Explicitly correlated configuration interaction investigation on low-lying states of SiO~+ and SiO

SiO~+ and SiO, which play vital roles in astrophysics and astrochemistry, have long attracted considerable attention.However, accurate information about excited states of SiO~+ is still limited. In this work, the structures of 14 Λ–S states and 30? states of SiO~+ are computed with explicitly correlated configuration interaction method. On the basis of the calculated potential energy curves of those Λ–S states and ? states, the spectroscopic constants of bound states are evaluated, which are in good agreement with the latest experimental results. The predissociation mechanism of B~2Σ~+ state is illuminated with the aid of spin–orbit coupling matrix elements. On the basis of the calculated potential energy curves and transition dipole moments, the radiative lifetime for each of low-lying vibrational states B~2Σ~+and A~2Π is estimated. The laser cooling scheme of SiO~+ is proposed by employing B~2Σ~+–X~2Σ~+ transition. Finally, the vertical ionization energy values from SiO(X~1Σ~+) to ionic states: SiO~+ , X~2Σ~+, B~2Σ~+, and A~2Π are calculated, which agree well with experimental measurements.     

Configuration interaction calculations on the spectroscopic and transition properties of magnesium chloride

The potential energy curves(PECs) of 14 Λ–S states for magnesium chloride(Mg Cl) have been calculated by using multi-reference configuration interaction method with Davidson correction(MRCI + Q). The core-valence correlation(CV), scalar relativistic effect, and spin–orbit coupling(SOC) effect are considered in the electronic structure computations.The spectroscopic constants of X~2Σ~+ and A ~2Π states have been obtained, which are in good agreement with the existing theoretical and experimental results. Furthermore, other higher electronic states are also characterized. The permanent dipole moments(PDMs) of Λ–S states and the spinorbit(SO) matrix elements between Λ–S states are also computed. The results indicate that the abrupt changes of PDMs and the SO matrix elements are attributed to the avoided crossing between the states with the same symmetry. The SOC effect is taken into account with Breit–Pauli operator, which makes the 14Λ–S states split into 30 ? states, and leads to a double-well potential of the ? =(3)1/2 state. The energy splitting for the A2Π is calculated to be 53.61 cm~(-1) and in good agreement with the experimental result 54.47 cm~(-1). The transition dipole moments(TDMs), Franck–Condon factors(FCFs), and the corresponding radiative lifetimes of the selected transitions from excited ? states to the ground state X~2Σ + 1/2 have been reported. The computed radiative lifetimes τν of low-lying excites ? states are all on the order of 10 ns. Finally, the feasibility of laser cooling of Mg Cl molecule has been analyzed.     

Molecule opacities of X~2Σ~+, A~2Π, and B~2Σ~+ states of CS~+

Carbon sulfide cation(CS~+) plays a dominant role in some astrophysical atmosphere environments. In this work, the rovibrational transition lines are computed for the lowest three electronic states, in which the internally contracted multireference configuration interaction approach(MRCI) with Davison size-extensivity correction(+Q) is employed to calculate the potential curves and dipole moments, and then the vibrational energies and spectroscopic constants are extracted. The Frank–Condon factors are calculated for the bands of X~2~+Σ~+–A~2Π and X~2Σ~+–B~2Σ~+systems, and the band of X~2Σ~+–A~2Π is in good agreement with the available experimental results. Transition dipole moments and the radiative lifetimes of the low-lying three states are evaluated. The opacities of the CS~+ molecule are computed at different temperatures under the pressure of 100 atms. It is found that as temperature increases, the band systems associated with different transitions for the three states become dim because of the increased population on the vibrational states and excited electronic states at high temperature.     

Configuration interaction study on low-lying states of AlCl molecule

High-level ab initio calculations of the Λ–S states for aluminum monoiodide(Al Cl) molecule are performed by utilizing the explicitly correlated multireference configuration interaction(MRCI-F12) method. The Davidson correction and scalar relativistic correction are investigated in the calculations. Based on the calculation by the MRCI-F12 method, the spin–orbit coupling(SOC) effect is investigated with the state-interacting technique. The adiabatic potential energy curves(PECs) of the 13 Λ–S states and 24 Ω states are calculated. The spectroscopic constants of bound states are determined,which are in accordance with the results of the available experimental and theoretical studies. Finally, the transition properties of 0~+(2)–X0~+, 1(1)–X0~+, and 1(2)–X0~+ transitions are predicted, including the transition dipole moments(TDMs),Franck–Condon factors(FCFs), and the spontaneous radiative lifetimes.     

Low-lying electronic states of aluminum monoiodide

High-level ab initio calculations of aluminum monoiodide(AlI) molecule are performed by utilizing the multireference configuration interaction plus Davidson correction(MRCI+Q) method. The core-valence correlation(CV) and spin–orbit coupling(SOC) effect are considered. The adiabatic potential energy curves(PECs) of a total of 13 Λ–S states and 24 ? states are computed. The spectroscopic constants of bound states are determined, which are in accordance with the results of the available experimental and theoretical studies. The interactions between the Λ–S states are analyzed with the aid of the spin–orbit matrix elements. Finally, the transition properties including transition dipole moment(TDM),Frank–Condon factors(FCF) and radiative lifetime are obtained based on the computed PEC. Our study sheds light on the electronic structure and spectroscopy of low-lying electronic states of the AlI molecule.     

Ab initio study on the electronic states and laser cooling of AlCl and AlBr

We investigate whether AlCl and AlBr are promising candidates for laser cooling. We report new ab initio calculations on the ground state X~1Σ~+ and two low-lying states(A~1Π and a~3Π) of AlCl and AlBr. The calculated spectroscopic constants show good agreement with available theoretical and experimental results. We also obtain the permanent dipole moments(PDMs) curve at multi-reference configuration interaction(MRCI) level of theory. The transition properties of A~1Π and a~3Π states are predicted, including the transition dipole moments(TDMs), Franck–Condon factors(FCFs), radiative times and radiative width. The calculated radiative lifetimes are of the order of a nanosecond, implying that they are sufficiently short for rapid laser cooling. Both AlCl and AlBr have highly diagonally distributed FCFs which are crucial requirement for molecular laser cooling. The results demonstrate the feasibility of laser cooling AlCl and AlBr, and we propose laser cooling schemes for AlCl and AlBr.     

MRCI+Q study of the low-lying electronic states of CdF including spin-orbit coupling

Cd F molecule, which plays an important role in a great variety of research fields, has long been subject to numerous researchers. Due to the unstable nature and heavy atom Cd containing in the Cd F molecule, electronic states of the molecule have not been well studied. In this paper, high accurate ab initio calculations on the Cd F molecule have been performed at the multi-reference configuration interaction level including Davidson correction(MRCI + Q). Adiabatic potential energy curves(PECs) of the 14 low-lying Λ–S states correlating with the two lowest dissociation limits Cd(~1S_g) + F(~2P_u) and Cd(~3P_u) + F(~2P_u) have been constructed. For the bound Λ–S and ? states, the dominant electronic configurations and spectroscopic constants are obtained,and the calculated spectroscopic constants of bound states are consistent with previous experimental results. The dipole moments(DMs) of 2 Σ+ and 2Π are determined, and the spin–orbit(SO) matrix elements between each pair of X2Σ+, 22Σ+, 12Π, and 22Π are obtained. The results indicate that the sudden changes of DMs and SO matrix elements arise from the variation of the electronic configurations around the avoided crossing region. Moreover,the Franck–Condon factors(FCFs), the transition dipole moments(TDMs), and radiative lifetimes of low-lying states-the ground state X2Σ+are determined. Finally, the transitional properties of 22Π–X2Σ+and 22Σ+–X2Σ+are studied. Based on our computed spectroscopic information of Cd F, the feasibility and challenge for laser cooling of Cd F molecule are discussed.     

Configuration interaction studies on the spectroscopic properties of PbO including spin-orbit coupling

Lead oxide(Pb O), which plays the key roles in a range of research fields, has received a great deal of attention. Owing to the large density of electronic states and heavy atom Pb including in Pb O, the excited states of the molecule have not been well studied. In this work, high level multireference configuration interaction calculations on the low-lying states of Pb O have been carried out by utilizing the relativistic effective core potential. The effects of the core-valence correlation correction, the Davidson modification, and the spin–orbital coupling on the electronic structure of the Pb O molecule are estimated. The potential energy curves of 18 Λ-S states correlated to the lowest dissociation limit(Pb(~3P_g) + O(~3P_g)) are reported. The calculated spectroscopic parameters of the electronic states below 30000 cm~(-1), for instance, X~1Σ~+, 1~3Σ~+,and 1~3Σ~-, and their spin–orbit coupling interaction, are compared with the experimental results, and good agreements are derived. The dipole moments of the 18 Λ-S states are computed with the configuration interaction method, and the calculated dipole moments of X~1Σ~+and 1~3Σ~+are consistent with the previous experimental results. The transition dipole moments from 1~1Π, 2~1Π, and 2~Σ to X~1Σ~+and other singlet excited states are estimated. The radiative lifetime of several low-lying vibrational levels of 1~1Π, 2~1Π, and 2~1Σ~+ states are evaluated.     

Theoretical study of spin-forbidden cooling transitions of indium hydride using ab initio methods

The feasibility of spin-forbidden cooling of the In H molecule is investigated based on ab initio quantum chemistry calculations. The potential energy curves for the X~1Σ_(0~+)~+, a~3Π_~(0~-), a~3Π_(0~+), a~3Π_1, a~3Π_2, A~1Π_1, 1~3Σ_(0~-)~+, and 1~3Σ_1~+states of In H are obtained based on multi-reference configuration interaction plus the Davidson corrections method. The calculated spectroscopic constants are in good agreement with the available experimental data. In addition, the influences of the active space and spin–orbit coupling effects on the potential energy curves and spectroscopic constants are also studied. For Re of a~3Π_(0~-), a~3Π_(0~+), a~3Π_1, and a~3Π_2 states, the error from large active space is small. The potential energy curve of the A~1Π_1state is not smooth for small active space. The spin–orbit coupling effects have great influences on the potential well depth and equilibrium internuclear distance of the A~1Π state. The Franck–Condon factors and radiative lifetimes are obtained on the basis of the transition dipole moments of the a~3Π_(0~+) → X~1Σ_(0~+)~+, a~3Π_1 → X~1Σ_(0~+)~+, and A~1Π_1 → X~1Σ_(0~+)~+ transitions. Our calculation indicates that the a~3Π_1( ν'= 0) → X~1Σ_(0~+)~+(ν = 0) transition provides a highly diagonally distributed Franck–Condon factor and a short radiative lifetime for the a3Π1 state, which can ensure rapid and efficient laser cooling of In H.The proposed laser drives a~3Π_1 → X~1Σ_(0~+)~+ transitions by using three wavelengths.     

Laser cooling of CH molecule: Insights from ab initio study

The feasibility of laser cooling a CH molecule is investigated theoretically by employing the ab initio method. The potential energy curves for the five ∧-S states and eight Ω states of CH are determined by the multi-reference configuration interaction with the Davidson corrections(MRCI+Q) level of theory. The results agree well with the available experimental data and other theoretical values. Also, the permanent dipole moments and transition dipole moments of the CH molecule are calculated at the multi-reference configuration interaction(MRCI) level. We find highly diagonally distributed FranckCondon factors(f_(00) = 0.9950 and 0.9998) and branching ratios(R_(00) = 0.983 and 0.993) for the A~2△→ X2Π and C~2∑~+→X~2Π transitions. Moreover, the values of suitable radiative lifetime τ of the A2 A and C~2∑~+ states are evaluated to be9.64×10~(-7) s and 2.02×10~(-7) s, respectively, for rapid laser cooling. A scheme for laser cooling the CH molecule is designed. In the proposed cooling scheme, three wavelengths for A~2△→X~2Π and C~2∑~+→X~2Π transitions are used, and the main pump lasers are λ_(00)=430.86 nm and 313.45 nm, respectively. The feasibility of laser cooling the CH molecules is demonstrated for each of these schemes, and this study offers a theoretical basis for experimental research into preparation of cold CH molecules.     

Theoretical study on the transition properties of AlF

Potential energy curves of the X$^{1}\Sigma ^{+}$ and A$^{1}\Pi $ states of the AlF molecule are studied through the combination of the multi-reference configuration interaction (MRCI) approach and Davidson corrections (MRCI$+$Q). The AWCV5Z basis set is employed in the calculations. The transition dipole moments (TDMs) of the A$^{1}\Pi \leftrightarrow {\rm X}^{1}\Sigma^{+}$ transition are explored based on the AWCV5Z basis set and (4, 2, 2, 0) active space. The Schrödinger equation is solved via the LEVEL 8.2 program, and the vibrational levels and rotational constants of the X$^{1}\Sigma^{+}$ and A$^{1}\Pi $ states are calculated. It is shown that the AlF molecule has high diagonal Franck-Condon factors ($f_{00}=0.9949$ and $f_{11}=0.9854$) and large Einstein coefficients for the transition of A$^{1}\Pi {(\nu }'=0)\leftrightarrow {\rm X}^{1}\Sigma^{+}{\rm (\nu }'=0)$. In addition, the radiative lifetimes of the vibrational levels are close to 10$^{-9}$ s for the A$^{1}\Pi $ state. The line intensities of the A$^{1}\Pi {\rm (\nu }'=4-15)\leftrightarrow {\rm X}^{1}\Sigma^{+}{\rm (\nu }'=0)$ transitions are also calculated. The calculated TDMs and transition probabilities in this work are credible and provide some guidance for the study of similar transitions, particularly for exploring interstellar space.     

Relativistic calculations on the transition electric dipole moments and radiative lifetimes of the spin-forbidden transitions in the antimony hydride molecule

Calculations on the spectroscopic constants and transition properties of the first three states (${\rm a}^{1}\Delta $, ${\rm b}^{1}\Sigma^{+}$, and X$^{3}\Sigma^-$) of the SbH molecule were performed under the relativistic framework using the exact two-component Hamiltonian (X2C). The potential energy curves in the Franck-Condon region were computed and compared with the previous values. Furthermore, the transition dipole moments for the weak spin-forbidden transitions (${\rm b}0^{+}$-X$_{1}0^{+}$, ${\rm b}0^{+}$-X$_{2}$1, X$_{1}0^{+}$-X$_{2}$1, and X$_{2}$1-${\rm a}$2) were reported. The spontaneous radiative lifetime of the ${\rm b}^{1}\Sigma^{+}$ ($\upsilon '=0$) state was calculated as 163.5 $\pm$ 7.5 μs, which is in reasonable agreement with the latest experimental value of 173 $\pm$ 3 μs. The spontaneous radiative lifetimes of the X$_{2}$1 ($\upsilon '=0$) state and the ${\rm a}$2 ($\upsilon '=0$) state were calculated to be 48.6 s and $\sim 8 $ ms, respectively. Our study is expected to be a benchmark transition property computation for comparison with other theoretical and experimental results. The datasets presented in this paper, including the transition dipole moments, are openly available at https://dx.doi.org/10.11922/sciencedb.j00113.00018.     

The splitting of low-lying states for hydroxyl molecule under spin--orbit coupling

The splitting of potential energy curves for the states $X^{2}\Pi _{3/2}$, $^{2}\Pi _{1/2}$ and $A^{2}\Sigma ^{ +}$ of hydroxyl OH under spin--orbit coupling (SOC) has been calculated by using the SO multi-configuration quasi-degenerate perturbation theory (SO-MCQDPT). Their Murrell--Sorbie (M--S) potential functions have been derived, then, the spectroscopic constants for $X^{2}\Pi _{3/2}$,$^{ 2}\Pi _{1/2}$ and $A^{2}\Sigma ^{ + }$ have been derived from the M--S function. The calculated dissociation energies for the three states are $D_{0}$[OH($X^{2}\Pi _{3/2})$]=34966.632cm$^{-1}$, $D_{0}$[OH($^{2}\Pi _{1/2})$]=34922.802cm$^{-1}$, and $D_{0}$[OH($A^{2}\Sigma ^{ + })$]=17469.794cm$^{-1}$, respectively. The vertical excitation energy $\nu [ {{ }^2\Pi _{1/2} ( {\nu = 0} ) \to {X}{ }^2\Pi _{3/2} ( {\nu = 0} )} ] = 139.6{\rm cm}^{-{\rm 1}}$. All the spectroscopic data for the $X^{2}\Pi _{3/2}$ and $^{2}\Pi _{1/2 }$ are given for the first time except the dissociation energy of $X^{2}\Pi _{3/2}$.     

激光冷却SH~–阴离子的理论研究

本文采用多组态相互作用及Davidson修正方法和全电子基组计算了SH~-阴离子的X~1∑~+,a~3∏和A~1∏态的势能曲线、电偶极矩和跃迁偶极矩.计算的光谱常数与实验值及已有的理论值符合得很好.在计算中考虑了自旋-轨道耦合效应.计算得到a~3∏_1(v'=0)?X~1∑_(0+)~+(v"=0)和A~1∏_1(v'=0)?X~1Σ_(0+)~+(v"=0)跃迁具有高对角分布的弗兰克-康登因子,分别为0.9990和0.9999;计算得到a~3∏_1和A~1∏_1态的自发辐射寿命分别为1.472和0.188 ms.A~1∏_1?X~1∑_(0+)~+跃迁存在中间态a~3∏_(0+)和a~3∏_1,但中间态对激光冷却SH~-阴离子的影响可以忽略.分别利用a~3∏_1(v'=0)? X~1∑_(0+)~+(v"=0)和A~1∏_1(v'=0)? X~1∑_(0+)~+(v"=0)跃迁构建了准闭合的能级系统,冷却所需的激光波长分别为492.27和478.57 nm.最后预测了激光冷却SH~-阴离子能达到的多普勒温度和反冲温度.这些结果为进一步实验提供了理论参数.     

Spin polarization effect for Os2 molecule

Density functional Theory （DFT） （B3p86） of Gaussian03 has been used to optimize the structure of Os2 molecule. The result shows that the ground state for Os2 molecule is 9-multiple state and its electronic configuration is ^9∑^＋g, which shows spin polarization effect of Os2 molecule of transition metal elements for the first time. Meanwhile, we have not found any spin pollution because the wavefunction of the ground state does not mingle with wavefunctions with higher energy states. So, the fact that the ground state for Os2 molecule is a 9-multiple state is indicative of spin polarization effect of Os2 molecule of transition metal elements. That is, there exist 8 parallel spin electrons. The non-conjugated electron is greatest in number. These electrons occupy different spacious tracks, so that the energy of Os2 molecule is minimized. It can be concluded that the effect of parallel spin of Os2 molecule is larger than the effect of the conjugated molecule, which is obviously related to the effect of electron d delocalization. In addition, the Murrell-Sorbie potential functions with the parameters for the ground state ^9∑^＋g and other states of Os2 molecule are derived. Dissociation energy De for the ground state of Os2 molecule is 3.3971eV, equilibrium bond length Re is 0.2403nm, vibration frequency ωe is 235.32cm^-1. Its force constants f2, f3, and f4 are 3.1032×10^2aJ·nm^-2, -14.3425×10^3aJ·nm^-3 and 50.5792×10^4aJ·nm^-4 respectively. The other spectroscopic data for the ground state of Os2 molecule ωexe, Be and ae are 0.4277cm^- 1, 0.0307cm^- 1 and 0.6491 × 10^-4cm^-1 respectively.     

Isotopic effect of Cl2+ rovibronic spectra in the A-X system

This paper studies the isotopic effect of Cl2+ rovibronic spectra in the A2Πu(Ω=1/2) X 2Πg(Ω= 1/2) system.Based on the experimental results of the molecular constants of 35 Cl2+,it calculates the vibrational isotope shifts of the(2,7) and(3,7) band between the isotopic species 35 Cl+2,35 Cl 37 Cl+and 37 Cl2+,and estimates the rotational constants of both A 2 Π u and X 2 Π g states for the minor isotopic species 35 Cl 37 Cl+and 37 Cl2+.The experimental results of the spectrum of 35 Cl 37 Cl+(3,7) band proves the above mentioned theoretical calculation.The molecular constants and thus resultant rovibronic spectrum for 37 Cl2+ were predicted,which will be helpful for further experimental investigation.     

Mutual recombination in slow Si^＋ ＋ H^- collisions

This paper studies the process of mutual neutralization of Si^＋ and H^- ions in slow collisions within the multichannel Landau-Zener model. All important ionic-covalent couplings in this collision system are included in the collision dynamics. The cross sections for population of specific final states of product Si atom are calculated in the CM energy range 0.05 e∨/u-5 ke∨/u. Both singlet and triplet states are considered. At collision energies below -10 e∨/u, the most populated singlet state is Si（3p4p, ^1S0）, while for energies above -150e∨/u it is the Si（3p, 4p, ^1P1） state. In the case of triplet states, the mixed 3p4p（^3S1 ＋^3P0） states are the most populated in the entire collision energy range investigated. The total cross section exhibits a broad maximum around 200 300e∨/u and for ECM ≤ 10e∨/u it monotonically increases with decreasing the collision energy, reaching a value of 8 × 10^-13 cm^2 at ECM = 0.05 e∨/u. The ion-pair formation process in Si（3p^2 ^3PJ）＋H（1s） collisions has also been considered and its cross section in the considered energy range is very small （smaller than 10^-20 cm^2 in the energy region below 1 ke∨/u）.     

Quantum numbers of the pentaquark states ${{\rm{P}}}_{{\rm{c}}}^{+}$ via symmetry analysis

We investigate the quantum numbers of the pentaquark states ${{\rm{P}}}_{{\rm{c}}}^{+}$, which are composed of 4 (three flavors) quarks and an antiquark, by analyzing their inherent nodal structure in this paper. Assuming that the four quarks form a tetrahedron or a square, and the antiquark is at the ground state, we determine the nodeless structure of the states with orbital angular moment L≤3, and in turn, the accessible low-lying states. Since the inherent nodal structure depends only on the inherent geometric symmetry, we propose the quantum numbers J^P of the low-lying pentaquark states ${{\rm{P}}}_{c}^{+}$ may be ${\tfrac{3}{2}}^{-}$, ${\tfrac{5}{2}}^{-}$, ${\tfrac{3}{2}}^{+}$and ${\tfrac{5}{2}}^{+}$, independent of dynamical models.     

Multireference configuration interaction potential curve and analytical potential energy function of the ground and low-lying excited states of CdSe

The potential energy curves (PECs) of the ground state ($^{3}\Pi )$ and three low-lying excited states ($^{1}\Sigma $, $^{3}\Sigma $,$^{ 1}\Pi )$ of CdSe dimer have been studied by employing quasirelativistic effective core potentials on the basis of the complete active space self-consistent field method followed by multireference configuration interaction calculation. The four PECs are fitted to analytical potential energy functions using the Murrel--Sorbie potential function. Based on the PECs, the vibrational levels of the four states are determined by solving the Schr\"{o}dinger equation of nuclear motion, and corresponding spectroscopic constants are accurately calculated. The equilibrium positions as well as the spectroscopic constants and the vibrational levels are reported. By our analysis, the $^{3}\Pi $ state, of which the dissociation asymptote is Cd($^{1}$S) + Se($^{3}$P), is identified as a ground state of CdSe dimer, and the corresponding dissociation energy is estimated to be 0.39\,eV. However, the first excited state is only 1132.49\,cm$^{ - 1}$ above the ground state and the $^{3}\Sigma $ state is the highest in the four calculated states.     

Lifetime vibrational interference during the NO 1s-1π* resonant excitation studied by the NO+(A 1Π → X 1Σ+) fluorescence

Dispersed fluorescence from fragments formed after the de-excitation of the 1s^-1π^* resonances of N^*O and NO^* has been measured in the spectral range of 118–142 nm. This range is dominated by lines of atomic nitrogen and oxygen fragments and by the bands in the NO⁺ ion which result from the participator Auger decay of the 1s^-1π^* resonances. Ab-initio calculations of the transition probabilities between vibrational levels during the reaction NO N^*O ⇒ NO were used to explain the observed intensity dependence for the fluorescence bands on the exciting-photon energy across the resonances and on both v^′ and v^′′ vibrational quantum numbers. The multiplet structure of the 1s^-1π^* resonance and lifetime vibrational interference explain the observed exciting-photon energy dependence of the fluorescence intensity. A strong spin-orbit coupling between singlet and triplet states of NO⁺ is proposed to reduce additional cascade population of the state via radiative transitions from the and states and to explain remaining differences between measured and calculated integral fluorescence intensities.