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.     

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.     

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.     

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.     

An ab initio investigation of the low-lying electronic states of BeH

Potential energy curves(PECs) for the ground state(X 2 Σ +) and the four excited electronic states(A 2 Π,B 2 Π,C 2 Σ +,4 Π) of a BeH molecule are calculated using the multi-configuration reference single and double excited configuration interaction(MRCI) approach in combination with the aug-cc-pVTZ basis sets.The calculation covers the internuclear distance ranging from 0.07 nm to 0.70 nm,and the equilibrium bond length R e and the vertical excited energy T e are determined directly.It is evident that the X2Σ+,A2Π,B2Π,C2Σ+ states are bound and 4Π is a repulsive excited state.With the potentials,all of the vibrational levels and inertial rotation constants are predicted when the rotational quantum number J is set to be equal to zero(J = 0) by numerically solving the radial Schr¨odinger equation of nuclear motion.Then the spectroscopic data are obtained including the rotation coupling constant ω e,the anharmonic constant ωexe,the equilibrium rotation constant Be,and the vibration-rotation coupling constant αe.These values are compared with the theoretical and experimental results currently available,showing that they are in agreement with each other.     

MRCI study of spectroscopic and molecular properties of X1Σg+ and A1Πu electronic states of the C2 radical

The potential energy curves (PECs) of X1Σ+g and A1Πu electronic states of the C2 radical 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 conjunction with the aug-cc-pV6Z basis set for internuclear separations from 0.08 nm to 1.66 nm. With these PECs of the C2 radical,the spectroscopic parameters of three isotopologues ( 12C2 ,12C13C and 13C2 ) have been determined. Compared in detail with previous studies reported in the literature,excellent agreement has been found. The complete vibrational levels G(υ),inertial rotation constants B υ and centrifugal distortion constants D υ for the 12C2 ,12C13C and 13C2 isotopologues have been calculated for the first time for the X1Σ+g and A1Πu electronic states when the rotational quantum number J equals zero. The results are in excellent agreement with previous experimental data in the literature,which shows that the presented molecular constants in this paper are reliable and accurate.     

Theoretical investigations of spectroscopic parameters and molecular constants for electronic ground state of Cl2 and its isotopes

The potential energy curve of the Cl 2(X1Σg+) is investigated by the highly accurate valence internally contracted multireference configuration interaction (MRCI) approach in combination with the largest correlation-consistent basis set, aug-cc-pV6Z, in the valence range. The theoretical spectroscopic parameters and the molecular constants of three isotopes, 35Cl2, 35Cl37Cl and 37Cl2, are studied. For the 35Cl2 (X1Σg+), the values of D0 , De , Re , ωe , ωeχe , αe and Be are obtained to be 2.3921 eV, 2.4264 eV, 0.19939 nm, 555.13 cm-1 , 2.6772 cm-1 , 0.001481 cm-1 and 0.24225 cm-1 , respectively. For the 35Cl37Cl(X1Σg+), the values of D0 , De , Re , ωe , ωeχe , αe and Be are calculated to be 2.3918 eV, 2.4257 eV, 0.19939 nm, 547.68 cm-1 , 2.6234 cm-1 , 0.00140 cm-1 and 0.23572 cm-1 , respectively. And for the 37C2 (X1Σg+), the values of D0 , De , Re , ωe , ωeχe , αe and Be are obtained to be 2.3923 eV, 2.4257 eV, 0.19939 nm, 540.06 cm-1 , 2.5556 cm-1 , 0.00139 cm-1 and 0.22919 cm-1 , respectively. These spectroscopic results are in good agreement with the available experimental data. With the potential of Cl2 molecule determined at the MRCI/aug-cc-pV6Z level of theory, the total of 59 vibrational states is predicted for each isotope when the rotational quantum number J equals zero (J = 0). The theoretical vibrational levels, classical turning points, inertial rotation and centrifugal distortion constants are determined when J = 0, which are in excellent accordance with the available experimental findings.     

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.     

Investigations on analytic potential energy function,spectroscopic parameters and vibrational manifolds （d = 0） of the SD^＋（X^3∑^-） ion

This paper investigates the spectroscopic properties of the SD + (X 3 Σ ) ion by employing the coupled-cluster singles-doubles-approximate-triples [CCSD(T)] theory combining with the quintuple correlation-consistent basis set augmented with diffuse functions (aug-cc-pV5Z) of Dunning and co-workers. The accurate adiabatic potential energy function is obtained by the least-squares fitting method with the 100 ab initio points, which are calculated at the unrestricted CCSD(T)/aug-cc-pV5Z level of theory over the internuclear separation range from 0.09 to 2.46 nm. Using the potential, it accurately determines the spectroscopic parameters (D e , ω e χ e , α e and B e ). The present D e , R e , ω e , ω e χ e , α e and B e results are of 3.69119 eV, 0.13644 nm, 1834.949 cm 1 , 25.6208 cm 1 , 0.1068 cm 1 and 4.7778 cm 1 , respectively, which are in remarkably good agreement with the experimental findings. A total of 29 vibrational states has been predicted by numerically solving the radial Schro¨dinger equation of nuclear motion when the rotational quantum number J equals zero. The complete vibrational levels, classical turning points, inertial rotation and centrifugal distortion constants are reported when J = 0 for the first time, which are in good accord with the measurements wherever available.     

Study on spectroscopic parameters and molecular constants of HCl(X~1Σ~+) molecule by using multireference configuration interaction approach

Equilibrium internuclear separations, harmonic frequencies and potential energy curves (PECs) of HCl($X^{1}\Sigma ^{ + })$ molecule are investigated by using the highly accurate valence internally contracted multireference configuration interaction (MRCI) approach in combination with a series of correlation-consistent basis sets in the valence range. The PECs are all fitted to the Murrell--Sorbie function, and they are used to accurately derive the spectroscopic parameters ($D_{\rm e}$, $D_{0}$, $\omega_{\rm e}\chi_{\rm e}$, $\alpha_{\rm e}$ and $B_{\rm e})$. Compared with the available measurements, the PEC obtained at the basis set, aug-cc-pV5Z, is selected to investigate the vibrational manifolds. The constants $D_{0}$, $D_{\rm e}$, $R_{\rm e}$, $\omega_{\rm e}$, $\omega_{\rm e}\chi_{\rm e}$, $\alpha_{\rm e}$ and $B_{\rm e}$ at this basis set are 4.4006~eV, 4.5845~eV, 0.12757~nm, 2993.33~cm$^{ - 1}$, 52.6273~cm$^{ - 1}$, 0.2981~cm$^{ - 1}$ and 10.5841~cm$^{ - 1}$, respectively, which almost perfectly conform to the available experimental results. With the potential determined at the MRCI/aug-cc-pV5Z level of theory, by numerically solving the radial Schr\"{o}dinger equation of nuclear motion in the adiabatic approximation, a total of 21 vibrational levels are predicted. Complete vibrational levels, classical turning points, inertial rotation and centrifugal distortion constants are reproduced, which are in excellent agreement with the available Rydberg--Klein--Rees data. Most of these theoretical vibrational manifolds are reported for the first time to the best of our knowledge.     

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.     

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.     

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.     

Accurate potential energy function and spectroscopic study of the X~2Σ~+,A~2Ⅱ and B~2Σ~+ states of the CP radical

This paper calculates the equilibrium internuclear separations,the harmonic frequencies and the potential energy curves of the X 2 Σ +,A 2Ⅱ and B 2 Σ + states of the CP radical by the highly accurate valence internally contracted multireference configuration interaction method with correlation-consistent basis sets(aug-cc-pV6Z for C atom and aug-cc-pVQZ for P atom).The potential energy curves are all fitted with the analytic potential energy function by the least-square fitting.Employing the analytic potential energy function,we determine the spectroscopic constants(B e,α e and ω e χ e) of these states.For the X 2 Σ + state,the obtained values of D e,B e,α e,ω e χ e,R e and ω e are 5.4831 eV,0.792119 cm 1,0.005521 cm 1,6.89653 cm 1,0.15683 nm,12535.11 cm 1,respectively.For the A 2Ⅱ state,the present values of D e,B e,α e,ω e χ e,R e and ω e are 4.586 eV,0.703333 cm 1,0.005458 cm 1,6.03398 cm 1,0.16613 nm,1057.89 cm 1,respectively.For the B 2 Σ + state,the present values of D e,B e,α e,ω e χ e,R e and ω e are 3.506 eV,0.677561 cm 1,0.00603298 cm 1,5.68809 cm 1,0.1696 nm,822.554 cm 1,respectively.For these states,the vibrational states with the rotational quantum number J equals zero(J = 0) are studied by solving the radial nuclear Schro¨dinger equation using the Numerov method.For each vibrational state,the vibrational level,the classical turning points,the rotational inertial and the centrifugal distortion constants are calculated.Comparison is made with recent theoretical and experimental results.     

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.     

Elastic collisions between Si and D atoms at low temperatures and accurate analytic potential energy function and molecular constants of the SiD（χ^2П） radical

Interaction potential of the SiD(X2Π) radical is constructed by using the CCSD(T) theory in combination with the largest correlation-consistent quintuple basis set augmented with the diffuse functions in the valence range. Using the interaction potential, the spectroscopic parameters are accurately determined. The present D0, De, Re, ωe, αe and Be values are of 3.0956 eV, 3.1863 eV, 0.15223 nm, 1472.894 cm-1, 0.07799 cm-1 and 3.8717 cm-1, respectively, which are in excellent agreement with the measurements. A total of 26 vibrational states is predicted when J=0 by solving the radial Schro¨dinger equation of nuclear motion. The complete vibrational levels, classical turning points, initial rotation and centrifugal distortion constants when J=0 are reported for the first time, which are in good accord with the available experiments. The total and various partial-wave cross sections are calculated for the elastic collisions between Si and D atoms in their ground states at 1.0×10-11–1.0×10-3 a.u. when the two atoms approach each other along the SiD(X2Π) potential energy curve. Four shape resonances are found in the total elastic cross sections, and their resonant energies are of 1.73×10-5, 4.0×10-5, 6.45×10-5 and 5.5×10-4 a.u., respectively. Each shape resonance in the total elastic cross sections is carefully investigated. The results show that the shape of the total elastic cross sections is mainly dominated by the s partial wave at very low temperatures. Because of the weakness of the shape resonances coming from the higher partial waves, most of them are passed into oblivion by the strong s partial-wave elastic cross sections.     

Multireference calculation of lifetime of A~2Π_u state in nitrogen-molecule cation

This paper utilizes multireference configuration interaction theory to calculate the lifetime of A2Πu state for nitrogen molecular ion N+2.It obtains the transition moment function for A2Πu→X2Σ+ g,Franck-Condon factors between vibrational levels of the two states.The calculated lifetimes are 16.81,14.62,13.10,12.18,11.40,and 11.64 μs forv'= 0,1,2,3,4,5 vibrational levels of A2Πu state,respectively,which are in excellent agreement with available experimental values.     

The effect of the rotational excitation of NO on the stereodynamics for the reaction C(~3P)+NO(X~2Π)→CN(X~2Σ~+)+O(~3P)

The stereodynamic properties of the reaction C(3P)+NO(X2Π)→CN(X2Σ+)+O(3P) in different rotational states of reactant NO are studied theoretically by using the quasiclassical trajectory method on 2A' and 2A' potential energy surfaces(PESs) at a collision energy of 0.06 eV.The vector properties in different rotational states on the two surfaces are discussed in detail.The results indicate that the rotational excitation of NO has considerable influence on the stereodynamic property of the reaction occurring on the two surfaces.At the same time,the calculated polarization-dependent differential cross sections(PDDCSs) in different initial rotational states manifest that products are strongly polarized at three scattering angles.     

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.     

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.