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∏） and three low-lying excited states （^1∑, ^3∑,^1∏） 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 Schrodinger 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∏ state, of which the dissociation asymptote is Cd（^1S） ＋ Se（^3p）, is identified as a ground state of CdSe dimer, and the corresponding dissociation energy is estimated to be 0.39eV. However, the first excited state is only 1132.49cm^-1 above the ground state and the ^3∑ state is the highest in the four calculated states.

Ab initio calculation of accurate dissociation energy, potential energy curve and dipole moment function for the A^1∑＋ state ^7LiH molecule

The reasonable dissociation limit of the A^1∑＋ state ^7LiH 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 the A^1∑＋ 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 Re=0.2487 nm and De=1.064eV, respectively. The unusual negative values of the anharmonicity constant and the vibration-rotational coupling constant are of ωeXe=-4.7158cm^-1 and αe=0.08649cm^-1, respectively. The vertical excitation energy from the ground to the A^1∑＋ state is calculated and the value is of 3.613eV 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 502.47cm^-1 about this state is approximately estimated. Careful comparison of the theoretical determinations with those obtained by previous theories about the A^1∑＋ state dissociation energy clearly shows that the present calculations are much closer to the experiments than previous theories, thus represents an improvement.

Theoretical study of potential energy curves,spectroscopic constants,and radiative lifetimes of low-lying states in an SeO molecule

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~）rbit coupling） effects. The spectroscopic constants of Ω states for X3∑-, a1△, b2∑＋, A3П , 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-lying Ω states are theoretically obtained. Comparisons of the natural lifetimes of Ω states with previous experimental results and those of isovalent TeO molecule are made.

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 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.

Potential energy curves, transition dipole moments, and radiative lifetimes of KBe molecule

An ab initio calculations on the ground and low-lying excited statesX2∑＋,2^2∑＋,3^2∑＋,1^4∏,2^4∏,1^4∑＋,2^4∑＋,and 3^4∑＋of KBe molecule have been performed using multireference configuration interaction （MRCI） plus Davidsoncorrections （MRCI＋Q） approach with all electron basis set aug-cc-pCV5Z-DK for Be and def2-AQZVPP-JKFI for K.3^2∑＋,1^4∏,2^4∏,1^4∑＋,2^4∑＋and3^4∑＋states are investigated for the first time. Inner shell electron correlations are computed on the potential energy curves （PECs） calculations. The spectroscopic and molecular parameters are also predicted. In addition, The transition properties including transition dipole moment, Franck-Condon factors qv′v″, Einstein coefficients Av′v″, and the radiative lifetimesτ′for the2^2∑＋-X2∑＋,3^2∑＋-X2∑＋,and 2^4∏-1^4∏ transitions are predictedat the same time.

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.

Examination of Potential Energy Curves of CFCl by Multi-reference Configuration Interaction Method

We give a detailed examination of potential energy curves of the singlet and triplet states of CFC1 correlated with the lowest three dissociation limits. The calculations are carried out at the internally contracted multi- reference configuration interaction/cc-pV（T＋d）Z level with the other two geometric parameters fixed at the state equilibrium conformation. The vertical transition energy, the oscillator strength, the main configuration and the electron transition are also investigated at the same level.

Potential energy curves and spectroscopic properties of X^2Σ^+ and A^2Π states of ^(13)C^(14)N

The potential energy curves （PECs） of X2∑ and A2П states of the CN molecule have been calculated with the multi- reference configuration interaction method and the aug-cc-pwCVSZ basis set. Based on the PECs, all of the vibrational and rotational levels of the 13C14N molecule are obtained by solving the Schrrdinger 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.

Theoretical Study on the Potential Energy Curve and Vibration-rotation Spectra of BeF Radical

The potential energy curve （PEC） of BeF（X2Σ＋） radical is investigated by using the complete active space self-consistent field （CASSCF） method followed by the highly accurate valence internally contracted multireference configuration interaction （MRCI） approach over the internuclear separation range from 0.0522 to 2.0472 nm. The PEC is fitted to the analytic Murrell-Sorbie function, which is employed to accurately determine the spectroscopic parameters. The present D0, De, Re, ωe, ωeχe, αe and Be are 6.14 eV, 6.22 eV, 0.1372 nm, 1236.12 cm-1, 9.11 cm-1, 0.0175 cm-1 and 1.4651 cm-1, respectively. These parameters have been compared with those of previous investigations reported in the literature. With PEC determined at the present level of theory, a total of 75 vibrational states have been predicted for the first time by numerically solving the radial Schrdinger equation of nuclear motion using the Numerov method. For each vibrational state, the complete vibrational levels, classical turning points, inertial rotation and centrifugal distortion constants are determined for the first time. Comparing with the available experiments and other theories, we find that the present spectroscopic parameter and molecular constant results are more accurate and complete than the previous theoretical investigations.

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.

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∑＋, 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.

Theoretical study of the structure and analytic potential energy function for the ground state of the PO_2 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.

Potential sediment sources identification of debris flows in the Jiangjia Gully,China

It is of great significance for gully prevention and management to identify the potential sediment source of debris flow.Debris flow in a gully always originates from tributaries that have different gravity potential energies and sediment condition.In this study,tributaries of the Jiangjia Gully(JJG) in Yunnan province,China,are taken as the study area to determine the possible sediment sources of debris flow.It was found that tributaries with a high evolution index(EI,the integral of the hypsometric curve) always had high gravity potential energy,which favors the occurrence of landslide activity.Furthermore,the relationship between sediment distribution,gravity potential energy,and EI is compared,respectively.The results showed that the EI had a greater influence on the occurrence of landslides,and sediments were concentrated in tributaries with EI between 0.5 and 0.6.Accordingly,tributaries with EI > 0.5 were identified as the sediment sources of debris flow.In addition,the shape of a tributary was related to EI and can reflect the condition of water and sediment storage.

Spin-orbit ab initio curves of ^(80)Se_2^+ ion and the assignment of photoelectron spectra of ^(80)Se_2 molecule

This paper carries out ab initio calculations to study the ^80Se2（X^3Σg^-） state and ^80Se2^＋（X^2Πg）, ^80Se2^＋（a^4Πg） states by using completed active space self-consistent field and multi-reference second order perturbation theory. The electronic curves of these states including spin-orbit coupling are calculated, and then the spectroscopic parameters are obtained. The photoelectron spectra of ^80Se2 molecule in gas phase are assigned according to Franck-Condon analysis based on calculated potential energy curves. The ionization energies of ^80Se2 molecule are determined by the present calculation.

Peculiar features of the interaction potential between hydrogen and antihydrogen at intermediate separations

This paper evaluates the interaction potential between a hydrogen and an antihydrogen using the second-order perturbation theory within the framework of the four-body system in a separable two-body basis. It finds that the H-H interaction potential possesses the peculiar features of a shallow local minimum located around interatomic separations of r ～ 6a.u. and a barrier rising at τ ≤5a.u.

Electronic Structures and Properties of V, Nb and Ta Metals

The electronic structures of pure V, Nb and Ta metals with bcc structure were determined by one atom (OA) theory. According to the electronic structures of these metals, their potential curves, cohesive energies, lattice parameters, elasticity and the dependence of linear thermal expansion coefficients on temperature were calculated. The electronic structures and characteristic properties of these metals with fcc and hcp structures and liquid states were studied.

Oxygen pressure acid leaching of artificial sphalerite catalyzed by Fe^3+/Fe^2+self-precipitation

The mechanism of oxygen pressure acid leaching of sphalerite catalyzed by Fe^3+/Fe^2+self-precipitation was investigated in this study.Artificial sphalerite was fabricated with varying amounts of iron content via the sintering of ZnS and FeS and used for the pressure acid leaching experiment.The variations in the potential of the pressure leaching system were investigated by using a self-designed potential autoclave.The results showed that compared to the non-iron sphalerite,there was a violent redox reaction between the 25.70%Fe-artificial sphalerite and dissolved oxygen during the process of pressure leaching;and the catalytic mechanism was attributed to the redox couple Fe^3+/Fe^2+,where Fe3+oxidizes the H2S gas film and the reduced Fe2+state is subsequently oxidized by the dissolved oxygen.Furthermore,the effect of temperature,H2SO4 concentration,and oxygen partial pressure on the artificial sphalerite with different iron contents was studied.The sphalerite samples with iron content were observed to dissolve more easily in sulfuric acid compared to the non-iron samples.Moreover,the activation energy of artificial sphalerite was observed to be lower in the sample with 25.70%iron content(22.26 kJ/mol)compared to that with no iron(32.31 kJ/mol);and the apparent reaction orders were obtained with respect to H2SO4 concentration(1.10 and 1.36)and oxygen partial pressure(1.29 and 1.41),respectively.A comprehensive kinetic model was developed on the basis of the experimental data and the fitted leaching ratio plot;and the kinetic equations for the leaching of sphalerite catalyzed by Fe^3+/Fe^2+self-precipitation were determined.

Ab Initio Calculation on Spectroscopic Properties and Radiative Lifetimes of Low-Lying Excited States of NaK

We performed high-level ab initio calculations on electronic structure of Na K. The potential energy curves (PECs) of 10 Λ-S states correlated with the three lowest dissociation limits have been calculated. On the basis of the calculated PECs, the spectroscopic constants of the boundΛ-S states are obtained, which are in good agreement with experimental results. The maximum vibrational quantum numbers of the singlet ground state X^1Σ^+ and the triplet ground state a^3Σ^+ have been analyzed with the semiclassical scattering theory. Transition properties including transition dipole moments, Franck-Condon factors, and radiative lifetimes have been investigated. The research results indicate that such calculations can provide fairly reliable estimation of parameters for the ultracold alkali diatomic molecular experiment.

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

Potential energy curves （PECs） for the ground state （X2∑＋） and the four excited electronic states （A2∏, B2∏, C2∑＋, 4∏） of a Bell 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 Re and the vertical excited energy Te are determined directly. It is evident that the X2∑＋, A2∏, B2∏, C2∑＋ states are bound and 4∏ 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 SchrSdinger equation of nuclear motion. Then the spectroscopic data are obtained including the rotation coupling constant w e, the anharmonic constant WeXe, the equilibrium rotation constant Be, and the vibration-rotation coupling constant ae. These values are compared with the theoretical and experimental results currently available, showing that they are in agreement with each other.