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.     

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.     

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.     

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.     

Configuration Interaction of Electronic Structure and Spectroscopy of AlH and Its Cation

We carry out a detailed study of the low-lying states of AlH and AlH~+,using a multireference configuration interaction method.Based on the computed potential energy curves,the spectroscopic constants of bound A-S states are fitted;these agree with the results for the measurements.The values of the permanent dipole moment of the A-S states are calculated,and the charge transfer mechanism is discussed.Based on the calculated transition dipole moments and vibrational levels,the radiative lifetimes of bound states are determined.Finally,tunneling lifetimes,and v'=0-2 vibrational levels of 4~2∑~+ and 3~2Π states with a potential barrier are investigated.     

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.     

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.     

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.     

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.     

Potential energy curves,transition dipole moments,and radiative lifetimes of KBe molecule

An ab initio calculations on the ground and low-lying excited states(X~2Σ+, 2~2Σ+, 3~2Σ+, 1~4Π, 2~4Π, 1~4Σ~+, 2~4Σ~+,and 3~4Σ~+) of KBe molecule have been performed using multireference configuration interaction(MRCI) plus Davidson corrections(MRCI+Q) approach with all electron basis set aug-cc-p CV5Z-DK for Be and def2-AQZVPP-JKFI for K.The 3~2Σ+, 1~4Π, 2~4Π, 1~4Σ~+, 2~4Σ~+, and 3~4Σ~+states are investigated for the first time. Inner shell electron correlations are computed on the potential energy curves(PECs) calculations. The spectroscopic and molecular parameters are also predicted. In addition, The transition properties including transition dipole moment, Franck–Condon factors qv'v', Einstein coefficients Av'v', and the radiative lifetimes τυ for the 2~2Σ~+–X~2Σ~+, 3~2Σ~+–X~2Σ~+, and 2~4Π–1~4Π transitions are predicted at the same time.     

Absorption spectra and isotope shifts of the(2, 0),(3, 1), and(8, 5) bands of the A~2Π_u-X~2Σ_g~+ system of ~(15)N_2~+ in near infrared

The high-resolution absorption spectra of the(2, 0),(3, 1), and(8, 5) bands of the A~2Π_u–X~2Σ_g~+system of~(15) N_2~+ have been recorded by using velocity modulation spectroscopy technique in the near infrared region. The rotational constants of the X~2Σ_g~+and A~2Π_u states of~(15) N_2~+ were derived from the spectroscopic data. The isotope shifts of these bands of the A~2Π_u–X~2Σ_g~+system of~(14) N_2~+ and~(15) N_2~+ were also analyzed and discussed.     

BaF radical: A promising candidate for laser cooling and magneto-optical trapping

Recently, there have been great interest and advancement in the field of laser cooling and magneto-optical trapping of molecules. The rich internal structure of molecules naturally lends themselves to extensive and exciting applications. In this paper, the radical~(138)Ba~(19) F, as a promising candidate for laser cooling and magneto-optical trapping, is discussed in detail.The highly diagonal Franck–Condon factors between the X~2Σ~+_(1/2)and A~2Π_(1/2) states are first confirmed with three different methods. Afterwards, with the effective Hamiltonian approach and irreducible tensor theory, the hyperfine structure of the X~2Σ~+_(1/2)state is calculated accurately. A scheme for laser cooling is given clearly. Besides, the Zeeman effects of the upper(A~2Π_(1/2)) and lower(X~2Σ~+_(1/2)) levels are also studied, and their respective g factors are obtained under a weak magnetic field.Its large g factor of the upper state A~2Π_(1/2) is advantageous for magneto-optical trapping. Finally, by studying Stark effect of Ba F in the X~2Σ~+_(1/2), we investigate the dependence of the internal effective electric field on the applied electric field. It is suggested that such a laser-cooled Ba F is also a promising candidate for precision measurement of electron electric dipole moment.     

Low-lying electronic states of CuN calculated by MRCI method

The high accuracy ab initio calculation method of multi-reference configuration interaction(MRCI) is used to compute the low-lying eight electronic states of CuN.The potential energy curves(PECs) of the X~3∑~-,1~3Π,2~3∑~-,1~3△,1~1△,1~1∑~-,1~1Π,and ~5∑~- in a range of R=0.1 nm-0.5 nm are obtained and they are goodly asymptotes to the Cu(~2S_g) + N(~4S_u) and Cu(~2S_g)+N(~2D_u) dissociation limits.All the possible vibrational levels,rotational constants,and spectral constants for the six bound states of X~3∑~-,1~3Π,2~3∑~-,1~1△,1~1∑~-,and 1~1 Π are obtained by solving the radial Schrdinger equation of nuclear motion with the Le Roy provided Level 8.0 program.Also the transition dipole moments from the ground state X~3∑~- to the excited states 1~3Π and 2~3∑~- are calculated and the result indicates that the 2~3∑-X~3∑ transition has a much higher transition dipole moment than the 1~3Π-X~3∑~- transition even though the l~3Π state is much lower in energy than the 2~3∑~- state.     

Study on the A~2Π_(3/2u), B~2Δ_(3/2u), and X~2Π_(3/2g) states of Cl_2~+ including its isotopologues

Adopting the experimentally available vibrational constants in a recent analysis of the strong perturbation between the A22Π3/2u and BΔ3/2u states of Cl+2in the A–X band system [Gharaibeh et al. 2012 J. Chem. Phys. 137 194317], an unambiguous vibrational assignment of the bands reported previously is carried out. The equilibrium rotational constants Be and α e of the X2Π3/2g and A2Π3/2u states for35Cl+2and35Cl37Cl+and those of the B2Δ3/2u state for35Cl+2are obtained by fitting the experimental values of Bυ. In addition, the values of Be and α e of these three states for the minor isotopologues35Cl37Cl+and37Cl+2are predicted by employing the isotopic effect. The values of equilibrium internuclear distance Re of the three states for the three isotopologues are calculated as well.     

Theoretical study of potential energy curves,spectroscopic constants,and radiative lifetimes of low-lying states in an SeO molecule

<正>The low-lying potential energy curves of the SeO molecule are computed by means of an ab initio multireference configuration interaction technique,taking into account relativistic(scalar plus spin-orbit coupling) effects.The spectroscopic constants ofΩstates for X~3∑~-,a~1△,b~1∑~+,A~3Π,A′~3△,and A″~3∑~+ states are obtained,and they are in good accordance with available experimental values.The Franck-Condon factors and transition dipole moments to the ground state are computed,and the natural radiative lifetimes of low-lyingΩstates are theoretically obtained. Comparisons of the natural lifetimes ofΩstates with previous experimental results and those of isovalent TeO molecule are made.     

Pressure-broadened atomic Li(2s-2p) line perturbed by ground neon atoms in the spectral wings and core

Full quantum calculations are performed to investigate the broadening profiles of the atomic lithium Li(2s-2p) resonance line induced by interactions with ground Ne(2s~22p~6) perturbers in the spectral wings and core. The X~2Σ~+, A~2Π,and B~2Σ~+ potential-energy curves of the two first low lying Li Ne molecular states, as well as the corresponding transition dipole moments, are determined with ab initio methods based on the SA-CASSCF-MRCI calculations. The emission and absorption coefficients in the wavelength range 550-800 nm and the line-core width and shift are investigated theoretically for temperatures ranging from 130 K to 3000 K. Their temperature dependence is analyzed, and the obtained results are compared with the previous experimental measurements and theoretical works.     

State-to-state dynamics of F(~2P) + HO(~2Π) → O(~3P) + HF(~1Σ~+)reaction on 1~3A〞 potential energy surface

State-to-state time-dependent quantum dynamics calculations are carried out to study F(~2P) + HO(~2Π) → O(~3P) +HF(~1Σ~+) reaction on 1~3A〞 ground potential energy surface(PES). The vibrationally resolved reaction probabilities and the total integral cross section agree well with the previous results. Due to the heavy–light–heavy(HLH) system and the large exoergicity, the obvious vibrational inversion is found in a state-resolved integral cross section. The total differential cross section is found to be forward–backward scattering biased with strong oscillations at energy lower than a threshold of 0.10 eV, which is the indication of the indirect complex-forming mechanism. When the collision energy increases to greater than 0.10 eV, the angular distribution of the product becomes a strong forward scattering, and almost all the products are distributed at θ_t = 0°. This forward-peaked distribution can be attributed to the larger J partial waves and the property of the F atom itself, which make this reaction a direct abstraction process. The state-resolved differential cross sections are basically forward-backward symmetric for v' = 0, 1, and 2 at a collision energy of 0.07 eV; for a collision energy of 0.30 eV,it changes from backward/sideward scattering to forward peaked as v increasing from 0 to 3. These results indicate that the contribution of differential cross sections with more highly vibrational excited states to the total differential cross sections is principal, which further verifies the vibrational inversion in the products.     

An Accurate Calculation of Potential Energy Curves and Transition Dipole Moment for Low-Lying Electronic States of CO

In this paper, potential energy curves for the X 1 Σ+ , a3 Π, a′3 Σ+ , d3 , A1 Π and I 1 Σ states of CO have been calculated using complete active space self-consistent field and multi-reference configuration interaction methods. The calculations have been performed at 108 nuclear separations from 0.7 to 4.0 A by the aug-cc-PV5Z basis set. Spectroscopic constants for the six low-lying electronic states are found in good agreement with experimental data. The vibrational states of the X1Σ+ and A1Π states are also calculated, which are reliable and accurate by comparison with the experimental data and the other theoretical values. The transition dipole moment (TDM) shows that the TDM of the two states (X1Σ + A1Π) are reduced strongly with increase of bond length.     

Franck--Condon factors and r-Centroids for the A 1∑+u-X1∑+g Band System of 107,109Ag2: Comparison of the Observed and Calculated Absorption Band Strengths

Franck-Condon factors and r-centrolds for the, A^1 ∑^＋ u-X^1∑^＋ 9 band system of ^107,109Ag2 are computed using Morse and Rydberg-Klein-Rees potentials for both lower and upper electronic states. The differences between the two sets of results are typically in the third decimal place for transitions involving vibrational levels with ν＇ and ν＂ up to about 15. Somewhat larger deviations appear for higher vibrational levels, but both sets of results follow the same pattern, which is to match well with the relative absorption band strength distribution in our experimental spectrum. The relative absorption band strengths are calculated by assuming that the electronic transition moment has only a weak dependence on the internuclear distance r. Good agreement between our measured and calculated absorption band strength ratios is found, which provides an excellent test of the calculated Franck- Condon factors and relative absorption band strengths. The r-centrold value for the （ν＇ = 0, ν＂ = 0） band is found to be approximately equal to the average value of r＇ and r＇＇e , indicating that the potentials of both states are not significantly aaharmonic around their minimum regions.     

Theoretical study of the radiative decay processes in H~+(D~+,T~+)–Be collisions

The potential energy curves of X~1Σ~+, A~1Σ~+, C~1Σ~+, and B~1Π are calculated with high-level MRDCI method, and the calculated spectroscopic constants of those states are in good agreement with most recent experimental data. On the basis of high precision PECs, the radiative processes of H~++ Be collisions are studied by using the fully quantum, optical potential and semiclassical methods in the energy ranges of 10~(-8) eV/u–0.1 eV/u, and the radiative decay, the radiative charge transfer,and the radiative association cross-sections are computed. It is found that the radiative association process is dominant in the energy region of 10~(-8) eV/u–0.02 eV/u, while radiative charge transfer becomes important at higher energies. Rich resonance structures are present in the radiative association and charge transfer cross-sections in the whole energy region considered, which result from the interaction between the quasi-bound rovibrational(J, v) states in the entrance channel with the final continuum state. Significant isotope effects have been found in the radiative decay processes of H~++ Be collisions.