Multireference configuration interaction study of ground and low-lying excited states of the AlC radical

This work explored the spectroscopic parameters and vibrational properties of the 21 Λ–S and 42 Ω states of the AlC radical. The PECs were calculated with the CASSCF method, which was followed by the icMRCI+Q approach. The A⁴Π, a²Π, 5²Π, 2²Δ, and 1²Φ states as well as the first well of B⁴Σ^? state were inverted with the spin–orbit coupling (SOC) effect included; the 1⁴Δ, 1⁴Σ⁺, and 2²Σ^? states as well as the second wells of the B⁴Σ^?, 2²Σ⁺, 3²Σ⁺, 4²Π and 5²Π states were weakly bound, which well depths were less than 650 cm^?1; the B⁴Σ^?, 2²Σ⁺, 3²Σ⁺, 4²Π, 5²Π, and 2²Δ states had double wells and the second wells of these states except for B⁴Σ^? had only several vibrational states; the avoided crossings existed between the 2²Σ⁺ and 3²Σ⁺ states, the 3²Σ⁺ and 4²Σ⁺ states, the B⁴Σ^? and 3⁴Σ^? states, the 2²Δ and 3²Δ states, the 4²Π and 5²Π states, the 5²Π and 6²Π states, as well as the 2⁴Π and 3⁴Π states. The extrapolation scheme, core–valence correlation and scalar relativistic corrections were included. The spectroscopic parameters and vibrational properties were determined. The TDM curves between two different Λ–S states were calculated and Franck–Condon factors of some transitions were evaluated. The SOC effect on the spectroscopic and vibrational properties was evaluated.     

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

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.     

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

Potential energy curves(PECs) for the ground state(X 2 Σ +) and the four excited electronic states(A 2 Π,B 2 Π,C 2 Σ +,4 Π) of a BeH 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 R e and the vertical excited energy T e are determined directly.It is evident that the X2Σ+,A2Π,B2Π,C2Σ+ states are bound and 4Π 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 Schr¨odinger equation of nuclear motion.Then the spectroscopic data are obtained including the rotation coupling constant ω e,the anharmonic constant ωexe,the equilibrium rotation constant Be,and the vibration-rotation coupling constant αe.These values are compared with the theoretical and experimental results currently available,showing that they are in agreement with each other.     

MRSDCI study on potential energy curves and ro-vibrational spectra of the BBr molecule

Four low-lying electronic states of the BBr molecule, including Σ⁺ symmetry and Π symmetry with singlet and triplet spin multiplicities, have been studied using the complete active space self-consistent-field method followed by multi-reference single and double excitation configuration interaction calculation. For the ground state, four isotopes (¹¹B⁷⁹Br, ¹¹B⁸¹, ¹⁰B⁷⁹Br, ¹⁰B⁸¹Br) of the BBr molecule have been studied, since their experimental spectroscopic constants and ro-vibrational energy levels are abundant. For the three excited states, just the most natural abundance isotope–¹¹B⁷⁹Br–is investigated. The spin–orbital coupling effect for the a³Π state is also considered. Finally, the analytical potential energy functions of these states are fitted except for the ³Σ⁺ state because its potential well is too shallow to be fitted with available functions. These results have been compared in detail with those of the investigations reported in the literature.     

多参考组态相互作用方法计算研究XOn(X=S,Cl; n=0,±1)的解析势能函数和光谱常数

采用从头计算的多参考组态相互作用方法和含扩散基的3个基组aug-cc-PVXZ(X=D,T,Q)计算了SO和ClO分子及其分子离子的势能曲线,确定了平衡几何结构、离解能,并采用Feller拟合递推方法得到了基函数为无穷大计算水平值.确定了SO-,ClO ,ClO-分子离子的基态.通过Murrell-Sorbie势能函数和最小二乘法拟合得到了解析势能函数.基于所得的势能函数,通过解核运动的薛定谔方程得到振动能级,精确计算了相应的光谱常数,并与现有的理论值和实验值进行了比较.     

Ab initio study of ground and low-lying excited states of MgLi and MgLi+ molecules with valence full configuration interaction and MRCI method

The ground and low-lying excited states of MgLi and MgLi⁺ molecules have been investigated. The potential energy curves and the permanent and transition dipole moments of the MgLi and MgLi⁺ molecules are determined making use of the multi-reference configuration interaction and valence full configuration interaction with large basis sets. The core–valence correlation and scalar relativistic correction are also taken into account with aug-cc-pCVQZ basis set and the third-order Douglas–Kroll Hamiltonian approximation, respectively. The transition dipole moments are used to evaluate the radiative lifetimes of the vibrational levels for the low-lying excited states of the MgLi and MgLi⁺ molecules. The derived spectroscopic constants of the ground and low-lying excited states are in good agreement with available experimental and theoretical works.     

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

Nine low-lying electronic states of the AsP molecule, including Σ , Ⅱ, and △ symmetries 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.     

Multireference configuration interaction study on spectroscopic properties of low-lying electronic states of As2 molecule

The potential energy curves (PECs) of four electronic states (X1Σ+g , e3△u , a 3 Σ-u , and d 3Πg ) of an As 2 molecule are investigated employing the complete active space self-consistent field (CASSCF) method followed by the valence internally contracted multireference configuration interaction (MRCI) approach in conjunction with the correlation-consistent aug-cc-pV5Z basis set. The effect on PECs by the relativistic correction is taken into account. The way to consider the relativistic correction is to employ the second-order Douglas-Kroll Hamiltonian approximation. The correction is made at the level of a cc-pV5Z basis set. The PECs of the electronic states involved are extrapolated to the complete basis set limit. With the PECs, the spectroscopic parameters (Te , Re , ωe , ωexe , ωeye , αe , βe , γe , and Be ) of these electronic states are determined and compared in detail with those reported in the literature. Excellent agreement is found between the present results and the experimental data. The first 40 vibrational states are studied for each electronic state when the rotational quantum number J equals zero. In addition, the vibrational levels, inertial rotation and centrifugal distortion constants of d 3Πg electronic state are reported which are in excellent agreement with the available measurements. Comparison with the experimental data shows that the present results are both reliable and accurate.     

Analytical potential energy functions for the ground and some excited states of N2

The analytical potential energy functions have been calculated for the ground state X¹Σ⁺_g and four excited electronic states a¹Π_g, A³Σ⁺_u, B′³Σ^?_u and B³Π_g of N₂ molecule using the algebraic and energy-consistent methods (AM-ECM). Based on our previously published full AM vibrational energies and spectroscopic constants, the low-lying force constants f_n, the expansion coefficients a_n and the variational parameters λ in the AM–ECM potentials are determined for these states. The computed AM–ECM potential energy curve of each state is in excellent agreement with the experimental data and better than other analytical potentials.     

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 (X1∑) as well as three low-lying excited states (3∑, 1∏, 3∏) of ZnCd dimer. Potential 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(o)dinger equation of nuclear motion, and corresponding spectroscopic parameters are accurately calculated using the APEFs. The present values of spectroscopic parameters including equilibrium positions and dissociation energies areompared with other theoretical reports available at 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.     

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.     

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.     

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.     

Profiling the binding motif between Be and Mg in the ground state via a single-reference coupled cluster method

We present a study on the performance of our iterative triples correction for the coupled cluster singles and doubles excitations (CCSDT-1a+d) method for computation of potential energy surface (PES), spectroscopic constants, and vibrational spectrum for the ground state (X¹Σ⁺) BeMg, where the ostensible inadequacy of the CCSD and CCSD(T) methods is quite expected. We compare our results with those obtained using state-of-the-art multireference configuration interaction (MRCI) investigations reported earlier by Kerkines and Nicolaides. Our estimated dissociation energy (417.37 cm^?1), equilibrium distance (3.285 Å), and vibrational frequency (82.32 cm^?1) are in good agreement with recent results of advanced MRCI calculations for X¹Σ⁺ BeMg PES, which exhibits a shallow well of 469.4 cm^?1 with a minimum at 3.241 Å and a harmonic vibrational frequency of 85.7 cm^?1. Very weakly bound nature of X¹Σ⁺ BeMg is clearly reflected from these values. In accord with MRCI studies, a comparison of BeMg with iso-valence weakly bound ground-state species, Be₂ and Mg₂, suggests that its characteristics do not exhibit any resemblance to Be₂ rather, it shows a close kinship to Mg₂. The agreement of our derived vibrational levels with those obtained via the high-level MRCI calculations is very encouraging reflecting the potential of the suitably modified single-reference coupled cluster (SRCC) method, CCSDT-1a+d as a tool for the study of multireference van der Waals systems.     

Further investigations of the low-lying electronic states of AsO~+ radical

The high level quantum chemistry ab inito multi-reference configuration interaction （MRCI） method with large V5Z basis set is used to calculate the spectroscopic properties of the 15 A-S electronic states （X1∑＋, A I П, 1 △, 1 ∑, 3∑＋, 3П, 3△, 3△ , 5∑＋, 5П, 5△, 1П （II）, ofAsO＋ radical correlated to the dissociation limit As＋（3pg） ＋ O（3pg） and As＋（IDg） ＋ O（1Dg）. In order to obtain better potential curves and more accurate spectroscopic properties, the Davidson modification is taken into account. With the potential energy curves （PECs） determined here, vibrational levels G（v） and inertial rotation constants Bu are computed for all the bound electronic states when the rotational quantum number J equals zero （J = 0）. Except for the states X1∑＋, A1П , it is the first time that the multi-reference configuration calculation has been used on the 13 A-S electronic states of the AsO＋ radical. The potential energy curves of all the A-S electronic states are depicted according to the avoided crossing rule of the same symmetry. Spin-orbit coupling effect （SOC） is introduced into the states X1 ∑＋, A1 П, 3П to consider its effects on the spectroscopic properties. Transition dipole moments （TDMs） from A1П 1, 3 П1 states to the ground state X1∑0＋ are predicted as well.     

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.     

The splitting of low-lying or low excited states for hydride molecules （cations） of the third period under spin-orbit coupling

This paper reports that the splitting of potential energy curves for the low-lying or low excited states for hydride molecules （cations） （MgH, AlH^＋, SiH, PH^＋, SH,ClH^＋） of the third period under Spin-Orbit Coupling has been calculated by using the Spin-Orbit Multi-Configuration Quasi-Degenerate Perturbation Theory （SO-MCQDPT） method. Then, spectroscopic constants of the split states have been derived from the Murrell-Sorbie function. The calculated dissociation energies for the spectrum branch terms have been given, respectively. The spectroscopic constants and dissociation energies for the spectrum branch terms are given for the first time in this paper.