Ab initio configuration interaction study on the electronic structure of the X2Σ+, B2Σ+ and 32Σ+ states of SiO+

The energy levels and electronic structure of the X²Σ⁺, B²Σ⁺ and 3²Σ⁺ states of SiO⁺ are studied using ab initio configuration interaction (CI) calculations at and around their equilibrium internuclear distances R _e. Spectroscopic constants and the vertical excitation energy from the SiO⁺ X²Σ⁺ state are predicted for the 3²Σ⁺ state. Based on the calculated CI wavefunctions, avoided crossings of the potential energy curve for the 3²Σ⁺ state and a near-degeneracy effect in the avoided crossing region are examined. The effects of the mixing of excited configuration state functions in the total electronic wavefunctions for the 1–3 ²Σ⁺ states are investigated by analysing correlation energies in terms of the contributions from classes of excited configurations. The importance of both the near-degeneracy effect and the correlation energy effect in describing correctly the electronic structure of the 3 ²Σ⁺ state in the neighbourhood of its R _e is discussed.     

Ab initio study of PN electronic states – a qualitative interpretation of the perturbation and predissociation effects on observed transitions

Valence and high electronic states of PN have been calculated with accurate quantum chemistry methods. The variety of theoretical methods used includes complete active space self-consistent field, multireference configuration interaction and the newly developed explicitly correlated coupled cluster methods. The large correlation-consistent atomic orbitals basis sets AVQZ, AV5Z and AV(5+d)Z are used for the potential energy curves calculations in the bonding and long-range regions. The spectroscopic constants (R_e, B_e, ω_e, ω_ex_e, α_e, D_e, T_e) and the vibrational levels of the bound valence states (X¹Σ⁺, A¹Π, a³Σ⁺, d ³Δ, e³Σ^?, C¹Σ^?, b³Π, D ¹Δ and E¹Σ⁺ and some higher bound states) are determined and compared with experimental findings when available. Significant spin–orbit interactions between triplet states and A¹Π and E¹Σ⁺ excited states are found near the crossing points of the potential energy curves and could explain predissociation phenomena and the perturbations of the vibrational levels experimentally observed for PN in their A¹Π and E¹Σ⁺ states.     

The electronic states of silicon monofluoride: Rydberg states

SCF-CI calculations are reported for the Rydberg states converging to the ground state of the SiF⁺ ion. The adjustment between the observed and calculated values for the energy of the first Rydberg B²Σ⁺ state has allowed the characterization of 15 observed ²Σ⁺ and ²Π Rydberg states. A value of 58960 cm^?1 has been obtained for the ionization potential of SiF. The A²Σ⁺ state appears to be a valence state with some Rydberg character.     

Theoretical study of spectral parameters for the γ and β band systems of NO for atmosphere and high temperature

Highly correlated ab initio calculations were performed for accurate determination of γ (A²Σ⁺-X²П) and β (B²П-X²П) band systems of NO molecule. Highly accurate multi-reference configuration interaction approach was used to investigate the potential energy curves (PECs) and transition dipole moment curves. We correctly and fully described their diffuse wave functions by the obvious balance between the valence and Rydberg character of the X²П, A²Σ⁺, B²П, C²П and D²Σ⁺ states. The PECs of the three states (X²П, A²Σ⁺ and B²П) by using the aug-cc-pV5Z (aV5Z) basis set for N and O atoms agreed well with the Rydberg–Klein–Rees potential. Moreover, the Einstein A coefficients were calculated to predict the lifetimes, where the vibrational bands included v′ = 0–8, v″ = 0–29 for γ system and v′ = 0–11, v″ = 0–31 for β system. The spectral line intensities of the γ and β systems for atmosphere and high temperature were provided.     

Low-lying electronic states of BeH+ with the effect of inner electrons

The potential energy curves of the low-lying electronic states of BeH⁺ molecular ion are performed by using highly accurate multi-reference configuration interaction with AV5Z basis sets for H atom and ACV5Z basis set for Be atom, 1s inner shell of Be is considered as the core orbit and the active orbit, respectively, which are used to characterise the spectroscopic properties of a manifold of singlet and triplet states. Fourteen electronic states correlated with eight dissociation channels are investigated, we have found that the a³Σ⁺ and c³Σ⁺ both are bound states, the 3³Σ⁺ possesses double wells, and the C¹Σ⁺, 3³Σ⁺, 2³Π, 2¹Π, 1¹Δ, 1³Δ, 2³Δ and 2¹Δ states are studied for the first time. Transition dipole moment, Franck–Condon factors q_υ′υ^″ and Einstein coefficients A_υ′υ^″ for A¹Σ⁺–X¹Σ⁺, 2¹Π–B¹Π, c³Σ⁺–a³Σ⁺ and b³Π–a³Σ⁺ systems have been calculated. Radiative lifetime of A¹Σ⁺–X¹Σ⁺ band system has also been determined.     

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.     

Structural and spectroscopic properties of the diazocarbene radical (CNN) and its ions CNN+ and CNN−: a high-level theoretical investigation

The diazocarbene radical, CNN, and the ions CNN⁺ and CNN^? were investigated at a high level of theory. Very accurate structural parameters for the states X ³Σ^? and A ³Π of CNN, and X ²Π of both CNN⁺ and CNN^? were obtained with the UCCSD(T) method using correlated-consistent basis functions with extrapolations to the complete basis set limit, with valence only and also with all electrons correlated. Harmonic and anharmonic frequencies were obtained for all species and the Renner parameter and average frequencies evaluated for the Π states. At the UCCSD(T)/CBS_T-5 level of theory, Δ_f H(0 K) = 138.89 kcal/mol and Δ_f H(298 K) = 139.65 kcal/mol were obtained for diazocarbene; for the ionization potential and the electron affinity of CNN, 10.969 eV (252.95 kcal/mol), and 1.743 eV (40.19 kcal/mol), respectively, are predicted. Geometry optimization was also carried out with the CASSCF/MRCI/CBS_T-5 approach for the states X ³Σ^?, A ³Π, and a ¹Δ of CNN, and with the CASSCF/MRSDCI/aug-cc-pVTZ approach for the states b ¹Σ⁺, c ¹Π, d ¹Σ^?, and B ³Σ^?, and excitation energies (T_e) evaluated. Vertical energies were calculated for 15 electronic states, thus improving on the accuracy of the five transitions already described, and allowing for a reliable overview of a manifold of other states, which is expected to guide future spectroscopic experiments. This study corroborates the experimental assignment for the vertical transition X ³Σ^? ← E ³Π.     

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.     

BH分子基态和激发态解析势能函数和光谱性质

运用多参考组态相互作用的方法和Dunning’s相关调和基函数并含扩散基的大基组aug-cc-pV5Z,获得了BH分子基态（X¹Σ⁺）和6个电子激发态（a³П, A¹П, B¹Σ⁺, b³Σ⁺, b³ 关键词： 势能曲线 解析势能函数 多参考组态相互作用方法 光谱常数     

Accurate spectroscopic calculations of the 19 Λ-S states and 36 Ω states of the BC+ cation

This work computed the potential energy curves of 19 Λ-S states, which arose from the first five dissociation limits of BC⁺ cation, B⁺(¹S_g) + C(³P_g), B⁺(¹S_g) + C(¹D_g), B⁺(¹S_g) + C(¹S_g), C⁺(²P_u) + B(²P_u), and B⁺(¹S_g) + C(⁵S_u). The calculations were done for internuclear separations from 0.08 to 1.07 nm. The potential energy curves of 36 Ω states yielded from these Λ-S states were also calculated. Core-valence correlation and scalar relativistic correction, basis set extrapolation as well as Davidson correction were accounted for. Of these Λ-S states, the c¹Σ⁺, D³Π, 2¹Π, 2³Σ⁺, 2¹Δ, 3¹Σ⁺, and 4¹Σ⁺ had double wells; the 3³Π and 3¹Π states had three wells; the C³Σ^? and D³Π states were inverted with the spin-orbit coupling effect included; and the second wells of c¹Σ⁺, D³Π and 3¹Σ⁺ states, the second and the third wells of 3³Π state as well as the third well of 3¹Π state were very weakly bound, which well depths were smaller than 400 cm^?1. The spectroscopic parameters were determined for all the states. The vibrational properties were predicted only for some weakly bound states. The spin-orbit coupling effect on the spectroscopic parameters was evaluated.     

boldmath B3Σu-–X3Σg- transition in selenium dimer: ab initio multireference configuration interaction calculations

Theoretical investigation of low-lying electronic states and B³Σ_u^-–X³Σ_g^- transition properties of selenium dimer using size-extensivity singly and doubly excitation multireference configuration interaction theory with nonrelativistic all-electron basis set and relativistic effective core potential plus its split valence basis set is presented in this paper. The spectroscopic constants of ten low-lying Λ-S bound states have been obtained and compared with experiments. Spin-orbit calculations for coupling between B³Σ_u^- sates and repulsive ¹Π_u, ⁵Π_u states have been made to interpret the predissociation mechanisms of the B³Σ_u^- state. The lifetimes of B³Σ_u^- (v=0～6) have been calculated with scalar relativistic effects included or excluded, respectively, and reasonably agree with experimental values.     

Investigations of spectroscopic parameters and molecular constants for X1Σg+, w3Δu, and W1Δu electronic states of P2 molecule

The potential energy curves (PECs) of three low-lying electronic states (X¹Σ_g⁺, w³Δ_u, and W¹Δ_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 w³Δ_u, and W¹Δ_u electronic states when the rotational quantum number J equals zero and the vibrational level G(v), the inertial rotation constant B_v, and the centrifugal distortion constant D_v 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.     

CrHn(n=0,+1,+2)分子及离子的势能函数

用原子分子反应静力学原理推导出CrHⁿ(n=0，+1，+2)的电子状态及其离解极限. 对H原子采用6-311++G^**基组，对Cr原子采用SVP(split valence polarization)全电子基组，用B3PW91方法计算了它们的平衡几何、电子状态，在此基础上分别计算CrH，CrH⁺的Murrell-Sorbie解析势能函数和CrH²⁺的解析势能函数及其对应的力常数、光谱参数，理论计算值与实验值和文献计算值符合较好. 从离解极限和通道解释了不同的势能函数形状. 计算表明：CrH⁺的势能曲线均具有对应于稳定平衡结构的极小点，说明CrH⁺可稳定存在. 而CrH²⁺离子的势能曲线对应于不稳定的排斥态，说明CrH²⁺是不稳定的. 关键词： n(n=0')" href="#">CrHⁿ(n=0 +2) 势能函数 光谱参数 稳定性     

Quantum mechanical calculation of rotational constants and Franck-Condon factors of diatomic molecules

In this paper, the question of reliability of the Morse potential as a potential curve for a diatomic molecule is investigated on the basis of calculating the rotational constant. It is shown that the Morse potential describes well potential curves of X¹Σ _q ⁺ and B¹Π_u electronic states of a Na₂ molecule. Calculations of Franck-Condon factors for X¹Σ _q ⁺ ? B¹Π_u band of a Na₂ molecule using wave functions of the Morse potential confirm the known correlation between the values of Franck-Condon factors and rotational constants of combined electronic states.     

采用多参考组态相互作用方法研究AsN( X1 Σ+ )自由基的光谱常数与分子常数

采用内收缩多参考组态相互作用方法和相关一致基对AsN(X ¹ Σ⁺)自由基的势能曲线进行了研究. 计算过程中对两原子分别采用不同基组,As原子为aug-cc-pV5Z基组,N原子为aug-cc-pV6Z基组. 通过最小二乘法将势能曲线拟合成Murrell-Sorbie函数,并进一步计算得到AsN(X ¹ Σ⁺)自由基的光谱常数.光谱常数分别为D_e=4.97 eV,R_e=0.16259 nm, ω_e=1061.14 cm^-1, ω_ex_e=5.4715 cm^-1, B_e=0.53919 cm^-1和α_e=0.003409 cm^-1. 通过比较发现它们与实验值符合非常好. 利用得到的解析势能函数, 求解双原子分子核运动的径向Schrödinger方程, 找到了J=0时该自由基存在的全部67个振动态. 对于每一振动态, 分别计算了振动能级、经典转折点、惯性转动常数和离心畸变常数. 与实验结果比较后发现,计算结果达到了很高的计算精度. 关键词： AsN 势能曲线 光谱常数 分子常数     

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.     

On the representation of long-range potentials by a [1, 0] Padé approximant

The utility of the [1, 0] Padé approximant in the determination of long-range interaction constants is investigated using the recently calculated Rydberg-Klein-Rees potentials for the B³Π_Ou ⁺ states of I₂, Br₂ and Cl₂. The conditions under which the [1, 0] Padé approximant is a valid representation of the long-range potential outside the electron-overlap region are studied in detail, using as model systems the B states of I₂, Br₂ and Cl₂, and the X¹Σg⁺, B¹Σu⁺ and B′¹Σu⁺ states of H₂. In general, the validity of the representation depends on the nature of the potential, and is governed by

if the long-range potential can be adequately represented by a maximum number of three terms (n, m, m1) in the inverse-power expansion.     

MRCI studies on ground and excited states of CBr

Potential curves and spectroscopic constants for a large number of doublet and quartet states of CBr were obtained by multireference configuration interaction calculations, using valence triple-zeta basis sets with polarization and diffuse functions. Besides the X²Π ground state, 1⁴Σ^?, 1²Δ and 2²Σ⁺ have been found to be stable. Spectroscopic constants calculated for 1²Δ are in excellent agreement with experimental values obtained by Dixon and Kroto in 1963. Their observed predissociation of one component of 1²Δ can be explained by the crossing of the 1²Δ potential near equilibrium by 1²Σ⁺. The 1²Σ⁺ state is calculated to have a shallow long-range minimum at 2.31?Å. The dissociation energy of X²Π is calculated to be 3.43?eV. An observed T _e of 4.97?eV for 2²Σ⁺ agrees with the theoretical value. Several Rydberg states of the 2π→Ryd and 3σ→Ryd series, starting at T _e ?=?5.25?eV, were identified. Photodissociation of CBr by sunlight, important in the ozone cycle, can occur via direct dissociation of the ground state, or by excitation to 1²Δ followed by predissociation. Most dissocative repulsive states lie at higher energies, and are not expected to participate in the photodisscociation of CBr.