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.     

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.     

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.     

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.     

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 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.     

Multireference configuration interaction potential curve and analytical potential energy function of the ground and low-lying excited states of CdSe

The potential energy curves (PECs) of the ground state ($^{3}\Pi )$ and three low-lying excited states ($^{1}\Sigma $, $^{3}\Sigma $,$^{ 1}\Pi )$ of CdSe dimer have been studied by employing quasirelativistic effective core potentials on the basis of the complete active space self-consistent field method followed by multireference configuration interaction calculation. The four PECs are fitted to analytical potential energy functions using the Murrel--Sorbie potential function. Based on the PECs, the vibrational levels of the four states are determined by solving the Schr\"{o}dinger equation of nuclear motion, and corresponding spectroscopic constants are accurately calculated. The equilibrium positions as well as the spectroscopic constants and the vibrational levels are reported. By our analysis, the $^{3}\Pi $ state, of which the dissociation asymptote is Cd($^{1}$S) + Se($^{3}$P), is identified as a ground state of CdSe dimer, and the corresponding dissociation energy is estimated to be 0.39\,eV. However, the first excited state is only 1132.49\,cm$^{ - 1}$ above the ground state and the $^{3}\Sigma $ state is the highest in the four calculated states.     

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.     

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.     

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.     

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.     

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 multi-reference configuration interaction of the low-lying states of the AsP molecule

Nine low-lying electronic states of the AsP molecule,includingΣ~ ,Π,andΔsymmetries with singlet, triplet,and quintet spin multiplicities,are studied using multi-reference configuration interaction method. The potential energy curves and the spectroscopic constants of these nine states are determined,and compared with the experimental observed data as well as other theoretical works available at present. Three quintet states are reported for the first time.Furthermore,the analytical potential energy functions of these states are fitted using Murrell-Sorbie function and least square fitting method.     

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.     

Solving Dirac Equation with New Ring-Shaped Non-Spherical Harmonic Oscillator Potential

A new ring-shaped non-harmonic oscillator potential is proposed. The precise bound solution of Dirac equation with the potential is gained when the scalar potential is equal to the vector potential. The angular equation and radial equation are obtained through the variable separation method. The results indicate that the normalized angle wave function can be expressed with the generalized associated-Legendre polynomial, and the normalized radial wave function can be expressed with confluent hypergeometric function. And then the precise energy spectrum equations are obtained. The ground state and several low excited states of the system are solved. And those results are compared with the non-relativistic effect energy level in Phys. Lett. A 340 （2005） 94. The positive energy states of system are discussed and the conclusions are made properly.     

Low-lying electronic states of aluminum monoiodide

High-level ab initio calculations of aluminum monoiodide(AlI) molecule are performed by utilizing the multireference configuration interaction plus Davidson correction(MRCI+Q) method. The core-valence correlation(CV) and spin–orbit coupling(SOC) effect are considered. The adiabatic potential energy curves(PECs) of a total of 13 Λ–S states and 24 ? states are computed. The spectroscopic constants of bound states are determined, which are in accordance with the results of the available experimental and theoretical studies. The interactions between the Λ–S states are analyzed with the aid of the spin–orbit matrix elements. Finally, the transition properties including transition dipole moment(TDM),Frank–Condon factors(FCF) and radiative lifetime are obtained based on the computed PEC. Our study sheds light on the electronic structure and spectroscopy of low-lying electronic states of the AlI molecule.     

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.     

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.     

Observation of Nano-Dots on HOPG Surface Induced by Highly Charged Arq+ Impact

Highly charged ions （HCIs） have huge potential energy due to their high charge state. When a HCI reaches a solid surface, its potential energy is released immediately on the surface to cause a nano-scale defect. Thus, HCIs are expected to be useful for solid-surface modifications on the nano-scale. We investigate the defects on a highly oriented pyrolytic graphite （HOPG） surface induced by slow highly charged Ar^q＋ ions with impact energy of 20-2000qeV with scanning probe microscopy （SPM）. In order to clarify the role of kinetic and potential energies in surface modification, the nano-defects are characterized in lateral size and height corresponding to the kinetic energy and charge state of the HCIs. Both the potential energy and kinetic energy of the ions may influence the size of nano-defect. Since potential energy increases dramatically with increasing charge state, the potential energy effect is expected to be much larger than the kinetic energy effect in the case of extremely high charge states. This implies that pure surface modification on the nano-scale could be carried out by slow highly charged ions. The mean size of nano-defect region could also be controlled by selecting the charge state and kinetic energy of HCI.