Accurate theoretical spectroscopic investigations of the 20 Λ-S and 58 Ω states of O2+ cation including the spin–orbit coupling effect

The potential energy curves (PECs) are calculated for the 20 Λ-S states (X²Π_g, A²Π_u, B²Σ^?_g, a⁴Π_u, b⁴Σ^?_g, b′⁴Π_g, c⁴Σ^?_u, 1²Σ⁺_g, 1²Σ⁺_u, 1²Σ^?_u, 1⁴Σ⁺_g, 1⁴Σ⁺_u, 1⁴Δ_g, 1⁴Δ_u, 1⁶Σ⁺_g, 1⁶Σ⁺_u, 1⁶Π_g, 1⁶Π_u, 2⁴Π_g and 2⁴Π_u) of O₂⁺ cation and their corresponding 58 Ω states. Of these 20 Λ-S states, the 1⁶Π_u state is found to be repulsive. The 1²Σ⁺_g, 1⁴Σ⁺_u, c⁴Σ^?_u and 1⁴Δ_u states are found to possess the double well. The b⁴Σ^?_g, 1⁶Σ⁺_g, 1⁴Σ⁺_u, a⁴Π_u, A²Π_u, 1⁶Π_g and 2⁴Π_g states are found to be inverted with the spin–orbit coupling effect included. The b′⁴Π_g, 1⁶Π_g, 1⁶Σ⁺_g, 1⁴Σ⁺_u and 1⁴Δ_u states, and the second well of the 1²Σ⁺_g state are found to be the weakly bound states. The b′⁴Π_g state is found to possess one well with one barrier. The PECs are calculated by the complete active space self-consistent field method, which is followed by the internally contracted multireference configuration interaction approach with the Davidson correction in combination with the aug-cc-pV6Z basis set. The core–valence correlation and scalar relativistic corrections are included. The convergent behaviour of present calculations is discussed with respect to the basis set and theoretical level. The spin–orbit coupling effect is accounted for. The PECs are extrapolated to the complete basis set limit. The spectroscopic parameters are evaluated, and compared with available measurements. It demonstrates that the spectroscopic parameters reported here can be expected to be reliably predicted ones.     

Low-lying energy levels of the FeH molecule

Multireference configuration interaction (MRCI) and complete active space second-order perturbation theory (CASPT2) calculations are performed on Fe₂ and Fe^? ₂. Although it is not possible to definitively identify the ground states of Fe₂ and Fe^? ₂, the calculations suggest that the ground state of Fe^? ₂ in ⁸Σ^? _u derived from 3d¹³4σ² _g4σ² _u and that the states observed in photodetachment are the ⁹Σ^? _g and ⁷Σ^? _g states with a 3d¹³4σ² _g4σ¹ _u occupation, but that the ground state of Fe₂ is ⁷Δ_u(3d¹⁴4σ² _g) and is not observed in the photo-detachment spectra.     

Li2分子自旋一致激发态a3Σ+u和b3Πu的分析势能函数的从头算

使用对称性匹配簇-组态相互作用方法首次计算了Li₂分子自旋一致激发态a³Σ⁺_u和b³Π_u的离解能、平衡几何及其谐振频率。使用最小二乘法、利用Murrell-Sorbie函数形式拟合出了Li₂分子三重态的第一激发态a³Σ⁺_u 和第二激发态b³Π_u的完整势能函数，并计算了这两个态的光谱常数 (B_e, α_e, ω_e 和 ω_eχ_e) 和力常数 (f₂, f₃和f₄)。得到了Murrell-Sorbie函数形式既适用于基态、又适用于激发态的结论。将计算得到的激发态（a³Σ⁺_u和b³Π_u）的离解能、平衡几何及其谐振频率与实验结果及其它理论计算结果进行了比较。从比较的结果中可以清楚地看出，本文的计算结果在计算精度方面有很大的改进。     

Analytical potential energy functions for the ground and some excited states of N2

The analytical potential energy functions have been calculated for the ground state X¹Σ⁺_g and four excited electronic states a¹Π_g, A³Σ⁺_u, B′³Σ^?_u and B³Π_g of N₂ molecule using the algebraic and energy-consistent methods (AM-ECM). Based on our previously published full AM vibrational energies and spectroscopic constants, the low-lying force constants f_n, the expansion coefficients a_n and the variational parameters λ in the AM–ECM potentials are determined for these states. The computed AM–ECM potential energy curve of each state is in excellent agreement with the experimental data and better than other analytical potentials.     

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.     

A numerical study of the convergency of second and approximate second-order multiconfiguration Hartree-Fock procedures

A detailed numerical study has been made of the convergency of second-and approximate second-order multiconfigurational Hartree-Fock procedures. Calculations were performed on the excited 2p ^{2 1} S state of Be and on the lowest states of ³Σ _g ^-, ¹δ _g , ¹Σ _g ⁺, ¹Δ _g and ³Δ _g symmetry in O₂. The O₂ calculations included all configurations that could be formed from doubly occupied core orbitals with eight electrons in the valence orbitals, 3σ _g , 1π _u , 1π _g and 3σ _u . All second-order calculations converged in between 4 and 6 iterations even for a case where approximate second-order procedures did not converge.     

Ab initio calculation of transition dipole moments for transitions between valence states in oxygen molecules

Results of ab initio calculations of potential-energy curves for 20 singlet and 20 triplet valence states of oxygen with configuration interaction taken into account in the 6-31G basis are presented. Transition dipole moments of triplet-triplet (1³Π_g ← B ³Σ _u ^? , 1³Π_g ← A ³Σ _u ⁺ , 1³Π_g ← A′ ³Δ_u, B ³Σ _u ^? ← X ³Σ _g ^? , 2³Π_u ← 1³Π _g, 2³Σ _g ^? ← B ³Σ _u ^? , 1³Π_u ← X ³Σ _g ^? , 2³Π_u ← X ³Σ _g ^? , 2³Π _g ← A′³Δ_u, 3³Π_g ← A′ ³Δ _u, 2³Δ_u ← 2³Π_g, 3³Π_g ← B ³Σ _u ^? , and 2³Π_g ← A ³Σ _u ⁺ ) and singlet-singlet (2¹Σ _g ⁺ ← 2¹Π_u, 2¹Π_u ← 1¹Π ^g, ¹Π_u ← 2¹Δ_g, 1¹Π_g ← c ¹Σ _u ^? , ¹Π_u ← b ¹Σ _g ⁺ , 1¹Δ _u ← a ¹Δ_g, 2¹Π_u ← a ¹Δ_g, 2¹Δ_g ← 1¹Δ_u, ¹Π _u ← a ¹Δ _g, 1¹Π_u ← b ¹Σ _g ⁺ , 2¹Π_g ← 1¹Π_u, 2¹Π _g ← c ¹Σ _u ^? , 1¹Δ _u ← 1¹Π _g, f′Σ _u ⁺ ← b ¹Σ _g ⁺ , 2¹Σ _g ⁺ ← f ′¹Σ _u ⁺ , 3¹Π_g ← 1¹Δ_u) radiative transitions are calculated as functions of internuclear separation. The possibility of observing these transitions under experimental conditions is discussed.     

Spectroscopic and molecular properties of 14 selected electronic states of Si2 molecule

The potential energy curves (PECs) of the X³Σ_g⁻, D³Π_u, a¹Δ_g, b¹Π_u, H′³Σ_u⁻, K³Σ_u⁻, 1³Σ_u⁺, 1³Π_g, 2³Σ_u⁺, 2³Π_g, 3³Π_g, 3³Σ_u⁺, 2³Π_u and 2³Σ_g⁻ electronic states of the Si₂ molecule are investigated using the complete active space self-consistent field (CASSCF) method followed by the valence internally contracted multireference configuration interaction (MRCI) approach with the correlation-consistent basis sets of Dunning and co-workers. The effects on the PECs by the core-valence correlation and relativistic corrections are included. The way to consider the relativistic correction is to use the third-order Douglas-Kroll Hamiltonian approximation. The core-valence correlation correction is made with the aug-cc-pCV5Z basis set. And the relativistic correction is performed at the level of cc-pV5Z basis set. To obtain more reliable results, the PECs determined by the MRCI calculations are also corrected for size-extensivity errors by means of the Davidson modification (MRCI+Q). The PECs of all these electronic states are extrapolated to the complete basis set limit by the total-energy extrapolation scheme. Using the PECs, the spectroscopic parameters are determined and compared with those reported in the literature. With these PECs determined by the MRCI+Q/CV+DK+56 calculations, the vibrational levels and inertial rotation constants of the first 20 vibrational states are evaluated and compared with the RKR data for these electronic states when the rotational quantum number J equals zero. On the whole, as expected, the most accurate spectroscopic parameters and molecular constants of the Si₂ molecule are determined by the MRCI+Q/CV+DK+56 calculations. And the spectroscopic parameters of the 1³Σ_u⁺, 1³Π_g, 2³Σ_u⁺, 2³Π_g, 3³Π_g, 3³Σ_u⁺, 2³Π_u and 2³Σ_g⁻ electronic states obtained by the MRCI+Q/CV+DK+56 calculations should be good prediction for future laboratory experiment.     

Studies on the Vibrational and Rovibrational Energies and Vibrational Force Constants of Diatomic Molecular States Using Algebraic and Variational Methods

Alternative expressions for vibrational and rotational spectrum constants and energies of diatomic molecular electronic states based on perturbation theory are suggested. An algebraic method (AM) is proposed to generate a converged full vibrational spectrum from limited energy data, and a potential variational method (PVM) is suggested to produce the vibrational force constants f_n and rotational spectrum constants using the perturbation formulae and the AM vibrational constants. The AM and PVM have been applied to study 10 diatomic electronic states: the X¹Σ_g⁺ and C¹Π_u⁻ states of H₂; the X¹Σ_g⁺, A³Σ_u⁺, B′³Σ_u⁻, and B³Π_g states of N₂; the X³Σ_g⁻, A³Σ_u⁺, and c¹Σ_u⁻ states of O₂; and the X¹Σ_g⁺ state of Br₂. Calculations show that (1) the AM E_υmax converges to the correct molecular dissociation energy; (2) the AM not only reproduce the input energies, but also generate the E_υ's of high vibrational excited states which may be difficult to obtain experimentally or theoretically; (3) the PVM vibrational force constants f_n may be used to measure the relative chemical bondstrengths of different diatomic electronic states for a molecule quantitatively.     

Fine and hyperfine structure in three low-lying 3Σ+ states of molecular hydrogen

The fine structure constant (electron spin-spin coupling) and the hyperfine structure parameters (electron-nuclear spin coupling, including spin-rotation and electron-nuclear quadrupole coupling) in the low-lying triplet states b³Σ⁺ _u, a³Σ⁺ _g and e³Σ⁺ _u of molecular hydrogen and deuterium are calculated using a recently developed technique with full configuration interaction and multiconfiguration self-consistent field wave functions. The second-order spin-orbit coupling contribution to the ³Σ⁺ states splitting is negligible, and the calculations therefore provide a good estimate of the zero-field splitting based only on the electron spin-spin coupling values. For the bound a³Σ⁺ _g state a negligible zero-field splitting is found, in qualitative agreement with the e-a spectrum. The zero-field splitting parameter is considerable for the repulsive b³Σ⁺ _u state (?1 cm^?1) and of intermediate size for the bound e³Σ⁺ _u state. The isotropic hyperfine coupling constant is very large not only for the valence b³Σ⁺ _u state (1580 MHz) but also for the Rydberg a and e triplet states (?1400 MHz). The quadrupole coupling constants for the deuterium isotopes are negligible (0.04–0.07 MHz) for all studied triplet states. The electric dipole activity of the spin sublevels in the triplet-singlet transitions to the ground state is estimated by means of the quadratic response technique.     

Energy levels of rare-earth ions in Gd<Subscript>2</Subscript>O<Subscript>2</Subscript>S

The energies of the ground 4f ⁿ levels of tri- and divalent rare-earth ions with respect to the conduction and valence bands of Gd₂O₂S crystal has been determined. It is shown that the Pr³⁺, Tb³⁺, and Eu³⁺ ions can be luminescence centers in Gd₂O₂S. The levels of the Nd³⁺, Dy³⁺, Er³⁺, Tm³⁺, Sm³⁺, and Ho³⁺ ions lie in the valence band; therefore, these ions cannot play the role of activators. The ground 4f level of the Ce³⁺ ion is near the midgap, due to which Ce³⁺ effectively captures holes from the valence band and electrons from the conduction band and significantly decreases the afterglow level of the Gd₂O₂S:Pr and Gd₂O₂S:Tb phosphors.     

High-resolution optogalvanic study of the c4(0)1Πu, c′5(0)1Σu+, and a″(0)1Σg+ Rydberg states of N2

A new optogalvanic technique with an rf discharge was applied to a high-resolution study of the Rydberg states of N₂. The Ledbetter band, c₄(0)¹Π_u ← a″(0)¹Σ_g⁺, and a new visible band, c′₅(0)¹Σ_u⁺ ← a″(0)¹Σ_g⁺, were studied at a Doppler-limited resolution of 0.05 cm^?1. A Doppler-free method was also applied to resolve overlapped lines. Precise wavenumbers were determined for the rotational transitions of the two Rydberg bands. The rotational and the centrifugal constants for the lowest Rydberg state, a″(0)¹Σ_g⁺, were determined to be B₀ = 1.913748(42) cm^?1 and D₀ = 6.088(99) × 10^?6 cm^?1, where the numbers in parentheses are the standard deviation and apply to the last digits.     

Electronic states and transitions of the TeX (X = C1, Br,I) radicals

Ab initio multireference configuration interaction calculations including spin-orbit coupling have been carried out for the first time for valence electronic states of the TeX (X = Cl, Br, I) radicals and compared with the results for the isovalent TeF and IO systems obtained earlier at a similar level of theoretical treatment. The calculated spectroscopic constants are in good agreement with experimental data in the rare cases when the latter are available. It is shown that the X² II(σ²π⁴π?³) ground state bonding becomes consistently weaker down the TeX group (calc. D_e, = 25480cm^?1 for TeF, 12 100cm^?1 for Tel) due to the more covalent character of bonding in the heavier radicals. The first excited state, A ⁴Σ^? (π?→ σ?), is calculated to be bound in all systems. It is split into Ω 1/2 and 3/2 components, with regular ordering in the Franck-Condon region, opposite to that of the ground X²II state. For larger internuclear distances, the A₁ ⁴Σ^? _1/2 state undergoes an avoided crossing with X₂ ²II_1/2, which causes a shoulder in the X₂ potential curve and also leads to a crossing between the A₁, and A₂ curves and large distinctions in their vibrational frequencies. The π? → σ? B²Σ^?, C²δ, and 1 ²Σ⁺ states are calculated to lie next in energy. They are all bound in the lightest of the TeX radicals, TeF, but successively lose their bonding character down the group. In contrast to oxygen monohalides, the 2²II(σ²π³ π?⁴) state has a repulsive potential curve. Electric dipole transition moments and radiative lifetimes have also been calculated for the low lying bound states in all systems. Most of them are found to be quite weak. The A^1,2 → X^1,2 spectra are dominated by parallel contributions, with the A₂ → X₁ being the strongest one. The T values for this transition are quite similar and lie in the 17–30 μs range. Radiative lifetime values for the B → X^1,2 transitions demonstrate very irregular behaviour for various, TeX radicals, due to strong admixture of A⁴Σ^? character to the X^1,2 states near the B²Σ^? potential minimum. The A^{1,2 4}Σ^? _1/2,3/2 and B²Σ^? _1/2 states of TeX (X = Cl, Br, I) still await their experimental observation.     

Singlet-triplet anticrossings between ungerade states of H2

Singlet-triplet anticrossings in the H₂ molecule have been observed between two ungerade states, B′(3p)¹Σ_u⁺ and f(4p)³Σ_u⁺. This is the first time that an observed H₂ anticrossing has involved a state which can radiate directly to the ground state. Analysis yields accurate values for the zero field separations between two pairs of rotational and vibrational levels. It also yields a value for the Fermi contact interaction in the triplet state as well as the difference in the orbital angular momentum g factors for the two states. From linewidth measurements, we deduce a rigorous lower limit to the radiative lifetime of the B′¹Σ_u⁺ state and a (nearly equal) most reasonable value for it. It is shown that the perturbation between the two states is quite weak leading to little singlet-triplet mixing in zero field. The experimental data establish that the oscillator strength for the forbidden transition from the ground state to the f(4p)³Σ_u⁺ state is at least seven orders of magnitude smaller than that of the allowed transition to the B′¹Σ_u⁺ state.     

Threshold energy electron impact excitation of carbon dioxide and carbon disulphide

The threshold energy electron impact excitation spectra of CO₂ and CS₂ have been studied using the sulfur hexafluoride scavenger technique. The main results are triplet state excitation and autoionisation of negative ions associated with resonant excited states of the molecules. This confirms previous data concerning diatomic molecules. Furthermore, transitions such as ¹Π_g?X¹Σ_g⁺ and ¹Π_u?X ¹Σ_g⁺ are only weakly induced by low energy electrons, while the corresponding triplet excitations are probably more easily produced. Structures at 5.6, 6.1 and 6.6 eV observed in CS₂ are due to negative ions and/or to ³Π_u, ³Π_g excitation.The autoionisation of CO₂^?(X²Π_u) proceeds also by ejection of a thermal energy electron and leads to highly excited vibrational levels (3–5 eV) of the ground electronic state of CO₂.     

Theoretical study of hyperfine coupling constants and electron spin g factors for X2Σ+ diatomics from Groups 1 and 2

The ESR parameters of the cations Be⁺ ₂, Mg⁺ ₂, Ca⁺ ₂, BeMg⁺, BeCa⁺, MgCa⁺ and the mixed radicals ZBe, ZMg, ZCa (Z = Li, Na, K), all having a X ²Σ⁺ _u(1σ² _g1σ_u)/X ²Σ⁺(1σ²2σ) ground state, have been studied theoretically. The A _iso and A _dip constants have been calculated with UHF, CISD, MP2, B3LYP, PW91PW91 wavefunctions, and 6–311+G(2df) basis sets. The electron spin g factors (magnetic moment μ_s) have been evaluated from correlated (MRDCI) wavefunctions, using a Hamiltonian based on Breit-Pauli theory with perturbation expansions up to second order, and 6–311 + G(2d) basis sets. As expected for s-rich radicals, the hyperfine spectra are governed by the A _iso terms. Both Δg∥ and Δg⊥ values are negative, but Δg∥ lies close to zero. For Δg⊥, the coupling with 1 ²Π_(u) dominates the sum-over-states expansions. Although the singly occupied MOs (SOMO) are mostly of s character, the |Δg⊥| are relatively large, up to 5200 ppm for cationic, and up to 7850 ppm for neutral radicals. These large values are caused by low excitation energies and high magnetic transition moments, the latter due to the fact that the σ?(s-s) SOMO has the same nodal properties as a pσ orbital. Of the radicals considered here, an ESR spectrum is available only for Mg⁺ ₂. Our theoretical A _iso of ?287 MHz reproduces well the matrix result (-291 MHz). Calculated values of ?10 ppm for Δg∥ and of ?1280 ppm for Δg⊥ give an average 〈Δg〉 = ?860 ppm that lies within the experimental range of ?600(±300) ppm in Ne, and of ?1300(±500) ppm in Ar matrices.     

Calculation of molecular constants for the X 1Σ g + , A 1Σ u + , B 1Πu, and a 3Σ u + electronic states of 39K2

The molecular constants are calculated for the X ¹Σ _g ⁺ , A ¹Σ _u ⁺ , B ¹Π_u, and a ³Σ _u ⁺ and electronic states of a potassium dimer. The wave functions and vibrational energies necessary for calculating the molecular constants are determined by solving the radial wave equation with the use of potential energy curves constructed by the semiempirical method. The vibrational terms, the rotational constants, and the centrifugal distortion constants calculated from the potential curves are compared with those determined from the experimental data.     

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.     

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.     

Fourier Transform Emission Spectroscopy of the FΣ-XΣ System of RuN

Emission spectra of RuN have been recorded at high resolution in the region 12 000-35 000 cm⁻¹ using a Fourier transform spectrometer. The molecules were excited in a ruthenium hollow cathode lamp in the presence of about 2.5 Torr of Ne and 5 m Torr of N₂. New bands with origins near 17 758.1, 18 866.4, 19 800.4 and 20 721.5 cm⁻¹ have been assigned as the 0-1, 0-0, 1-0, and 2-0 bands of a new ²Σ⁺-²Σ⁺ system with the lower state as the ground state. This transition has been labeled as F²Σ⁺-X²Σ⁺, with the F²Σ⁺ state arising from the 1σ²2σ²1π⁴1δ⁴4σ¹ configuration. A rotational analysis of these bands has been carried out and spectroscopic constants have been extracted. The principal equilibrium constants for the ground state of RuN are ΔG(1/2)″=1108.3235(22) cm⁻¹, B_e″=0.5545023(42) cm⁻¹, α_e″=0.0034468(57) cm⁻¹, r_e″=1.5714269(60) Å, while the equilibrium constants for the excited state are ω_e′=946.8471(40) cm⁻¹, ω_ex_e′=6.4229(14) cm⁻¹, B_e′=0.50085(21) cm⁻¹, α_e′=0.00375(10) cm⁻¹, r_e′=1.65345(34) Å. This transition is analogous to the E²Σ⁺-X²Σ⁺ system of RhC (W. J. Balfour et al., J. Mol. Spectrosc.198, 393 (1999)).