculated with a cc-pCVTZ basis set. Scalar relativistic correction is included using the third-order Douglas–Kroll Hamiltonian approximation at the level of cc-pVTZ basis set. The spectroscopic parameters of all the Λ-S and Ω bound states are evaluated. The spectroscopic parameters are compared with those reported in the literature. Fair agreement is found between the present results and available measurements. In particular, the energy splitting of 204.43 cm^?1 in the A²Π Λ-S state agrees well with the measurements of 201 cm^?1. Analyses demonstrate that the spectroscopic parameters reported here can be expected to be reliably predicted ones.     

Ab initio study of PN electronic states – a qualitative interpretation of the perturbation and predissociation effects on observed transitions

Valence and high electronic states of PN have been calculated with accurate quantum chemistry methods. The variety of theoretical methods used includes complete active space self-consistent field, multireference configuration interaction and the newly developed explicitly correlated coupled cluster methods. The large correlation-consistent atomic orbitals basis sets AVQZ, AV5Z and AV(5+d)Z are used for the potential energy curves calculations in the bonding and long-range regions. The spectroscopic constants (R_e, B_e, ω_e, ω_ex_e, α_e, D_e, T_e) and the vibrational levels of the bound valence states (X¹Σ⁺, A¹Π, a³Σ⁺, d ³Δ, e³Σ^?, C¹Σ^?, b³Π, D ¹Δ and E¹Σ⁺ and some higher bound states) are determined and compared with experimental findings when available. Significant spin–orbit interactions between triplet states and A¹Π and E¹Σ⁺ excited states are found near the crossing points of the potential energy curves and could explain predissociation phenomena and the perturbations of the vibrational levels experimentally observed for PN in their A¹Π and E¹Σ⁺ states.     

Accurate spectroscopic calculations of the 19 Λ-S states and 36 Ω states of the BC+ cation

This work computed the potential energy curves of 19 Λ-S states, which arose from the first five dissociation limits of BC⁺ cation, B⁺(¹S_g) + C(³P_g), B⁺(¹S_g) + C(¹D_g), B⁺(¹S_g) + C(¹S_g), C⁺(²P_u) + B(²P_u), and B⁺(¹S_g) + C(⁵S_u). The calculations were done for internuclear separations from 0.08 to 1.07 nm. The potential energy curves of 36 Ω states yielded from these Λ-S states were also calculated. Core-valence correlation and scalar relativistic correction, basis set extrapolation as well as Davidson correction were accounted for. Of these Λ-S states, the c¹Σ⁺, D³Π, 2¹Π, 2³Σ⁺, 2¹Δ, 3¹Σ⁺, and 4¹Σ⁺ had double wells; the 3³Π and 3¹Π states had three wells; the C³Σ^? and D³Π states were inverted with the spin-orbit coupling effect included; and the second wells of c¹Σ⁺, D³Π and 3¹Σ⁺ states, the second and the third wells of 3³Π state as well as the third well of 3¹Π state were very weakly bound, which well depths were smaller than 400 cm^?1. The spectroscopic parameters were determined for all the states. The vibrational properties were predicted only for some weakly bound states. The spin-orbit coupling effect on the spectroscopic parameters was evaluated.     

Accurate ab initio potential energy curves and spectroscopic properties of the low-lying electronic states of OH− and SH− molecular anions

ABSTRACT

Multireference configuration interaction method was used in order to generate accurate potential energy curves of the OH, SH, OH^? and SH^? electronic states correlating to the three lowest dissociation limits. These curves were used in addition with core–valence correlation and scalar relativistic corrections for the calculations of accurate spectroscopic constants of bound states, which generally are found in excellent agreement with best available experimental and theoretical values in the literature. The spin–orbit interactions between electronic states have been calculated for the cases in which the couplings were assumed to be responsible for perturbations and used to explain the predissociation of A²Σ⁺ state of OH and SH by dissociative states 1⁴Σ^?, 1²Σ^? and 1 ⁴Π. Dipole moment functions were also computed along internuclear distances and used to explain polarity of these molecules in different calculated electronic states. In addition, stability and metastability of electronic states (X ¹Σ⁺, A¹Π and a³Π) of OH^? and SH^? molecular anions have been studied relatively to curves of neutral parent electronic states. Finally, we have computed adiabatic electron affinity of OH and SH and these values have been found in very good agreement with the best experimental values and resort as among the best achieved values.     

The C-N Stretching Vibronic Bands of the MgNC ÃΠ-X?Σ Transition

We have generated MgNC in supersonic free jet expansions and measured the laser-induced fluorescence excitation spectra of the C-N stretching vibronic bands of the òΠ-X?²Σ⁺ transition. Rotational analysis yields the molecular constants of the vibronic levels, (1,0,0) and (1,0,1), in the Ã²Π state. We cannot find any anomalies in the constants of these vibronic levels, while they are predicted to lie above the barrier of the isomerization reaction pathway, MgNC↔MgCN, on the Ã²Π state. On the basis of the molecular constants obtained, we discuss the fine structures of both the ground X?²Σ⁺ and excited Ã²Π states.     

The lower excited states of CS: A study of extensive spin-orbit perturbations

We present previously unpublished data on the A¹Π, e³Σ^?, d³Δ_i, $\text{a′}{}^3\text{Σ}{}^{\mathrm{+}}$, and a³Π states of CS from uv emission and absorption transitions to the X¹Σ⁺ ground state. Term values obtained from d³Δ_i ← a³Π ir emission bands are also included. Rotational analyses are presented for about 50 new fine-structure components in some 30 new vibrational levels, together with extended data and analyses for many of the previously observed levels. The data now availabe for these five electronic states more than triples that previously published. Vibrational numbering for the e, d, and a′ states is established by data for minor isotopes. In a Hund's case a-b basis, off-diagonal spin-orbit elements (incipient case c effects) produce extensive coupling among these levels, not only for perturbation crossings but also between levels widely separated in energy. A systematic deperturbation requires two stages, which are iterated. Term values computed from the spectral lines are used to fit parameters of Hamiltonian matrices for groups of nearby, coupled levels. Additional shifts are computed by second-order perturbation theory from the electronic interactions deduced from vibronic coupling elements. The resultant parameters satisfy certain tests for self-consistency; they conform to low-order polynomials in $\text{v +}\text{1}\text{2}$, and vibrational overlap factors from wave-functions computed with RKR potential curves are proportional to the vibronic coupling elements, to within experimental error in most cases. To obtain this self-consistency, we have computed and applied normally neglected centrifugal distortion effects in the off-diagonal coupling elements and in the second-order perturbation sums. We also present and interpret the diagonal spin-orbit fine structure in the a and d states, including the centrifugal distortion parameters, A_D, for the latter, and values for several fitted second-order elements. Possible assignments for three additional perturbations of the A¹Π state and one faint band are discussed in view of ¹Δ, ¹Σ^?, and ⁵Π states that are also expected to occur in the region studied. Tentative parameters for the D¹Δ state are obtained from one possible set of assignments.     

Fourier transform spectroscopy of CrO: Rotational analysis of the A5Σ-X5Π (0,0) band near 8000 cm−1

The emission spectrum of CrO has been investigated by Fourier transform spectroscopy in the near infrared. New weak electronic bands have been found in the 6000- to 10 000-cm^?1 region, the strongest of which, near 8000 cm^?1, is shown to be the (0,0) band of a ⁵Σ-⁵Π transition where the ⁵Π lower state is the ground state. Fifty branches have been assigned in this band, which have permitted the first detailed characterizations of quintet electronic states in the gas phase. Accurate values have now been obtained for the spin-orbit coupling and Λ-doubling intervals in the ground state (which could only be estimated in the previous laser-induced fluorescence work in the visible region by Hocking et al. [Canad. J. Phys.58, 516–533 (1980)]). The relative branch intensities are not consistent with those calculated for a pure ⁵Σ-⁵Π(a) transition, and indicate considerable spin-orbit contamination such that there are interference effects between two or more competing transition moments. It is not known whether the ⁵Σ excited state is ⁵Σ⁺ or ⁵Σ^?.     

Electronic states and spectroscopic properties of GeSi

Electronic structure and spectroscopy of the GeSi molecule have been investigated by performing ab initio based multireference configuration interaction calculations. Potential energy curves of 29 Λ-S states of singlet, triplet, and quintet spin multiplicities have been constructed. Spectroscopic constants of 24 bound states within 36 000 cm⁻¹ are reported and compared with the available data. The calculated dissociation energy of GeSi in the ground state is 2.80 eV. Effects of the spin-orbit coupling on the spectroscopic properties of the molecule have been found to be small. However, the computed zero-field-splitting of the ground state compares well with the earlier prediction. Transitions such as 2³Σ⁻-X³Σ⁻, 3³Σ⁻-X³Σ⁻, 4³Π-A³Π, 5³Π-A³Π etc. are relatively strong. Radiative lifetimes for several dipole allowed and spin-forbidden transitions are calculated. The estimated lifetimes of the 2³Σ⁻, 3³Σ⁻, and 5³Π states are about 109, 33, and 62 ns, respectively. Dipole moments of most of the low-lying states of GeSi are also reported.     

The electronic spectrum of PN. A configuration interaction study

Potential energy curves were calculated for the ground state of PN and for all excited singlet and triplet states resulting from the 2π → 3π, 7σ → 3π, 2π → 8σ, and 7σ → 8σ orbital excitations. CI studies at 4 Å served to establish dissociation energies. Spectroscopic constants were calculated, and are in good agreement with those of the known X¹Σ⁺ and A¹Π states. Overall, their similarity with those observed for N₂ is striking. Various states considered to perturb the known excitations are discussed. The recently discovered second ¹Σ⁺ state is included.     

Accurate potential energy curves and spectroscopic properties of the 27 Λ-S states and 73 Ω states of the PO radical

The potential energy curves (PECs) were calculated for the 27 Λ-S states and 73 Ω states of PO radical. The calculations were done using the CASSCF method, which was followed by the internally contracted multireference configuration interaction (icMRCI) approach. To improve the quality of PECs, core-valence correlation and scalar relativistic corrections as well as Davidson correction were included. Of the 27 Λ-S states, the 1⁶Σ⁺ state was repulsive at any case. The 1⁴Φ and 1⁶Π states were bound, but they became repulsive with the spin-orbit coupling (SOC) effect accounted for. The 3⁴Σ⁺, a⁴Π, C′²Δ, D′²Π, 1⁴Δ, 1²Φ, 1⁶Σ⁺ and 1⁶Π states were inverted with the SOC effect included. The F²Σ⁺ state had double wells. The avoided crossings existed between the B²Σ⁺ and F²Σ⁺ states, the F²Σ⁺ and 3²Σ⁺ states, the C′²Δ and 2²Δ states, the 1⁴Δ and 2⁴Δ states, the 2⁴Δ and 3⁴Δ states, the 2⁴Π and 3⁴Π states and the 3⁴Π and 4⁴Π states. The c⁴Σ⁺, 2⁴Σ⁺, 3⁴Σ⁺, 3⁴Π, 4⁴Π, 5⁴Π, 3⁴Δ, 1⁴Φ and 1⁶Π states were weakly bound, which well depths were within several hundred cm^?1. The spectroscopic parameters were derived. The SOC effect on the spectroscopic properties was evaluated. The spectroscopic results obtained here could be expected to be reliably predicted ones.     

MRCI studies on ground and excited states of CBr

Potential curves and spectroscopic constants for a large number of doublet and quartet states of CBr were obtained by multireference configuration interaction calculations, using valence triple-zeta basis sets with polarization and diffuse functions. Besides the X²Π ground state, 1⁴Σ^?, 1²Δ and 2²Σ⁺ have been found to be stable. Spectroscopic constants calculated for 1²Δ are in excellent agreement with experimental values obtained by Dixon and Kroto in 1963. Their observed predissociation of one component of 1²Δ can be explained by the crossing of the 1²Δ potential near equilibrium by 1²Σ⁺. The 1²Σ⁺ state is calculated to have a shallow long-range minimum at 2.31?Å. The dissociation energy of X²Π is calculated to be 3.43?eV. An observed T _e of 4.97?eV for 2²Σ⁺ agrees with the theoretical value. Several Rydberg states of the 2π→Ryd and 3σ→Ryd series, starting at T _e ?=?5.25?eV, were identified. Photodissociation of CBr by sunlight, important in the ozone cycle, can occur via direct dissociation of the ground state, or by excitation to 1²Δ followed by predissociation. Most dissocative repulsive states lie at higher energies, and are not expected to participate in the photodisscociation of CBr.     

Feshbach resonances of the C3H− anion: laser autodetachment spectroscopy and ab initio calculations

The electronic spectra of the C₃H^? and C₃D^? anions have been studied above the lowest electron detachment threshold. On the basis of the vibrational, rotational analysis and ab initio calculations, the photodetachment spectrum is assigned to the d³ A″←a³ A″ Feshbach resonance in the bent chain C₃H(D)^? anion. The vibronic system is characterized by a long vibrational progression involving the CCH in plane bending mode ν₄. The potential curves along this coordinate obtained from the spectral analysis and theoretical calculations reveal the importance of vibronic coupling in the electronic excited states. A strong Renner–Teller effect is thought to be the reason for the existence of the Feshbach resonance because the ⁴Σ^? neutral parent and the ³Π anion excited states are close in energy. As for the neutral, ν₄ appears to be the active mode and drives the interaction between the Feshbach and the dipole bound states.     

The electronic states of silicon monofluoride: Rydberg states

SCF-CI calculations are reported for the Rydberg states converging to the ground state of the SiF⁺ ion. The adjustment between the observed and calculated values for the energy of the first Rydberg B²Σ⁺ state has allowed the characterization of 15 observed ²Σ⁺ and ²Π Rydberg states. A value of 58960 cm^?1 has been obtained for the ionization potential of SiF. The A²Σ⁺ state appears to be a valence state with some Rydberg character.     

The rotational spectrum of 13C2HD in the ground and excited bending states

The pure rotational spectrum of ¹³C₂HD was recorded in the range 100–700 GHz. Lines belonging to the ground vibrational state were observed from J^″ = 1 to J^″ = 11. Several absorption lines were also detected in the bending states v₄ = 1 (Π), v₅ = 1 (Π), v₄ = 2 (Σ⁺ and Δ), v₅ = 2 (Σ⁺ and Δ), v₄ = v₅ = 1 (Σ^?, Σ⁺ and Δ), v₄ = 3 (Π and Φ) and v₅ = 3 (Π and Φ). The transition frequencies measured in this work were fitted together with all the infrared lines available in the literature. The global fit allowed a very accurate determination of the vibrational, rotational and ?-type interaction parameters for the bending states of this molecule.     

Theoretical electronic structure of the lowest-lying states of ScCl molecule below 22 500 cm

Potential energy curves and theoretical spectroscopic constants are obtained for 18 electronic states of ScCl molecule in the representation ^2s+1Λ^+/− by CASSCF/MRCI calculations in all electron schemes for both atoms scandium and chlorine. The theoretical computational results of the lowest 10 singlet states and of 5 triplet states are in good agreement with experimental values and confirm the relative order of these states. In this work, three unobserved triplet states (2)³Π, (1)³Σ⁻ and (3)³Π are predicted for the first time in the transition energy range of 22 500 cm⁻¹.