MRCI potential energy curves and analytical potential energy functions for the X^2∑^＋ and 2^∏ states of BO molecule

The potential energy curves （PECs） of BO molecule, including ∑^＋and ∏ symmetries with doublet spin multiplicities, are obtained employing multi-reference configuration interaction （MRCI） method and Dunning＇s correlation consistent basis sets. The analytical potential energy functions （APEFs） are fitted using the Murrell-Sorbie （MS） function and the least square method. Based on the PECs, the spectroscopic constants of the states have been determined and compared with the theoretical and experimental results available to affirm the accuracy and liability of the calculations. The root-mean-square （RMS） errors between the fitted results and the ab initio values are too little in comparison with the chemical accuracy （349.755 cm^-1）. It is shown that the present APEFs are accurate and can display the interaction between the atoms well. The present APEFs can be used to construct more complicated APEF or do some dynamic investigations.     

Potential energy curves and analytical potential energy functions of the metastable states of B2^＋＋

The multi-reference configuration interaction method and aug-cc-pvqz （AVQZ） have been used to calculate potential energy curves （PECs） of the singlet and triplet states of the riu and rig symmetry of B2＋＋. All of the four states （^l∏u, ^1∏g, ^3∏u and ^3∏g） are found to be metastable states, though the potential well of ^3∏u symmetry is very shallow. Based on the PECs, the analytical potential energy functions （APEFs） of these states have been fitted using the least square fitting method and two models of function. The spectroscopic parameters of each state are also calculated, and are compared with other investigations in the literature. The credibility and veracity of the two functions are evaluated. Some ideas to improve the fitting accuracy are presented. Also the vibrational levels for each state are predicted by solving the SchrSdinger equation of nuclear motion.     

Accurate potential energy function and spectroscopic study of the X^2∑＋, A^2П and B^2∑＋ states of the CP radical

This paper calculates the equilibrium internuclear separations, the harmonic frequencies and the potential energy curves of the X^2∑＋, A^2П and B^2∑＋ 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 （Be, αe and ωeχe） of these states. For the X2∑＋ state, the obtained values of De, Be, αe, ωeχe, Re and ωe 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 A2H state, the present values of De, Be,αe, ωeχe, Re and We 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 B2E＋ state, the present values of De, Be, αe, ωeχe, Re and We 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 Schr6dinger 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.     

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.     

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.     

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.     

Potential energy curve study on the ^3Π electronic states of GaX （X=F,Cl, and Br） molecules

The potential energy curves （PECs） of the 3Π states of GaX （X=F, Cl, and Br） molecules are calculated using the multireference configuration interaction method with a large contracted basis set aug-cc-pV5Z. The PECs are accurately fitted to analytical potential energy functions （APEFs） using the Murrell–Sorbie potential function. The spectroscopic parameters for the states are determined using the obtained APEFs, and compared with the theoretical and experimental data available presently in the literature.     

Ab initio calculation on accurate analytic potential energy functions and harmonic frequencies of c^3∑g^＋ and B^1-Пu states of dimer 7Li2

The comparison between single-point energy scanning （SPES） and geometry optimization （OPT） in determining the equilibrium geometries of c^3∑g^＋ and B^1-Пu states of dimer 7Li2 is made at numerous basis sets by using a symmetryadapted-cluster configuration-interaztion （SAC-CI） method in the Gaussian 03 program package. In this paper the difference of the equilibrium geometries obtained by SPES and by OPT is reported. The results obtained by SPES are found to be more reasonable than those obtained by OPT in full active space at the present SAC-CI level of theory. And the conclusion is attained that the cc-PVTZ is a most suitable basis set for these states. The calculated dissociation energies and equilibrium geometries are 0.8818 eV and 0.3090 nm for c^3∑g^＋ state, and 0.3668 eV and 0.2932 nm for B^1-Пu state respectively. The potential energy curves are calculated over a wide internuclear distance range from about 2.5α0 to 37α0 and have a least-squares fit into the Murrell-Sorbie function. According to the calculated analytic potential energy functions, the harmonic frequencies （We） and other spectroscopic data （ωeXe, Be and αe） are calculated. Comparison of the theoretical determinations at present work with the experiments and other theories clearly shows that the present work is the most complete effort and thus represents an improvement over previous theoretical results.     

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 of accurate dissociation energy and analytic potential energy function for the second excited state B1∏ of 7LiH

The reasonable dissociation limit of the second excited singlet state B¹∏ of ⁷LiH molecule is obtained. The accurate dissociation energy and equilibrium geometry of the B¹\Pi state are calculated using a symmetry-adapted-cluster configuration--interaction method in full active space. The whole potential energy curve for the B¹∏ state is obtained over the internuclear distance ranging from about 0.10nm to 0.54nm, and has a least-square fit to the analytic Murrell--Sorbie function form. The vertical excitation energy is calculated from the ground state to the B¹∏ state and compared with previous theoretical results. The equilibrium internuclear distance obtained by geometry optimization is found to be quite different from that obtained by single-point energy scanning under the same calculation condition. Based on the analytic potential energy function, the harmonic frequency value of the B¹∏ state is estimated. A comparison of the theoretical calculations of dissociation energies, equilibrium interatomic distances and the analytic potential energy function with those obtained by previous theoretical results clearly shows that the present work is more comprehensive and in better agreement with experiments than previous theories, thus it is an improvement on previous theories.     

Analytical potential energy function for the electronic states 2^∏1/2 and 2^∏3/2 of O^x2 （x=＋1, -1）

The splitting of potential energy levels for ground state X^2∏g of O^x2 （x = ＋1,-1） under spin-orbit coupling （SOC） has been calculated by using the spin-orbit （SO） multi-configuration quasi-degenerate perturbation theory （SO-MCQDPT）. Their Murrell-Sorbie （M S） potential functions are gained, and then the spectroscopic constants for electronic states 2^∏1/2 and 2^∏3/2 are derived from the M S function. The vertical excitation energies for O^x2 （x = ＋1,-1） are v[O2＋1^（2∏3/2→X^2∏1/2）] =195.652cm^-1, and v[O2^-1（2^∏1/2 →X^2∏3/2）] =182.568cm^-1, respectively. All the spectroscopic data for electronic states 2^∏1/2 and 2^∏3/2 are given for the first time.     

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.     

Ab initio calculation of accurate dissociation energy, potential energy curve and dipole moment function for the A1∑ + state 7LiH molecule

The reasonable dissociation limit of the A¹∑⁺ state $^{7}$LiH molecule is obtained. The accurate dissociation energy and the equilibrium geometry of this state are calculated using a symmetry-adapted-cluster configuration-interaction method in complete active space for the first time. The whole potential energy curve and the dipole moment function for theA¹∑⁺ state are calculated over a wide internuclear separation range from about 0.1 to 1.4\,nm. The calculated equilibrium geometry and dissociation energy of this potential energy curve are of R_{\e}=0.2487\,nm and D_{\e}=1.064\,eV, respectively. The unusual negative values of the anharmonicity constant and the vibration-rotational coupling constant are of \textit{\omega }_{\e}\textit{\chi }_{\e}=--4.7158cm^{ - 1} and \textit{\alpha }_{\e}=--0.08649cm^{ -1}, respectively. The vertical excitation energy from the ground to the A¹∑⁺ state is calculated and the value is of 3.613\,eV at 0.15875nm (the equilibrium position of the ground state). The highly anomalous shape of this potential energy curve, which is exceptionally flat over a wide radial range around the equilibrium position, is discussed in detail. The harmonic frequency value of 502.47cm¹ about this state is approximately estimated. Careful comparison of the theoretical determinations with those obtained by previous theories about the A¹∑⁺ state dissociation energy clearly shows that the present calculations are much closer to the experiments than previous theories, thus represents an improvement.