Spectroscopic investigations on NO~+(X~1Σ~+, a~3Σ~+, A~1Π) ion using multi-reference configuration interaction method and correlation-consistent sextuple basis set augmented with diffuse functions

Three low-lying electronic states (X1Σ+, a3Σ+, and A1Π) of NO+ ion are studied using the complete active space self-consistent-field (CASSCF) method followed by highly accurate valence internally contracted multi-reference configuration interaction (MRCI) approach in combination of the correlation-consistent sextuple basis set augmented with diffuse functions, aug-cc-pV6Z. The potential energy curves (PECs) of the NO+(X1Σ+, a3Σ+, A1Π) are calculated. Based on the PECs, the spectroscopic parameters Re, De, ωe, ωeχe, αe, Be, and D0 are reproduced, which are in excellent agreement with the available measurements. By numerically solving the radial Schrdinger equation of nuclear motion using the Numerov method, the first 20 vibrational levels, inertial rotation and centrifugal distortion constants of NO+(X1Σ+, a3Σ+, A1Π) ion are derived when the rotational quantum number J is equal to zero (J = 0) for the first time, which accord well with the available measurements. Finally, the analytical potential energy functions of these states are fitted, which are used to accurately derive the first 20 classical turning points when J = 0. These results are compared in detail with those of previous investigations reported in the literature.     

Investigations of spectroscopic parameters and molecular constants for X1Σg+, w3Δu, and W1Δu electronic states of P2 molecule

The potential energy curves (PECs) of three low-lying electronic states (X¹Σ_g⁺, w³Δ_u, and W¹Δ_u)of P₂ molecule are 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 in conjunction with the correlation-consistent basis set in the valence range. The PECs of the electronic states involved are modified by the Davidson correction and extrapolated to the complete basis set (CBS) limit. With these PECs, the spectroscopic parameters of the three electronic states are determined and compared in detail with the experimental data. The comparison shows that excellent agreement exists between the present results and the available experimental data. The complete vibrational states are computed for the w³Δ_u, and W¹Δ_u electronic states when the rotational quantum number J equals zero and the vibrational level G(v), the inertial rotation constant B_v, and the centrifugal distortion constant D_v of the first 30 vibrational states are reported, which accord well with the experimental data. The present results show that the two-point extrapolation scheme can obviously improve the quality of spectroscopic parameters and molecular constants.     

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 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.     

Investigations of spectroscopic parameters and molecular constants for X1Σg+, w3△u, and W1△u electronic states of P2 molecule

The potential energy curves （PECs） of three low-lying electronic states （X～1Σ_g～+,w～3△u,and W～1△u） of P₂ molecule are 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 in conjunction with the correlation-consistent basis set in the valence range.The PECs of the electronic states involved are modified by the Davidson correction and extrapolated to the complete basis set （CBS） limit.With these PECs,the spectroscopic parameters of the three electronic states are determined and compared in detail with the experimental data.The comparison shows that excellent agreement exists between the present results and the available experimental data.The complete vibrational states are computed for the w～3△u and W～1△u electronic states when the rotational quantum number J equals zero and the vibrational level G（v）,the inertial rotation constant Bv,and the centrifugal distortion constant Dv of the first 30 vibrational states are reported,which accord well with the experimental data.The present results show that the two-point extrapolation scheme can obviously improve the quality of spectroscopic parameters and molecular constants.     

Accurate spectroscopic constants of the lowest two electronic states in S_2 molecule with explicitly correlated method

A computational scheme for accurate spectroscopic constants was presented in this work and applied to the lowest two electronic states of sulfur dimer. A high-level ab initio calculation utilizing explicitly correlated multireference configuration interaction method(MRCI-F12) was performed to compute the potential energy curves(PECs) of the ground triplet X3-Σgand first excited singlet a1?g states of sulfur dimer with cc-p CVX Z-F12(X = T, Q) basis sets. The effects of Davidson modification, core–valence correlation correction, and scalar relativistic correction on the spectroscopic constants were examined. The vibration–rotation spectra of the two electronic states were provided. Our computational results show excellent agreement with existing available experimental values, and the errors of main spectroscopic constants are within 0.1% order of magnitude. The present computational scheme is cheap and accurate, which is expected for extensive investigations on the potential energy curves or surfaces of other molecular systems.     

B~3Σ_u~- X~3Σ_g~- transition in selenium dimer:ab initio multireference configuration interaction calculations

Theoretical investigation of low-lying electronic states and B 3Σu-X3Σg- transition properties of selenium dimer using size-extensivity singly and doubly excitation multireference configuration interaction theory with nonrelativistic all-electron basis set and relativistic effective core potential plus its split valence basis set is presented in this paper. The spectroscopic constants of ten low-lying Λ-S bound states have been obtained and compared with experiments. Spin-orbit calculations for coupling between B3Σu- sates and repulsive 1Πu,5Πu states have been made to interpret the predissociation mechanisms of the B3Σu- state. The lifetimes of B3Σu-(ν=0～6) have been calculated with scalar relativistic effects included or excluded,respectively,and reasonably agree with experimental values.     

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.     

Ab initio calculations on the spectroscopic constants, vibrational levels and classical turning points for the 21∏u state of dimer 7Li2

The accurate dissociation energy and harmonic frequency for the highly excited 2^1Пu state of dimer ^7Li2 have been calculated using a symmetry-adapted-cluster configuration-interaction method in complete active space. The calculated results are in excellent agreement with experimental measurements. The potential energy curves at numerous basis sets for this state are obtained over a wide internuclear separation range from about 2.4a0 to 37.0a0. And the conclusion is gained that the basis set 6-311＋＋G（d,p） is a most suitable one. The calculated spectroscopic constants De, Re, ωe, ωeχe, ae and Be at 6-311＋＋G（d,p） are 0.9670 eV, 0.3125 nm, 238.6 cm^-1, 1.3705 cm^-1, 0.0039 cm^-1 and 0.4921 cm^-1, respectively. The vibrational levels are calculated by solving the radial SchrSdinger equation of nuclear motion. A total of 53 vibrational levels are found and reported for the first time. The classical turning points have been computed. Comparing with the measurements, in which only the first nine vibrational levels have been obtained so far, the present calculations are very encouraging. A careful comparison of the present results of the parameters De and We with those obtained from previous theories clearly shows that the present calculations are much closer to the measurements than previous theoretical results, thus representing an improvement on the accuracy of the ab initio calculations of the potentials for this state.     

Structural, Spectroscopic and Vibrational Properties for Low-Lying Electronic States of LiCl

A multireference configuration interaction(MRCI) study has been carried out on the LiCl molecule. The potential energy has been calculated over a wide range of internuclear separation for the 21 low-lying electronic states of the LiCl molecule dissociating into Li(2S,2P,3S)+Cl(2P). The(4)1Σ+,(3)1Π, 1-33Σ+, 1-33Π,1,3,1,3Σ,(5)1Σ+,(4)3Σ+,(4)1Π,(4)3Π excited states are studied for the first time in theory. Molecular spectroscopic constants(Re, De,ωe, ωeχe, Be and αe) have been derived for the 9 bound states(X1Σ+,(3)1Σ+,(2)3Σ+,1,3,1,3Σ,(4)1Π,(4)3Π) with a regular shape, and the spectroscopic constants of ground states X1Σ+are in good agreement with available experimental and theoretical values. The relative diferences between experimental values and our values for Re, De, ωe, ωeχe, Be andαe are 1.02%, 0.60%, 1.72%, 9.46%, 2.0%, and 0.75%, respectively. Moreover, vibrational levels of 9 bound states, which have not been investigated experimentally, are computed.     

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.     

Potential energy curves and spectroscopic properties of X2∑ and A2П states of 13C14N

The potential energy curves(PECs) of X2+Σand A2Π states of the CN molecule have been calculated with the multireference configuration interaction method and the aug-cc-pwCV5Z basis set. Based on the PECs, all of the vibrational and rotational levels of the13C14N molecule are obtained by solving the Schro¨dinger equation of the molecular nuclear motion.The spectroscopic parameters are determined by fitting the Dunham coefficients with the levels. Both the levels and the spectroscopic parameters are in good qualitative agreement with the experimental data available. The analytical potential energy functions are also deduced from the calculated PECs. The present results can provide a helpful reference for future spectroscopy experiments or dynamical calculations of the molecule.     

Accurate ab initio study of low-lying electronic states of phosphorus nitride radical

This paper employs the highly accurate valence internally contracted multireference configuration interaction method to investigate the potential energy curves (PECs) for the ground state (X 1 Σ +) and two low-lying excited states (A 1 Π and D 1 of phosphorus nitride (PN) radical with the correlation-consistent basis set,aug-cc-pV6Z,in the valence range.Relativistic effects are considered in these calculations.The spectroscopic constants of the X 1 Σ + and A 1 Π states are calculated based on the PECs,and the results are in good accord with the available experimental data.The first 30 vibrational states for the X 1 Σ + state and the first 40 vibrational states for theA 1 Π state are determined when J=0.For each vibrational state,molecular constants G(υ),B(υ) and D(υ) are also attained.     

Spectroscopic investigations on NO＋（X1∑＋, a3∑＋, A1II） ion using multi-reference configuration interaction method and correlation-consistent sextuple basis set augmented with diffuse functions

Three low-lying electronic states （X1∑, a3∑＋, and A1II） of NO＋ ion are studied using the complete active space self-consistent-field （CASSCF） method followed by highly accurate valence internally contracted multi-reference configuration interaction （MRCI） approach in combination of the correlation-consistent sextuple basis set augmented with diffuse functions, aug-cc-pV6Z. The potential energy curves （PECs） of the NO＋（X1∑＋, a3∑＋, A1II） are calculated. Based on the PECs, the spectroscopic parameters Re, De, We, WeXe, ae, Be, and D0 are reproduced, which are in excellent agreement with the available measurements. By numerically solving the radial SchrSdinger equation of nuclear motion using the Numerov method, the first 20 vibrational levels, inertial rotation and centrifugal distortion constants of NO＋（X1∑＋, a3∑＋, A1II） ion are derived when the rotational quantum number J is equal to zero （J = 0） for the first time, which accord well with the available measurements. Finally, the analytical potential energy functions of these states are fitted, which are used to accurately derive the first 20 classical turning points when J = 0. These results are compared in detail with those of previous investigations reported in the literature.     

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.     

Study of hot bands in the B2Σ+u-X2Σ+g system of C-2 anion

Optical heterodyne magnetic rotation enhanced velocity modulation spectroscopy was employed to observe the visible absorption spectra of the B^2Σ^+_u-X^2Σ^+_g electronic transition of C^-_2. Four hot bands (0,1), (1,2), (2,3) and (3,4) have been observed and the band (3,4) is measured directly for the first time, so far as we know, by absorption. A rotational analysis was carried out to obtain molecular constants. With the Franck－Condon principle and the vibrational Boltzmann distribution, we have estimated the vibrational temperature of C^-_2 to be about 3000K.     

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.     

Band （5,0） in the Red System A^2Π1—X^2Σ^＋ of CN Studied by Optical Heterodyne Magnetic Rotation Enhanced Oncentration Modulation Spectroscopy

We study the CN radical using optical heterodyne magnetic rotation enhanced concentration modulation apectroscopy in the visible region.The radical has been produced in the ac glow discharge of acetonitrile with helium as the carrier gas.The (5,0) hand of the red system A^2Π1-X^2Σ^ in the range 17450-17830cm^-1 has been observed and rotationally analysed.We determine a set of precise molecular constants for the υ=5 vibrational level of CN in the A^2Π1 state.     

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.     

OPTICAL-OPTICAL DOUBLE-RESONANCE EXCITATION SPECTRA OF THE (6d)1Πg, (7d)1Πg HIGH-LYING RYDBERG STATES IN Na2

Two ¹Π_g states of Na₂ for v≤13 have been observed by using optical-optical double resonance (OODR) fluorescence excitation spectroscopy. The intermediate levels in B¹Π_u state are identified by the numerical calculations with the molec-ular constants for B¹Π_u←X¹Σ_g⁺ transitions and confirmed by the complemen-tary A¹Σ_g⁺←X¹Σ_g⁺ polarization spectra. Absolute vibrational numberings of the (6d)¹Π_g and (7d)¹Π_g states are determined by comparing the experimental OODR excitation intensities with the simulated Franck-Condon factors. The Dnnham coef-ficients and the Rydberg-Klein-Rees (RKR) potential energy curves of the (6d)¹Π_g, (7d)¹Π_g states are reported.