A UNIVERSAL ANALYTIC POTENTIAL-ENERGY FUNCTION BASED ON A PHASE FACTOR

Using a field equation with a phase factor, a universal analytic potential-energy function applied to the interactions between diatoms or molecules is derived, and five kinds of potential curves of common shapes are obtained adjusting the phase factors. The linear thermal expansion coefficients and Young's moduli of eleven kinds of face-centered cubic (fcc) metals - Al, Cu, Ag, etc. are calculated using the potential-energy function; the computational results are quite consistent with experimental values. Moreover, an analytic relation between the linear thermal expansion coefficients and Young's moduli of fcc metals is given using the potential-energy function. Finally, the force constants of fifty-five kinds of diatomic moleculars with low excitation state are computed using this theory, and they are quite consistent with RKR (Rydberg-Klein-Rees) experimental values.

Structure and analytical potential energy function for the ground state of the BC^x （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.

The Analytical Potential Energy Function of NH Radical Molecule in External Electric Field

The geometric structures of an Nit radical in different external electric fields are optimized by using the density functional B3P86/cc-PVSZ method, and the bond lengths, dipole moments, vibration frequencies and IR spectrum are obtained. The potential energy curves are gained by the CCSD （T） method with the same basis set. These results indicate that the physical property parameters and potential energy curves may change with the external electric field, especially in the reverse direction electric field. The potential energy function of zero field is fitted by the Morse potential, and the fitting parameters are in good accordance with the experimental data. The potential energy functions of different external electric fields are fitted adopting the constructed potential model. The fitted critical dissociation electric parameters are shown to be consistent with the numerical calculation, and the relative errors are only 0.27% and 6.61%, hence the constructed model is reliable and accurate. The present results provide an important reference for further study of the molecular spectrum, dynamics and molecular cooling with Stark effect.

Ab initio calculations of accurate dissociation energy and analytic potential energy function for the second excited state B^1∏ 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 B^∏ state are calculated using a symmetry-adaptedcluster configuration interaction method in full active space. The whole potential energy curve for the B1H state is obtained over the internuclear distance ranging from about 0.10 nm to 0,54 nm, 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 B^1∏ 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 B^1∏ 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.

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.

Analytical Potential Energy Function,Spectroscopic Constants and Vibrational Levels for A^1E_u^+ State of Dimer ~7Li_2

The symmetry-adapted-duster configuration-interaction method is used to investigate the spectroscopicproperties of ~7Li_2(A^1∑_u^+) over the internuclear distance ranging from 2.4ao to 37ao.The complete potential energycurves are calculated at numbers of basis sets.All the ab initio calculated points are fitted to the analytic MurrellSorbie function and then employed to compute the spectroscopic constants.By comparison,the spectroscopic constantsreproduced by the potential attained at D95(3df,3pd) are found to be very close to the experiments,a^d the values (T_e,D_e,R_e,ω_e,ω_eχ_e,α_e and B_e) are of 1.732 93 eV,1.161 36 eV,0.313 27 nm,251.95 cm^(-1),1.623 cm^(-1),0.005 35 cm^(-1),and0.490 cm^(-1),respectively.With the potential obtained at D95(3df,3pd),the totally 75 vibrational states are found whenJ=0.The vibrational levels,the classical turning points and the inertial rotation constants of the first 68 vibrationalstates are calculated for the first time and compared with the available measurements.Good agreement is obtained.The centrifugal distortion constants of the first 32 vibrational states are also reported for the first time.The reasonabledissociation limit for ~7Li_2(A^1∑_u^+) is deduced using the calculated results at present.

The theoretical study on the potential energy curves for X^1Σ^+, A^1Π and C^1Σ^- states of SiO molecule

This paper applies the symmetry-aziapted-cluster/symmetry-adapted-cluster configuration-interaction （SAC/SACCI） method to optimize the structures for X^1∑^＋, A^1 Ⅱ and C^1 ∑^- states of SiO molecule with the basis sets D95＋＋, 6-311＋＋G and 6-311＋＋G^＊＊. Comparing the obtained results with the experiments, it gets the conclusion that the basis set 6-311＋＋G^＊＊ is most suitable for the optimal structure calculations of X^1.∑^＋, A^Ⅱ and C^1∑^- states of SiO molecule. The whole potential energy curves for these electronic states are further scanned by using SAC/6-311＋＋G^＊＊ method for the ground state and SAC-CI/6-311＋＋G^＊＊ method for the excited states, then use a least square method to fit Murrell^Sorbie functions, at last the spectroscopic constants and force constants are calculated, which are in good agreement with the experimental data.

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 X3A 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 X3A 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.

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 S2（a^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 AV6 Z 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.

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, X2AH） molecule has been calculated and compared with available theoreticM values. The obtained results show that the AlSO molecule has a most stable structure with bond lengths of ROA1= 0.1864 nm, ROS=0.1623 nm, RAIS=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.

The molecular structure and analytical potential energy function of HCO （X^2A＇）

In this paper the equilibrium structure of HCO has been optimized by using density functional theory （DFT）/ B3P86 method and CC-PVTZ basis. It has a bent （Cs, X^2A＇） ground state structure with an angle of 124.4095 °. The vibronic frequencies and force constants have also been calculated. Based on the principles of atomic and molecular reaction statics, the possible electronic states and reasonable dissociation limits for the ground state of HCO molecule have been determined. The analytic potential energy function of HCO （X^2A＇） molecule has been derived by using the many-body expansion theory. The contour lines are constructed, which show the static properties of HCO （X^2A＇）, such as the equilibrium structure, the lowest energies, etc. The potential energy surface of HCO （X^2A＇） is reasonable and very satisfactory.

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.

The molecular structure and the analytical potential energy function of S2^- and S3^-

In this paper, the equilibrium geometry, harmonic frequency and dissociation energy of S2^- and S3^- have been calculated at QCISD/6-311＋＋G（3d2f） and B3P86/6-311＋＋G（3d2f） level. The S2^- ground state is of 2IIg, the S3^- ground state is of 2B1 and S3^- has a bent （C2v） structure with an angle of 115.65° The results are in good agreement with these reported in other literature. For S3^- ion, the vibration frequencies and the force constants have also been calculated. Base on the general principles of microscopic reversibility, the dissociation limits has been deduced. The Murrell-Sorbie potential energy function for S2^- has been derived according to the ab initio data through the least- squares fitting. The force constants and spectroscopic data for S2^- have been calculated, then compared with other theoretical data. The analytical potential energy function of S3^- have been obtained based on the many-body expansion theory. The structure and energy can correctly reappear on the potential surface.

Accurate calculation of the potential energy curve and spectroscopic parameters of X^2Σ^+ state of ^(12)Mg^1H

High level calculations on the ground state of 12Mg1H molecule have been performed using multi-reference configuration interaction （MRCI） method with the Davidson modification. The core-valence correlation and scalar relativistic corrections are included into the present calculations at the same time. The potential energy curve （PEC） of the ground state, all of the vibrational levels and spectroscopic parameters are fitted. The results show that the levels and spectroscopic parameters are in good agreement with the available experimental data. The analytical potential energy function （APEF） is also deduced from the calculated PEC using the Murrell-Sorbie （M-S） potential function. The present results can provide a helpful reference for the future spectroscopic experiments or dynamical calculations of the molecule.

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.

Precise calculations on spectroscopic parameters of diatomic molecules using a novel potential energy function

A novel scheme for potential energy functions of diatomic molecules is derived using a function with phase factors. Six kinds of potential curves of common shapes are obtained by adjusting the phase factors. Spectroscopic parameters of the ground states for ten kinds of molecules are calculated using the potential energy functions. The results agree well with experimental data.

The structure and the analytical potential energy function of NH_2(X^2B_1)

This paper reports that the equilibrium structure of NH2 has been optimized at the QCISD/6-311＋＋G （3df, 3pd） level. The ground-state NH2 has a bent （C2v, X^2B1） structure with an angle of 103.0582°. The geometrical structure is in good agreement with the other calculational and experimental results. The harmonic frequencies and the force constants have also been calculated. Based on the group theory and the principle of microscopic reversibility, the dissociation limits of NH2（C2v, X^2B1） have been derived. The potential energy surface of NH2（X^2B1） is reasonable. The contour lines are constructed, the structure and energy of NH2 reappear on the potential energy surface.

A universal potential energy function and precise calculations on the molecular spectra

By using a function with a phase factor,a universal analytic potential energy function applied to the interactions between diatoms or molecules is derived and six kinds of potential curves of common shapes are obtained by adjusting the phase factor.The spectroscopic parameters of ten diatomic molecules are calculated by using the potential energy function;as a consequence,all calculation results are in good agreement with experimental data.

The analytical potential energy function of flue gas SO_2(X^1A_1)

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.

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.