Accurate spectroscopic calculations of the 12 Λ-S states and 27 Ω states of NF+ cation including the spin–orbit coupling effect

This paper studies the potential energy curves (PECs) of 27 Ω states generated from the 12 Λ-S states (X²Π, 1²Σ⁺, 1²Σ^?, 2²Σ^?, A²Π, 1²Δ, 1⁴Σ⁺, 1⁴Σ^?, 2⁴Σ^?, 1⁴Π, 2⁴Π and 1⁴Δ), which are attributed to the first dissociation channel of NF⁺ cation. Of these 12 states, only 2²Σ^? and 2⁴Π are the repulsive ones, which are very different from those reported by G.-S. Kim and D. M. Hirst, Mol. Phys. 86, 1183–1193 (1995) G.-S. Kim and D.M. Hirst, Mol. Phys. 86, 1183–1193 (1995).[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]. In addition, the 1²Δ and 1⁴Σ^? states are found to possess the double well. 1⁴Σ⁺, 1⁴Σ^? and 1⁴Δ are found to be the inverted states with the spin–orbit coupling effect taken into account, and 1²Σ⁺, 1²Σ^?, 1²Δ, 1⁴Σ⁺, 2⁴Σ^? and 1⁴Δ are found to be the weakly bound states. 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 Davidson correction. The convergent behaviour of the present calculations is discussed with respect to the basis set and level of theory. All the PECs are extrapolated to the complete basis set limit. Core–valence correlation and scalar relativistic corrections are included at the same time. The spin–orbit coupling effect is accounted for by the state interaction method with the Breit–Pauli Hamiltonian. The spectroscopic parameters are evaluated and compared with available measurements and other theoretical results. The effect of spin–orbit coupling on the spectroscopic parameters is discussed. The Franck–Condon factors and radiative lifetimes of the transitions from the 1⁴Π_3/2, 1⁴Σ^?_3/2, 1²Δ_3/2 and A²Π_1/2 states to the X²Π_1/2 state are calculated for several low vibrational levels and some necessary discussion is done. It shows that the spectroscopic results reported in this paper can be expected to be reliably predicted ones.     

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 calculations of the 18 Λ-S states and 50 Ω states of PO+ cation: potential energy curves and spectroscopic parameters including the spin-orbit coupling effect

The potential energy curves (PECs) of 5 Ω states generated from the 18 Λ-S states (X ¹ Σ ⁺, A¹Σ^?, 1¹ Δ, 1¹ Π, 2¹Σ⁺, 2¹ Π, a ³ Σ ⁺, 1³ Δ, 1³ Π, 1³Σ^?, 2³Σ⁺, 2³ Π, 1⁵Σ⁺, 1⁵ Π 2⁵ Π, 1⁵Σ^?, 2⁵Σ⁺ and 1⁵ Δ) of PO⁺ cation are studied for the first time for internuclear separations from about 0.08 to 1.0 nm. Of these Λ-S states, only the 2⁵Σ⁺ and 1⁵ Δ are the replusive ones. The a ³ Σ ⁺, 2³Σ⁺, 1⁵Σ^?, 2³ Π, 1³ Δ, 2⁵Σ⁺ , and 1⁵ Δ are the inverted states with the spin-orbit coupling effect included. The 1¹ Π, 1³ Π, 1⁵ Π and 2³ Π states possess the double well. The 1⁵Σ^?, 2¹ Π and 2⁵ Π states and the second wells of 1¹ Π, 1³ Π, 2³ Π and 1⁵ Π states are the rather weakly bound states. The PEC calculations are performed by the CASSCF method, which is followed by the icMRCI approach with Davidson correction in combination with the aug-cc-pV6Z basis set. Core-valence correlation and scalar relativistic corrections are included at the same time. The spin-orbit coupling effect is accounted for. All the PECs are extrapolated to the complete basis set limit. The spectroscopic parameters are evaluated for all the Λ-S and Ω bound states, and compared with the measurements and other theoretical results. Fair agreement is found between the present spectroscopic parameters and the measurements. The vibrational properties are evaluated for the weakly bound states. The effect of spin-orbit coupling on the spectroscopic parameters is discussed. The results reported in this paper can be expected to be reliable predicted ones.     

Accurate spectroscopic properties of 10 Λ-S states and 25 Ω states of BS<Superscript>+</Superscript> cation including the electronic transition properties

The potential energy curves of 10 Λ–S states of BS⁺ yielded from the first four dissociation limits are calculated by the internally contracted multireference configuration interaction approach with the Davidson correction. The core-valence correlation and scalar relativistic corrections are included. Basis on the calculated potential energy curves, the spectroscopic parameters are evaluated. All the PECs are extrapolated to the complete basis set limit. The spin-orbit coupling are taken into account by the state interaction method with the Breit-Pauli Hamiltonian. Finally, the transition dipole moments, Franck-Condon Factors and radiative lifetimes of transitions from the 2³Π_0-, 2³Π₀₊, 2³Σ₀ ^- and 2³Σ₁ ^- states to ground state 1³Π₂ are predicted for future experiment.     

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.     

Highly accurate theoretical study on spectroscopic properties of SH including spin–orbit coupling

The multi-reference configuration interaction method plus Davidson correction(MRCI+Q) are adopted to study the low-lying states of SH with consideration of scalar relativistic effect, core-valence(CV) electron correlation, and spin–orbit coupling(SOC) effect. The SOC effect on the low-lying states is considered by utilizing the full Breit–Pauli operator. The potential energy curves(PECs) of 10 Λ–S states and 18 ? states are calculated. The dipole moments of 10 Λ–S states are calculated, and the variation along the internuclear distance is explained by the electronic configurations. With the help of calculated SO matrix elements, the possible predissociation channels of A~2Σ+, c4Σ-and F~2Σ-are discussed. The Franck–Condon factors of A~2Σ~+–X~2Π, F~2Σ~-–X~2Π and E~2Σ~+–X~2Π transitions are determined, and the radiative lifetimes of A~2Σ+and F~2Σ-states are evaluated, which are in good agreement with previous experimental results.     

Excited-states and spectroscopic properties of superoxide anion: a theoretical study including spin–orbit coupling

ABSTRACT

The potential energy curves (PECs) of 24 Λ–S electronic states of superoxide anion (O₂^?), which correlated with the first dissociation channel, were calculated using a high-accuracy internally contracted multireference configuration interaction (icMRCI) methodology with the Davidson correction in conjunction with the correlation-consistent basis sets. The core electron correlation and scalar relativistic corrections as well as basis set extrapolation were included. The spin–orbit coupling was also taken into account by using the state interaction approach with the Breit–Pauli Hamiltonian. The PECs of 54 Ω states generated from the 24 Λ–S states were constructed and described in detail. The spectroscopic constants of the seventeen Λ–S and 37 Ω bound states were evaluated and the vibrational properties of some weakly bound states were predicted. Comparing with the available experimental and theoretical data shows that the computational strategy employed is suitable and highly accurate for this system.     

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.     

Electronic states and spectroscopic properties of MgH in absence and presence of spin–orbit coupling − a configuration interaction study

Electronic spectrum of astrophysically important molecule magnesium hydride (MgH) has been studied using configuration interaction methodology excluding and including spin–orbit coupling. Potential energy curves of several spin-independent (Λ?S) electronic states have been constructed and spectroscopic constants of low-lying bound Λ?S states within 8.2 eV of term energy are reported in the first stage of calculations. The X²Σ⁺ is identified as the ground state in the Λ?S level. In the subsequent stage, the spin–orbit interaction has been incorporated and its effects on the potential energy curves and spectroscopic features of different electronic states of the species have been investigated. The X²Σ⁺_1/2 is identified as the spin–orbit (Ω) ground state of the species. Transition moments of several dipole-allowed transitions are computed in both the stages and radiative lifetimes of the corresponding excited states are computed. Electric dipole moments (µ) for a number of low-lying bound Λ?S states as well as several low-lying Ω-states are also calculated in the present study.     

Accurate calculations on the 12 electronic states and 23 Ω states of the SiBr<Superscript>+</Superscript> cation: potential energy curves,spectroscopic parameters and spin-orbit coupling

The potential energy curves (PECs) of 23 Ω states generated from the 12 electronic states (X¹ Σ ⁺, 2¹ Σ ⁺, 1¹ Σ ^?, 1¹ Π, 2¹ Π, 1¹ Δ, 1³ Σ ⁺, 2³ Σ ⁺, 1³ Σ ^?, a³ Π, 2³ Π and 1³ Δ) are studied for the first time. All the states correlate to the first dissociation channel of the SiBr⁺ cation. Of these electronic states, the 2³ Σ ⁺ is the repulsive one without the spin-orbit coupling, whereas it becomes the bound one with the spin-orbit coupling added. On the one hand, without the spin-orbit coupling, the 1¹ Π, 2¹ Π and 2³ Π are the rather weakly bound states, and only the 1¹ Π state possesses the double well; on the other hand, with the spin-orbit coupling included, the a³ Π and 1¹ Π states possess the double well, and the 1³ Σ ⁺ and 1³ Σ ^? are the inverted states. The PECs are calculated by the CASSCF method, which is followed by the internally contracted MRCI approach with the Davidson modification. Scalar relativistic correction is calculated by the third-order Douglas-Kroll Hamiltonian approximation with a cc-pVTZ-DK basis set. Core-valence correlation correction is included with a cc-pCVTZ basis set. The spin-orbit coupling is accounted for by the state interaction method with the Breit-Pauli Hamiltonian using the all-electron aug-cc-pCVTZ basis set. All the PECs are extrapolated to the complete basis set limit. The variation with internuclear separation of the spin-orbit coupling constant is discussed in brief. The spectroscopic parameters are evaluated for the 11 bound electronic states and the 23 bound Ω states, and are compared with available measurements. Excellent agreement has been found between the present results and the experimental data. It demonstrates that the spectroscopic parameters reported here can be expected to be reliably predicted ones. The Franck-Condon factors and radiative lifetimes of the transitions from the a³ Π _{0 +} and a³ Π ₁ states to the X¹ Σ ⁺ ₀₊ state are calculated for several low vibrational levels, and some brief discussion has been made.     

Influence of the spin–orbit interaction in the impurity-band states of n-doped semiconductors

We study numerically the effects of an extrinsic spin–orbit interaction on the model of electrons in n-doped semiconductors of Matsubara and Toyozawa (MT). We focus on the analysis of the density of states (DOS) and the inverse participation ratio (IPR) of the spin–orbit perturbed states in the MT set of energy eigenstates in order to characterize the eigenstates with respect to their extended or localized nature. The finite sizes that we are able to consider necessitate an enhancement of the spin–orbit coupling strength in order to obtain a meaningful perturbation. The IPR and DOS are then studied as a function of the enhancement parameter.     

Mesoscopic Fano effect modulated by Rashba spin–orbit coupling and external magnetic field

By employing non-equilibrium Green's function method, the mesoscopic Fano effect modulated by Rashba spin–orbit (SO) coupling and external magnetic field has been elucidated for electron transport through a hybrid system composed of a quantum dot (QD) and an Aharonov–Bohm (AB) ring. The results show that the orientation of the Fano line shape is modulated by the Rashba spin–orbit interaction kRL$k_{R}L$ variation, which reveals that the Fano parameter q will be extended to a complex number, although the system maintains time-reversal symmetry (TRS) under the Rashba SO interaction. Furthermore, it is shown that the modulation of the external magnetic field, which is applied not only inside the frame, but also on the QD, leads to the Fano resonance split due to Zeeman effect, which indicates that the hybrid is an ideal candidate for the spin readout device.     

Spin Hall effect and spin current generation in two-dimensional systems with random Rashba spin–orbit coupling

We consider a new effect induced by spin–orbit coupling in a two-dimensional electron gas confined in a semiconductor quantum well, i.e. the possibility of spin current generation by fluctuating random Rashba spin–orbit interaction, with the corresponding mean value of the interaction being equal to zero. Our main results suggest that – in contrast to the spatially uniform Rashba spin–orbit interaction – the spin Hall effect does not vanish for typical disorder strengths. We also point out some other possibilities of using such a random Rashba coupling for the generation of spin density and spin current in two-dimensional nonmagnetic structures.     

Effects of the spin–orbit coupling on magnetic and superconducting properties in iron-based superconductors

We analyze the magnetic properties through two-orbital Hubbard model with the spin–orbit coupling (SOC) interaction in the iron-based superconductors. With the help of the Ising approximation for the Hund’s coupling between the itinerant electrons and the localized spins, we give a self-consistent account of the various magnetic orders observed in pnictides and the pairing symmetry. We also calculate the local density of states (LDOS) of the vortex state when a magnetic field is applied. The LDOS without SOC shows no resonant peak at the vortex core center in the superconducting state, while it shows an obvious resonant peak when SOC is applied.     

Effects of the spin–orbit coupling on the vacancy-induced magnetism on the honeycomb lattice

The local magnetism induced by vacancies in the presence of the spin–orbit interaction is investigated based on the half-filled Kane–Mele–Hubbard model on the honeycomb lattice. Using a self-consistent mean-field theory, we find that the spin–orbit coupling will enhance the localization of the spin moments near a single vacancy. We further study the magnetic structures along the zigzag edges formed by a chain of vacancies. We find that the spin–orbit coupling tends to suppress the counter-polarized ferrimagnetic order on the upper and lower edges, because of the open of the spin–orbit gap. As a result, in the case of the balance number of sublattices, it will suppress completely this kind of ferrimagnetic order. But, for the imbalance case, a ferrimagnetic order along both edges exists because additional zero modes will not be affected by the spin–orbit coupling.     

Characteristics of persistent spin current components in a quasi-periodic Fibonacci ring with spin–orbit interactions: Prediction of spin–orbit coupling and on-site energy

In the present work we investigate the behavior of all three components of persistent spin current in a quasi-periodic Fibonacci ring subjected to Rashba and Dresselhaus spin–orbit interactions. Analogous to persistent charge current in a conducting ring where electrons gain a Berry phase in presence of magnetic flux, spin Berry phase is associated during the motion of electrons in presence of a spin–orbit field which is responsible for the generation of spin current. The interplay between two spin–orbit fields along with quasi-periodic Fibonacci sequence on persistent spin current is described elaborately, and from our analysis, we can estimate the strength of any one of two spin–orbit couplings together with on-site energy, provided the other is known.     

Effect of in-plane magnetic field on spin polarization in the presence of the Dresselhaus spin–orbit effect

In this paper, we theoretically study the effect of the in-plane magnetic field on spin polarization in the presence of the Dresselhaus spin–orbit effect. It is shown that the large spin polarization can be achieved in such a nanostructure due to the effects of both the Dresselhaus spin–orbit term and the in-plane magnetic field, but the latter plays a main role in the tunneling process. It is also shown that with the increase of in-plane magnetic field, the degree of spin splitting obviously becomes larger.