Multireference configuration interaction study on spectroscopic properties of low-lying electronic states of As2 molecule

The potential energy curves (PECs) of four electronic states (X1Σ+g , e3△u , a 3 Σ-u , and d 3Πg ) of an As 2 molecule are investigated employing the complete active space self-consistent field (CASSCF) method followed by the valence internally contracted multireference configuration interaction (MRCI) approach in conjunction with the correlation-consistent aug-cc-pV5Z basis set. The effect on PECs by the relativistic correction is taken into account. The way to consider the relativistic correction is to employ the second-order Douglas-Kroll Hamiltonian approximation. The correction is made at the level of a cc-pV5Z basis set. The PECs of the electronic states involved are extrapolated to the complete basis set limit. With the PECs, the spectroscopic parameters (Te , Re , ωe , ωexe , ωeye , αe , βe , γe , and Be ) of these electronic states are determined and compared in detail with those reported in the literature. Excellent agreement is found between the present results and the experimental data. The first 40 vibrational states are studied for each electronic state when the rotational quantum number J equals zero. In addition, the vibrational levels, inertial rotation and centrifugal distortion constants of d 3Πg electronic state are reported which are in excellent agreement with the available measurements. Comparison with the experimental data shows that the present results are both reliable and accurate.     

Ab initio study of ground and low-lying excited states of MgLi and MgLi+ molecules with valence full configuration interaction and MRCI method

The ground and low-lying excited states of MgLi and MgLi⁺ molecules have been investigated. The potential energy curves and the permanent and transition dipole moments of the MgLi and MgLi⁺ molecules are determined making use of the multi-reference configuration interaction and valence full configuration interaction with large basis sets. The core–valence correlation and scalar relativistic correction are also taken into account with aug-cc-pCVQZ basis set and the third-order Douglas–Kroll Hamiltonian approximation, respectively. The transition dipole moments are used to evaluate the radiative lifetimes of the vibrational levels for the low-lying excited states of the MgLi and MgLi⁺ molecules. The derived spectroscopic constants of the ground and low-lying excited states are in good agreement with available experimental and theoretical works.     

MRCI study on spectroscopic and molecular properties of four low-lying electronic states of the BO radical

The potential energy curves (PECs) of four low-lying electronic states of the BO radical, including two ²Σ⁺ and two ²Π states, have been studied using the full valence complete active space self-consistent field (CASSCF) method followed by the highly accurate valence internally contracted multireference configuration interaction (MRCI) approach in combination with the cc-pV5Z basis set for internuclear separations from 0.05 to 2.0 nm. The effect on the PECs by the relativistic correction has been taken into account. With these PECs, the spectroscopic parameters (T_e, D₀, D_e, R_e, ω_e, ω_ex_e, α_e and B_e) of two main isotopologues (¹¹B¹⁶O and ¹⁰B¹⁶O) have been determined. These parameters have been compared in detail with those of previous investigations reported in the literature, and excellent agreement has been found between the available data and the present results. By solving the radial Schrödinger equation of nuclear motion, 60 vibrational states for the ¹¹B¹⁶O(X²Σ⁺), 60 for the ¹⁰B¹⁶O(X²Σ⁺), 66 for the ¹¹B¹⁶O(A²Π) and 64 for the ¹⁰B¹⁶O(A²Π) are predicted for the non-rotating molecule. For each vibrational state of the ¹¹B¹⁶O(X²Σ⁺), ¹⁰B¹⁶O(X²Σ⁺), ¹¹B¹⁶O(A²Π) and ¹⁰B¹⁶O(A²Π), the vibrational level G(υ), inertial rotation constant B_υ and centrifugal distortion constant D_υ have been determined. Comparison with the available data shows that the present molecular constants are reliable and accurate. The ro-vibrational levels have been calculated for the X²Σ⁺ and A²Π states of two main species for future laboratory research.     

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.     

Ab initio configuration interaction study of the ground and low-lying excited states of ZnCd

The multi-reference configuration interaction (MRCI) electronic energy calculations have been carried out on the ground state (X1∑) as well as three low-lying excited states (3∑, 1∏, 3∏) of ZnCd dimer. Potential energy curves (PECs) are therefore generated and fitted to the analytical potential energy functions (APEFs) using the Murrel-Sorbie(MS) potential function. Based on the PECs, the vibrational levels of each state are determined by solving Schr(o)dinger equation of nuclear motion, and corresponding spectroscopic parameters are accurately calculated using the APEFs. The present values of spectroscopic parameters including equilibrium positions and dissociation energies areompared with other theoretical reports available at present.     

Ab initio MRCI＋Q study on potential energy curves and spectroscopic parameters of low-lying electronic states of CS＋

Carbon monosulfide molecular ion （CS＋）, which plays an important role in various research fields, has long been attracting much interest. Because of the unstable and transient nature of CS＋, its electronic states have not been well investigated. In this paper, the electronic states of CS＋ are studied by employing the internally contracted multireference configuration interaction method, and taking into account relativistic effects （scalar plus spin–orbit coupling）. The spin–orbit coupling effects are considered via the state-interacting method with the full Breit–Pauli Hamiltonian. The potential energy curves of 18 Λ–S states correlated with the two lowest dissociation limits of CS＋ molecular ion are calculated, and those of 10 lowest Ω states generated from the 6 lowest Λ–S states are also worked out. The spectroscopic constants of the bound states are evaluated, and they are in good agreement with available experimental results and theoretical values. With the aid of analysis of Λ–S composition of Ω states at different bond lengths, the avoided crossing phenomena in the electronic states of CS＋ are illuminated. Finally, the single ionization spectra of CS （X1Σ＋） populating the CS＋（X2Σ1/2＋, A2Π3/2, A2Π1/2, and B2Σ1/2＋） states are simulated. The vertical ionization potentials for X2Σ1/2＋, A2Π3/2, A2Π1/2, and B2Σ1/2＋ states are calculated to be 11.257, 12.787, 12.827, and 15.860 eV, respectively, which are accurate compared with previous experimental results, within an error margin of 0.08 eV~0.2 eV.     

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.     

Low-lying electronic states of BeH+ with the effect of inner electrons

The potential energy curves of the low-lying electronic states of BeH⁺ molecular ion are performed by using highly accurate multi-reference configuration interaction with AV5Z basis sets for H atom and ACV5Z basis set for Be atom, 1s inner shell of Be is considered as the core orbit and the active orbit, respectively, which are used to characterise the spectroscopic properties of a manifold of singlet and triplet states. Fourteen electronic states correlated with eight dissociation channels are investigated, we have found that the a³Σ⁺ and c³Σ⁺ both are bound states, the 3³Σ⁺ possesses double wells, and the C¹Σ⁺, 3³Σ⁺, 2³Π, 2¹Π, 1¹Δ, 1³Δ, 2³Δ and 2¹Δ states are studied for the first time. Transition dipole moment, Franck–Condon factors q_υ′υ^″ and Einstein coefficients A_υ′υ^″ for A¹Σ⁺–X¹Σ⁺, 2¹Π–B¹Π, c³Σ⁺–a³Σ⁺ and b³Π–a³Σ⁺ systems have been calculated. Radiative lifetime of A¹Σ⁺–X¹Σ⁺ band system has also been determined.     

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.     

Spectroscopic properties and radiative lifetimes of SiTe:A high-level multireference configuration interaction investigation

The 18 A-S states correlated to the lowest dissociation limit of SiTe were calculated by using a high-level multirefer-ence configuration interaction （MRCI） method, including scalar relativistic and spin-orbit coupling effects. Based on the calculated potential energy curves, the spectroscopic constants of bound states were determined, which are well consistent with previous experimental results. The spin-orbit matrix elements between the A-S states were computed, which lead to an in-deoth understanding, of oerturbations on the electronic state a^3∏. Finally. the transition dioole moments of allowed transitionsA^1∏-X^1∑^＋,E^1∑^＋-X^1∑^＋,a^3∏-d^3△,a^3∏-d^3△,a^∏-a′^3∑^＋,a^3∏-e^3∑^-,and the radiative lifetimes of A^1∏,E^1∑^＋,and a^3∏ were evaluated.     

Ab initio multi-reference configuration interaction of the low-lying states of the AsP molecule

Nine low-lying electronic states of the AsP molecule, including Σ , Ⅱ, and △ symmetries with singlet, triplet, and quintet spin multiplicities, are studied using multi-reference configuration interaction method.The potential energy curves and the spectroscopic constants of these nine states are determined, and compared with the experimental observed data as well as other theoretical works available at present.Three quintet states are reported for the first time.Furthermore, the analytical potential energy functions of these states are fitted using Murrell-Sorbie function and least square fitting method.     

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.     

Theoretical study of the SrLi+ molecular ion: structural,electronic and dipolar properties

ABSTRACT

The structural and electronic properties of (SrLi)⁺ molecular ion have been determined by the use of ab initio approaches. Potential energy curves (PECs) with their spectroscopic constants (R_e, D_e, ω_e, T_e, B_e and ω_eχ_e) have been calculated. Also, the vibrational properties and the electric dipole moments, either permanent (PDM) or transition (TDM) ones, have been investigated and analysed. Large Gaussian basis sets, the full valence configuration interaction (FCI) and the formalism of non-empirical pseudo-potential including the two approaches, effective core potential (ECP) and core polarisation potential (CPP), are analysed. Therefore, (SrLi)⁺ is considered as a two effective electrons system. Numerous excited states of symmetries ^1,3Σ⁺, ^1,3Π and ^1,3Δ dissociating below the ionic limit Sr²⁺Li^? have been investigated. This study shows interesting behaviours around the avoided crossing related to charge transfer involving important processes in physics and astrophysics such as dynamics, pre-dissociation and inelastic transitions.     

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.     

Further investigations of the low-lying electronic states of AsO~+ radical

The high level quantum chemistry ab inito multi-reference configuration interaction （MRCI） method with large V5Z basis set is used to calculate the spectroscopic properties of the 15 A-S electronic states （X1∑＋, A I П, 1 △, 1 ∑, 3∑＋, 3П, 3△, 3△ , 5∑＋, 5П, 5△, 1П （II）, ofAsO＋ radical correlated to the dissociation limit As＋（3pg） ＋ O（3pg） and As＋（IDg） ＋ O（1Dg）. In order to obtain better potential curves and more accurate spectroscopic properties, the Davidson modification is taken into account. With the potential energy curves （PECs） determined here, vibrational levels G（v） and inertial rotation constants Bu are computed for all the bound electronic states when the rotational quantum number J equals zero （J = 0）. Except for the states X1∑＋, A1П , it is the first time that the multi-reference configuration calculation has been used on the 13 A-S electronic states of the AsO＋ radical. The potential energy curves of all the A-S electronic states are depicted according to the avoided crossing rule of the same symmetry. Spin-orbit coupling effect （SOC） is introduced into the states X1 ∑＋, A1 П, 3П to consider its effects on the spectroscopic properties. Transition dipole moments （TDMs） from A1П 1, 3 П1 states to the ground state X1∑0＋ are predicted as well.     

Effects on spectroscopic properties for several low-lying electronic states of CS molecule by core-valence correlation and relativistic corrections

The potential energy curves (PECs) of six low-lying electronic states (X¹Σ⁺, a³Π, a′³Σ⁺, d³Δ, e³Σ⁻ and A¹Π) of CS molecule have been investigated using the full valence complete active space self-consistent field (CASSCF) method followed by the highly accurate valence internally contracted multireference configuration interaction (MRCI) approach with large correlation-consistent basis sets. Effects on the PECs by the core-valence correlation and relativistic corrections have been taken into account. And the two corrections are performed at the level of cc-pV5Z basis set. The way to consider the relativistic corrections is to use the second-order Douglas-Kroll Hamiltonian approximation. Using the CCSD(T), MRCI and MRCI with the Davidson modification (MRCI + Q), the PECs of electronic states involved are extrapolated to the complete basis set (CBS) limit. With the PECs, the spectroscopic parameters (T_e, R_e, ω_e, ω_ex_e, ω_ey_e, α_e, β_e, γ_e and B_e) of the six low-lying electronic states are determined. These parameters are in excellent agreement with the experimental data. The complete vibrational states are computed for the six low-lying electronic states when the rotational quantum number J equals zero, and the inertial rotation constants of the first 23 vibrational states are reported, which agree favorably with the RKR data. Comparison with the measurements shows that the two-point total-energy extrapolation scheme can obviously improve the quality of spectroscopic parameters and molecular constants.