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The paper presents the Morse potential-based calculation of Franck–Condon factors which have not been investigated from the point of view of allowed transitions associated with the first negative and second positive systems. For nonallowed transitions, it is shown that the Morse potential provides an exact calculation of factors, depending on vibrational constants. During the vibrational number increase, the deviation is observed between calculated Franck–Condon factors and those determined by the more accurate Rydberg–Klein–Rees potential. [ABSTRACT FROM AUTHOR]

This paper calculates the potential energy curves of 21 Λ–S and 42 Ω states, which arise from the first two dissociation asymptotes of the CO + cation. The calculations are conducted using the complete active space self–consistent field method, which is followed by the valence internally contracted multireference configuration interaction approach with the Davidson correction. To improve the reliability and accuracy of the potential energy curves, core–valence correlation and scalar relativistic corrections, as well as the extrapolation of potential energies to the complete basis set limit are taken into account. The spectroscopic parameters and vibrational levels are determined. The spin–orbit coupling effect on the spectroscopic parameters and vibrational levels is evaluated. To better study the transition probabilities, the transition dipole moments are computed. The Franck–Condon factors and Einstein coefficients of some emissions are calculated. The radiative lifetimes are determined for a number of vibrational levels of several states. The transitions between different Λ–S states are evaluated. Spectroscopic routines for observing these states are proposed. The spectroscopic parameters, vibrational levels, transition dipole moments, and transition probabilities reported in this paper can be considered to be very reliable and can be used as guidelines for detecting these states in an appropriate spectroscopy experiment, especially for the states that were very difficult to observe or were not detected in previous experiments. [ABSTRACT FROM AUTHOR]

This paper investigates the spectroscopic parameters and transition probabilities of 25 low-lying states, which come from the first five dissociation channels of AlC + cation. The potential energy curves are calculated with the complete active space self-consistent field method, which is followed by the valence internally contracted multireference configuration interaction approach with Davidson correction. Of these 25 states, only the 3 5 Σ − s tate is repulsive; the c 1 Σ + , f 1 Π, and 1 5 Π states have the double well; the first well of c 1 Σ + state and the second well of 1 5 Π state are very weakly bound; the first well of c 1 Σ + state has no vibrational levels; the 2 5 Π state and the double well of f 1 Π state have only several vibrational states; the B 3 Σ − , E 3 Σ + , D 3 Π, 1 5 Σ + , 2 5 Σ − , and 1 5 Π states are inverted when the spin-orbit coupling effect is included. The avoided crossings exist between the B 3 Σ − and 3 3 Σ − states, the c 1 Σ + and d 1 Σ + states, the f 1 Π and 3 1 Π states, the 1 5 Π and 2 5 Π states, as well as the 2 5 Π and 3 5 Π states. Core-valence correlation and scalar relativistic corrections are considered. The extrapolation of potential energies to the complete basis set limit is done. The spectroscopic parameters and vibrational levels are determined for all the Λ–S and Ω bound states. The transition dipole moments are calculated. Franck–Condon factors of a great number of electronic transitions are evaluated. On the whole, the spin-orbit coupling effect on the spectroscopic parameters and vibrational levels is small except for very few states. The results determined in this paper could provide some powerful guidelines to observe these states in a spectroscopy experiment. [ABSTRACT FROM AUTHOR]

The potential energy curves of 23 states of AlN radical are calculated to accurately determine the first several lowest-lying singlet and triplet states. The calculations are done using the CASSCF method, which is followed by the valence internally contracted MRCI approach. The rotationless radiative lifetimes of the vibrational levels are approximately 10−7–10−8 s for the C3Π, D3Π, and E3Δ states, 101–10−4 s for the A3Σ− state, and 10−4–10−5 s for the B3Σ+ state. The origins of the vibronic bands and the radiative lifetimes agree well with the available experimental and other theoretical results. The Einstein coefficients of many vibronic emissions are large for the C3Π–X3Π, C3Π–A3Σ−, D3Π–X3Π, D3Π–A3Σ−, and E3Δ–X3Π transitions and therefore, these transitions are strong. The emissions of the E3Δ–D3Π system are so weak that it is difficult to measure them through spectroscopy. The spectral distribution of the vibronic emissions is evaluated for the transitions of 12 pairs of states. In terms of the radiative lifetimes and transition probabilities obtained here, several spectroscopic routines for observing these states via spectroscopy are proposed. This paper calculates the potential energy curves, spectroscopic parameters, transition dipole moments, and transition probabilities of the AlN radical. The rotationless radiative lifetimes of the vibrational levels are of the order of 10−7 to 10−8 s for the C3Π, D3Π, and E3Δ states, 10−4 to 10−5 s for the B3Σ+ state, and 101 to 10−4 s for the A3Σ− state. The lifetimes of the C3Π, D3Π, and E3Δ states are almost determined by the C3Π–X3Π, D3Π–X3Π, D3Π–A3Σ, and E3Δ–X3Π systems, respectively. Overall, the C3Π–X3Π, C3Π–A3Σ−, D3Π–X3Π, and E3Δ–X3Π transitions, followed by the D3Π–A3Σ− and D3Π–C3Π transitions; the emissions are weak for the A3Σ−–X3Π, D3Π–B3Σ+, and E3Δ–D3Π systems. Curves of the TDM versus internuclear separation of 5pairs of states of the AlN. Unlabelled Image • Lifetimes are of the order of 10−7–10−8 s for the C3Π, D3Π, and E3Δ states. • C3Π–X3Π, C3Π–A3Σ−, D3Π–X3Π, D3Π–A3Σ−, and E3Δ–X3Π transitions are strong. • Lifetimes are 101–10−4 s for the A3Σ− state and 10−4–10−5 s for the B3Σ+ state. • Vibronic emissions of the E3Δ–D3Π system are weak. [ABSTRACT FROM AUTHOR]

This study calculates the potential energy curves of 12 Λ-S and 27 Ω states, which belong to the first dissociation channel of SiC + cation. The potential energy curves are computed with the complete active space self–consistent field method, which is followed by the valence internally multireference configuration interaction approach with the Davidson correction. The transition dipole moments are determined. Core-valence correlation and scalar relativistic correction, as well as extrapolation of the potential energies to the complete basis set limit are included. The spin-orbit coupling effect on the spectroscopic parameters and vibrational properties is evaluated. The vibrational band origins, Franck–Condon factors, and Einstein coefficients of spontaneous emissions are calculated. The rotationless radiative lifetimes of the vibrational levels are approximately 10 −5  s long for the e 2 Π state. The partial radiative lifetimes of vibrational levels are approximately 10 −7  s long for the 2 4 Π and 2 4 Σ − states, 10 −5 to 10 −6  s long for the 2 2 Σ − state and the first well of the 1 4 Π state, and very short for the second well of the 1 4 Π state. Overall, the emissions are strong for the 2 2 Σ − –c 2 Σ − , 2 4 Σ − –X 4 Σ − , 2 4 Π–X 4 Σ − transitions, and for the second well of the 1 4 Π–1 4 Σ + transition. The spectral range of emissions is determined. In terms of the radiative lifetimes and transition probabilities obtained in this paper, some guidelines for detecting these states are proposed via spectroscopy. These results can be used to measure the emissions from the SiC + cation, in particular, in interstellar clouds. [ABSTRACT FROM AUTHOR]

This work calculates the potential energy curves of 9 Λ-S and 28 Ω states of the NCl + cation. The technique employed is the complete active space self-consistent field method, which is followed by the internally contracted multireference configuration interaction approach with the Davidson correction. The Λ-S states are X 2 Π, 1 2 Σ + , 1 4 Π, 1 4 Σ + , 1 4 Σ − , 2 4 Π, 1 4 Δ, 1 6 Σ + , and 1 6 Π, which are yielded from the first two dissociation channels of NCl + cation. The Ω states are generated from these Λ-S states. The 1 4 Π, 1 4 Δ, 1 6 Σ + , and 1 6 Π states are inverted with the spin-orbit coupling effect included. The 1 4 Σ + , 1 6 Σ + , and 1 6 Π states are very weakly bound, whose well depths are only several-hundred cm − 1 . One avoided crossing of PECs occurs between the 1 2 Σ + and 2 2 Σ + states. To improve the quality of potential energy curves, core-valence correlation and scalar relativistic corrections are included. The potential energies are extrapolated to the complete basis set limit. The spectroscopic parameters and vibrational levels are calculated. The transition dipole moments are computed. The Franck-Condon factors, Einstein coefficients, and radiative lifetimes of many transitions are determined. The spectroscopic approaches are proposed for observing these states according to the transition probabilities. The spin-orbit coupling effect on the spectroscopic and vibrational properties is evaluated. The spectroscopic parameters, vibrational levels, transition dipole moments, as well as transition probabilities reported in this paper could be considered to be very reliable. [ABSTRACT FROM AUTHOR]

In this work, we calculate the potential energy curves of 16 Λ-S and 36 Ω states of beryllium boride (BeB) radical using the complete active space self-consistent field method, followed by the valence internally contracted multireference configuration interaction approach with Davidson correction. The 16 Λ-S states are the X 2 Π, A 2 Σ + , B 2 Π, C 2 Δ, D 2 Ʃ − , E 2 Σ + , G 2 Π, I 2 Σ + , a 4 Σ − , b 4 Π, c 4 Σ − , d 4 Δ, e 4 Σ + , g 4 Π, h 4 Π, and 2 4 Σ + , which are obtained from the first three dissociation channels of the BeB radical. The Ω states are obtained from the Λ-S states. Of the Λ-S states, the G 2 Π, I 2 Σ + , and h 4 Π states exhibit double well curves. The G 2 Π, b 4 Π, and g 4 Π states are inverted with the spin-orbit coupling effect included. The d 4 Δ, e 4 Σ + , and g 4 Π states as well as the second well of the h 4 Π state are very weakly bound. Avoided crossings exist between the G 2 Π and H 2 Π states, the A 2 Σ + and E 2 Σ + states, the c 4 Σ − and f 4 Σ − states, the g 4 Π and h 4 Π states, the I 2 Σ + and 4 2 Σ + states, as well as the 2 4 Σ + and 3 4 Σ + states. To improve the quality of the potential energy curves, core-valence correlation and scalar relativistic corrections, as well as the extrapolation of the potential energies to the complete basis set limit, are included. The transition dipole moments are computed. Spectroscopic parameters and vibrational levels are determined along with Franck–Condon factors, Einstein coefficients, and radiative lifetimes of many electronic transitions. The transition probabilities are evaluated. The spin-orbit coupling effect on the spectroscopic parameters and vibrational levels is discussed. The spectroscopic parameters, vibrational levels, and transition probabilities reported in this paper can be considered very reliable and can be employed to predict these states in an appropriate spectroscopy experiment. [ABSTRACT FROM AUTHOR]

This paper calculates the potential energy curves of the 14 Λ-S and 49 Ω states, which come from the first three dissociation channels of the SiN- anion. These calculations are conducted using the valence internally contracted multireference configuration interaction and the Davidson correction approach. Core-valence correlation and scalar relativistic corrections are taken into account. The potential energies are extrapolated to the complete basis set limit. The spin-orbit coupling is computed using the state interaction approach with the Breit-Pauli Hamiltonian. We found that the X¹ Σ+ (ν" = 0-23) and a³ Σ+ (ν' = 0-2) states of SiN- are stable at the computed adiabatic electron affinity value of 23,262.27 cm-1 for SiN. Based on the calculated potential energy curves, the spectroscopic parameters and vibrational levels were determined for all stable and metastable Λ-S and Ω states. The computed adiabatic electron affinity of SiN and the spectroscopic constants of SiN- (X¹ Σ+) are all in agreement with the available experimental data. The D³ Σ+, 25Σ+, 15 Δ, and 15 Σ- quasi-bound states caused by avoided crossings were found. Calculations of the transition dipole moment of a³ Σ+1 to X¹ Σ+0+ are shown. Franck-Condon factors, Einstein coefficients, and radiative lifetimes of the transition from the a³ Σ+(ν' = 0-2) to the X¹ Σ+0+ state are evaluated. [ABSTRACT FROM AUTHOR]

This paper calculated the potential energy curves of 21 Λ-S and 42 Ω states of the OF radical. The 21 Λ-S states were the X 2 Π, A 2 Σ − , B 2 Σ − , C 2 Δ, D 2 Σ + , E 2 Σ + , 2 2 Π, a 4 Σ − , b 4 Δ, 2 4 Σ − , 1 4 Σ + , 1 4 Π, 2 4 Π, 3 2 Σ + , 3 2 Σ − , 3 2 Π, 4 2 Π, 5 2 Π, 2 2 Δ, 3 2 Δ, and 1 2 Φ, which arose from the first two dissociation limits. The 42 Ω states were generated from these Λ-S states. All the potential energy curves were calculated with the CASSCF method, which was followed by the icMRCI + Q approach. The 1 4 Π, 2 4 Π, 2 2 Π, 4 2 Π, 5 2 Π, 3 2 Σ + , and 3 2 Δ states were repulsive whether the spin-orbit coupling effect included or not, but the A 2 Σ − , D 2 Σ + , 3 2 Σ − , 2 2 Δ, and 1 2 Φ states became repulsive with the spin-orbit coupling effect included. Only the 16 Ω states were bound. With the spin-orbit coupling effect accounted for, the X 2 Π state was inverted among the bound states; the X 2 Π, a 4 Σ − , and E 2 Σ + states were strongly bound; and the 3 2 Π, b 4 Δ, B 2 Σ − , C 2 Δ, 2 4 Σ − , and 1 4 Σ + states were very weakly bound. The spectroscopic and vibrational properties were determined. Franck–Condon factors of some transitions were evaluated. The spin-orbit coupling effect on the spectroscopic parameters and vibrational properties was discussed. It is very difficult to explore the X 2 Π, a 4 Σ − , and E 2 Σ + states by observing the electronic transitions between them because all these strong transitions originating only from the highly-vibrational states of the X 2 Π or a 4 Σ − state. It is also very hard to detect the 3 2 Π, b 4 Δ, B 2 Σ − , C 2 Δ, 2 4 Σ − , and 1 4 Σ + states by observing the transitions originating from these states, because these states are very weakly bound and unstable, though some transitions originating from them are very strong. These results can well explain why the OF radical is very difficult to detect in a spectroscopic experiment by observing the electronic transitions between different states. [ABSTRACT FROM AUTHOR]

The spectroscopic properties are in detail studied for the 1 1 Σ − , 2 1 Σ − , b 1 Σ + , c 1 Π, 2 1 Π, 3 1 Π, a 1 Δ, 2 1 Δ, X 3 Σ − , C 3 Σ − , 3 3 Σ − , 1 3 Σ + , A 3 Π, B 3 Π, 3 3 Π, 1 3 Δ, 2 3 Δ, 1 5 Σ − and 1 5 Π states, which are yielded from the first two dissociation limits, P( 4 S u ) + Cl( 2 P u ) and P( 2 D u ) + Cl( 2 P u ), of the PCl radical. Of the nineteen states, the 3 3 Σ − , 1 3 Σ + , 1 3 Δ, 2 3 Δ and 1 5 Π states are the repulsive ones. The 2 1 Σ − , 2 1 Δ and 1 5 Σ − states and the second well of A 3 Π state are very weakly-bound ones. The A 3 Π and B 3 Π states, the B 3 Π and 3 3 Π states, and the 2 1 Π and 3 1 Π states have the avoided crossings. The A 3 Π state is found to possess the double well. The potential energy curves (PECs) are calculated with the CASSCF method followed by the internally contracted MRCI approach with Davidson correction together with the Dunning’s correlation-consistent basis sets, aug-cc-pV6Z. To improve the quality of PECs, core–valence correlation and scalar relativistic correction calculations are included simultaneously. The PECs are extrapolated to the complete basis set limit. The vibrational properties are evaluated for several weakly-bound states. The spectroscopic parameters are determined, and compared with those available in the literature. The Franck–Condon factors and radiative lifetimes of the transitions from the A 3 Π, B 3 Π and 3 3 Π states to the X 3 Σ − state and from the c 1 Π, 2 1 Π and 3 1 Π states to the a 1 Δ state are calculated for several low vibrational states. And some necessary discussion is performed. Analyses demonstrate that the spectroscopic properties of PCl radical reported in this paper can be expected to be reliably predicted ones. [ABSTRACT FROM AUTHOR]

The potential energy curves (PECs) of 74 Ω states generated from the 21 Λ-S states of AsN molecule are studied for the first time for internuclear separations from 0.1 to 1.0 nm. Of these 21 Λ-S states, the X 1 Σ + , a′ 3 Σ + , 1 5 Σ + , 1 3 Δ, 1 3 Σ − , a 3 Π, 1 5 Π, 2 5 Σ + , 3 5 Σ + , 2 3 Δ, 2 3 Π, 3 3 Π, 3 5 Π, and A 1 Π states are found to be bound, and the 2 3 Σ + , 3 3 Σ + , 1 5 Σ − , 1 5 Δ, 2 5 Δ, 2 5 Π, and 1 7 Σ + states are found to be repulsive ones. The 3 3 Π state possesses the double well. The 2 5 Σ + , 3 5 Σ + , 3 5 Π, and 3 3 Π states possess the shallow well. The a′ 3 Σ + , 1 3 Σ − , 2 3 Π, 1 3 Δ, 1 5 Π, 2 5 Π, 3 5 Π, and 1 7 Σ + states are found to be the inverted ones with the spin–orbit coupling effect taken into account. The PECs are calculated using the CASSCF method, which is followed by the internally contracted MRCI approach with Davidson correction. Core–valence correlation and scalar relativistic corrections are included. The vibrational properties are evaluated for the 2 5 Σ + , 3 5 Σ + , and 3 5 Π states and the second well of the 3 3 Π state. The spin–orbit coupling effect is accounted for by the state interaction method with the Breit–Pauli Hamiltonian. The PECs are extrapolated to the complete basis set limit. The spectroscopic parameters are evaluated, and compared with available measurements and other theoretical results. The Franck–Condon factors and radiative lifetimes of the transitions from the a′ 3 Σ + 1 , a 3 Π 1 , A 1 Π 1 , 1 3 Δ 1 and a 3 Π 0− states to the X 1 Σ + 0+ state are calculated for several low vibrational levels, and some necessary discussion is performed. Analyses show that the spectroscopic parameters reported in this paper can be expected to be reliably predicted ones. [ABSTRACT FROM AUTHOR]