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.     

The theoretical character of the X^1∑^＋ and A^1∑^＋ states of ScN

This paper calculates the potential energy curves (PECs) of the ground state (X 1 Σ + ) and excited state (A 1 Σ + ) of ScN molecule by multireference configuration interaction method. The correct character of the PECs has been gripped while they had been improperly reported in the literature. Based on the PECs, the spectroscopic parameters and vibrational energy levels are determined, and compared with experimental data and other theoretical works available at the present.     

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

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

The analytical potential energy function of flue gas SO₂（X¹A₁）

The equilibrium structure of flue gas SO 2 is optimized using the density functional theory (DFT)/ B3P86 method and CC-PV5Z basis. The result shows that it has a bent (C2V ,X1A1) ground state structure with an angle of 119.1184 . The vibronic frequencies and the force constants are also calculated. Based on the principles of atomic and molecular reaction statics (AMRS), the possible electronic states and reasonable dissociation limits for the ground state of SO2 molecule are determined. The potential functions of SO and O2 are fitted by the modified Murrell–Sorbie+c6 (M-S+c6) potential function and the fitted parameters, the force constants and the spectroscopic constants are obtained, which are all close to the experimental values. The analytic potential energy function of the SO2 (X1A1) molecule is derived using the many-body expansion theory. The contour lines are constructed, which show the static properties of SO2 (X1A1), such as the equilibrium structure, the lowest energies, the most possible reaction channel, etc.     

Theoretical study of the structure and analytic potential energy function for the ground state of the PO₂ molecule

In this paper, the energy, equilibrium geometry, and harmonic frequency of the ground electronic state of PO2 are computed using the B3LYP, B3P86, CCSD(T), and QCISD(T) methods in conjunction with the 6-311++G(3df, 3pd) and cc-pVTZ basis sets. A comparison between the computational results and the experimental values indicates that the B3P86/6-311++G(3df, 3pd) method can give better energy calculation results for the PO 2 molecule. It is shown that the ground state of the PO2 molecule has C2v symmetry and its ground electronic state is X2 A1 . The equilibrium parameters of the structure are R P O = 0.1465 nm, ∠OPO = 134.96°, and the dissociation energy is Ed = 19.218 eV. The bent vibrational frequency ν 1 = 386 cm-1 , symmetric stretching frequency ν 2 = 1095 cm-1 , and asymmetric stretching frequency ν 3 = 1333 cm-1 are obtained. On the basis of atomic and molecular reaction statics, a reasonable dissociation limit for the ground state of the PO2 molecule is determined. Then the analytic potential energy function of the PO2 molecule is derived using many-body expansion theory. The potential curves correctly reproduce the configurations and the dissociation energy for the PO2 molecule.     

Structure and analytical potential energy function for the ground state of the BCx (x=0, －1)

In this paper, the electronic states of the ground states and dissociation limits of BC and BC- are correctly determined based on group theory and atomic and molecular reaction statics. The equilibrium geometries, harmonic frequencies and dissociation energies of the ground state of BC and BC- are calculated by using density function theory and quadratic CI method including single and double substitutions. The analytical potential energy functions of these states have been fitted with Murrell-Sorbie potential energy function from our ab initio calculation results. The spectroscopic data （αe, ωe and ωeχe） of each state is calculated via the relation between analytical potential energy function and spectroscopic data. All the calculations are in good agreement with the experimental data.     

Molecular structure and analytical potential energy function of SeCO

The density functional method(B3P86/6-311G) is used for calculating the possible structures of SeC, SeO, and SeCO molecules. The result shows that the ground state of the SeC molecule is1Σ, the equilibrium nuclear distance is RSeC= 0.1699 nm, and the dissociation energy is De = 8.7246 eV. The ground state of the SeO molecule is3Σ, with equilibrium nuclear distance RSeO= 0.1707 nm and dissociation energy De = 7.0917 eV. There are two structures for the ground state of the SeCO molecule: Se=C=O and Se=O=C. The linear Se=C=O is1Σ. Its equilibrium nuclear distances and dissociation energy are RSeC= 0.1715 nm, RCO= 0.1176 nm and 18.8492 eV, respectively. The other structure Se=O=C is1Σ. Its equilibrium nuclear distances and dissociation energy are RCO= 0.1168 nm, RSeO= 0.1963 nm and 15.5275 eV,respectively. The possible dissociative limit of the SeCO molecule is analyzed. The potential energy function for the SeCO molecule has been obtained from the many-body expansion theory. The contour of the potential energy curve describes the structure characters of the SeCO molecule. Furthermore, contours of the molecular stretching vibration based on this potential energy function are discussed.     

Theoretical study on the complexes of He, Ne and Ar

This paper investigates the effect of basis sets through the potential energy curves(PECs) of six rare gas complexes He 2,Ne 2,Ar 2,He-Ne,He-Ar,and Ne-Ar.The coupled cluster singles and doubles method with perturbative treatment of triple excitations,doubly augmented basis sets of d-aug-cc-pVQZ,bond functions,and basis set superposition errors are employed.The diffuse function is more effective than the polarization function on describing the dissociation energy.The PECs are fitted into analytical potential energy functions(APEFs) using three expressions.It is found that all the expressions are suitable for describing the complexes of rare gases.Based on these APEFs,the spectroscopic parameters are calculated and the results are compared with the theoretical and experimental data available in the literature.     

The structure and the potential energy function of AlSO(C_S,X~2A″)

By using the B3P86/aug-cc-pvtz method,the accurate equilibrium geometry of the AlSO(CS,X2A″) molecule has been calculated and compared with available theoretical values.The obtained results show that the AlSO molecule has a most stable structure with bond lengths of R OAl = 0.1864 nm,R OS = 0.1623 nm,R AlS = 0.2450 nm,together with a dissociation energy of 13.88 eV.The possible electronic states and their reasonable dissociation limits for the ground state of the AlSO molecule were determined based on the principle of atomic and molecular reaction statics.The analytic potential energy function of the AlSO molecule was derived by the many-body expansion theory and the contour lines were constructed for the first time,which show the internal information of the AlSO molecule,including the equilibrium structure and stable point.The analysis demonstrates that the obtained potential energy function of AlSO is reasonable and successful and the present investigations provide important insights for further study on molecular reaction dynamics.     

Accurate ab initio-based analytical potential energy function for S_2(~1△_g) via extrapolation to the complete basis set limit

The potential energy curves(PECs)of the first electronic excited state of S_2(~1△_g) are calculated employing a multi-reference configuration interaction method with the Davidson correction in combination with a series of correlationconsistent basis sets from Dunning:aug-cc-p VX Z(X=T,Q,5,6).In order to obtain PECs with high accuracy,PECs calculated with aug-cc-p V(Q,5)Z basis sets are extrapolated to the complete basis set limit.The resulting PECs are then fitted to the analytical potential energy function(APEF)using the extended Hartree–Fock approximate correlation energy method.By utilizing the fitted APEF,accurate and reliable spectroscopic parameters are obtained,which are consistent with both experimental and theoretical results.By solving the Schr o¨dinger equation numerically with the APEFs obtained at the AV6Z and the extrapolated AV(Q,5)Z level of theory,we calculate the complete set of vibrational levels,classical turning points,inertial rotation and centrifugal distortion constants.     

Investigation of analytical harmonic frequency and potential energy function,vibrational levels for the X^2∑^＋ and A^2Л states of CN radical

This paper calculates the equilibrium structure and the potential energy functions of the ground state （X^2∑^＋） and the low lying excited electronic state （A^2Л） of CN radical are calculated by using CASSCF method. The potential energy curves are obtained by a least square fitting to the modified Murrell-Sorbie function. On the basis of physical theory of potential energy function, harmonic frequency （ωe） and other spectroscopic constants （ωeχe, βe and αe） are calculated by employing the Rydberg-Klei-Rees method. The theoretical calculation results are in excellent agreement with the experimental and other complicated theoretical calculation data. In addition, the eigenvalues of vibrational levels have been calculated by solving the radial one-dimensional SchrSdinger equation of nuclear motion using the algebraic method based on the analytical potential energy function.     

The theoretical study on the potential energy curve for X~3△ state of TiO molecule

This paper applies the density functional theory method to optimise the structure for X ³Δ state of TiO molecule with the basis sets 6-31G, 6-31++G and 6-311G^**. Comparing the attained results with the experiments, it obtains the conclusion that the basis set 6-31++G is most suitable for the optimal structure calculations of X ³Δ state of TiO molecule. The whole potential energy curve for the electronic state is further scanned by using B3P86/6-31++G method for the ground state, then it uses a least square fitted to Murrell--Sorbie functions, at last it calculates the spectroscopic constants and force constants, which are in better agreement with the experimental data.     

Ab initio calculations on accurate dissociation energy, equilibrium geometry, and analytic potential energy function for the 6~3Π state of ~7LiH molecule

The accurate dissociation energy and equilibrium geometry of the 63Π state of 7LiH molecule is calculated using a symmetry-adapted-cluster configuration-interaction method in full active space. And the calculated results are 0.2580 eV and 0.1958 nm for the dissociation energy and equilibrium geometry, respectively. The whole potential energy curve for the 63Π state is also calculated over the internuclear separation range from about 0.10 to 0.54 nm. The results are fitted by the Murrell-Sorbie function. It is found that the Murrell-Sorbie function form, which is mainly used to fit the ground-state potential energy function, is well suitable for the excited triplet b3Π state. The vertical excitation energy from the ground state to the 63Π state is calculated to be 4.233 eV. Based on the analytic potential energy function, the harmonic frequency of 610.88 cm-1 about this state is firstly estimated. Compared with other theoretical results, this work is the most complete effort to deal with the analytic potential energy function and the harmonic frequency of this state.     

Analytical potential energy function and spectroscopy parameters for B~1Π state of KH

Multi-reference configuration interaction is used to produce potential energy curves(PECs) for the excited B1Π state of KH molecule.To investigate the correlation effect of core-valence electrons,five schemes are employed which include the different correlated electrons and different active spaces.The PECs are fitted into analytical potential energy functions(APEFs).The spectroscopic parameters,ro-vibrational levels,and transition frequencies are determined based on the APEFs and compared with available experimental and theoretical data.The molecular properties for B1Π obtained in this letter,which are better than those available in literature,can be reproduced with calculations using the suitable correlated electrons and active space of orbitals.     

The analytical potential energy function of flue gas SO2（X1A1）

The equilibrium structure of flue gas SO2 is optimized using the density functional theory （DFT）/B3P86 method and CC-PV5Z basis. The result shows that it has a bent （C2v, X1A1） ground state structure with an angle of 119.1184°. The vibronic frequencies and the force constants are also calculated. Based on the principles of atomic and molecular reaction statics （AMIIS）, the possible electronic states and reasonable dissociation limits for the ground state of SO2 molecule are determined. The potential functions of SO and 02 are fitted by the modified Murrell-Sorbie＋c6 （M-S＋c6） potential function and the fitted parameters, the force constants and the spectroscopic constants are obtained, which are all close to the experimental values. The analytic potential energy function of the SO2 （X1A1） molecule is derived using the many-body expansion theory. The contour liues are constructed, which show the static properties of SO2 （XIA1）, such as the equilibrium structure, the lowest energies, the most possible reaction channel, etc.     

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.     

Triple-differential cross section for single ionization of H2 by electron impact

The triple-differential cross section (TDCS) for the (e,2e) ionization of a hydrogen molecule is calculated using the molecule distorted-wave Born approximation (MDWBA). Distorted waves are obtained by solving momentum-space coupled-channel Lippmann-Schwinger equations, including the ground state and the lowest-lying electronic state of b3Σu . TDCSs at the incident energy 100 eV in coplanar asymmetric geometry are reported. The present calculations are compared with the available experimental measurements and the theoretical results.     

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.     

Theoretical study of the structure and analytic potential energy function for the ground state of the PO2 molecule

In this paper, the energy, equilibrium geometry, and harmonic frequency of the ground electronic state of PO2 are computed using the B3LYP, B3P86, CCSD（T）, and QCISD（T） methods in conjunction with the 6-311＋＋G（3df, 3pd） and cc-pVTZ basis sets. A comparison between the computational results and the experimental values indicates that the B3P86/6-311＋＋G（3df, 3pd） method can give better energy calculation results for the PO2 molecule. It is shown that the ground state of the PO2 molecule has C2v symmetry and its ground electronic state is X2A1. The equilibrium parameters of the structure are Rp-o = 0.1465 am, ZOPO = 134.96°, and the dissociation energy is Ed = 19.218 eV. The bent vibrational frequency Ul = 386 cm-1, symmetric stretching frequency v2 = 1095 cm-1, and asymmetric stretching frequency ua = 1333 em-1 are obtained. On the basis of atomic and molecular reaction statics, a reasonable dissociation limit for the ground state of the PO2 molecule is determined. Then the analytic potential energy function of the PO2 molecule is derived using many-body expansion theory. The potential curves correctly reproduce the configurations and the dissociation energy for the PO2 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.